RADIO THEORY HANDBOOK

Beginner to Advanced

Ron. Bertrand. VK2DQ

Second Edition

Copyright © 2019 Ron. Bertrand.

All rights reserved.

Contents

1 BASIC ELECTRICITY - I 

2 BASIC ELECTRICITY - II

3 BASIC ELECTRICITY - Ill

4 OHM'S LAW 

5 SERIES CIRCUITS 

6 PARALLEL CIRCUITS 

7 SERIES-PARALLEL CIRCUITS 

8 MAGNETISM

9 ALTERNATING CURRENT- I 

10 ALTERNATING CURRENT - II 

11 CAPACITANCE - I

12 CAPACITANCE - II 

13 CAPACITIVE REACTANCE 

14 INDUCTANCE 

15 METERS

16 ELECTRIC CELLS & BATTERIES 

17 MICROPHONES

18 TRANSFORMERS

19 RESISTIVE, INDUCTIVE & CAPACITIVE CIRCUITS 

20 POWER SUPPLIES

21 ELECTRON TUBES

22 DECIBELS

23 ELECTROMAGNETIC RADIATION 

24 SEMICONDUCTORS - I 

25 SEMICONDUCTORS - II

26 AMPLIFIERS

27 OSCILLATORS

28 PROPAGATION

29 AMPLITUDE MODULATION

30 AM TRANSMITTERS & RECEIVERS - I 

31 AM TRANSMITTERS & RECEIVERS - II

32 FILTERS IN RADIOCOMMUNICATIONS 

33 INTERFERENCE

34 FREQUENCY MODULATION

35 DIGITAL MODULATION 

36 TRANSMITTER FAULTS

37 ANTENNAS

38 TRANSMISSION LINES 

39 TEST EQUIPMENT & MEASUREMENTS 

40 OTHER OPERATING MODES 

41 MATHEMATICS -AC CIRCUITS 

1 - Basic Electricity - I

This book begins with the basics of electrical and radio theory and then progressively builds to a solid understanding of Advanced Amateur Radio operator level as it applies to Australia, U.K. USA, Canada and Europe. While starting at beginner level, the target standard of this book is CEPT Radio Experimenter Advanced Licence (T/R61-01) and higher. It is imperative to have a thorough understanding of the fundamentals of electricity before any study of radio and communications. We start our study from the beginning, thus benefiting readers with a limited knowledge of the basics whilst also providing a convenient refresher for those who may have long since covered the material. Once we have the fundamentals down rock solid, we will progress to the Advanced Radio Theory.

ELECTRICITY

The complicated electronic systems involved in modern day communication, satellites, nuclear power plants, radio and television and even up to date automobiles, do not require technicians to understand the functioning of electric and electronic circuits. Modern day electronics is very modular. A remove and replace, or substitution of the suspected 'faulty module' is the approach to modern electronics servicing. This, in itself, is not a bad thing, as in the real world, getting an electronic device up and going is the most important thing. However, to have a true understanding requires a strong foundation in the basics of electricity. The term "electronic" infers circuits ranging from the first electronic device, the electron tube, to the newer solid state devices such as diodes and transistors, as well as integrated circuits (ICs). The term "electric" or "electrical" is usually applied to systems or circuits in which electrons flow through wires but which involve no vacuum tubes or solid state devices. Many modern electrical systems are now using electronic devices to control the electric current that flows in them.

What makes such a simple thing as an electric lamp glow? It is easy to pass the question off with the statement, "The switch connects the light to the power lines and it glows" or something to that effect. But what does connecting the light to the power lines do? How does energy travel through solid copper wires? What makes a motor turn? A radio play? What is behind the dial that allows you to pick out one radio station from thousands of others operating at the same time? How fast is electricity? There are no single, simple answers to any of these questions. Each question requires the understanding of many basic principles. By adding one basic idea to another, it is possible to answer, eventually, all of the questions that may be asked about the intriguing subjects of electricity, electronics and radio.

When a light switch is turned on and elsewhere the light suddenly glows, energy has found a path through the switch to the light. The path used is usually along copper wires and the tiny particles that do the moving and carry the energy are called electrons. These electrons are important to anyone studying electronics and radio since they are usually the only particles that are considered to move in electric circuits.

To explain what is meant by an electron, it will be necessary to investigate more closely the make-up of all matter. The word "matter" means, in a general sense, anything that can be touched. It includes substances such as rubber, salt, wood, water, glass, copper and air. The whole world is made of different kinds of stuff. The ancient Greek philosophers were always trying to find the 'stuff' that made up the universe. Even before the Greeks, the Alchemists were trying to find the basic building blocks that all matter was made from, though most of the time their driving force was not so much science but the pursuit of wealth. They figured that if they could isolate the building blocks of matter, then they would be able to 'create' matter themselves. One of their primary pursuits was the creation of the precious metal gold.

Water is one of the most common forms of 'stuff' that we call matter. If a drop of water is divided in two and then divided again and again until it can be divided no longer and still be water, then we have arrived at the smallest possible piece of water. We have a water molecule. The ancient Greeks would have called the smallest droplet of water an atomos (atom). The word atomos means indivisible. We know today that substances such as water can be divided into more fundamental bits.

The water molecule can be broken down into still smaller particles, but these new particles will not be water. Physicists have found that three smaller particles make up a molecule of water. Two atoms of hydrogen (H) and one atom of oxygen (O) are shown in figure 1-1. The symbols 'H' and 'O' are universal symbols used to represent Hydrogen and Oxygen. Oxygen, at average temperatures, is one of the several gases that constitute the air we breathe. Hydrogen is also a gas in its natural state; it is found in everyday use as part of the gas used for heating or cooking. If a gaseous mixture containing two parts of hydrogen and one part of oxygen is ignited, a violent chemical reaction, an explosion, will occur as water is formed and excess energy released. This is not an experiment that I would recommend.

Water is made up of two types of atoms, hydrogen and oxygen. Water is a molecule. A molecule is a substance that is made up of groups of atoms. If you divided a droplet of water down to its smallest possible size, you would have a single molecule of water. If you had the means to split the water molecule further, you would no longer have water; you will have the atoms (hydrogen and oxygen) that make up water. The chemical name of water then is Dihydrogen Oxide. It has been found that atoms are also divisible. An atom is made up of at least two types of particles: protons and electrons and a third particle called a neutron. Don't let these names concern you too much. For our purposes, the primary particle is the electron. Electrons and protons are called electrical particles and neither one is divisible (in typical environments). All the molecules that make up all matter in the universe are composed of these electrical proton-electron pairs.

ELECTRONS AND PROTONS

Electrons are the smallest and lightest of the fundamental particles. They are said to have a negative charge, meaning that they are surrounded by an invisible force field that will react in an electrically negative manner with other matter.

Protons are said to have a positive charge and are surrounded by an invisible force field that causes them to react in an electrically positive manner. The words negative and positive are just names to describe the so called charge of electrons and protons and their charge describes how they interact with each other. We could just as easily call the charge of the electron the white charge and the charge of the proton the black charge. My point is, 'charge' is an electric behaviour and since there are two types of charge we need to name them so that when we talk about them we will know which behaviour we are speaking of: either the positive charge behaviour or the negative charge behaviour.

AN EXPERIMENT WITH CHARGE

You may have already done this if you have, please try it again. Tear up some tiny strips of paper and place them on the table in front of you. Make sure no one is watching! Now run a hair comb through your hair briskly several times and put the comb close to the bits of paper. Before the comb touches the paper, a bit of paper will leap off the table, move through the air and cling to the comb. This happens because you have produced a charge on the comb, which will physically interact with matter around it (in our case the bits of paper).

The charge on the comb was created by friction between the comb and your hair. Protons are about eighteen hundred times more massive than electrons and have a positive electric field surrounding them.

The proton is exactly as positive as the electron is negative; each has a unit of electric charge.

When an electron and a proton are far apart, only a few of their lines of force (the invisible field around them) join and pull together. The attracting pull between the two charges is, therefore, small. When brought closer together, the electron and proton can link more of their lines of force and will pull together with greater force. If close enough, all the lines of force from the electron are joined to all the lines of force of the proton and there is no external field and they attract each other strongly. Together, a positive charged proton and the negative charge of an electron cancel out and they form a neutral, or uncharged, group. The neutral atomic particle, known as a neutron, exists in the nucleus of all atoms heavier than hydrogen. The fact that electrons repel other electrons, protons repel other protons, but electrons and protons attract each other gives us the basic law of charges:

LIKE CHARGES REPEL, UNLIKE CHARGES ATTRACT

Because the proton has about 1,800 times more mass than the electron, it seems reasonable to assume that when an electron and a proton attract each other, it will be the lower mass and free to move electrons that will do most of the actual moving. Such is the case. It is the electron which moves in electricity. If the proton was the lower mass particle and not in the nucleus, we would probably have called what we know today as 'electricity', something like 'proton'icity. Regardless of the difference in apparent size and mass, the negative field of an electron is just as strong negatively as the positive field of a proton is positive.

Though physically small, the field near the electron is quite strong. If the field strength (field strength = the strength of the invisible field) around an electron at a distance of one millionth of a metre is a certain amount, at two-millionths of a metre it will be one quarter as much; at four millionths of a metre it will be one-sixteenth as much; and so on. If the field decreases as distance increases, the field is said to vary inversely with distance. It varies inversely with the distance squared.

Note: A millionth of a metre has a name; it is called a 'micron'. A micron is not an International System (SI) Unit, but it is a unit which has stuck and is still often used. It is too nice of a name not to be used.

When an increase in something produces an increase in something else, the two things are said to vary directly rather than inversely. Two million electrons on an object produce twice as much negative charge as one million electrons would. The charge is directly proportional to the number of electrons. The invisible fields surrounding electrons and protons are known as electrostatic fields. The word 'static' means, in this case, "stationary', or "not caused by movement", When electrons are made to move, the result is dynamic electricity. The word "dynamic" indicates that motion is involved. To produce a movement of an electron, it will be necessary to have either, a negatively charged field to push it, or positively charged field to pull it. Normally in an electric circuit, both a negative and a positive charge are used (a pushing and pulling pair of forces).

THE ATOM AND ITS FREE ELECTRONS

As of 2019 there are 118 different kinds of atoms, or elements, from which the millions of different forms of matter found in the universe, are composed. Let me elaborate on the last paragraph. About 100 different atoms are found in nature. Many atoms do not occur naturally. Many are only manufactured in very powerful particle colliders or inside stars.

The heavy atoms, those containing a large number of protons, electrons and neutrons, like uranium and radium are unstable. They throw off energy (they are radioactive) and decompose until they become stable non-radioactive atoms. A material, which is only made from one type of atom, is called an element. Water is not an element because it contains two types of atoms, hydrogen and oxygen. Water is, therefore, a molecule. Copper contains only copper atoms, so copper is an element. There are many other common elements.

The simplest and lightest atom (or element) is hydrogen. An atom of hydrogen consists of one electron and one proton, as shown in figure 1-4. In one respect the hydrogen atom is similar to all others: the electron whirls (orbits) around the proton, or nucleus, of the atom, much as planets rotate around the sun. Electrons whirling around the nucleus are termed planetary, or orbital, electrons! This is not an accurate model but is accurate for our purposes in radio physics. Electrons are more like clouds around the nucleus with electrons having a probability that they are more likely to be in the vicinity of one or more bands. We really can't say that they are just like planets around the sun, however we can use this analogy for our purposes.

The nucleus is just a name given to the 'centre' of an atom. The next atom in terms of atomic weight is helium, having two protons and two electrons. The third atom is lithium, with three electrons and three protons and so on. All elements are grouped in families with the atomic weights in the Periodic table of elements.

Most atoms have a nucleus (centre) consisting of all the protons of the atom and also one or more neutrons. The electrons (always equal in number to the protons in the nucleus) are whirling around (orbiting) the nucleus in various layers. The first layer of electrons outside the nucleus can accommodate only two electrons. If the atom has three electrons, two will be in the first layer and the third will be in the next layer. The second layer is completely filled when eight electrons are whirling around in it. The third is filled when it has eighteen electrons. Some of the electrons in the outer orbit, or shell, of the atoms of many materials such as copper or silver, exist in a higher "conduction level" and can be dislodged easily. These electrons travel out into the wide open spaces between the atoms and molecules and may be termed free electrons.

Other electrons in the outer orbit will resist dislodgement and are called bound or valence electrons. Materials consisting of atoms (or molecules) having many free electrons will allow an easy interchange of their outer shell electrons while atoms with only bound electrons will hinder any electron exchange. Copper, for example, has one electron in its outer orbit or layer.

This lonely little outer electron of the copper atom is very easy to 'steal' from the copper atom and made to move. The outer electron is called a free electron. It is not free but loosely bound to the atom and easy to encourage away and made to move, so we call it a free electron. Copper does not resist the movement of its outer electrons strongly, or in other words, it does not offer much resistance to us if we try to get its outer electrons to move. We will talk about how we get them to move later. A material, which does not have free electrons, is said to have a high resistance. All metals have free electrons. Most common metals when heated cause greater energy to be developed in their free electrons. The more energy electrons have the greater they resist orderly movement through the material. The material is said to have an increased resistance to the movement of electrons through it.

THE ELECTROSCOPE

The charge on the comb was created by friction between the comb and your hair. Protons are about eighteen hundred times more massive than electrons and have a positive electric field surrounding them.

An example of electrons and electric charges acting on one another is demonstrated by the action of an electroscope. An electroscope consists of two very thin gold or aluminium leaves attached to the bottom of a metal rod. The delicate metal foil leaves and rod are encased in a glass bottle to protect them from air movement.

To understand the operation of the electroscope, it is necessary to recall these facts:

Normally an object has a neutral charge.

Like charges repel; unlike charges attract.

Electrons are negative.

Metals have free electrons.

Normally the metal rod of the electroscope has a neutral charge and the leaves hang downward parallel to each other, as shown in figure 1-5A. The leaves are shown in charged position in figure 1-5B and 1-5C. With no charge the leaves hang vertically down from the rod.

Rubbing a piece of hard rubber with wool causes the wool to lose electrons to the rubber and the excess electrons on the rubber, charge the rubber negatively. When such a negatively charged object is brought near the top of the rod, some of the free electrons at the top are repelled and travel down the rod, away from the negatively charged object. Some of these electrons force themselves onto one of the leaves and some onto the other. Now the two leaves are no longer neutral but are slightly negative and repel each other, moving outward from the vertical position as shown. When the charged object is removed, electrons return up the rod to their original areas. The leaves again have a neutral charge and hang down parallel to each other.

Since the charged object did not touch the electroscope, it neither placed electrons on the rod nor took electrons from it. When electrons were driven to the bottom, making the leaves negative, these same electrons leaving the top of the rod left the top positive. The overall charge of the rod remained neutral. When the charged object was withdrawn, the positive charge at the top of the rod pulled the displaced electrons up to it. All parts of the rod were then neutral again. If a positively charged object, such as a glass rod vigorously rubbed with a piece of silk, is brought near the top of the electroscope rod, some of the free electrons in the leaves and rod will be attracted upward toward the positive object. This charges the top of the rod negatively because of the excess of free electrons there. Both leaves are left with a deficiency of free electrons which means they are positively charged. Since both leaves are similarly charged again, they repel each other and move outward a second time.

A deficiency of electrons on an object leaves the object with a positive charge. An excess of electrons gives it a negative charge. If a negatively charged object is touched to the metal rod, some excess electrons will be deposited onto the rod and will be immediately distributed throughout the electroscope. The leaves spread apart. When the object is taken away, an excess of electrons remains on the rod and the leaves. The leaves stay spread apart. If the negatively charged electroscope is touched to a large body that can accept the excess free electrons, such as a person, a large metal object, or earth (the ground), the excess electrons will have a path to leave the electroscope and the leaves will collapse as the charge returns to neutral. The electroscope has been discharged. If a positively charged object is touched to the top of the metal rod, the rod will lose electrons to it and the leaves will separate. When the object is taken away, the rod and leaves still lack free electrons and are therefore positively charged and the leaves will remain apart.

A large neutral body touched to the rod will drain some of its free electrons to the electroscope discharging it and the leaves will hang down once more. The electroscope demonstrates the free movement of electrons that can take place through metallic objects or conductors when electric pressures, or charges, are exerted on the free electrons.

2 - Basic Electricity - II

THE THREE BIG NAMES IN ELECTRICTY

Without calling them by name, we have touched on the three elements always present in operating electric circuits:  

Current: A progressive movement of free electrons along a wire or other conductor caused by electrical pressure.

Voltage: The electron moving force in a circuit that pushes and pulls electrons (current) through the circuit. Also called electromotive force and electrical pressure.

Resistance: Any opposing effect that hinders free electron progress through wires when an electromotive force is attempting to produce a current in the circuit.

We will be talking a lot about these three properties of an electric circuit and how they relate to each other.

A SIMPLE CIRCUIT 

The simplest of electric circuits consists of some electron moving force, or source, such as that provided by a dry cell, or battery, and a load, such as an electric light, connecting wires and a control device. A pictorial representation and the electric diagram of a simple circuit is shown in figure 2-1.

The diagram in figure 2-1 is called a schematic diagram and is much easier to draw. The control device is a switch, to turn the bulb ON and OFF. In effect, the switch disconnects one of the wires from the cell. In our circuit, the switch could be connected anywhere to turn the bulb ON and OFF. In this circuit, the light bulb is the load. Although the wires connecting the source of electromotive force (the dry cell) to the load may have some resistance, it is usually tiny in comparison with the resistance of the load and is ignored in most cases.

A straight line in a schematic diagram is considered to connect components electrically and does not represent any resistance in the circuit. In the simple circuit shown, the cell produces the electromotive force (voltage) that continually pulls electrons to its positive terminal from the bulb's filament and pushes them out of the negative terminal to replace the electrons that were lost to the load by the pull of the positive terminal. The result is a continual flow of electrons through the lamp filament, connecting wires and source. The special resistance wire of the lamp filament heats when a current of electrons flows through it. If enough current flows, the wire becomes white hot and the bulb glows and gives off light (incandescence).

CURRENT

A stream of electrons forced into motion by an electromotive force is known as a current. Here we have a definition of electric current:

Current is the ordered movement of electrons in a circuit

In a good conducting material such as copper, one or more free electrons in the outer ring are constantly flying off at a high rate. Electrons from other nearby atoms fill in the gaps. There is a constant aimless movement of billions of electrons in all directions at all times in every part of any conductor. This random movement of electrons is not an electric current, as there is not yet movement in any one direction.

Only when a voltage is applied, do we get an ordered movement of electrons. When an electric force is applied across the conductor (from a battery), it drives some of these aimlessly moving free electrons away from the negative force toward the positive. It is unlikely that any one electron will move more than a fraction of a centimetre in a second, but an energy flow takes place along the conductor at a significant fraction of the velocity of light .

Notice that I said the energy flow in the circuit is very fast (almost the speed of light - but not quite). The speed of the electrons in a circuit - or the current flow is in fact very slow. I won't bore you with calculations. However, I did once calculate how fast the electron flow was in a typical circuit and it came to be about walking speed. Electron flow or current flow is very slow. The effect of an electric current at a distance through a conductor, on the other hand, is very fast.

If you have trouble with this and many do, think about how fast water travels through a pipe. The dam where the water comes from may be many kilometres away from the tap. When you turn the tap on the water comes out immediately does it not? Did the water travel all the way from the dam to the tap in an instant? I am sure you would agree that it did not. If I tried to tell you that it did you would most probably laugh at me and say the water was already in the pipe, all you did by turning the tap on was to make the water move in the pipe between the dam and the tap.

Similarly, the electrons are already in the wire (conductor). When we close a switch in the circuit and apply an electromotive force, all we are doing is making all the electrons move in the conductor at the same time. It may take a very long time for an electron leaving the source to reach the load if it ever does.

HOW FAST ARE MARBLES?

Let's do another analogy to make sure we have got this clear. Suppose a pipe was connected between Sydney and Melbourne. Imagine if we blocked off one end of the pipe and filled it with marbles until we could not fit any more in. We now unblock the pipe and we have a crowd of people at each end to witness the experiment and find out how fast marbles travel. The two crowds are in contact by telephone or radio and anxiously awaiting the big moment. One too many marbles is about to be inserted into the full pipe. As soon as a marble is inserted in Sydney, a marble drops out in Melbourne. The effect of pushing a marble into the pipe in Sydney caused an immediate result or effect in Melbourne. The newspaper's report "Eccentric experimenter proves that marbles travel at the speed of light". Is this right?

I hope you are shaking your head and saying 'no'. The marble, which fell out of the pipe in Melbourne, was sitting there ready to fall out as soon as the marble was pushed in at the Sydney end. So, marbles definitely do not travel at the speed of light any more than do electrons in a conductor. The marbles were already in the pipe just as the electrons were already in the conductor.

The effect of an electric current at a distance is almost instantaneous; however, the speed of the electrons is very slow.

A source of electrical energy does not increase the number of free electrons in a circuit; it merely produces a concerted pressure on loose, aimlessly moving electrons. If the material of the circuit is made of atoms or molecules that have no freely interchanging electrons, the source cannot produce any current in the material. Such a material is known as an insulator, or a non-conductor.

The amount of current in a circuit is measured in Amperes, abbreviated 'A' or Amp. An ampere is a certain number of electrons passing or drifting passed a single point in an electric circuit in one second. Therefore, an ampere is a rate of flow, similar to litres (or marbles) per minute in a pipe.

The quantity of electrons used in determining an ampere (and other electrical units) is the Coulomb, abbreviated 'C'. An ampere is one Coulomb per second. A single coulomb is 6,250,000,000,000,000,000 electrons. This large number is more easily expressed as 6.25 x 1018, which is read verbally as 6 point 25 times 10 to the eighteenth power". "Ten to the eighteenth power" means the

ELECTROMOTIVE FORCE OR VOLATGE

The electron moving force in electricity, variously termed electromotive force (emf), electric potential, potential difference (PD), electric pressure and voltage (V), is responsible for the pulling and pushing of the electric current through a circuit. The force is the result of an expenditure of some form of energy to produce an electrostatic field.

An emf (I like to read this as 'electron-moving force') exists between two objects whenever one of them has an excess of free electrons and the other has a deficiency of free electrons. An object with an excess of electrons is negatively charged. Similarly, an object with a deficiency of electrons is positively charged. Should two objects with a difference in charge be connected by a conductor, a discharge current will flow from the negative body to the positive one.

Instead of writing negatively or positively charged all the time it is easier to say '-Ve' or '+Ve.' I tend not to use this notation, but you should know what it means.

An emf also exists between two objects whenever there is a difference in the number of free electrons per unit volume of the objects. In other words, both objects may have a negative charge, but one is more negative than the other. The less negative object is said to be positive with respect to the more negative object.

In the electrical trades, it is common to hear of current flow from positive to negative. This is called the conventional direction of current flow. This is just what it says, a convention (popular method). Current flow is electron flow and it is from negative to positive. Conventional current flow is mostly used in Electrical Engineering. In Radio, there is a greater tendency to do what I have done in this book and that is to use electron flow; current flows from negative to positive.

The unit of measurement of electric pressure, or emf, is the Volt (V). A single torch dry cell produces about 1.5V. A volt can also be defined as the pressure required to force a current of one ampere through a resistance of one ohm.

PRODUCING AN ELECTRON-MOVING FORCE

NOTE: A battery is a collection of cells (like a battery of cannons). There is no such thing as an AA battery; it is an AA cell. On the other hand, a 9 volt transistor battery or a car battery are samples of real batteries because they are constructed from a number of cells connected together (in series).

Chemical (cells and batteries).

Electromagnetic (generators).

Thermal (heating the junction of dissimilar metals).

Magnetostriction (filters and special energy converters called transducers).

Static (laboratory static electricity generators).

Photoelectric (light sensitive cells).

Magnetohydrodynamics (MHD, a process that converts hot gas directly to electric current).

Piezoelectricity - some materials produce a voltage when physical pressure is applied to them.

EFFECTS OF AN ELECTRIC CURRENT

Heat and light - current flowing in a conductor causes the conductor's temperature to increase. If the temperature increases sufficiently, the conductor will become incandescent and radiate light.

Magnetic - a conductor carrying a current will produce a magnetic field around the conductor.

Chemical - electroplating, charging batteries. An electric current is able to cause a chemical reaction.

THE BATTERY IN A CIRCUIT

In the explanations thus far, "objects," either positively or negatively charged, have been used. A common method of producing an emf is by the chemical action in a battery. Without going into the chemical reactions that take place inside a cell, a brief outline of the operation of a Leclanche cell is given here.

Consider a torch battery. Such a battery (two or more cells form a battery) is composed of a zinc container, a carbon rod down the middle of the cell and a black, damp, paste like electrolyte between them. The zinc container is the negative terminal. The carbon rod is the positive terminal. The active chemicals in such a cell are the zinc and the electrolyte.

The materials in the cell are selected substances that permit electrons to be pulled from the outer orbits of the molecules or atoms of the carbon terminal, chemically by the electrolyte, and be deposited onto the zinc can. This leaves the carbon positively charged and the zinc negatively charged.

The number of electrons that move is dependent upon the types of chemicals used and the relative areas of the zinc and carbon electrodes. If the cell is not connected to an electric circuit, the chemicals can pull a certain number of electrons from the rod over to the zinc. The massing of these electrons on the zinc produces a backward pressure of electrons, or an electric strain, equal to the chemical energy of the cell and no more electrons can move across the electrolyte.

If a wire is connected between the positive and negative terminals of the cell, the 1.5 V of emf starts a current of electrons flowing through the wire. The electrons flowing through the wire start to fill up the deficient outer orbits of the molecules of the positive rod.

The electron movement away from the zinc into the wire begins to neutralise the charge of the cell. The electron pressure built up on the zinc, which held the chemical action in check, is decreased. The chemicals of the electrolyte can now force an electron stream from the positive rod through the cell to the zinc, maintaining a current of electrons through the wire and battery as long as the chemicals hold out.

As soon as the wire begins to carry electrons; the electrolyte also has an electric current moving through it. This motion produces an equal amount of current through the whole circuit at the same time. This is a very important concept to understand. There are no bunches of electrons moving around an electric circuit like a group of racehorses running around a track. A closed circuit is more like the racetrack with a single lane of cars, bumper to bumper. Either all must move at the same time, or none can move. In an electric circuit, when electrons start flowing in one part, all parts of the circuit can be considered to have the same value of current flowing in them instantly. Most circuits are so short that the energy flow velocity, 300,000,000 meters per second, may be disregarded. Figure 2-4 shows the construction of a typical 9V batteries from individual cells.

IONISATION

When an atom loses an electron, it lacks a negative charge and is therefore positive. An atom with a deficiency of one or more electrons is called a positive ion. On the other hand, if an atom were to gain an electron, albeit temporarily, it is a negative ion.

In most metals the atoms are constantly losing and regaining free electrons. They may be thought of as constantly undergoing ionisation. Because of this, metals are usually good electrical conductors. Atoms in a gas are not normally ionised to any great extent and therefore, a gas is not a good conductor under low electric pressures.

However, if the emf is increased across an area in which gas atoms are present, some of the outer orbiting electrons of the gas atoms will be attracted to the positive terminal of the source of emf and the remainder of the atom will be attracted toward the negative. When pressure increases enough, one or more free electrons may be torn from the atoms. The atoms are ionised. If ionisation happens to enough of the atoms in the gas, a current flows through the gas. For any particular gas at any particular pressure, there is a certain voltage value that will produce ionisation. Below this value, the number of ionised atoms is small. Above the critical value, more atoms are ionised, producing greater current flow, which tends to hold the voltage across the gas at a constant value. In an ionised condition the gas acts as an electric conductor.

Examples of ionisation of gases are lightning, neon lights and fluorescent lights. Ionisation plays an important part in electronics and radio.

TYPES OF CURRENT AND VOLTAGE

Different types of currents and voltages that are dealt with in electricity:

Direct current (DC). There is no variation of the amplitude (strength) of the current or voltage. Supplied from batteries, DC generators and power supplies.

Varying direct current (VDC). The amplitude of the current or voltage varies but never falls to zero. Found in many radio and electronic circuits. A telephone is a good example of the use of varying direct current.

Pulsating direct current (PDC). The amplitude drops to zero periodically (such as our light bulb circuit if it was repeatedly switched on and off).

Alternating current (AC). Electron flow reverses (alternates) periodically and usually changes amplitude in a more or less regular manner.

AC is produced in AC generators, oscillators, some microphones and radios in general. Household electricity is alternating current.

RESISTANCE

Resistance is that property of an electric circuit which opposes the flow of current. Resistance is measured in Ohms. The higher the resistance in an electric circuit the lower the current flow. The symbol used for resistance is the Greek letter Omega - 0. If a circuit with an electric pressure of 1 volt causes a current of 1 Ampere to flow, then the circuit has a Resistance of 10.

What is resistance? It is all well and good to say it is the opposition to current flow but from where does the opposition come? Resistance causes heat. In fact, resistance is the only electrical property that produces heat. Resistance is the effort or energy that it takes to get electrons moving. When we do get them moving some of the energy is dissipated as heat. It is lost energy. So resistance is the energy lost making electrons move in an orderly manner.

WHATS IN A NAME

We have learned quite a few new terms. Some of these terms are taken from people's names. These people were usually pioneers in the fields of physics, electricity or electronics. Read the very short biographies below and think about the person's name and what it represents in an electric circuit.

George Simon Ohm. Born March 16, 1789, Erlangen, Bavaria [Germany]. Died July 6, 1854, Munich. German physicist who discovered the law named after him, which states that the current flow through a conductor is directly proportional to the potential difference (voltage) and inversely proportional to the resistance.

Andre-Marie Ampere. Born Jan. 22, 1775, Lyon, France. Died June 10, 1836, Marseille. French physicist who founded and named the science of electrodynamics, now known as electromagnetism. Ampere was a prodigy who mastered all mathematics then existing by the time he was 12 years old. He became a professor of physics and chemistry at Bourg in 1801 and a professor of mathematics at the Ecole Polytechnique in Paris in 1809.

Allesandro Giuseppe Antonio Anastasia Volta. Born Feb. 18, 1745, Como, Lombardy [Italy]. Died March 5, 1827, Como. Italian physicist whose invention of the electric battery provided the first source of continuous current. He became a professor of physics at the Royal School of Como in 1774 and discovered and isolated methane gas in 1778. One year later he was appointed to the chair of physics at the University of Pavia.

Charles Augustin de Coulomb. Born June 14, 1736, Angouleme, France. Died Aug. 23, 1806, Paris. French physicist best known for the formulation of Coulomb's law, which states that the force between two electrical charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Goerges Leclanche. Born 1839, Paris. Died Sept. 14, 1882, Paris. French engineer who in about 1866 invented the battery bearing his name. In slightly modified form, the Leclanche battery, now called a dry cell, is produced in great quantities and is widely used in devices such as torches and portable radios.

3 - Basic Electricity - III

MORE ON RESISTANCE

As discussed briefly in Basic Electricity Part II, resistance is the opposition to current flow in any circuit. Resistance is measured in ohms and the symbol for resistance is Ω, though for equations (we will be using them soon) the letter 'R' is used.

Copper and silver are excellent conductors of electric current. When the same emf (voltage) is applied across an iron wire of equivalent size compared to silver, only about one-sixth as much current flows. Iron is considered to be good conductor.

When the same voltage (emf) is applied across a length of rubber or glass, no electron drift results. These materials are insulators. Insulators are used between conductors when it is desired to prevent electric current from flowing between them. To be more precise, in a normal 'electric' circuit the current flow is negligible through an insulator.

Silver is one of the better conductors and glass is one of the best insulators. Between these two extremes are found many materials of intermediate conducting ability. While such materials can be catalogued as to their conducting ability, it is more usual to think of them by their resisting ability. Glass (when cold) completely resists the flow of current. Iron resists much less. Silver has the least resistance to current flow.  

The resistance of a wire or other conducting material is dependent on four physical factors:

The type of material from which it is made (silver, iron, etc.).

The length (the longer the conductor, the greater the resistance).

The cross-sectional area of the conductor (larger area, more free electrons and less resistance).

Temperature (the higher the temperature, the greater the resistance, except for carbon and other semiconductor materials).

A piece of silver wire of given dimensions will have less resistance than an iron wire of the same dimensions. It is reasonable to assume that if a 1-metre piece of wire has a 1 ohm resistance, then 2 metres of the same wire will have 2 ohms of resistance.

On the other hand, if a 1 metre piece of wire has 1 ohm of resistance then two pieces of this wire placed side by side will offer twice the cross-sectional area, will conduct current twice as well and therefore will have half as much resistance.

R=ρL/A

Where:

R = resistance in ohms.

ρ = resistivity of the material in ohms per metre cube.

L = length in metres.

A = cross-sectional area of the wire in square metres.

ρ is a Greek letter spelt 'rho' and pronounced the same as in 'row-your- boat.'

RESISTIVITY ρ

Since the resistance of a wire (or any other material) depends on its shape, we must have a standard shape to compare the conducting properties of different materials. This standard is a cube measuring 1 metre on each side. That's a pretty big cube! Smaller material sizes are measured and then the results extrapolated to an Ohm-metre. The resistance measured between opposite faces of the cube is called the resistivity.

Resistivity should not be confused with resistance. The resistivity of a material is the resistance measured for a standard size cube of that material. If you look at the table below you will see for example that the resistivity of copper is 1.76 x 10-8• The part of this number shown as 10-8 is called the exponent and the 'minus 8' means that the decimal point must be moved 8 places to the left. If we take 1.76 and move the decimal point 8 places to the left, we get:

0.000 000 017 6 ohm-metre (Ω.m)

Now this is a very low resistance indeed. It is the resistance that would be measured across the opposite faces of a cubic metre of solid copper. Resistivity is not resistance. Resistivity is a measure of the resistance of a material of a standard size to allow us to compare how well that material conducts or resists current compared to other materials.

The Resistivity of Metals and Alloys at 20 degrees C.  

The most common conducting material used in radio is, of course, copper, for it is a good conductor and relatively cheap. You can see in the table that aluminium is not as good a conductor as copper. However, aluminium is used for conductors more than any other material because of its light weight and corrosion resistance. In overhead power line distribution, weight is a crucial consideration, so aluminium is the conductor of choice. In radio and communications, antennas are made of aluminium, because of the light weight and ability to withstand corrosion.

CALCULATING THE RESISTANCE OF A WIRE

A 100 metre length of copper wire is used to wind the primary of a transformer and the wire has a diameter of 0.5 millimetres. What is the resistance of the winding?

Solution:

We need to use the equation R=ρl/A

Since the wire is copper, we look at the Resistivity table and get a ρ of 1. 76x10-8 for copper. The length (L) = 100 metres. We need to calculate 'A' (the cross-sectional area) from the equation for the area of a circle.

A= πd2/4 or πr2 

Where:

π = Another Greek letter, the mathematical constant Pi, approximated by 22/7

d = diameter of the circle (wire).

A= 22/7 x (0.5 x 10-3)2 / 4

A= 3.142 x 0.00000025 / 4

A= 0.000000196375 square metres

R = ρl/A

R = 1. 76x10-8 x 100 / 0.000000196375

R = 8.96 ohms

R=ρL/A  ← What does this say?

We shall look at the numerator and the denominator on the right-hand side separately.

R=ρL

This means that resistance is directly proportional to the resistivity and to the length. As either p or L changes so does R. If p or L increases by say a factor of 2 then so does R. In other words, doubling the length of a wire doubles its resistance. If we increase the length by 3.25 times the resistance is increased 3.25 times. So, from the equation, we say R is directly proportional to length and resistivity.

The cross-sectional area is in the denominator of the equation on the right-hand side. Ignoring the numerator for the moment, we can rewrite this relationship as:

R=1/A

This means that resistance is inversely proportional to the cross-sectional area, A. If the cross-sectional area of a wire was to be doubled then its resistance would be halved. This would be the same as twisting two wires together and using them as one. If the cross-sectional area of a wire was increased by a factor of say 4.5 times, then the resistance would be R/4.5 of what it originally was.

We have avoided bringing temperature into our calculations. The resistance of metals increases with temperature - we will discuss this further later.

In the real world, conductors are not round. Wire is not truly round. Copper circuit board track is definitely not round. In these cases, we work with the cross-sectional area given by the manufacturer. I would like you to know what this equation 'says' to you about the resistance of a wire.

Resistance is directly proportional to the length and resistivity and inversely proportional to the cross-sectional area.

THE METRIC SYSTEM

Scientific measurements are mostly done using the metric system. The metric system uses multiples of base 10. The basic prefixes of metric units of measurement are:

The common prefixes used in radio and electronics that you need to learn are underlined. You will need to memorise all of these.

Volts, amperes, ohms, etc. may use metric based prefixes. Some examples of the utilisation of these prefixes are: 1 kV = 1000 volts.

1mV = one thousandth of a volt.

10MΩ = 10 million ohms

56mΩ = 56 thousandths of an ohm.

25mA = 25 thousandths of an ampere.

65µA = 65 millionths of an ampere.

CONVERTING FROM ONE PREFIX TO ANOTHER

Many a mark has been lost in Advanced Radio exams when a question asks you to convert from one unit to another.

Questions like; convert Megahertz to Kilohertz? - and other similar unit conversions.

Hertz is the UNIT. Mega and Kilo are prefixes of the unit.

Let's try the one above.

Megahertz is 106 - 106 means 1,000,000 or one million.

Kilohertz is 103 - 103 means 1,000 or one thousand.

Megahertz is a larger unit than kilohertz. How much larger is a megahertz than a kilohertz? How many times will one thousand divide into one million?

It takes 1,000 kilohertz to make one megahertz. A megahertz is 1000 times larger than a kilohertz, so to convert megahertz to kilohertz, we must multiply megahertz by 1000.

144MHz is the same as 144,000 kilohertz.

If you were asked to do it the other way round, that is, convert kilohertz to megahertz you would DIVIDE by 1000.

100kHz is 0.1MHz.

I think this looks all too easy to some and for this reason, it is done too quickly and very often the wrong answer is picked in the exam and 2 marks are lost all too easily.

Let's do another.

How do you convert microfarads to picofarads?

Please do it step by step, not what you immediately think it should be, unless you are very confident.

This would be my reasoning.

Micro= 1/1,000,000 or one millionth.

Pico = 1/1,000,000,000,000 or one millionth of a millionth.

This means that picofarads are one million times SMALLER than microfarads. To convert microfarads to picofarads MULTIPLY by 1,000,000.

Example - convert 0.001 microfarads to picofarads.

If we multiply 0.001 by 1,000,000, we get 1000 picofarads.

The easiest way to multiply by 1,000,000 is to move the decimal point 6 places to the right. Can you see that moving the decimal point in 0.001 six places to the right gives you 1000? Do it on a piece of paper - it's the way I do it. Simply put your pen on the decimal point in 0.001 and draw 6 'hoops' moving to the right. Then add "zeros" to the 'hoops' that have nothing in them.

TIP: Learn to use the ENG key on your scientific calculator. If you need to do a conversion then just enter the number you are given in scientific notation and then repeatedly press the ENG until you get the exponent you want. If the numbers go the wrong way press SHIFT ENG to reverse the direction. ENG and SHIFT ENG never change the number you have entered they just manipulate the exponent.

This may seem like a silly way of doing it, but it is a safe way. If you had to divide by 1 million (converting picofarads to microfarads), use the same method only move the decimal point 6 places to the left.

You can use pen and paper in the exam. Using this method, you can convert any prefix to another prefix. Do not try and memorise the conversions, but do memorise what each prefix means, then work out how to convert one to the other using the techniques described above.

SYMBOLS IN TEXT

Since some assignments (when this book is used as part a course) are done using plain text you cannot show superscripts, subscripts and symbols. Many email programs do allow this, but you should avoid using symbols as when your email is received the symbols could be stripped out.

This is the method I use (but you can use your own as long as it is clear).

For example, show:

106 (10 to the power 6) as 10^6 

10-6 (10 to the power minus 6) as 10^-6 

Use the '^' which is a 'shifted 6' to indicate that what follows is a superscript. For symbols, you can type the symbol name in brackets. Take the formula for the resistance of a conductor that we used earlier in this chapter.

R=ρL/A

The Greek letter ρ can be typed as (rho): R = (rho)L/A

If you have to type the Greek letter π in a formula you can just type (Pi).

THE RESISTOR COLOUR CODE

Resistors can be very small electronic components. Too small to write the resistor's value on, so instead, each resistor has colour coded bands which tell you its value and tolerance. The tolerance is the percentage of error, about which the resistor may vary from its coded value.

Resistors are manufactured in what are called preferred values. Usually, you will require a certain value of resistance in ohms and normally you will choose a resistance with the closest preferred value. If you want a specific resistance that does not match any preferred value, then you may have to make up a resistor especially for the job, or more commonly, you will use a variable resistance and adjust it using an ohmmeter.

There are only so many numerical values in a decade, i.e. from 0-10, or 0-100, 0-1,000, etc. Simple resistors only have 12 values in a decade e.g. 1.0, 1.2, 1.5, 1.8, 2.2, 2. 7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2. This is called the E12 series

A newer series called E24 has 24 standard values and closer tolerances.

Resistors can have either 4 or 5 coloured bands. With each type, the last band is the tolerance. Five band resistors simply have room for three significant figures even though the E24 series only really needs two bands. Most of the time these resistors are 1 or 2% tolerance (within +/- 1 or +/- 2% of the stated resistance). This will be either a brown or red band, respectively, at one end of the resistor, separated from the other bands. The value of the resistor starts at the other end.

The tolerance band is always a band on the end and separated slightly from the other bands.

The second last band is the multiplier for both 4 and 5 colour banded resistors. The first letter of each word in the following sentence may help you to remember the colour code.

Big Boys Race Our Young Girls But Violet Generally Wins.

Example 1: 

A resistor has 4 coloured bands. From left to right the bands are coloured:

Yellow, Violet, Yellow and Gold

The first significant digit is: 4.

The second significant digit is: 7.

The third band is the multiplier, in this case, 4 and means add four zeros.

So we get 470000Ω or 470kΩ.

The tolerance is (gold) +/- 5%.

So the final result is 470kΩ +/-5%.

Example 2: 

A resistor has 5 coloured bands. From right to left the bands are coloured:

Green, Blue, Black, Red, Brown

The first significant digit is: 5.

The second significant digit is: 6.

The third significant digit is: 0.

The multiplier in the fourth band is 2 (add two more zeros).

So we get 56000 Ohms or 56kΩ.

The tolerance band is 1, therefore, 1% tolerance.

So the final result is 56kΩ +/- 1%

The fourth band on a five-banded resistor can be Gold or Silver. Gold means the multiplier is 0.1 and Silver means 0.01. To multiply by 0.1, move the decimal place one place to the left. To multiply by 0.01, move the decimal place two places to the left.

SURFACE MOUNT RESISTORS

Surface mounted resistors (SMD) are so small the resistor colour code is impractical. These resistors have a 3 or 4 character code to convey their resistance

CONDUCTANCE

There is no need for you to be concerned about the term 'conductance'. I mention it only for your information and you will occasionally see the term. You will not see the term in your exam.

For some (not myself) it is more convenient to work in terms of the ease with which a current can be made to flow, rather than the opposition to current flow (resistance). Conductance is merely the reciprocal of resistance. The symbol for conductance is 'G' and G=l/R. Conductance is measured in Siemens 'S', formerly the 'Mho'.

The term 1/R is simply resistance divided into 1 giving the conductance in siemens. Taking any quantity 'x' and dividing that quantity into 1 is called the reciprocal of the quantity - this you will need to remember.

RESISTORS

Pictured are some of the types and sizes that resistors are packaged in. They are all just resistors. Resistors can be made to vary; these are called rheostats, potentiometers, or just plain variable resistors.

The resistors in figure 3-3 are not shown to scale.  

(a)  fixed low wattage carbon film resistor

(b)  a variable motorised resistor.

(c)  two  potentiometers  on  the  one  shaft.  

(d)  a variable resistor - potentiometer.

(e)  a surface mount resistor

(f)  a  variable  'slider'  resistor.  

(g) high wattage  wire  wound  resistors.  

(h) a very high power resistor with heat sink.

(i)  a  multi-turn  circuit  board  mounted  variable  resistor.  

(j)  a  circuit  board  mounted  variable  resistor  -  trim  pot.  

The only reason that resistors are made large is so they can dissipate (give off to their surroundings) heat. I only add this because a physically large resistor does not mean a large resistance. The large resistor in figure 3-3(h) may only be a few ohms and the tiny one in figure 3-3(a) could be 1MΩ. Large physical resistors will often not use the colour code and have their value written on them in ohms.

SCHEMATIC SYMBOLS OF RESISTORS

(a)  fixed resistor.

(b)  variable resistor.

(c)  a  trimmer  potentiometer.  

(d)  rheostat  -  essentially  the  same  as  (e).  

(e)  a potentiometer.

(f)   an  alternative  symbol  for  a  fixed  resistor.  

4 - Ohm's Law

Ohm's Law describes the relationship between current, voltage and resistance in an electric circuit.

Ohm's Law states:

The current in a circuit is directly proportional to voltage and inversely proportional to the resistance.

Let:

I = current

E = voltage

R = resistance

Part of Ohm's Law says: current is directly proportional to voltage.

Using the symbols given, we can write an equation to show a direct proportion between current and voltage.

I=E

Normally the above equation is read I 'equals' E. It can just as easily and more understandably be read as: I is directly proportional to E.

I know I harp on about the direct proportion and inverse proportion stuff a lot. I do so because it is so important to understand this thoroughly before we come to do more complex equations.

I=E

Means that if the voltage is increased or decreased in a circuit, then the current will increase or decrease by the same amount. Double the voltage and you double the current. Halve the voltage and you halve the current. This is a direct proportion.

The other part of Ohm's Law says that current is inversely proportional to the resistance. This can be written as:

I=1/R

Now 1/R is a fraction with a numerator (the top part, 1) and a denominator, R. 1/R is a fraction just like 1/4, 1/2 and 3/8 are fractions.

R is the denominator in the fraction. What happens to the whole fraction if the denominator is changed? Watch.

1/2, 1/3, 1,4, 1/5, 1/6

As the denominator increases, the fraction decreases. In fact, if the denominator doubles then the fraction is half the size. 1/4 is half the size of 1/2.

'I' is the same as 1/R. This is an inverse proportion. If I is the same as 1/R and R is increased in size by three times, then the fraction 1/R is a third the size now and since 1/R is the same as the current, then the current is a third the size also.

The complete equation for Ohm's Law then is:

This equation, derived from Ohm's law, enables us to find the current flowing in any circuit if we know the voltage (E) and resistance (R) of the circuit.

For example, a resistor of 20 ohms has a 10 volt battery connected across it. How much current will flow through the resistor?

I=E/R =10/20 = 1/2 = 0.5 amperes

The equation I=E/R can be transposed for E or for I.

In some texts a diagram called the Ohm's Law triangle is used to help you rewrite the equation for E and R. This is okay, however, you do really need to know how to transpose equations - not just this one. If you learn to transpose this equation, then you will be able to do it with many others. There is a memory wheel at the end of this chapter that can help you remember equations for Ohm's law and power. You will also find a tutorial on transposing equations and using a calculator in the RES downloads area if you feel you might need some extra help. Always write to your facilitator if you require assistance.

We want to transpose I=E/R for E and R. The rule is: do whatever you like to the  equation and it will always be correct as long as you do the same to each side of the equal sign. For example, if I multiply both sides of the equal sign by R, we get:

On the left-hand side (LHS) we have I x R. On the RHS we have E multiplied by Rand divided by R. Can you see that the R's cancel on the RHS? R/R is 1/1.

There is no need to show the 1s at all since multiplying or dividing a number by 1 does not change the number, therefore:

Re-writing the above with E on the LHS we get:

When there is no sign between two letters in an equation, like IR above, it is assumed the IR means Ix R.

Now transpose the equation for R:

Multiply both sides by 1/E (which is the same as dividing both sides by E):

On the RHS the E's cancel out so we can rewrite the equation as:

or

Turning both sides upside down (remember we can do anything as long as we do the same to both sides):

Remove the '1' and reverse the sides to get:

So the three equations are:

I have probably bored you by now - however; it is really important to be able to transpose equations for yourself. For one thing, you don't need to remember so many equations.

So if you know any two of the three in 'E', 'R' and 'I' then you can transpose like we did here to calculate the missing one.

Finding I when you know E and R:

Finding E when you know I and R:

Finding R when you know I and E:

POWER

The unit of electrical power is the Watt (W), named after James Watt. One watt of power equals the work done in one second by one Volt of potential difference in moving one Coulomb of charge.

Remember that one coulomb per second is an ampere. Therefore, power in watts equals the product of amperes times volts.

Power (P) in watts= volts x amperes

P =E x I

Example: A toaster takes 5A from the 240V power line. How much power is used?

P = E x I = 240V x 5A

P = 1200 watts

Example: How much current flows in the filament of a household 75 watt light bulb connected to the standard 240 volt supply?

You know P (power) and E (volts). You need to transpose P=EI for 'I' and you get:

I=P/E Therefore:

I=75/240

I=0.3125 amperes

This amount of current is best expressed in milliAmperes. To convert amperes to milliamperes multiply by 1000 or think of it as moving the decimal point 3 places to the right, which is the same thing. This gives:

312.5mA Power in watts can also be calculated from:

P=I2R, read, "power equals I squared R".

P=E2/R, read, "power equals E squared divided by R".

Watts and Horsepower Units. 746W=1 horsepower.

This relationship can be remembered more easily as 1 horsepower equals approximately 3/4 kilowatt. One kilowatt= 1000W.

WORK

Work= Power x Time

Practical Units of Power and Work. Starting with the watt, we can develop several other important units. The fundamental principle to remember is that power is the time rate of doing work, while work is the power used during a period. The formulas are:

Power= work/time and

Work= power x time

The unit of power is the watt. One watt used during one second equals the work of one joule. In other words, one watt is one joule per second. Therefore, 1W = 1J/s. The joule is a basic practical unit of work or energy.

A unit of work that can be used with individual electrons is the Electron-Volt. Note: that the electron has charge, while the volt is potential difference. Now 1eV is the amount of work required to move an electron between two points having a potential difference of one volt. Since 6.25 x 1018 electrons equal 1C and a joule is a volt-coulomb, there must be 6.25 x 1018 eV in 1J.

Kilowatt-hours. This is a unit commonly used for large amounts of electrical work or energy. The amount is calculated simply as the product of the power in kilowatts multiplied by the time in hours during which the power is used. This is the unit of energy you need to know.

Example: A light bulb uses 100W or 0.1kW for 4 hours (h), the amount of energy used is:

Kilowatt-hours= kilowatts x hours

= 0.1 X 4

= 0.4kWh.

We pay for our household electricity in kilowatt-hours of energy.

POWER DISSIPATION IN RESISTANCE

When current flows through a resistance, heat is produced due to the energy consumed in moving free electrons and the atoms obstructing the path of electron flow. The heat is evidence that power is used in producing current. This is how a fuse opens, as heat resulting from excessive current melts the metal link in the fuse.

The power is generated by the source of applied voltage and consumed in the resistance in the form of heat. As much power as the resistance dissipates in heat must be supplied by the voltage source; otherwise, it cannot maintain the potential difference required to produce the current.

Any one of the three formulas can be used to calculate the power dissipated in a resistance. The one to be used is just a matter of convenience, depending on which factors are known.

In the following diagram, the power dissipated with 2A through the resistance and 6V across it is 2x6=12W. Or, calculating in terms of just the current and resistance, we get 22 times 3, which equals 12W. With voltage and resistance, the power can be calculated as 6x2 or 36 divided by 3, which also equals 12W.

Resistance is the "only" electrical property that dissipates heat

We have introduced a new schematic symbol here too. The schematic symbol of a battery is shown at the left. Note the small bar at the top is the negative terminal. The direction of current (electron) flow is shown correctly, from negative to positive.

No matter which equation is used, 12W of power is dissipated, in the form of heat. The battery must generate this amount of power continuously in order to maintain the potential difference of 6V that produces the 2A current against the opposition of 3Ω.

In some applications, the electrical power dissipation is desirable because the component must produce heat in order to do its job. For instance, a 600W toaster must dissipate this amount of power to produce the necessary amount of heat. Similarly, a 300W light bulb must dissipate this power to make the filament white hot so that it will have the incandescent glow that furnishes the light. In other applications, however, the heat may be just an undesirable by-product of the need to provide current through the resistance in a circuit. In any case, though, whenever there is current in a resistance, it dissipates power equal to 12R.

The term 12R is used many times to describe unwanted resistive power losses in a circuit. You will hear of the expression 12R losses as we go through this course.

ELECTRIC SHOCK

While you are working on electric circuits, there is often the possibility of receiving an electric shock by touching the "live" conductors when the power is on. The shock is a sudden involuntary contraction of the muscles, with a feeling of pain caused by current through the body. If severe enough, the shock can be fatal.

The greatest shock hazard is from high voltage circuits that can supply appreciable amounts of power. The resistance of the human body is also an important factor. If you hold a conducting wire in each hand, the resistance of the body across the conductors is about 10,000 to 50,000Ω. Holding the conductors tighter lowers the resistance. If you hold only one conductor, your resistance is much higher. It follows that the higher the body resistance, the smaller the current that can flow through you. Dry skin has much higher resistance than wet skin.

A safety rule, therefore, is to work with only one hand if the power is on. Also, keep yourself insulated from earth ground when working on power line circuits since one side of the line is usually connected to earth. Also, the metal chassis of radio and television receivers is often connected to the power line ground for your safety. The final and best safety rule is to work on the circuits with the power disconnected if at all possible and make resistance tests.

Note that it is current through the body, not through the circuit, that causes the electric shock. This is why care with high voltage circuits is more important since sufficient potential difference can produce a dangerous amount of current through the relatively high resistance of the body. For instance, 500V across a body resistance of 25,000Ω produces 0.02A, or 20mA, which can be fatal. As little as 10μA through the body can cause an electric shock. In an experiment on electric shock to determine the current at which a person could release the live conductor, this value of "let go" current was about 9 mA for men and 6 mA for women.

In addition to high voltage, the other important consideration in how dangerous the shock can be is the amount of power the source can supply. The current of 0.02A through 25,000Ω means the body resistance dissipates 10W. If the source cannot supply 10W, its output voltage drops with the excessive current load. Then the current is reduced to the amount corresponding to how much power the source can produce.

In summary, then, the greatest danger is from a source having an output of more than about 30V with enough power to maintain the load current through the body when it is connected across the applied voltage.

RESISTANCE OF EARTH

The earth, no not the ground, I am speaking of planet earth, is not made of metal (in any great concentrated amount) so one may expect that it is not a good conductor. However, if you recall the equation R = pl/ A, where A is the cross-sectional area - well the earth indeed does have an enormous cross-sectional area. This means for many applications the earth itself can be used as a conductor to save us having to run two conductors from the source to the load. Such circuits are called earth return and they have been used for power distribution and telephone communications.

Some Revision

By now you should have a good concept of current, voltage and resistances. It should be clear in your mind that current flows in a circuit pushed and/or pulled along by voltage. Current is restricted from flowing in a circuit by resistance.

You should be aware by now that statements like; "the voltage through the circuit" are in error. Voltage is electrical pressure. Voltage is never through anything. You can have voltage across the circuit or a component, but you can never have voltage through anything. Current flows through the circuit pushed along by voltage and restricted by resistance.

VOLTS PUSH AMPS THROUGH OHMS

A final point. You can have voltage without current. However, you cannot have current without voltage. A battery sitting on a bench has a voltage on its terminals - but no current is flowing. Voltage is electric pressure just like the water pressure in your tap. Current is the flow of electrons just like the flow of water from a tap. If the tap is turned off, you do not have a water flow. However, the pressure is definitely still there. Likewise, it is possible (with a disconnected battery) to have voltage (electric pressure) and no current (flow).

However, you cannot have any flow without pressure. So voltage can exist on its own, current cannot.

The unit of current is the Ampere. When 6.25x1018 electrons flow past a given point in a circuit in one second, the current is said to be one ampere.

Since 6.25 x 1018 electrons is a coulomb, this can be used in the definition of an ampere. An ampere of current is said to flow when one coulomb passes a given point in one second.

OHM'S LAW WHEEL

5 - Series Circuits

When components in a circuit are connected in serial order with the end of each joined up to the other end of the next as shown below in figure 5-1, they form a series circuit.

An electric current consists of an ordered movement of electrons. In the schematic shown in figure 5-1, the current leaves the negative terminal of the battery and flows through R1, R2 and R3, then returns to the positive terminal.

It does not matter where we measure the current in a series circuit as we will always get the same value of current everywhere, as:

Current is the same in all parts of a series circuit

The total resistance of any number of resistances in series is simply the sum of the individual resistances:

Rt=R1+R2+R3..n

Suppose the resistors in figure 5-1 were 10, 20 and 30 ohms respectively and the applied voltage was 10 volts. What is the current flowing in the circuit?

Rt=R1+R2+R3

Rt=10+20+30
Rt=60 ohms

We now know the total resistance (60 ohms) and the applied voltage is 10 volts, so we can use Ohm's law to calculate the current flowing in the circuit.

l=E/R = 10/60 = 1/6 A or 0.1666 A or 166.6 milliamps

All of the resistances shown in the four circuits of figure 5-2 are in series. The circuits are drawn differently, but nevertheless, they are all series circuits and the current is  the same in every part of the circuit. The rectangle symbol is an alternative method of drawing a resistor. In this circuit the rectangle could be any type of component.

Another rule that you must learn is:

The sum of the voltage drops in a series circuit is equal to the applied voltage.

Going back to figure 5-1, we have three resistances R1, R2 and R3 in series, connected to a 10 volt supply. We can calculate the voltage across R1 because we know the resistance and we know the current through R1.

Let's call the voltage across R1 'ER1',

then:

ER1 = I x R1 = 0.1666 x 10 = 1.666 volts

And for the other two resistances:

ER2 =I x R2 = 0.1666 x 20 = 3.332 volts

ER3 =I x R3 = 0.1666 x 30 = 4.998 volts  

The sum of the voltage drops across each resistance will equal the applied voltage. There will be a small error in our example due to rounding of decimals.

Et=ER1+ER2+ER3 = 1.666 + 3.332 + 4.998 = 9.996 volts (with rounding error).

Notice how the supply voltage is distributed around the circuit - think about it for a while. The least resistance has the smallest voltage drop across it and the largest  resistance has the most voltage across it. This makes sense when we realise that the current in a series circuit must be the same through all components. R3 needs nearly half of the supply voltage to get 0.1666 amps to flow through it and R1 requires only 1.666 volts to produce the same current through it.

If two resistances of equal value were connected in series across a supply voltage of say 20 volts, then each resistance would have exactly half the supply voltage across it. You can work out the voltage drops in a series circuit by using a method known as 'proportion'.

Let's use our series circuit again and this time, we will work out the voltage drops for R1, R2 and R3 without using the current.

The total resistance of the circuit is 60 ohms (Rt) and the supply voltage is 10 volts.

ER1 = R1/Rt x 10 = 10/60 x 10 = 1.6667 volts (rounded)

ER2 = R2/Rt x 10 = 20/60 x 10 = 3.3334 volts (rounded)

ER3 = R3/Rt x 10 = 30/60 x 10 = 5 volts

AN EXAMPLE OF A SERIES CIRCUIT

The best example I can think of for a common series circuit which will also demonstrate one of the problems with series circuits is Christmas tree lights. These lights are low voltage lights of about 10 volts. Christmas tree lights plug into the mains voltage of 240 volts. Suppose each bulb requires 10 volts and you connect 24 of them in series, then each bulb will have 10 volts across it.

At least this is the way Christmas tree lights are supposed to work. Darn dangerous things if you ask me because if you break a bulb you are exposing yourself to potentially (no pun intended) 240 volts.

So, from the point of view of Christmas tree lights, series circuits have an advantage. The disadvantage is, should a bulb blow, no current will flow in the circuit and all the lights will go out.

What would happen if you placed a short circuit where a bulb had blown (don't do this by the way)? The remaining 23 lights would come on again as you have completed the circuit. However, they would all be a little brighter than intended as they will now have slightly more than their designated 10 volts each. Of course running them at a higher voltage will cause them to burn out faster, so if you continued down this track and survived, you would find that the bulbs would blow faster and faster until eventually they would blow immediately.

POWER IN A SERIES CIRCUIT

The total power in a series circuit is found from P=EI where E is the applied voltage and I is the total current.

In our example: 10 x 0.1666 = 1.666 watts

You can use any of the power equations to calculate the power dissipated in R1, R2 or R3. Of course, the sum of the power dissipated in each resistance should equal the total power in the circuit (1.666 watts).

PR1 = 12 x R1 = (0.1666)2 x 10 = 0.2775556 watts

PR2 = 12 x R2 = (0.1666)2 x 20 = 0.5551112 watts

PR3 = 12 x R3 = (0.1666)2 x 30 = 0.8326668 watts

Pt= PR1 + PR2 + PR3 

Pt= PR1 + PR2 + PR3 = 1.6653336 watts (slight rounding error)

THE VOLTAGE DIVIDER 

A voltage divider is a simple way to adjust the voltage in a particular part of a larger circuit. The supply voltage might be 9V and the component requires 2V on one terminal. A voltage divider can be used to produce the required 2 volts. Two resistors can be connected to produce such a voltage divider. Such a circuit is shown in figure 5-3.

Since we have not looked at parallel circuits yet, we will assume that the total resistance of the transistor is 8000Ω and this is represented by the resistance R2. This is a real problem we will learn more about this later when we look at transistors. For now, R2 is 8000Ω and we want to workout the value of R1 that will produce 2 volts across R2.

Our problem then is to find the value of R1.  

We know that the sum of the voltage drops across R1 and R2 must equal the supply voltage of 9 volts. R2 has 2 volts across it so R1 must have 7 volts across it. It should be evident that the resistance value of R1 must be higher than that of R2 since it has the higher voltage across it.

Let's try this:-

ER2 we know is 2 volts and R2 is 8000Ω.

We can calculate the current through R2:

IR2 = ER2/R2 = 2/8000 = 0.25 milliamperes

We now know the current through R1 since R2 and R1 are in series.

R2=ER2/IR2 

In case the abbreviations are confusing you - ER2 means the voltage across R2 and IR2 means the current through R2.

R1= 7 volts/ 0.25 milliamperes ← remember this is milliamperes
R1 = 28000Ω

We can check this by saying:

8000/36000th of the supply voltage should be across R1,
or 8/36 x 9 which gives 2 volts which is correct.

Also:

28000/36000th of the supply voltage should be across R2,

We know that the sum of the voltage drops across R1 and R2 must equal the supply 28/36 x 9 = 7 volts.

In electronic circuits we often use voltage dividers to bias transistors or establish the correct operating voltage of a component when the supply voltage is too high.

6 - Parallel Circuits

When two or more components are connected directly across one voltage source, they form a parallel circuit. The two lamps in figure 6-1 are in parallel with each other and with the battery. Each parallel path is called a branch, with its own individual current. Parallel circuits have one common voltage across all the branches, but the individual branch currents can be different.

The voltage is the same across all components in a parallel circuit 

In figure 6-1 a pictorial diagram and the schematic equivalent circuit is shown. The two lamps are directly connected to the battery terminals. This is always the case with parallel circuits. If you had 10 components (they don't have to be lamps) connected in parallel, then each side of each component is connected directly to the battery.

BRANCH CURRENTS 

Each resistance (or other component) in a parallel circuit is connected by a conductor directly to the source voltage. Each resistor will draw current from the source according to Ohm's law, l=E/R, for each branch. The sum of all the branch currents must then be equal to the total current drawn from the source. In a parallel circuit the sum of the branch currents equals the total current.

In applying Ohm's law, it is important to note that the total current equals the voltage applied across the circuit divided by the total resistance of the circuit. lT=ET/RT.

ln figure 6-2, 10V is applied across the 10Ω of R1, resulting in a current of 1 Ampere being drawn from the battery through R1. Similarly, the 10 volts applied to the 5Ω of R2 will cause 2 amperes to be drawn from the battery.

The two branch currents in the circuit are then 1 ampere and 2 amperes. The total current drawn from the battery is then 3 amperes.

Just as in a circuit with only one resistance, any branch that has less resistance will draw more current. If R1 and R2 were equal, however, the two branch currents would have the same value. For instance, if R1 and R2 were both 50Ω then each branch would draw 2 amperes and the total current drawn from the battery would be 4 amperes.

The current can be different in parallel circuits having different resistances because the voltage is the same across all the branches. Any voltage source generates a potential difference across its two terminals. This voltage does not move. Only current flows around the circuit.

The source voltage is available to make electrons move around any closed path connected to the generator terminals. How much current flowing in the separate paths depends on the amount of resistance in each branch.

For a parallel circuit with any number of branch currents we can then write an equation for calculating the total current (IT):

IT=I1+I2+I3..n

This rule applies to any number of parallel branches, whether the resistances are equal or unequal.

Example:

An R1 of 20Ω and an R2 of 40Ω and an R3 of 60Ω are connected in parallel across a 240 volt supply. What is the total current drawn from the supply?

Let's calculate the branch currents for R1, R2 and R3:

IR1 = E/R1 = 240/20 = 12 amps
IR2 = E/R2 = 240/40 = 6 amps
IR3 = E/R3 = 240/60 = 4 amps

The total current drawn from the 240 volt supply is the sum of the branch currents:

 IT= IR1 + IR2 + IR3 = 12 + 6 + 4 = 22 amperes.

RESISTANCES IN PARALLEL

In the example, above we could have worked out the total resistance to calculate the total current being drawn from the supply.

To find the total resistance of any number of resistors in parallel we find the reciprocal of the sum of the reciprocals for each resistance. This sounds like a bit of a mouthful so I will put it in equation form and you should see what I mean.

Let's calculate the total resistance of our example using this equation.

Firstly, find the reciprocal of each of the resistances:

Reciprocal of R1 = 1/R1 = 1/20 = 0.05
Reciprocal of R2 = 1/R2 = 1/40 = 0.025

Reciprocal of R3 = 1/R3 = 1/60 = 0.01667 (recurring decimal)

The sum of the reciprocals above is: 0.091667

Finally, to find Rt we take the reciprocal of the sum of the reciprocals, or:

1/0.091667 which equals 10.91 rounded.

So Rt= 10.91 ohms (with a little rounding error).

Since we know the total resistance and the applied voltage we can now calculate the total current from Ohm's law.

l=E/R = 240/10.91 = 21.998 amps, or close enough to the 22 amps we calculated earlier. When you get used to it, these calculations are very easy to do on a calculator. Many calculators have a reciprocal key '1/x' or 'x-1'.

Example: A parallel circuit consisting of two branches, with a current of 5A through each branch, is connected across a 90V source. What is the equivalent total resistance Rt?

To find the total resistance (Rt) we need to know the applied voltage (90V) and the total current drawn from the supply. Since we are told that there are two branches and each branch draws 5A then the total current must be 10A. We can now use Ohm's Law to calculate the total resistance:

R=E/I
R=90/10
R=90Ω 

PARALLEL BANK

A combination of parallel branches is often called a bank. Radio operators often use a device called a dummy load (we will go into detail about dummy loads later). A dummy load is typically just a resistance of 50Ω which is connected to the antenna socket of a transmitter for tuning purposes. The problem is the dummy load has to dissipate all of the transmitter power. If the operator purchased and used a typical 50 ohm carbon resistor, it would burn out, as carbon resistors cannot dissipate more than about 1W. A typical dummy load for a commercial transceiver should be able to dissipate 100W.

A good dummy load can be made from twenty 1000Ω, 5 watt resistors connected in parallel. Each of the twenty resistors, being 5 watts each are able to dissipate 5 watts, so the bank is able to dissipate 20 x 5 = 100 watts. The total resistance of twenty 1000Ω resistors in parallel is 50Ω with a total power rating of 100 watts.

In practice, the dummy load is usually cooled, perhaps by immersing the resistors in oil or some sort of air cooling which enables the resistors to dissipate more power without overheating and being destroyed.

A stumbling block for many is trying to understand how adding more resistors to a parallel circuit can reduce the total resistance.

In figure 6-3(a) you see a supply voltage of 60 volts connected to a 30Ω load. By Ohm's law the current drawn by the 30Ω load must be 2A.

If a second 30Ω resistor is now connected as in figure 6-3(b), then an additional 2A will flow through it. The total current drawn from the supply is now 4A.

Adding a third 30Ω resistor as in figure 3(c) causes a further 2A to be drawn from the supply, bringing the total current drawn from the supply to 6A.

The total resistance of this circuit would be:

R=E/I=60/6=10Ω

We can see that as we add parallel resistors to the supply, more current is drawn from the supply, so the total circuit resistance must be less. We could go on adding parallel resistors for as long as we wanted and each time we did, the total circuit resistance would become less with each added resistor.

So now you should be able to answer the question; why does adding more resistors to a parallel circuit increase the total current? Each additional parallel resistor creates an additional branch for current that would not otherwise be there.

DERIVING THE RECIPROCAL EQUATION

We discussed the reciprocal equation earlier, but we did not mention how this equation was derived.

We know the basic law: the sum of the branch currents is equal to the total current  flowing in a parallel circuit.

It= E/Rt and I1 = E/R1 and 12 = E/R2 ... n

We can substitute this into the rule for branch currents and get:

E/Rt = E/R1 + E/R2 + E/R3 ... n

Notice how E is in the numerator on both sides of the equal sign. If we divide both  sides by E, the E's cancel out and we are left with:

1/Rt = l/R1 + l/R2 + l/R3 ... n.

This gives us the reciprocal of the total resistance. The reciprocal of this is the total resistance.

SPECIAL CASE OF ALL RESISTANCES THE SAME

If all of the resistances are the same in a parallel circuit, as in our dummy load  example presented earlier, the total resistance can be found by dividing the number  of branches into the value of one of the parallel resistances. In the dummy load example, we had twenty, 1000Ω resistors. A quick method to find the total resistance is; 1000/20 = 50Ω. However, please do remember that this approach can only be used when all resistances are the same.

When there are two parallel resistances and they are not equal, it is usually quicker to calculate the combined resistance by the method known as 'product over sum'. This rule says that the combination of two parallel resistances is their product divided by their sum.

Rt=(R1 x R2) /(R1 +R2)

The symbol '/' means divided by.

Example:

A resistance of 100Ω is connected in parallel with a resistance or 200Ω. What is the total resistance of the circuit using the product over sum method?

Rt = (100x200)/(100+200)

Rt = 20000 / 300

Rt= 66.6670Ω (rounded).

Notice also that the total resistance of parallel resistors is always less than the lowest resistance.

TOTAL POWER IN PARALLEL CIRCUITS

Since the power dissipated in the branch resistances must come from the source  voltage, the total power equals the sum of the individual values of power in each branch.

Pt=PR1+PR2+PR3..n

Of course if you know the total current and the applied voltage, you can find the power using P=EI.

I can recall a question that was asked in a radiocommunications exam some years ago. I am sure the question was not meant to be as difficult as it turned out and my guess is that the person writing the question must have been anxious to knock off work at the time.

The question was:

Four 10Ω, 1 watt resistors are connected in series. What is the total power dissipation rating of the circuit?

That was it, no voltage or current mentioned. In fact, the resistance (10Ω) is totally irrelevant as is the series connection.

The answer is 4 watts.

The question was poorly phrased in my view and could have been put:

What is the maximum power that four, 1 Watt resistors can dissipate?

ADVANTAGE OF A PARALLEL CONNECTION

Household appliances, as you may know, are designed to operate at 240V. The  electrical wiring to all the power points and light fittings in your home are in the form of a parallel circuit. This ensures that each appliance receives the supply voltage of 240V. Imagine the problems if your house was wired as a series circuit. Each time you turned on a light all the lights in the house would get dimmer. If you turned on something with a high resistance (low wattage), the lights would not even glow. Supplying the same voltage to various devices in a house, a radio circuit, or a car requires parallel connections.

7 - Series Parallel Circuits

In many circuits, some components are connected in series so they have the same current, while others are in parallel for the same voltage. When analysing and doing calculations with series-parallel circuits, you simply apply what you have learned from the last two chapters.

In the circuit of figure 7-1, we could work out all the voltages across all of the resistances and the current through each resistance and then total resistance. For now, I am just going to walk through the simplification of this circuit to a single resistance connected across the 100V source.

Keep in mind that any circuit (resistive) can be reduced to a single resistance. This is particularly useful when we come to do transmission lines and antennas.

For now, let's have a go at simplifying the circuit of figure 7-1. There are many ways to go about this problem. The method I prefer is to start at the right-hand side and work my way back to the source, simplifying the circuit as I go. Let's try this together:-

On the right-hand side, we see R3 and R4 in parallel and each 12Ω. Do you remember the shortcut method when parallel resistances are all the same value? Divide the value of the branch by the number of branches: 12Ω /2 = 6Ω.

Replace the parallel pair of R3 and R4 with a single resistance R7 as shown in figure 7-2.

Always redraw the circuit.

The next logical step would be to combine the series resistance of R6 and R7 into a single resistance R8 by adding them, as shown in figure 7-3: 4Ω + 6Ω = 10Ω.

Redraw the circuit. 

Now combine the parallel and equal resistances of R5 and R8 into a single resistance R9 of 5Ω as shown in figure 7-4.

Redraw the circuit.

We are now left with a series circuit consisting of R1, R2 and R9. We find the total resistance of these by adding them: 15Ω + 30Ω + 5Ω =50Ω.

You guessed it! Redraw the circuit again for our final result shown in figure 7-5.

So the total resistance of the circuit we started with is equivalent to a single resistance of 50Ω.

We could now find out how much current is being drawn by the circuit from the supply, by using Ohm's law:

l=E/R = 100/50 = 2 amperes.

That's it! You will find that most circuits, even very complex ones, can be handled in the same manner i.e. by simplifying series and parallel branches as you work your way down to a single resistance.

I cannot emphasise enough the need to redraw the circuit as you work your way through it. The calculations for this circuit were easy arithmetically. If you found it was not so easy, then it is important for you to show all of your working out as well.

Refer to the circuit of figure 7-1. What is the voltage across R4?

We know that the total resistance of the circuit is 50Ω and from this we worked out that the current drawn from the supply was 2A.

Therefore, if we go back to the figure 7-1 circuit, R1 (15Ω) and R2 (30Ω) must have 2A flowing through them since they are in series with the supply.

The voltage across R1 will be: E=IR1 = 2 x 15 = 30V.

Likewise, the voltage across R2 will be: E=IR2 = 2 x 30 = 60V.

Now if there are 30 volts across R1 and 60 volts across R2 then this leaves 100-30-60 = 10 volts across R5.

R5 is in parallel with R6 and the parallel pair of R3 and R4.

R3 and R4 simplify to 6Ω.

So we have 10 volts across 4Ω and 6Ω in series. The voltage across the 6Ω will be the voltage across R4 (and R3 for that matter).

Some may see immediately without any calculation that 10 volts across a series combination of a 4Ω and a 6Ω resistor will result in 4 volts across the 4Ω and 6 volts across the 6Ω. If you can't see this then don't worry, let's solve it using Ohm's law.

I = E/R = 10/10 = 1 ampere.

So there is 1 ampere flowing through the 6Ω resistance that represents the combined resistance of R3 and R4 in parallel.

E = IR = 1 x 6 = 6 volts.

Therefore, the voltage drop across R4 is 6 volts.

8 - Magnetism

There are usually no questions in radio exams about magnetism. You are justified then in asking why we are doing this subject. Well, although there are not many, if any, questions in the exams, later on in this book we do have to cover topics like:

Inductance

Mutual Inductance

Alternating Current 

It is impossible to gain an understanding of these subjects without a basic understanding of magnetism. I will try to keep the topic as brief as possible, bearing in mind what has to be learned and more to the point 'understood' later on.

MAGNETISM AND ELECTRICITY

Any wire carrying a current of electrons is surrounded by area of force called a magnetic field. For this reason, any study of electricity or electronics must consider magnetism.

Almost everyone has had experiences with magnets or pocket compasses at one time or another. A magnet attracts pieces of iron but has little effect on practically everything else. Why does it single out iron? A compass, when laid on a table, swings back and forth, finally coming to rest pointing toward the North Pole of the world.

Why does it always point in the same direction?

These and other questions about magnetism have puzzled scientists for hundreds of years. It is only relatively recently that theories have begun to answer many of the perplexing questions about magnetism.

Radio and electronic apparatus such as relays, circuit breakers, earphones, loudspeakers, transformers, chokes, magnetron tubes, television tubes, phonograph pickups, tape and disk recorders, microphones, meters, motors and generators depend on magnetic effects to make them function.

Every coil (inductance) in a radio receiver or transmitter is utilising the magnetic field that surrounds it when current is flowing through it. But what is meant by the term magnetic field?

THE MAGNETIC FIELD 

An electron at rest has a negative electrostatic field of force surrounding it. When energy is imparted to an electron to make it move, a new type of field develops around it, at right angles to its electrostatic field. Whereas negative electrostatic lines of force are considered as radiating outward from an electron, the electromagnetic field of force develops as a ring around a moving electron, at right angles to the path taken, around the wire.

An interesting difference between a magnetic field and an electrostatic field is that an electrostatic field can exist around a single stationary charge such as an electron or a proton. This is not the case with magnetism. A North 'monopole' does not exist any more than a South 'monopole' exists. With magnetism, you always have two poles.

Electrons orbiting around the nucleus of an atom or a molecule produce electromagnetic fields around their paths of motion. These fields (electric and magnetic) are balanced or neutralised by the effect of proton movement in the nucleus. The movement of one orbital electron is counteracted by another orbital electron whirling in an opposite direction. In almost all substances, the net result is little or no external fields.

In the case of an electric conductor carrying current, the collective movement of electrons along the wire produces a magnetic field around the conductor. The greater the current, the more intense the magnetic field.

The diagram in figure 8-1 shows a method of determining the direction of the magnetic field around a current carrying conductor.

If you place a compass next to a conductor and then pass a current through the conductor, the compass needle will move indicating the presence of a magnetic field.

Under normal circumstances, the field strength around a current carrying conductor varies inversely as the distance from the conductor. At twice the distance from the conductor, the magnetic field strength is one-half as much, at five times the distance the field strength is one-fifth and so on. At a relatively short distance from the conductor, the field strength may be quite weak.

When the current in a conductor is increased, more electrons flow, the magnetic field strength increases and the whole field extends further outward.

By looping a conductor, as shown in figure 8-2A, magnetic lines of force are concentrated in the central core area of the loop.  

When two or more turns of wire are formed into a coil, as shown in figure 8-2B, the lines of force from each turn link to the fields of the other turns and a more concentrated magnetic field is produced in the core of the coil.

By forming a coil into many loops the magnetic field is stronger and more concentrated. With enough turns plus current a strong electromagnet can be created.

An experiment to try

Typically in face-to-face classes, I would demonstrate many things by experiment. This makes learning more enjoyable. We don't have that luxury. However, I will mention these experiments from time to time and perhaps you can try them yourself. If you have never made an electromagnet, I really encourage you to do so as it can be a lot of fun and fascinating.

Get an iron rod about 75mm long. A bolt with a head and a nut screwed onto one end is ideal. Wind as many turns of wire onto it as you can. I use single telephone wire. However, any small diameter wire will do the job. The more turns, the better. Connect the ends of the coil you have made to a 6 volt lantern battery and you will have yourself an electromagnet. You can use the electromagnet with other experiments down the track.

Besides just playing with your electromagnet you can use it to magnetise some tools such as screwdrivers etc. Don't leave it connected to the battery for very long as it draws a heavy current from it. Do not use a car battery as the coil will overheat and melt. The coil (inductor) is a very low resistance. However, current is limited by using a 6 volt lantern battery, which can only supply 3-4 amps. If you want to use a car battery you need to limit the current flow through the electromagnet. You could do this by connecting a 12 volt automotive light bulb in series with the magnet.

Figure 8-3 shows an electromagnet made from a bolt and some scrap wire; a permanent bar and horseshoe magnet.

The direction of the field of force (north and south pole) can be reversed by reversing the current direction or by reversing the winding direction.

At one end of the coil the field lines are leaving and at the other end, they are entering. When a coil or piece of metal has lines of force leaving one end of it, that end is said to have a north pole. The end with the lines entering is the south pole.

The terms "north" and "south" indicate magnetic polarity, just as "negative" and "positive" indicate electrostatic polarity. They should not be used interchangeably.

The negative end of a coil is the end connected to the negative terminal of the source and does not refer to the north or south magnetic polarity of the coil.

All magnetic lines of force are complete loops and may be considered somewhat similar in their action to stretched rubber bands. They will contract back into the circuit from which they came as soon as the force that produced them ceases to exist.

Magnetic lines of force never cross each other. When two lines of force have the same direction, they will oppose mechanically if brought near each other.

PERMEABILITY

When a coil of wire is wound with air as the core, a certain flux density will be developed in the core for a given value of current. If an iron core is inserted into the coil, the flux density will increase. This increase in flux density is achieved without increasing current or the number of turns.

With an air core coil, the air surrounding the turns of the coil may be thought of as pushing against the lines of force and tending to hold them close to the turns. With an iron core, the lines of force find a medium in which they can exist much more easily than in air. As a result, lines that were held close to the turns in the air core coil are free to expand into the highly receptive area afforded by the iron. This allows lines of force that would have been close to the surface of the wire to expand into the iron core. Thus, the iron core produces a greater flux density, although there are no extra magnetic lines of force. In other words, for the same number of turns and current, a coil will have a stronger magnetic field if an iron core is inserted. The iron core merely brings the lines of force out where they can be more readily used and concentrates them.

The ability of material to concentrate magnetic lines of force is called Permeability.

The permeability of most substances is very close to that of air, which may be considered as having a value of 1. A few materials, such as iron, nickel and cobalt, are highly permeable, with permeabilities of several hundred to several thousand times that of air. The word "permeability" is a derivation of the word "permeate," meaning "to pervade or saturate" and is not related to the word "permanent.")

Permeability is represented by the Greek letter µ (mu, pronounced mew).

Alloying iron makes it possible to produce a broad range of permeabilities. Most stainless steel exhibits practically no magnetic effect, although some steels may be magnetic.

Any substance that is not affected by magnetic lines of force and is reluctant to support a magnetic field is said to have the property of reluctance. Air, vacuum and most substances have unity reluctance, while iron has a very low reluctance.

In electric circuits, the reciprocal of resistance is called conductance. In magnetic circuits, the reciprocal of reluctance is called permeance. "Permeability" is used when discussing how magnetic materials behave.

THE ATOMIC THEORY OF MAGNETISM 

The discussion here will be a considerably condensed version of the atomic theory of magnetism.

From atomic theory, it is known that an atom is made up of a nucleus of protons surrounded by one or more electrons encircling it. The rotation of electrons and protons in most atoms is such that the magnetic forces cancel each other. Atoms or molecules of the elements iron, nickel and cobalt, arrange themselves into magnetic entities called domains. Each domain is a complete miniature magnet.

Groups of domains form crystals of the magnetic material. The crystals may or may not be magnetic, depending on the arrangement of the domains in them. Investigation shows that while any single domain is fully magnetised, the external resultant of all the domains in a crystal may be a neutral field.

Each domain has three directions of magnetisation: easy magnetisation, semi-hard magnetisation and hard magnetisation. If an iron crystal is placed in a weak field of force, the domains begin to line up in the easy direction. As the magnetising force is increased, the domains begin to roll over and start to align themselves in the semihard direction. Finally, as the magnetising force is increased still more, the domains are lined up in the hard direction. When all the domains have been lined up in the hard direction, the iron is said to be saturated. An increase in magnetising force no longer magnetically changes the material. The material is magnetically saturated.

FERROMAGNETISM 

Substances that can be made to form domains are said to be ferromagnetic, which means "iron magnetic." The ferromagnetic elements are iron, nickel and cobalt, but it is possible to combine some non-magnetic elements and form a ferromagnetic substance. For example, in the proper proportions, copper, manganese and aluminium, each by itself being non-magnetic, produce an alloy which is similar to iron magnetically.

Materials made up of non-ferromagnetic atoms, when placed in a magnetic field may weakly attempt either to line up in the field or to turn at right angles to it. If they line themselves in the direction of the magnetic field, they are said to be paramagnetic. If they try to turn from the direction of the field, they are called diamagnetic. There are only a few diamagnetic materials. Some of the more common are gold, silver, copper, zinc and mercury. All materials which do not fall in the ferromagnetic or diamagnetic categories are paramagnetic. The greatest percentage of substances are paramagnetic.

Ferromagnetic substances will resist being magnetised by an external magnetic field to a certain extent. It takes some energy to rearrange even the easy to move domains.

Once magnetised, however, ferromagnetic substances may also tend to oppose being demagnetised. They are said to have retentivity, or remanence, the ability to retain magnetism when an external field is removed.

As soon as the magnetising force is released from a magnetised ferromagnetic substance, it tends to return at least part way back to its original non-magnetised state, but it will always retain some magnetism. This remaining magnetism is residual magnetism. Paramagnetic and diamagnetic materials always become completely nonmagnetic when the external magnetising force is removed from them.

PERMANENT AND TEMPORARY MAGNETS 

Ferromagnetic substances that hold magnetic domain alignment well (have a high value of retentivity) are used to make permanent magnets. One of the strongest permanent magnets is made of a combination of iron, aluminium, nickel and cobalt called Alnico. It is used in horseshoe magnets, electric meters, headphones, loudspeakers, radar transmitting tubes and many other applications. Some magnetically hard, or permanent magnetic materials, are cobalt steel, nickel aluminium, steels and special steels.

Figure 8-5 shows the magnetic field surrounding permanent magnets. This picture was made by placing a piece of paper over the magnets and sprinkling iron filings onto the paper.

You can see the lines of force attracting when a north and a south pole are brought near to each other and repelling when two north poles are brought near to each other.

Ferromagnetic metals that lose magnetism easily (have a low value of retentivity) make temporary magnets. They find use in transformers, chokes, relays and circuit breakers.

Pure iron and permalloys ('perm' derived from "permeable," not from "permanent") are examples of magnetically soft, temporary magnet materials. Finely powdered iron, held together with a non-conductive binder, is used for cores in many applications. These are called ferrite cores.

MAGNETISING AND DEMAGNETISING 

There are two simple methods of magnetising a ferromagnetic material. One is to wrap a coil of wire around the material and force a direct current through the coil. If the ferromagnetic material has a high value of retentivity, it will become a permanent magnet.

If the material being magnetised is heated and allowed to cool while subjected to the magnetising force, a greater number of domains will be swung into alignment, and a greater permanent flux density may result. Hammering or jarring the material while under the magnetising force also tends to increase the number of domains that will be affected.

A less efficient method of magnetising is to stroke a high retentivity material with a permanent magnet. Have you ever magnetised a screwdriver using this approach? This will align some of the domains of the material and induce a relatively weak permanent magnetism.

If a permanent magnet is hammered, many of its domains will be jarred out of alignment and the flux density will be lessened. If heated, it will lose its magnetism because of an increase in molecular movement that upsets the domain structure. Strong opposing magnetic fields brought near a permanent magnet may also decrease its magnetism. It is important that equipment containing permanent magnets be treated with care. The magnets must be protected from physical shocks, excessive temperatures and strong alternating or other magnetic fields.

When heated, permanent magnets lose their magnetism quickly and also at a certain temperature. The temperature at which a magnet loses its magnetism is called the Curie temperature.

When tools or objects such as screwdrivers or watches become permanently magnetised, it is possible to demagnetise them by slowly moving them into and out of the core area of a many turn coil in which a relatively strong alternating current (AC) is flowing. The AC produces a continually alternating magnetising force. As the object is placed into the core area, it is alternately magnetised in one direction and then the other. As it is pulled further away, the alternating magnetising forces become weaker. When it is finally out of the field completely, the residual magnetism will usually be so low as to be of no consequence.

PERMANENT MAGNET FIELDS

When a piece of magnetically hard material is subjected to a strong magnetising force the domains are aligned in the same direction. When the magnetising force is removed, many of the domains remain in the aligned position and a permanent magnet results. A north pole is anywhere the direction of the magnetic lines of force move outward from the magnet. A south pole is any place where the direction of the lines of force are inward.

If a magnet is completely encased in a magnetically soft iron box, all its lines of force remain on the walls of the box and there is no external field. This is known as magnetic shielding. Shielding may be used in the opposite manner. An object completely surrounded by an iron shield will have no external magnetic fields affecting it, as all such lines of force will remain in the permeable shield.

THE MAGNETISM OF THE EARTH 

Sufficient quantity of the ferromagnetic materials making up the earth have domains aligned in such a way that the earth appears to be an enormous permanent magnet. The direction taken by the lines of force surrounding the surface of the earth is inward at a point near what is commonly known to be the north pole of the world and outward near the earth's south pole.

The simple magnetic navigational compass consists of a small permanent magnet balanced on a pivot point. The magnetic field of the compass needle lines itself up in the earth's lines of force.

As a result, the magnetic north end of the compass needle is pulled toward the earth's south magnetic pole, since unlike poles attract each other. This means that when the "north-pointing end" is pointing toward geographical north, this end (a magnetic north pole) is pointing toward a magnetic south pole.

RELAYS

A relay is a relatively simple magnetic device that generally consists of a coil, a ferromagnetic core and a movable armature on which make and/or break contacts are fastened. A simple relay may be used to close a circuit when the coil is energised. This type of relay is known as single pole single throw (SPST), normally open (NO), or "make contact" relay. The relay in figure 8-7 is a double pole single throw. The contacts can be used to turn something ON or OFF.

The core, of the relay and the pivoted armature bar, are made of magnetically soft ferromagnetic materials having high permeability and little retentivity. One of the relay contacts is attached by an insulating strip to the armature and the other to the relay body with an insulating material. The contacts are electrically separated from the operational parts of this particular relay.

When current flows through the coil, the core is magnetised and lines of force develop in the core and through the armature and the body of the relay. The gap between the core and the armature is filled with magnetic loops trying to contract. These contracting lines of force overcome the tension of the spring and pull the armature toward the core, operating the relay contacts. When the current in the coil is stopped, the magnetic circuit loses its magnetism and the spring pulls the armature up, opening the contacts.

Relays are useful in remote closing and opening of high voltage or high current circuits with relatively little voltage or current flow in the coil.

A relay can be used to switch an antenna between the transmitter and the receiver when the push-to-talk button is pressed on a microphone. Another example is the headlights or any other current drawing device in an automobile. The headlights need thick gauge wire to keep the resistance low. If we were to run heavy gauge wire to the switch of the dashboard it would require more wire and it would be difficult routing the wire and would have to connect it to a large heavy current switch.

Instead we run the heavy wire to the battery and relay contacts in series. The relay is very close to the battery so we do not need so much heavy gauge wire. Then we run small light wire to the dashboard to a lightweight low current switch. When we operate the switch to turn the lights on the relay operates and completes the circuit for the headlights.

Relay contacts are usually made of silver or tungsten. Silver oxidises but can be cleaned by using a very fine abrasive paper, or a piece of ordinary letterhead paper rubbed between the contacts. If the contacts are pitted by heavy currents, they may be smoothed with a fine file, but the original shape of the contacts should be retained to allow a wiping action during closing to keep them clean.

When I started out in electronics, relays were physically big components. These days relays for switching small currents can be made very small and look no larger than a medium sized integrated circuit.

The energy of a magnetic field.

Here is something for you to ponder. A magnetic field around a relay or a solenoid (electromagnet) has energy. The energy comes from the current flowing in the conductor coil. Suppose we switch the current OFF quickly by opening a switch. Where does the energy of the magnetic field go? It cannot just "disappear". Energy never disappears. It can change into another type of energy. Energy just can't go away.

Barkhausen Effect.

Earlier we explained how materials that can be magnetised contain many minute magnets in them called domains. For a long time, this was called the domain hypothesis of magnetism as it was not quite a fact. A scientist by the name of Barkhausen was experimenting with microphones attached to a soft iron bar while adjusting the strength of an external field. As he adjusted the strength of the external field, his microphone picked up the sound of the magnetic domains moving and the domain theory of magnetism was proven. He also noticed that the domains did not move smoothly. The domains moved in discrete steps. Staying still for a while as the magnetising force was increased; then suddenly jumping to their next position. This and other experiments led to the idea of what is known today as a quantum. A quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction. This became critical to the evolution of quantum mechanics.

9 - Alternating Current I

You may be thinking that when we speak of alternating current (AC), we are talking about the household electrical supply, however, so is the signal from a radio transmitter. The only difference is the frequency.

FARADAY'S LAW

When relative motion exists between a conductor and a magnetic field an emf is induced into the conductor. 

This is a fundamental law. We will take our time and try to understand it thoroughly. What Faraday discovered was a way of producing electrical pressure (voltage or emf) from a magnetic field.

Faraday's law requires relative motion. This means there must be motion between the conductor and the magnetic field. This is not to say that the magnetic field must move. Neither does it mean that the conductor must move. Provided there is relative motion between the magnetic field and the conductor; a voltage will be induced into the conductor. In practice, this means the conductor can be stationary and the magnetic field must be moved relative to it. Alternatively, the magnetic field can be stationary and the conductor moved through it.

A Mind Experiment

Imagine a cardboard tube. I have successfully used the cardboard tube from an empty kitchen wrap. The tube is wound with at least 50 turns of insulated conductor. So, in fact, we have made a simple coil. To the ends of the coil, we attach a voltmeter. We have not discussed meters yet, but I think you can follow along if I just say it is an instrument with a needle, which indicates if the voltage is present. I used a special type of voltmeter called a galvanometer. A galvanometer is a voltmeter that has zero volts at centre scale. The advantage of this is that the meter's pointer can deflect left or right of centre depending on the polarity of the voltage being measured.

In figure 9-1 we have a galvanometer connected to our coil. Now imagine taking a permanent magnet, a bar magnet, and inserting it quickly into the centre of the coil.

The pointer will deflect in one direction as you insert the magnet. When the magnet stops moving the meter will return to zero.

You still have the magnet inside the coil. Now pull the magnet out. The pointer will again deflect, indicating a voltage on the coil, but, this time, the deflection will be in the opposite direction to when we inserted the magnet.

What we have done is demonstrated Faraday's law of induction. When we inserted the bar magnet inside our coil, we produced relative motion between the coiled conductor and the magnetic field of the bar magnet. Once the magnet was in and stopped moving, the relative motion stopped and the induced voltage fell to zero again. When we removed the magnet from the coil, relative motion existed again, but since the magnet was being extracted rather than inserted, the polarity of the induced voltage was in the opposite direction and the meter's pointer deflected accordingly.

If you happened to have made the electromagnet we discussed in an earlier chapter, you could place it inside the coil. If you then energised the electromagnet by applying a voltage to it, the expanding magnetic field would induce a voltage in our coil. After a few moments, the induced voltage would fall to zero. Now, if we disconnected the voltage to the electromagnet, the magnetic field around it would collapse (relative motion) and voltage would be induced in the coil. You may not know it, but you have just demonstrated the operation of a device to be discussed shortly, called a transformer.

THE AMOUNT OF INDUCED VOLTAGE 

How much voltage is induced with our coil experiment is determined by the number of turns on the coil, the strength of the magnet we use and the speed of the relative motion.

Of course, if we were able to continue to move our bar magnet in and out of the coil at high speed without stopping, we would get a continuously induced voltage.

Remember how the needle of the galvanometer first defected one way and then the other? This is because when the magnet is inserted, the induced voltage is one polarity (negative or positive) and when the magnet is withdrawn the polarity reverses. This is an alternating voltage. An alternating voltage is one which changes polarity periodically. If we connect an alternating voltage to a circuit, we will get an alternating current. This is a current that flows in the circuit first in one direction and then in the other.

CYCLES PER SECOND 

Going back to our coil. Placing the magnet into the coil and then removing it is one cycle. If we could take the magnet in and out of the coil every second, the polarity of the induced voltage would go through one cycle in one second. Mechanics call this revolutions per second. In electronics, we once used cycles per second, but now use Hertz. So when you see 'hertz' just think of 'cycles per second'.

This method of inducing an emf was the first method used for household power generation. The first household power was direct current (DC). The method used to produce this direct current was electromagnetic induction. The generator converted the AC to DC.

The alternating voltage connected to the household supply from the power grid changes polarity 100 times a second (50 cycles per second) and reaches a peak of 325 volts in Australia. The mains voltage in some locations varies a great deal depending on consumer load.

WHERE HAVE ALL THE ELECTRONS GONE? 

A bit of a strange subtitle but it's all I could think of now. What I want you to think about is the electrons in your household wiring! They don't move from the power station through the conductors to your house. The household supply is AC at 50 hertz (Hz). So the electrons in the conductors in your house are probably the same electrons that were there when the wiring was installed in your home. The AC supply just causes them to move first one way and then the other. We discussed earlier how slowly electrons really move. So if they (the electrons) are changing direction 50 times a second, they would not be getting anywhere. They just see-saw back and forth. For the effects of an electric current to work, we don't have to make the electrons move in one direction all the time we just have to make them move. Think about that.

Let's look at how AC is produced in the power station. The device which creates the household power is called a generator. It works by creating relative motion between a conductor and a magnetic field.

Figure 9-2 is a simplified AC generator. The segments N and S are the north and south pole of a permanent magnet. Between the magnet, in the magnetic field, we have a coil of wire. Only one turn is shown but in practice, there would be many turns. The coil in a generator is called the armature. The ends of the coil are connected to a load via slip rings and brushes. We are going to make the armature rotate and we don't want the wires to become twisted where they connect to the load, so we feed them out through slip rings. We are going to rotate the armature through 360 degrees or one cycle and look what happens to the induced emf (voltage). When there is no relative motion between the armature and the magnetic field there will be no induced emf. When the armature is cutting across magnetic field line the relative motion will be the greatest and the induced emf will be at its greatest.

We can choose any starting position for the armature. In Figure 9-2 the armature is horizontal. We are going to start with the armature in the vertical position as shown in figure 9-3. In plan view we would see the armature as a straight line. In side view we would see all of the armature as shown. When the armature starts to rotate it will be at the instant rotation starts in line with the magnetic field and the induced voltage will be zero volts. As the armature continues to rotate it becomes more perpendicular to the magnetic lines of force the induced voltage increases rapidly, reaching a maximum when the armature reaches 90 degrees.

In figure 9-4 the armature has now reached 90 degree. Looking from above in plan view we see the entire armature which is now "in line" with the magnetic field line and has reached the peak value of the induced emf. The armature in 9-4 is in the same position as shown in figure 9-2.

In figure 9-4 the relative motion is the greatest because the armature is cutting across the magnetic field line at a right angle to those field lines. Figure 9-5 shows the position of the armature from 0 to 360 degrees in steps of 90 degrees.

Figure 9-5 shows when the armature is cutting across field lines at 90 and 120 degrees the relative motion is the greatest and the induced emf is the greatest. At 0 and 270 degrees the armature is travelling along field lines and the relative motion is least as is the induced emf. You might also notice that the polarity of the emf changes each half cycle. We have alternating voltage and the shape of that voltage is a sinewave.

10 - Alternating Current II

In the last chapter, we discussed how an alternating current, or voltage, can be produced using a generator.

We are now going to look more closely at the shape (waveform) of this AC voltage. Recall how we discussed that the voltage starts out at zero, builds up to a maximum, then falls to zero. The polarity of the voltage then reverses. It builds up to a maximum again and then falls back to zero. This is one cycle. The number of cycles in 1 second is called the frequency and is measured in hertz.

Now the shape (waveform) of the wave from a generator is called a sinewave or sinusoidal wave. Some textbooks just flash this shape in front of you and say here it is. When I was learning I found the concept of a sinewave a little difficult, so I am going to assume the same for you.

A sinewave is the graphical representation of the alternating current or voltage plotted against time.

AN EXPERIMENT

Get yourself a piece of paper, about A4. On the left-hand side of the paper place a pen down and draw a vertical line about 50mm long. Now continue to trace over the line going up and down, over and over. Consider the centre of this line to represent zero volts. Why aren't you doing it?

Continue to move your pen up and down, redrawing the line. I want you to think that the middle of the line represents zero volts. Your pen moving upwards toward the top of the line represents current or voltage increasing in one direction. When you get to the top move down again and you eventually pass through the zero point. Once through zero your pen movement is now representing a change in the direction of the current and it begins to increase towards the bottom of the line, which represents maximum voltage in this direction. When you reach maximum at the bottom your pen now moves back toward the zero point and so on.

So you are sitting there copying over this vertical line. Do it reasonably quickly and get used to it.

Now without stopping your up and down motion, move your hand to the right without even thinking about the pen.

This is what I got, shown below in figure 10-1, though I have added a couple of notations.

The graph is very rough, but it does illustrate clearly the waveshape of an alternating voltage plotted against time. The waveshape is called a sinewave.

An AC voltage can be fed into an oscilloscope and its screen will display the waveform precisely.

Figure 10-3 is how you will see the sinewave represented in most textbooks. Sometimes positive and negative symbols are drawn on the vertical axis. Just think of positive as being current flow in one direction and negative as current flow in the opposite direction. How many cycles you see will depend on the time scale on the horizontal axis. On an oscilloscope, the horizontal and vertical axes are calibrated accurately in time and voltage. So we can read things like the maximum voltage and we can work out the frequency in hertz (number of cycles per second).

The shape of the AC voltage delivered to your home is a sinewave. A signal from a radio transmitter, without modulation, is also a sinewave.

One cycle, or revolution, is 360 degrees. Figure 10-2 shows the values of the voltage or current for any sinewave at different parts of the cycle. Sine is a trigonometric function that can be used to calculate points on a sinewave. You will find the 'sin' key on most calculators and if you enter 30 (degrees) into the calculator and press 'Sin' you will get 0.5. At 30° the instantaneous value of a sinewave is 0.5; with 1 being its peak value. On some calculators you press 'Sin' then enter 30° and '='. This is why the waveform is called a sinewave.

VOLTAGE AND CURRENT VALUES FOR A SINEWAVE

Suppose you wanted to buy electricity from Edison or Tesla. Edison says he will supply you with 100 volts direct current (DC), none of this sinewave stuff from him. He offers to provide 100 volts just like you would get from a battery. No current reversals. Tesla offers you 100 volts AC. From whom would you buy electricity?

Well, Edison's offer is very straightforward. Tesla, on the other hand, is offering a sinusoidal wave and you would have to ask more questions. Tesla is offering you 100 volts but what and when is it 100 volts? Is it 100 volts at the peak value of each half cycle? Which would mean that you would only get 100 volts for a brief moment twice during each cycle. Does this matter? You bet it does. If you were in the middle of winter in front of the electric bar heater, you would want 100 volts all the time not just for a brief period, each half cycle.

100 volts peak AC will not produce the same heating effect as 100 volts DC. So there is a need to be able to compare AC with DC, in terms of their heating effect. That is the same as comparing how much work each can produce.

It can be found mathematically or by experiment that the equivalent heating effect of a sinusoidal waveform compared to DC is 0.707 of its peak value. This value is known as the root mean square or effective value and is written RMS.

So if Tesla was to supply 100 volts peak, the actual equivalent heating value would be:

0.707 x 100 = 70.7 volts RMS, in which case you would go for Edison's deal? The average value of a sinewave is:

Peak x 0.637

I have never found a use for this value.

Sometimes an AC voltage is given as peak-to-peak. So if the maximum peak voltage was 100 volts, then the peak to peak value would be 200 volts - again a need to know however, I have never found any use for the peak to peak value.

Your household electricity supply is 240 volts RMS. This means it provides the same heating value as 240 volts DC. What is the peak value of the household power supply in Australia? The Standard for AC mains in Australia is now 230V AC RMS. However, it is nearly always closer to 240V AC RMS.

RMS = 0. 707 x Peak 

Transpose for peak by dividing both sides by 0.707 Peak= RMS/0.707 = 240/0.707 = 339.46 volts

So twice during each cycle, the household mains voltage actually reaches 339 volts. The frequency of the household supply is 50 hertz. How many times a second does the mains voltage reach 339 volts?

Since there are 50 cycles per second and two peaks during each cycle, the supply voltage will reach 339 volts 100 times each and every second.

Summary of equations

RMS = 0. 707 x Peak

Peak= RMS/ 0.707

Average= Peak x 0.637

Peak-to-Peak = Peak x 2

Note: 1/0.707 is 1.414 and 1.414 is the square root of 2 The duration of one cycle in seconds is called the period. What is the period of the household mains in Australia?

Since the frequency is 50Hz, there are 50 cycles in 1 second. Therefore 1 cycle has a Period of 1/50th of a second or 20 milliseconds.

Period = 1 / frequency.

WHAT DOES ROOT MEAN SQUARE MEAN?

We have learned what the RMS value of an AC voltage means. We also know the RMS value is 0.707 of the peak. However, what is this term 'root mean square'?

The factor 0.707 for RMS is derived as the square root of the average (mean) of all the squares of a sinewave. Now, if that still sounds like gobbledygook, let me show you how it is done and at least we will take away the mystery of the term RMS.

Michael Faraday, who became one of the greatest scientists of the 19th century, began his career as a chemist. He wrote a manual of practical chemistry that revealed his mastery of the technical aspects of his art. He discovered a number of new organic compounds, among them benzene and was the first to liquefy a "permanent" gas (i.e., one that was believed to be incapable of liquefaction). His major contribution, however, was in the field of electricity and magnetism. He was the first to produce an electric current from a magnetic field; invented the first electric motor and dynamo; demonstrated the relationship between electricity and chemical bonding; discovered the effects of magnetism on light; and discovered and named diamagnetism, the peculiar behaviour of certain substances in strong magnetic fields. He provided the experimental and a good deal of the theoretical, foundation upon which James Clerk Maxwell worked out the classical electromagnetic field theory.

11 - Capacitance - I

In this chapter, we are going to talk about capacitance. We need to make a distinction between the capacitor and capacitance. A capacitor is a device, whereas capacitance is an electrical property. First, we will discuss the capacitor and then the property of capacitance.

As you can see a capacitor is a two-terminal device. Two conductive plates separated by an insulator. This should suggest to you that current never flows through a capacitor.

Capacitor types generally take their name from the type on insulation material used between the plates. This is called the dielectric of the capacitor. Some capacitors have their dielectrics made electrically. These capacitors are said to be polarised in that they have a positive and negative terminal. When connected in a circuit this polarity must be maintained, if not the dielectric will be destroyed and the capacitor could gas and explode.

Figure 11-2 shows the standard schematic symbols for a capacitor.

Some capacitor types and packages:-

Figure 11-3 shows a variety of capacitor types. The yellow/brown are ceramic capacitors (because they use ceramic as the dielectric). The green capacitor in the foreground is the polyester type. The blue and black cylindrical capacitors are called electrolytic. The pale blue bottom left is a tantalum capacitor. Electrolytic and tantalum capacitors have their dielectrics formed electrically, for this reason, they are polarised capacitors that have a negative and positive leg. Connected incorrectly they can create internal gas and explode.

Larger 200-400pF air variable capacitors are used in transmitter output stages and antenna tuners. Air dielectric capacitors can withstand higher voltages. It takes about 10kV to flash over 1cm of dry air. Notice that in addition to the capacitance in farads, capacitors also have a voltage rating.

Charging and discharging a capacitor

The interesting stuff starts to happen when we connect an emf to the plates of a capacitor. Have a look at the test circuit of figure 11-5.

The capacitor can be switched so that it will be connected to the 10 volt battery when the switch is thrown to the left, or when the switch is thrown to the right, it will be connected to the resistor. The capacitor can be connected by the switch to the battery or the resistor, but not both at the same time.

The negative terminal of the battery has an excess of electrons on it, created by the chemical action within the battery. The positive terminal has a deficiency of electrons. Now recall that unlike charges attract. If there was any way for the electrons to get from the negative terminal of the battery to the positive, they would.

Now I just want you to imagine a battery by itself with two terminals. There is an electrostatic field between the two terminals of any battery created by the unlike charges on each terminal. In other words, there is a very slight tugging from the positive terminal and a very slight pushing from the negative terminal

in a vain attempt to move electrons from the negative to the positive terminal. No current flows between the unconnected terminals of a battery because the electrostatic fields are very small due to the spacing of the battery terminals and the very high air resistance between them.

If you find this hard to imagine look at figure 11-6 of two charges separated by air.

Here we have two lumped charges Q- and Q+. There is an electrostatic field between them. This field is trying to pull electrons from the negative charge over to the positive charge. There is an electrical strain here. No current flows because the two charges are too far apart. Let's say they are 100mm to start with. Now move the two lumped charges so that they are only 50mm apart. The electrostatic field will now be stronger. The strain will be stronger. Still no current flows. Let's push the issue. Move the two lumped charges so that they are only 5mm apart. Now (depending on the charges) the electrostatic field will be much stronger. The tugging of electrons from the negative charge will be much greater. Still no current flows, as the air insulation resistance between the charges is too high.

The electrons on the negative lumped-charge want to traverse the gap to the positive charge. Do you think the electrons would be evenly distributed on the negative lump? On the side of the negative lump closest to the positive lump (the inside) the electrons will be crowding up trying to jump the gap.

Can you figure out what will happen if we continue to move them closer, say, to 1mm? I think you will agree that a point will be reached where the electrostatic field is so strong that electrons will jump off the negative lump and flow through the air to the positive lump. There will be an arcing of electric current. This is what happens in a lightning storm.

Returning to our capacitor that, at the moment, is not connected to anything. The switch is thrown to the left. The plates of the capacitor have a very large surface area.

The dielectric between the plates is extremely thin but still a very good insulator. When we throw the switch to the left as in figure 11-7, we are extending the charges on the battery terminals to the plates of the capacitor and there will be a strong electrostatic field across the plates of the capacitor and through the dielectric.

Electrons are going to move from the negative terminal of the battery and bunch up on the top plate of the capacitor. Similarly, electrons are going to move from the bottom plate and travel to the positive terminal of the battery. No electrons will be able to flow through the dielectric. Its insulating properties are too good. So, if you like, there is going to be a redistribution of charge. This movement of charge will continue until the electrons flowing into and out of the capacitor create a potential difference on the plates of the capacitor equal to the battery voltage, namely 10 volts. The capacitor is now said to be charged.

This charging of the capacitor does not happen instantaneously - it takes a little time. Suppose now we move the switch so the capacitor is disconnected from the circuit, as shown in figure 11-8.

The capacitor is now left charged, even though it has been disconnected from the battery. The capacitor has 10 volts across it. Older capacitors would not hold this charge for very long as a current would slowly leak through the dielectric and the capacitor would eventually self-discharge. Some modern capacitors can hold their charge for many days or even weeks.

The capacitor has stored energy due to the charge on the plates. If we connect a circuit to the capacitor, it will discharge as shown in figure 11-9.

Electrons will now flow from the top plate of the capacitor through the resistance until the capacitor becomes discharged. If the resistor was a small light bulb, it would flash brightly at first and then slowly dim as the capacitor discharges.

At no time did current flow through the dielectric of the capacitor. Current flows into and out of a capacitor giving the illusion that current flows through a capacitor.

Suppose the resistor was a lamp. Also, suppose we continue to move the switch rapidly back and forth between the left and right position. The lamp would perhaps flicker a bit, but continuously give off light.

So you should now see that a capacitor can be used to store charge and we can use that charge to do something.

Where is the energy stored?

Though we have said that energy has been stored due to the charge on the plates, it is more correct to say that the energy is stored in the electric field. It is the charge on the plates that forms the electric field between the plates. When current flows into a capacitor, charging it, the electric field becomes stronger (stores more energy). When the current flows out of the capacitor, the voltage across the plates decreases and hence the strength of the electric field decreases (energy moves out of the electric field).

UNIT OF CAPACITANCE

The unit of capacitance is called the Farad. The farad is the measure of a capacitor's ability to store a charge. If one volt is applied to the plates of a capacitor and this causes a charge of 1 coulomb to be stored on the plates, the capacitance is 1 farad.

In practice 1 farad is an enormous capacitance. More practical sub-units of the farad are used. Microfarad and picofarad are the most common sub-units.

1 microfarad = 1 x 10-6 farads

1 nanofarad = 1 x 10-9 farads

1 picofarads = 1 x 10-12 farads

Capacitors range from as small as 1 picofarad to as high as thousands of farads. The very high value capacitors are electrolytic and have a working voltage of about 2.5 to 3V. The very high capacity low voltage capacitors are called "Super Capacitors". These capacitors have not yet found an application in radio though I think they will come to be used in portable power supplies.

A 2.7V 3000F Super Capacitor Figure 11-10

PERMITTIVITY OR DIELECTRIC CONSTANT 

The insulating material between the plates (dielectric) determines the concentration of electric lines of force. Just like different materials will concentrate magnetic lines of force to a greater or lesser extent, materials also vary in their ability to concentrate electric lines of force.

If the dielectric was air, then a certain number of lines of force will be set up. Some papers have a dielectric constant twice that of air, which would cause the density of the electric lines of force to be double and the capacitance would be double. The ability of a dielectric to concentrate electric lines of force is called the dielectric constant or permittivity. The higher the dielectric constant, the greater the capacitance for a given plate area.

Suppose an air dielectric capacitor (dielectric constant close enough to 1) of 8 microfarads had its air dielectric replaced with mica, without changing the distance between the plates. The capacitance would increase in direct proportion to the dielectric constant.

In other words, the capacitance would increase from 8 microfarads to 5-7 times that value, or 40 to 56 microfarads proportional to the new dielectric constant.

DIELECTRIC CONSTANTS

FACTORS DETERMINING CAPACITANCE 

A formula to determine the capacitance of a two-plate capacitor is:

The constant 8.85 x 10-12 is the absolute permittivity of free space.

Example

Calculate C for two plates, each with an area of 2 square metres, separated by 1 centimetre (1 x 10-2 metres), with a dielectric of air.

We will take the dielectric constant of air as 1. Even though it is more accurately 1.0006, 1 is close enough, so that:

For examination purposes, you do not have to use this equation. However, you most definitely do need to know what the equation says about the factors determining capacitance.

Capacitance is directly proportional to the dielectric constant (Ke). Capacitance is directly proportional to the area of one of the plates (A). Capacitance is inversely proportional to the distance between the plates (d).

CAPACITORS IN SERIES AND PARALLEL

In figure 11-12 all the capacitors are the same. Let's say they are 10 microfarads. Think about what happens when you connect two identical capacitors in series. Think about it in terms of the factors that we just discussed; that affect capacitance. Can you visualise by looking at the series capacitors that we have actually doubled the thickness of the dielectric? Doubling the thickness of the dielectric is exactly the same thing as doubling the distance between the plates.

If the distance between the plates is doubled and capacitance is inversely proportional to the distance between the plates, then the capacitance must be half that of a single capacitor on its own. The total capacitance of two 10 microfarad capacitors in series must then be 5µF.

The equation for any number of capacitors of any value in series is:

The easiest way to use this equation on a calculator is:

1. Find the reciprocal of each capacitance.

2. Add all of the reciprocals together (sum them).

3. Find the reciprocal of this sum.

In other words, the reciprocal of the sum of the reciprocals.

Worked example 

Take three capacitors of 7, 8 and 12 microfarads in series.

Find the reciprocal of 7: 1/7 = 0.143 (rounded to 3 decimal places)

The reciprocal of 8: 1/8 = 0.125

The reciprocal of 12: 1/12 = 0.083

The sum of the above is: 0.351

Find the reciprocal of this sum: 1/0.351 = 2.85 microfarads.

Three capacitors of 7, 8 and 12 microfarads in series have a total capacitance of 2.85µF.

Notice how the total capacitance is always less than the lowest value capacitor.

If just two capacitors are in series then you can use the simplified product over sum formula.

For two capacitors (only) in series:

Ct = ( C1 x C2 ) / ( C1 + C2 )

When the same two capacitors are connected in parallel, the distance between the plates and all other factors remain the same, except we have doubled the effective area of the plates. So the capacitance has doubled.

The equation for any number of capacitors of any value in parallel is:

Ct= C1 + C2 + C3 + ... n

These equations are opposite to that of resistances in parallel and series, so be careful not to confuse the two. The shortcuts we took with resistors in parallel work the same for capacitors in series. For example, if we have just two capacitors of any value in series we can use the product over sum method to find the total capacitance.

VOLTAGE ACROSS SERIES CAPACITORS 

If two equal capacitors were connected in series across a 100 volt DC supply and we were to measure the voltage across each capacitor, we would get 50 volts across each. Since the capacitors are equal, we get an equal voltage drop.

For unequal capacitances in series the voltage across each C is inversely proportional to its capacitance. In other words, the smallest capacitance would have the largest voltage drop. The largest capacitance would have the smallest voltage drop.

The amount of charge on each series capacitor is given by:

Q=CE

If a 10µF capacitor was charged to 10 volts, then the charge in coulombs on the capacitors would be:

10µF x 10 volts= (10 x 10-6)F x (10)V = 1 x 10-4 coulombs. (100µC)

The equation can be transposed for voltage across a capacitor and we get:

E =Q/C

In a series circuit, each capacitor regardless of its capacitance will have the same charge. Q is the same for all capacitances in series. For a smaller capacitance to have the same charge as larger capacitors in a series circuit, it must have a higher E.

We could do numerical examples. However, you do not need this in practice or for examination purposes. You do need to understand and be able to visualise the voltage drops across capacitances in a series circuit.

Example.

Two capacitances of 1µF and 2µF are connected in series across a 900 volt DC supply. What is the voltage drop across each capacitor?

Now, the voltage drops have to be unequal because each capacitor will have the same charge (Q).

E=Q/C

E is inversely proportional to C. Therefore, the smallest C (1µF) must have the greatest voltage drop. But how much greater? Since the 1µF capacitor is half the value of the 2µF capacitor, it must have twice the voltage to achieve the same charge. The 1µF capacitor must then have 600 volts across it, leaving 300 volts on the 2µF capacitor.

VOLTAGE RATING OF CAPACITORS

All capacitors are given a maximum voltage rating. This is necessary as the dielectric of capacitors can breakdown and conduct causing the capacitor to fail and in most cases be destroyed. Some capacitors, if placed across a voltage which is too high, will create gas within them and explode somewhat violently.

Thomas Alva Edison was the quintessential American inventor in the era of Yankee ingenuity. He began his career in 1863, in the adolescence of the telegraph industry, when virtually the only source of electricity was primitive batteries putting out a low voltage.

Before he died in 1931, he had played a critical role in introducing the modern age of electricity. From his laboratories and workshops emanated the phonograph, the carbon-button transmitter for the

telephone speaker and microphone, the incandescent lamp, a revolutionary generator of unprecedented efficiency, the first commercial electric light and power system, an experimental electric railroad and key elements of motion-picture apparatus, as well as a host of other inventions.

Singularly or jointly he held a world-record 1,093 patents. In addition, he created the world's first industrial research laboratory.

Born in Milan, Ohio, on Feb. 11, 1847, Edison was the seventh and last of four surviving children of Samuel Edison Jr. and Nancy Elliott Edison. At an early age, he developed hearing problems, which have been variously attributed but were most likely due to a family tendency to mastoiditis. Whatever the cause, Edison's deafness strongly influenced his behaviour and career, providing the motivation for many of his inventions.

12 - Capacitance - II

TYPES OF CAPACITORS

AIR DIELECTRIC CAPACITORS

Capacitors using an air dielectric are used mostly as variable capacitors. Air dielectric variable capacitors are large but can withstand high voltages; this is just what is needed for transmitter output stages and antenna tuning units.

We have seen that capacitance is proportional to the plate area and inversely proportional to the spacing. Even with close spacing, the area of the plate must be large, in order to obtain the required capacitance. Instead of using two large plates, which would be inconvenient, a number of smaller plates can be interleaved.

The capacitance can easily be varied by sliding the plates in and out of mesh since the capacitance is proportional to the cross section of the dielectric between the plates connected to opposite terminals.

A practical capacitor is constructed with a set of fixed plates and a set of moving plates that rotate on a spindle. As the moving plates are rotated through 180 degrees the meshing and therefore the capacitance varies from a minimum to a maximum value. The maximum value of the capacitance is generally about 500pF. It is common practice to use two or three of these capacitors ganged together on a common spindle to form the main tuning control of a transmitter.

Over the years, the physical size of variable capacitors has decreased considerably due to the use of smaller spacing between the moving and fixed plates. However, with the introduction of small communication receivers; air spaced capacitors are too large. In receivers, a synthetic dielectric is now used. In these capacitors, a solid dielectric in the form of thin plastic sheets is placed between the plates. In this way, the capacitance is increased by the value of the relative permittivity of the dielectric. The sheets are a fairly loose fit between the plates so that the moving plates can still slide over the plastic sheets (which are fixed).

In radio transmitters of significant power, air-dielectric variable capacitors are the only option, as an air dielectric can withstand higher voltages at radio frequencies.

SILVER MICA CAPACITORS

This capacitor consists of thin mica sheets as the dielectric. The mica sheets are coated with a thin layer of silver, which forms the plates. A number of plates may be stacked together to obtain the required capacitance. The capacitor is protected by a wax, lacquer or plastic coating. These capacitors are available up to 10,000 pF and have a small loss, small tolerance (e.g. ± 1 %), are stable in capacitance value and have a low temperature coefficient. They are mainly used where an accurate, highly stable, good quality capacitor (high Q) is required. Typical applications of a mica capacitor include the crystal oscillators and other critical RF circuits.

There was a time not that long ago when you could identify most capacitors from the colour of the package and their general appearance. That is not always the case now. You may need to look up a manufacturer's code to identify a capacitor type. Mica capacitors are generally dark or light brown. Do watch out as these conventions may no longer apply. The package can be any shape and colour. An example of mica capacitors is shown in figure 12-2.

CERAMIC CAPACITORS

These capacitors use a ceramic for the dielectric and are very widely used as they are physically small and inexpensive. The term 'ceramic' covers a very large range of materials and the properties of the capacitor depend on the type of ceramic used.

The permittivity of some ceramic materials is very high, as much as 16,000; this results in a physically small capacitor. Capacitors can be made using relatively low permittivity ceramics, which have different temperature coefficients and can be used for temperature compensation. When a high permittivity ceramic is used the temperature coefficient may be very large and not linear, i.e. varies greatly with temperature. These also have a capacitance that changes with the applied voltage and because of this, the tolerance may be large, as much as 20% to +80%. Obviously, such capacitors must only be used where a precise capacitance value is not important.

The maximum working voltage may range from 100V to 10kV or more.

Ceramic capacitors are widely used owing to their small size, low cost and because so many types are available.

There are many bypass and coupling capacitors (discussed later) in a transceiver. There could be  thirty or more. These bypass and coupling capacitors then need to be small, inexpensive and stable. This is an ideal application for the ceramic capacitor. Remember that tip.

PAPER CAPACITORS

At one time paper capacitors were very common. They consisted of a metal foil for the electrodes and paper (impregnated with oil or wax) for the dielectric. Instead of a number of plates, two plates only are used, about 2 to 5 cm wide and of a length corresponding to the capacitance required. The plates and dielectric are now wound into a roll to form a tubular capacitor. Paper capacitors are rarely seen today.

PLASTIC FILM CAPACITORS

These are constructed similar to a paper capacitor, but with a plastic film instead of paper. There are several types: polystyrene, polycarbonate, polyester, polyethylene terephthalate or polypropylene. The plates may be foil (e.g. with polystyrene) or metallised plastic film. Polystyrene ones do not normally have a case, but the others are usually enclosed in a plastic case that may be cylindrical or rectangular. The various films have different detailed characteristics but will be considered as one class.

ELECTROLYTIC CAPACITORS

This type is used where a high value is required in a small space. It depends on the principle of depositing, by electrolytic action, an extremely thin insulating film on one plate, the film then acting as the dielectric. With such a thin dielectric, the capacitance for a given plate area is large. There are two basic types: aluminium and tantalum. These capacitors are polarised. If connected to the wrong polarity they will be destroyed.

ALUMINIUM CAPACITORS 

These are made in a similar way to a paper capacitor, but use two aluminium plates and an absorbent paper. The paper is impregnated with a suitable electrolyte, which produces an aluminium oxide coating on the positive plate. The paper acts as a conductor and container of the electrolyte, the only dielectric being the oxide coating. The capacitance may be increased by etching the positive plate (the one with the oxide coating), thus increasing the effective surface area. In normal capacitors, the aluminium coating must be maintained by the application of a direct voltage across the plates in the correct direction, i.e. the capacitor is polarised. If the voltage is reversed the coating will be removed and the capacitor ruined. Working voltages vary from 3 to 500 volts and it is important that the working voltage is not exceeded as they may explode. The capacitor passes a small leakage current, particularly when first switched on, reforming the oxide layer. This current rises rapidly if the working voltage is exceeded and damage then results. The capacitors are usually fitted into aluminium cases, the case often being one of the connections. These capacitors are commonly used in transistor equipment. Values are available from 1µF to 100,000µF. The tolerance is high, 25% to 100% and the losses are high, particularly at high frequencies.

There are some special electrolytic capacitors made that are not polarised, in which both plates have oxide coatings. They are used in a few special applications where a large electrolytic capacitor is require and polarity can change, e.g. crossover networks in loudspeakers.

Packages differ a great deal; from the small ones shown in 12-4 to large cylindrical packages. A typical application is coupling and bypassing in low frequency circuits to large filter capacitors found in low voltage DC power supplies.

When electrolytic capacitors fail they often bulge due to the internal generation of gas. When looking for a fault check for this bulging. If you find two or three electrolytic capacitors like this on the one circuit board it is good engineering practice to replace all of the electrolytics on that board.

TANTALUM CAPACITORS 

The basic principles are the same as aluminium, with tantalum in place of aluminium. They have a better shelf life and lower leakage current but are more expensive. There are three types: wet electrolyte sintered anode, foil electrode wet electrolyte and solid electrolyte sintered anode. The last type is the cheapest and the more commonly used in domestic equipment, so no further details will be given of the first two types. The solid type uses a sintered tantalum anode with a solid electrolyte of manganese dioxide. It comes in various forms, in particular, tubular and "tear drop" types. Capacitance values vary from 0.1 to at least 100µF with working voltages up to 50V.

TIME CONSTANT 

If a capacitor 'C' is connected to a DC supply through a resistor 'R', as shown in figure 12-5, a current will flow through R until the capacitor is charged to the supply voltage. As the capacitor charges, the voltage across it will rise to 63.2% of its final value, E, in a time equal to CR seconds (where C is in farads and R is in ohms). This time is known as the time constant of the circuit. The voltage across R is the difference between the supply voltage and the voltage across the capacitor and therefore decreases as the capacitor charges. As the capacitor charges the current will decrease and fall to zero at full charge.

If the supply is now disconnected the capacitor will remain charged, apart from the small leakage through the dielectric of the capacitor. It may remain nearly fully charged for hours or even days if it is a high Q (low loss) capacitor.

A large capacitor (e.g. 1 Farad) charged to a high voltage (say 500 volts) may store considerable energy and it is unwise to touch the terminals or a nasty shock will result. If the resistor is connected across the charged capacitor, it will discharge by passing a current through R, the value of the current being determined by Ohm's law. The voltage will now decrease by 63.2% in a time equal to the time constant 'CR'.

Example 

In figure 12-5, the resistance is 1MΩ and the capacitor 10µF. What is the time constant of the circuit?

T=CR = 10 x 10-6 x 1 x 106 = 10 seconds.

When the switch is closed, what will be the voltage on the charging capacitor after 10 seconds?

10 seconds is 1 time constant period. The capacitor will charge to approximately 63.2% of the applied voltage after 1 time constant period has elapsed. Hence, after 10 seconds, the voltage on the capacitor will be about 63.2% of 10 volts or 6.32 volts.

I would like to pause here for a moment to emphasise something. Consider a single resistor connected across a battery with a switch and the switch was closed. How long would it take for the supply voltage to appear across the resistor? Answer - immediately. With a capacitive and resistive circuit, however, the voltage is delayed from building up on the capacitor, determined by the RC time constant. This gives us a better definition of capacitance.

Capacitance is that property of an electric circuit, which opposes changes of voltage.

Going back to our circuit in figure 12-5. The capacitor has charged to 6.32 volts after 1 time constant period. How much further does it have to charge before it equals the supply voltage? The answer is: 10 - 6.32 = 3.68 volts.

During the next time constant period (10 seconds) the capacitor will charge a further 63.2% of the remaining voltage. That is, 63.2% of 3.68 volts, which is 2.325 volts. So after 20 seconds the capacitor will have charged to about 6.32 + 2.325 = 8.645 volts.

In other words, the capacitor charges to 6.32 volts in one time constant period (10 Sec) and it charges a further 2.325 volts in the second time constant period. So, after 20 seconds, the total voltage on the capacitor will be 8.645 volts. During the third time constant period the capacitor will again charge a further 63.2% of the remaining voltage and so on. A capacitor can be considered to be fully charged after 5 time constants.

The same time constant applies to discharging the capacitor through 'R". If the capacitor is charged to 10V then discharged through a resistor after one time constant it will discharge by 63.2% of the starting voltage of 10V. Then in the second time constant period discharge a further 63.2% of the remaining voltage. After 5 time constants the capacitor is considered to be discharged.

Using equation T=CR allows us to easily work the voltage on a charging or discharging capacitor. However you can only do it in increments of a time constant. It is also obvious that going by time constants the capacitor is never (at least mathematically) fully charged.

Figure 12-6 shows the charging voltage across a capacitor and the current through it. The top of the figure shows the voltage increasing on the capacitor over 5 time constants. Notice that at the instant the switch is closed the voltage on the capacitor is zero volts. Then after the first time constant the capacitor charges by 63.2% or to 0.63V of what will then be the final voltage of 1 V.

The bottom part of figure 12-6 shows the current flowing in to the capacitor over 5 time constants. Notice that at the instant the switch is closed; when time equals zero; the current into the capacitor is at maximum. The current slowly decrease and stops after 5 time constants.

THE CONCEPT OF LEADING CURRENT 

Compare the current and voltage in figure 12-6 to that of a resistive circuit. In a resistive circuit when the switch is closed the voltage across and the current through a resistance reaches the Ohm's Law value immediately.

If you were describing current and voltage in a capacitive circuit to someone you would have to say the current starts high and tapers off to nothing while the voltage starts at zero and increases to a maximum.

So current and voltage in a capacitive circuit are not in sync. Current is said to lead the voltage in a capacitive circuit. We describe this behaviour by saying:-

THE VOLTAGE AFTER ANY TIME -T

We can find out the voltage on a charging or discharging capacitor in increments of a time constant by using the equation T=CR. Suppose we wanted to know the voltage after any time period. Take a look at figure 12-7.

The time constant of this circuit is T=CR = 20kΩ x 10µF = 0.2 seconds.

Suppose we wanted to know the voltage across the capacitor 0.5 seconds after the switched was closed. We can use the equation below. We are able to do so because the charge and discharge curve is described by the natural logarithm.

The voltage across the capacitor 0.5 seconds after the switch is closed is 11 V.

RC time constants have many uses in radiocommunications. The de-emphasis and pre-emphasis networks in FM are produced by a simple RC time constant circuits. RC time constants are used for time delays, simple high and lowpass filters and key click filters.

Analogy of a charging capacitor

Suppose you were to blow up a balloon. Some balloons have an initial resistance to being inflated so let's take one that has already been blown up and deflated. The flow of your breath going in the balloon is current. The pressure you create with your breath is voltage. When you first start to inflate the balloon it is easy and there is a high inrush of air (current).

So air flow or current is high at first. After just one breath the balloon has pressure pushing back against you. After one breath the balloon does not have much back pressure (voltage).

As you continue to inflate the balloon, the backward pressure from it becomes greater. It becomes harder to inflate further. The amount of flow (current) into the balloon is less due to the amount of pressure (voltage) that the balloon is pushing back.

When the back pressure of the balloon matches your maximum inflating forward pressure - that is it - you cannot inflate the balloon further and the flow (current) comes to a stop. The balloon is now at maximum inflation, assuming it does not burst.

Can you see this is exactly how a capacitor behaves when it is being charged?

STRAY CAPACITANCE

When we build a capacitor, we want capacitance. However, all we need for capacitance are any two conductors separated by an insulator (dielectric). In any circuit, there are literally hundreds of stray and sometimes unwanted capacitances. More often these are not a problem, however, sometimes they can be. We will discuss this in more detail later.

A lifetime ago I was teaching PMG (telephone) linesmen about fixing telephone lines. A typical telephone line is just two insulated conductors twisted together and they can go for many kilometres.

A telephone line then by its very construction is a capacitor. Suppose a telephone line is only a kilometre long. Also nothing is connected to the telephone line - no telephone and no exchange equipment. The line is said to be open circuit. When a linesman connects an ohmmeter to the line an infinite resistance is expected. This is what an ohmmeter does on a good telephone line, but not immediately. The ohmmeter will swing across and to the right and slowly fall back to infinite ohms after one to two seconds. The ohmmeter shows the capacitance of the line charging.

An ohmmeter is a battery, resistor and a current meter connected in series. When the ohmmeter is attached to the line it shows at first a low resistance as the line acting as a capacitor and charging and after five time constants it is fully charged and the ohm meter reads open circuit. This technique can be used to estimate the length of the line.

13 - Capacitive Reactance

CAPACITOR IN A DC CIRCUIT

We have already discussed the operation of a capacitor in a DC circuit, let's just go over the main principles again.

If a capacitor is connected to a battery (or other DC source), it will charge according to its time constant (T=CR), to the battery voltage.

If a lamp is connected in series with the capacitor while it is charging, the lamp would give off light indicating that current is flowing. The lamp would be bright at first and then slowly dim and extinguish as the capacitor becomes charged. Current into the charging capacitor is high at first and then tapers off to zero when it is fully charged. The voltage on the capacitor is low at first and increases to the supply voltage when the capacitor is fully charged. We can see that the voltage across and the current into a capacitor, are not in sync (phase). Current in a purely capacitive circuit leads the voltage (by 90 degrees).

Imagine a capacitor and a lamp in series. Connect the circuit to a DC source and the lamp will light up momentarily. The capacitor is now charged and the lamp is extinguished. Suppose now we reverse the battery (or supply terminals). The capacitor will now discharge through the lamp and the battery and then recharge with the opposite polarity.

Imagine now continuing to do this very quickly, that is, reversing the battery every time the capacitor is charged or near to fully charged. Because the capacitor will be continually charging and discharging, there will be current flow in the circuit all the time and the lamp will be continuously lit.

Instead of reversing the battery, it would be much easier to supply the circuit with AC voltage, which by definition, automatically changes polarity each half cycle.

CAPACITOR IN AN AC CIRCUIT 

In the circuit of figure 13-1, a capacitor and a lamp are connected via a switch to a source of AC. The capacitor will continually charge and discharge as the AC supply changes polarity. AC current will flow in the circuit continuously and the lamp will remain lit. The two arrows indicate the charge and discharge currents.

So a capacitor 'appears' to allow an AC current to pass through it. I say 'appears' because while there is current flowing in the circuit at all times, at no point does current actually flow through the capacitor. Remember it has a dielectric which will not pass current. The current flows continuously in the circuit because the capacitor is constantly charging and discharging. This type of current is referred to as a displacement current.

Capacitance is the property of a circuit that opposes changes of voltage. A capacitor, therefore, has an opposition to current flow. The opposition to current flow produced by a capacitor is called Capacitive Reactance and is measured in ohms. The shorthand for capacitive reactance is XC.

FACTORS DETERMINING XC

What do you think we could do in the above circuit to increase the brightness of the lamp without changing the lamp or the supply voltage?

Firstly, let's reflect on the frequency of the AC supply. It helps to go to extremes and imagine a very low frequency supply. As a capacitor charges, a voltage builds up on its plates, which opposes the supply voltage. This is why the charge current of the capacitor is at first very high and then tapers off to zero as the capacitor becomes charged.

If the frequency of the AC supply is high enough (polarity reversal is fast enough) then the capacitor will be in the early part of its charge cycle, where the current is greatest when a polarity reversal takes place.

A high frequency will then cause the capacitor to charge and discharge in the early part of its first time constant period and this will cause a greater current to flow in the circuit for the same supply voltage.

We have deduced that capacitive reactance (XC) is dependent on the frequency of the AC supply. In fact, we have deduced that the higher the frequency of the AC supply the more current flows and therefore the lower the capacitive reactance.

A larger capacitance would allow higher charge currents to flow. Therefore, changing the capacitance to one of a higher value would increase the current and therefore decrease the capacitive reactance.

The two factors determining capacitive reactance are frequency and capacitance.

EQUATION FOR CAPACITIVE REACTANCE

XC=1/2πfC Where:

XC=capacitive reactance in ohms.

2π = a numeric constant.

f = frequency in hertz.

C = capacitance in farads.

Look at the equation. 2πfC is in the denominator. 2π is a constant (it does not change).

We can say then, that capacitive reactance is inversely proportional to both frequency and capacitance.

In other words, if either capacitance or frequency was to double then capacitive reactance would halve. If capacitance or frequency was to halve then, the capacitive reactance would double and so on.

EXAMPLE CALCULATION 

A capacitor of 0.05µF is connected to a 10 volt AC supply that has a frequency of 500kHz. What is the capacitive reactance in ohms and how much current will flow in the circuit?

XC=1/2πfC

XC=1/( 6.2831 X 500 X 103 X 0.05 X 10-6)

XC= 6.366 ohms

The current is found from Ohm's law by substituting XC for R in the equation.

I=E/XC =10/ 6.366=1.57 amps

If we are given the capacitive reactances of a circuit and you need to find the net total capacitive reactance, use the same rules as for finding the total resistance of a circuit. For example, two capacitive reactances of 100 ohms in series are equal to 200 ohms and in parallel, the same combination would be 50 ohms.

To reinforce what we have learned have a look at the circuit shown in figure 13-2.

We could deduce the voltage across the 1µF and 2µF capacitors using the proportion method. Instead, let's work out how much current is flowing in the circuit, then using Ohm's law work out the voltage across each of the capacitors.

Reactance of the 1µF capacitor:

XC1=1/2πfC

XC1=1/( 6.2831 X 1 X 106 X 1 X 10-6)

XC1= 0.159154943 ohms

Reactance of the 2µF capacitor (it should be half as much because the capacitance is double):

XC2 =1/2πfC

XC2=1/( 6.2831 X 1 X 106 X 2 X 10-6)

XC2= 0.079577471 ohms

The total capacitive reactance is the sum of the reactances:

XC (total) = XC1+XC2= 0.159154943 + 0.079577471 ohms

XC (total) = 0.238732414 ohms

The current flowing in the circuit is:

I=E/XC (total) = 900/0.238732414=3769.911194 amps

The voltage across the 1µF (it should be 600 volts):

E = IXC1 = 3769.911194 x 0.159154943 = 599.9998392 volts

The voltage across the 2µF (it should be 300 volts):

E = IXC2 = 3769.911194 x 0.079577471 = 299.9999987 volts

So C1 the smallest capacitor (1µF) has 600VAC RMS across it and C2 (2µF) has 300VAC RMS across it.

What if the circuit were DC? What would be the voltage across C1 and C2 in figure 13-3?

Well, we no longer have a frequency as it is DC; however, we do know that the highest voltage will be across the smallest capacitor and the lower voltage across the larger and that the sum of these voltages must equal 900V. Why?

Figure 13-3 is a series circuit. The current is the same in all parts of a series circuit. This means the amount of charge (Q) on C1 and C2 must be the same. For the smaller capacitor C1 to have the same charge on it as the larger C2, there must be more voltage across C1. (double the voltage in this case).

Q=CE and Q is the same for both capacitors. We also know the C1 is half the value of C2.

For C1 to have the same charge as C2, C1 must have twice the voltage of C2. Logically then; C1=600V and C2=300V and the sum, of course, the applied voltage of 900V

As you can see from the graph in figure 13-4, as frequency increases capacitive reactance decreases and as capacitance increases capacitive reactance decreases.

REACTANCE VERSUS F AND C

Capacitive reactance (XC) is inversely proportional to both frequency and capacitance. Now if you cannot see that, without graphs, you have forgotten to "read" equations that we did back in the early chapters.

XC=1/2πfC

This equation should be speaking to you. The 2πfC is in the denominator. The right hand side of the equal sign in this equation is a fraction. It has a numerator (1) and a denominator 2πfC. When the denominator becomes larger in any fraction the entire fraction (which is XC) becomes smaller.

So at a glance, even if you do not have a clue what the symbols mean you should recognise that XC is inversely proportional to frequency and capacitance.

That capacitive reactance decreases with increasing frequency becomes important later. As an example for now many amplifiers; transistors, FETs or valves have unwanted internal capacitance. At low frequencies the reactance of this internal capacitance is so high that this is not a problem. However as we move to higher frequencies the lower capacitive reactance becomes a real problem and ultimately determines the highest operating frequency of the amplifier.

POWER IN A CAPACITIVE CIRCUIT 

Capacitance does not dissipate power. The only circuit property that can dissipate power is resistance.

All of the power taken from a purely capacitive circuit during the charge cycle is returned during the discharge cycle. So a pure capacitance does not dissipate any power. In practice, every capacitor has some resistance in its leads and plates. Dielectric leakage and dielectric loss also dissipates some power.

In practical capacitors, a small amount of power is lost in the dielectric, called dielectric loss. The atoms within the dielectric of a capacitor are placed under stress and do move slightly due to the electric field. Particularly at higher frequencies, the dielectric loss can become significant.

The losses in a "real" capacitor are due to the small amount of resistance in the leads and the plates - this is called resistive losses. Dielectric loss accounts for the greatest amount of loss. All losses increase with increasing frequency. Dielectric loss is caused by the alternating stress placed on the dielectric's atomic structure. In industry, there are many processes that utilise dielectric heating. Food is a lossy dielectric and can be cooked through dielectric heating. Plastics can be welded. Laminated wooden furniture is shaped in a press and cured through dielectric heating.

Note: "real" means - a real world or actual capacitor as opposed to a pure capacitor which only exists on an engineering drawing.

ENERGY STORED IN A CAPACITOR

When a capacitor is charged by a supply and then removed from that supply, the negative plate has an excess of electrons and the positive plate a deficiency of electrons. There exists between the plates an electric field and this field places the molecules in the dielectric under stress. If a charged capacitor is placed across a lamp of the correct voltage the lamp will give off light as electrons move from the negative plate to the positive plate. This continues until there is no imbalance of charge on the plates.

While discharging through the lamp it gives off heat and light energy. There is no doubt then that a capacitor can store energy and later release that energy. Charge is stored on the plates of the capacitor and energy is stored in the electric field.

The amount of energy stored in a capacitor can be calculated in joules (watt-seconds) using the formula: -

In radio circuits we do not deal with large capacitances with the exception of power supplies. I did experiment with some 6 x 700F super-capacitors in series and charged them to 15 volts. I found the super-capacitors stored enough energy to start a car engine several times. With the battery removed of course.

QUANTITY OF CHARGE IN A CAPACITOR

The charge of a capacitor is a measure of the imbalance of electrons on the plates. The Coulomb is the unit of charge. One coulomb is equal to a charge of 6.25 x 1018 electrons.

The amount of charge in coulombs is given by:-

WORKING VOLTAGE 

The working voltage of a capacitor is the maximum voltage at which a capacitor operate without excessive current leaking or arcing through the dielectric.

The working voltage is usually rated as so many volts DC. A capacitor might be marked at 1µF 600 VDC. This capacitor can withstand up 600V of DC electrical pressure. In AC circuits the capacitor should be used at no more than half the DC working voltage. Unless of course the capacitor has an AC working voltage on it.

If we had 2 x 1µF 600V capacitors and we connected them in series then we would have the equivalent to 0.5µF and working voltage of 1200V. If we were to have a string of many capacitors in series then you might think we can just keep adding up the working voltage, and you can, but precautions are necessary to make sure the voltage is shared evenly with all the capacitors. See equalising resistors.

If we had 2 x 1µF 600V capacitors and we connected in parallel we have the equivalent of 2µF 600V - the working voltage does not change.

Suppose we charged a capacitor to a certain charge Q and removed the charging source. We will pretend that our capacitor is perfect in that it has no losses. With the charging source removed the charge remains on the plates. We also have a certain voltage on the plates.

Now if we could move the plates of the capacitor apart without discharging the capacitor what would happen to the voltage on the plates?

If the plates are moved apart then C is decreased. Q stays the same as the charge is trapped on the plates. What happens to E?

We can transpose Q=CE for E and we get E=Q/C.

If Q is constant and C is decreasing the E must be increasing!

What we have just observed in albeit a mind experiment is that a capacitor can amplify voltage! Capacitors are used at very high frequencies as voltage amplifiers using this method. The capacitor is no ordinary capacitor. We use a semiconductor capacitor called a Varactor Diode. These amplifiers are called parametric amplifiers - meaning "amplification by variation of a parameter". These amplifiers are used where there are extremely weak signals such as in a radio telescope. Parametric amplifiers are very low noise. This noise is often reduced further by super cooling the amplifier.

Summary of capacitance so far:-

Capacitance is the property of an electric circuit that opposes changes of voltage. The unit of capacitance is the Farad.

If a charge of 1 coulomb produces a potential difference of 1 volt across the plates of a capacitor, then the capacitance is 1 farad.

Current flows into and out of, but not through, a capacitor.

The capacitance of a capacitor is directly proportional to the area of the plates and the dielectric constant and inversely proportional to the distance between the plates.

The opposition to current flow in a capacitive circuit is called Capacitive Reactance and is measured in ohms.

Capacitive reactance is inversely proportional to both frequency and capacitance. A purely capacitive circuit does not dissipate any power.

Current leads the voltage in a capacitive circuit.

Capacitors in parallel are treated like resistors in series.

Capacitors in series are treated like resistors in parallel.

Capacitors are given a voltage rating, which if exceeded, could cause the dielectric to conduct, destroying the capacitor.

14 - Inductance

Coils of wire were mentioned in the chapter on magnetism when we discussed the magnetic field about a coil carrying a current. An equally important aspect of the operation of a coil is its property to oppose any change in current through it. This property is called inductance.

Inductance is that property of an electric circuit that opposes changes of current.

Not to be confused with capacitance, which is, the property of an electric circuit to oppose changes of voltage.

When a current of electrons starts to flow along any conductor, a magnetic field starts to expand from the centre of the conductor outward. These lines of force move outward, through the conducting material itself and then continue into the air. As the lines of force sweep outward through the conductor, they induce an emf in the conductor. This induced voltage is always opposing the current that produced it. Because of its opposing polarity, it is called a counter emf, or a back emf. This opposing affect is called Lenz's Law and it is much like one of Newton's law's; every action has an equal and opposite reaction.

The effect of this backward pressure built up in the conductor is to oppose the immediate establishment of maximum current. It must be understood that this is a temporary condition. When the current eventually reaches a steady value in the conductor, the lines of force will no longer be in the process of expanding or moving and a counter emf will cease to be produced. In other words, there will be no relative motion between the conductor and the magnetic field. At the instant when current begins to flow, the lines of force are expanding at their greatest rate and the greatest value of counter emf will be developed. At the starting instant, the counter emf value almost equals the applied source voltage.

Current is minimum at the start of current flow. As the lines of force move outward, the number of lines of force cutting the conductor per second becomes progressively smaller and the counter emf becomes progressively less. After a period of time the lines of force expand to their greatest extent, the counter emf ceases to be generated and the only emf in the circuit is that of the source. Maximum current can now flow in the wire or circuit since the inductance is no longer opposing the source voltage.

This property of a coil or more correctly an inductor to oppose changes of current by self-inducing an opposing (counter) emf is called inductance. The unit of inductance is the Henry and the symbol for inductance is 'L'.

SELF INDUCTION

When the switch in a current carrying circuit is suddenly opened, an action of considerable importance takes place. At the instant the switch breaks the circuit, the current due to the applied voltage would be expected to cease abruptly. With no current to support it, the magnetic field surrounding the wire will collapse back into the conductor at a fast rate, inducing a high amplitude emf in the conductor. Originally, when the field built outward, a counter emf was generated. Now, with the field collapsing inward, a voltage in the opposite direction is produced. This might be termed a counter-counter emf, but is usually known as a self-induced emf. This self induced emf is in the direction of the applied source voltage. Therefore, as the applied voltage is disconnected, the voltage due to self-induction tries to establish current flow through the circuit in the same direction, aiding the source voltage. The inductance induces a voltage to try and prevent the circuit current from decreasing. With the switch open it might be assumed that there is no path for the current, but the induced emf immediately becomes great enough to ionise the air at the opened switch contacts and a spark of current appears between them. Arcing lasts as long as energy stored in the magnetic field exists. This energy is dissipated as heat in any circuit resistance and the arc radiates energy as electromagnetic waves.

With circuits involving low current and short wires, the energy stored in the magnetic field will not be great and the switching spark may be insignificant. With long lines and heavy currents, inductive arcs many centimetres long may form between opened switch contacts on some power lines. The heat developed by arcs tends to melt the switch contacts and is a source of difficulty in high voltage high current switching circuits.

In a previous chapter, I gave you an example of the capacitance of a telephone line. A telephone line also has inductance. The normal operating voltage of a telephone line is about 50 volts DC. When a telephone line is suddenly open circuited by a technician or a linesman, the self-induced voltage on the line can be in the order of 2000 volts and this will produce a harmless but significant electric shock. The shock is harmless, as the amount of current is extremely small.

Remember, regardless of how current changes in a circuit containing inductance, the induced emf created by the inductance will oppose the change of current. The self induced emf of an inductor is often referred as a 'counter' or 'back emf'.

The unit of measurement of inductance is the Henry, defined as the amount of inductance required to produce an average counter emf of one volt when an average current change of one ampere per second is under way in the circuit. Inductance is represented by the symbol L in electrical problems and henrys are indicated by the letter 'H'.

COILING A CONDUCTOR 

It has been explained that a piece of wire has the ability to produce a counter emf and therefore has a value of inductance. A small length of wire will have an insignificant value of inductance by general electrical standards. One henry represents a relatively large inductance in many circuit applications, where milli, micro or nanohenries are typically more practical. A straight piece of No. 22 wire one meter long has about 1.66 µH. The same wire wound onto an iron nail, or other high permeability core may produce 50 or more times that inductance.

A given length of wire will have much greater inductance if wound into a coil. If two loops are wound on the same conductor but a distance apart then each loop will have a small inductance. If the two loops are wound together side by side, they will collectively have twice the inductance of one loop.

When ten loops are wound next to each other as shown in figure 14-1, with the same current flowing there will be ten times the number of magnetic lines of force cutting each turn. Compared to 1 turn, this coiled inductor would produce a counter emf, ten times greater.

If the turns are stretched out, the field intensity will be less and the inductance will be less. Stretching the coil but keeping the same number of turns increases the length of the magnetic circuit and the inductance decreases.

The larger the radius or diameter of the coil, the longer the wire used and the greater the inductance. In single layer air core coils with a length approximately equal to the diameter, a formula that will give the approximate inductance in microhenries is:

The inductance of straight wires is found in antennas, in power lines and in ultra-high frequency equipment. In most electronic and radio applications where inductance is required, space is limited and the wire is wound into either single layer or multilayer coils with air, mixed powdered iron compound (ferrite), or laminated iron (many thin sheets) cores. The advantage of multilayer coil construction for high values of inductance becomes obvious when it is considered that, while 2 closely wound turns produce 4 times the inductance of 1 turn, the addition of 2 more turns closely wound on top of the first 2 will provide almost 16 times the inductance. The direction of winding has no effect on the inductance value of a given coil.

In many applications, coils are constructed with ferrite cylinders (slugs) that can be screwed into or out of the core space of the coil. This results in a controlled variation of inductance, maximum when the ferrite core "slug" is in the coil and minimum with it out.

A particular type of coil is the toroid. It consists of a doughnut shaped ferrite core, either single or multilayer wound as shown in figure 14-2. Its advantages are high values of inductance with little wire and therefore little resistance in the coil and the fact that all the lines of force are in the core and none outside (provided there is no break in the core). As a result, it requires no shielding to prevent its field from interfering with external circuits and to protect it from effects of fields from outside sources. Two toroids can be mounted so close that they nearly touch and there will be almost no interaction (magnetic coupling) between them. Inductors come in a huge number of packages from tonnes to a few grams in weight. With some packages, it is not evident that the device is an inductor as they are small and encapsulated.

There are so many different packages for inductors it is too much to show them all. Some look very much like resistors. Others are copper tracks etched into a circuit board. Others may be formed with a length of transmission line.

THE TIME CONSTANT OF AN INDUCTANCE

The time required for the current to rise to its maximum value in an inductive circuit after the voltage has been applied will depend on both the inductance and the resistance in the circuit. The greater the inductance, the greater the counter emf produced and the longer the time required for the current to rise to maximum. With a constant value of inductance in a circuit and more resistance, then less current can flow.

As with capacitive and resistive circuits, the time required for the current to rise to about 63% (more precise 63.2%) of the maximum value (called the time constant) can be determined by:

T= L/R 

Where

T = time in seconds.

L = inductance in henrys (H).

R = resistance in ohms.

EXAMPLE

Calculate the time constant of a 10 henry inductance with 10 ohms of resistance.

T =L/R=10/10=1 second

Suppose the emf applied to this inductor was 10 volts. What would be the current flowing after 1 second?

The final current after 5 time constants will be:

I=E/R=10/10 =1A

After 1 time constant the circuit current will have reached 63.2% of what will be its final value, or 63.2% of 1A = 632mA.

CURRENT LAGS VOLTAGE IN AN INDUCTIVE CIRCUIT

In a resistive circuit, the current and voltage obey Ohm's law. If you increase the voltage across a resistance, the current increases straight away to the new Ohm's law value determined by l=E/R. In an inductive circuit, it takes time for the current to build up to its final value. The current lags behind the voltage. The current will eventually reach its Ohm's law value after 5 time constants. However, if the voltage is continually changing as in an AC circuit, the current will always lag the voltage across the inductor by 90 degrees.

Think of 'L' for inductance and 'L' for lag - current lags voltage in an inductive circuit.

THE ENERGY IN A MAGNETIC FIELD 

The current flowing in a wire or coil produces a magnetic field around itself. If the current suddenly stops, the magnetic field held out in space by the current will collapse back into the wire or coil. Unless the moving field has induced a voltage and current into some external load circuit, all the energy taken to build up the magnetic field will be returned to the circuit in the form of electric energy as the field collapses.

The amount of energy stored in the magnetic field of an inductor is given by;

CHOKE COILS

The ability of a coil to oppose any change of current can be used to smooth out varying or pulsating types of current. In this application, an inductor is known as a choke coil since it chokes out variations of amplitude of the current. For radio frequency (RF) AC or varying DC, an air core coil may be used. For lower frequency circuits greater inductance is required. For this reason, iron core choke coils are found in audio and power frequency applications.

A choke coil will hold a nearly constant inductance value until the core material becomes saturated. When enough current is flowing through the coil to saturate the core magnetically, variations of current above this value can produce no appreciable counter emf and the coil no longer acts as a high value of inductance to these variations. To prevent the core from becoming magnetically saturated, a small air gap may be left in the iron core. The air gap introduces so much reluctance in the magnetic circuit that it becomes difficult to make the core carry the number of lines of force necessary to produce saturation. The gap also decreases the inductance of the coil. An air coil cannot be saturated.

DEFINITION OF A HENRY

If a coil has a rate of change of current of 1 ampere per second and this produces a counter emf of 1 volt, then the coil is said to have an inductance of 1 henry.

MUTAL INDUCTANCE 

If one coil is placed near another so that the magnetic fields interact with each other, then the moving magnetic field in one will induce a voltage into the other. This ability of one coil to effect another is called mutual inductance.

The further apart the two coils are, the fewer the number of lines of force that interlink the two coils and the lower the voltage induced in the second coil.

The mutual inductance can be increased by moving the two coils closer together or by increasing the number of turns of either coil.

When all the lines of force from one inductor are linked to another, unity coupling is said to exist and the mutual inductance is:

Where M is the mutual inductance in henries.

The above formula assumes 100% coupling between the two inductors L1 and L2. This equation assumes that all the magnetic lines of force from L1 cut all the turns of L2. If this is not the case then M is determined by:

Where k is the percentage of coupling.

For example: suppose a 5 henry coil has 75% of its lines of force cutting a 3 henry coil. What is the mutual inductance?

COEFFICIENT OF COUPLING 

The degree of closeness of coupling of two coils can also be expressed as a number between 0 and 1 rather than as a percent. A percentage of 100 is equal to a coefficient of coupling of 1 or unity. 75% coupling is 0.75 as above. No coupling is 0.

The formula for mutual inductance can be transposed for coefficient of coupling:

INDUCTANCES IN SERIES 

When you add inductances in series, you are in effect simply increasing the number of turns on the inductor. Therefore, to find the total inductance, sum the individual inductances.

Lt= L 1 + L2 + L3 + ... n

INDUCTANCES IN PARALLEL 

If the inductances are connected in parallel, the total inductance is calculated by using a formula similar to the parallel resistance formula.

1/Lt = 1/L 1 + 1/L2 + 1/L3 + ... n 

Both of these equations assume that the magnetic lines of force from all the inductors are not coupled (linked) to the others i.e. the mutual inductance is zero. Another way of describing how inductances are linked is called coefficient of coupling (k). If k=O then there is no coupling. If k=L, the two inductances are completely coupled.

INDUCTIVE REACTANCE

It has been explained that DC flowing through an inductance produces no counter emf to oppose the current. With varying DC, as the current increases, the counter emf opposes the increase. As the current decreases, the counter emf opposes the decrease. Alternating current is in a constant state of change and the effect of the magnetic fields is a continually induced voltage opposition to the current. This reacting ability of the inductance to oppose a changing current is called inductive reactance. Inductive reactance is the opposition to current flow presented by an inductance in a circuit with changing current and is measured in ohms.

Inductive reactance is directly proportional to frequency and inductance.

Just as with resistance and capacitive reactance, the total inductive reactance in ohms is found using the same form of the equation.

In series:

XL(total) = XL1 + XL2 + XL3 + ... n

and parallel:

1/XL(total) = 1/XL1 + 1/XL2 + 1/XL3 + ... n

The voltage across and the current through an inductive reactance can be determined using Ohm's law.

EXAMPLE 

An inductance of 100µH is in series with an inductance of 200µH and connected to a 10 volt AC supply with a frequency of 500kHz. How much current will flow in this circuit?

We need to find the total inductive reactance of the circuit. We could find the individual reactances of each inductor and add them, or we could find the total inductance and then the total inductive reactance. I will do it using the latter method.

LT = L1 + L2 = 100µH + 200µH = 300µH

XL= 2πfL

XL = 2π X 500 x 103 x 300 x 10-6 

XL= 942Ω 

l=E/R = 10/942 (x 1000 for milliamps) = 10.6mA

How much power is dissipated in the above example?

There is no resistance in the circuit, so no power is dissipated. You cannot/must not substitute XL or XC for R in the power equations. For example, P=l2R is okay but P=l2XL is not. Reactance, either inductive or capacitive does not dissipate power - only resistance does.

Take a pure inductive reactance of 240 ohms and imagine it being connected to a power point. The current that flows would be l=E/ XL = 240/240 = 1 ampere. Even though 1 ampere would flow in the circuit, no power is dissipated as there is no resistance. All of the power supplied charging the inductor during one cycle is returned to the power point (the power supply) on the alternate half cycle. A pure inductor has no losses.

Only resistance dissipates power 

Power authorities dislike reactive loads like this as current drawn does not register on the energy meter. The power lines to your house carry the charge and discharge 'reactive' currents do have resistance - the lines do dissipate power - and this power loss is not metered.

LOSSES IN A REAL INDUCTOR

A real world inductor does have losses. These losses include resistive losses of the windings and core losses. Hysteresis loss is a core loss caused by the continuous realignment of the magnetic domains. Eddy currents are small circulatory currents (eddies) induced into a conductive core. Core losses increase substantially with increasing frequency. Hysteresis and eddy current loss will be discussed in more detail in the chapter on transformers.

PHASE AND INDUCTANCE 

In a purely inductive circuit (no resistance) the current lags the voltage by 90°. If there is inductance and resistance in the circuit then the phase angle between voltage and current will be less than 90° lagging. The actual phase angle will depend on the ratio of the inductive reactance and the resistance XL/R.

For example suppose we had and inductive reactance of 30Ω and a resistance of 30Ω then the phase angle, that is, how much the current lags the voltage is given by phase angle θ = tan XL/R or tan(30/30) = 45° lagging.

In an LR circuit the phase angle can be between 0° to 90° lagging.

In a CR circuit the phase angle (from tan XC/R) can be between 0 to 90° leading. Leading means the current leads the voltage.

This lead and lag occurs because Inductance is the electrical property that opposes changes of current and capacitance is the electrical property that opposes changes of voltage. We will be doing more on phase angle later when we study LCR circuits.

The man that did the most work on Inductance was Joseph Henry and the unit of inductance is named after him.

Joseph Henry was the first to coil insulated wire tightly around an iron core in order to make a more powerful electromagnet. Henry shared his knowledge freely and to some extent has not been given full credit. Samuel Morse acquired much of the knowledge to build the Telegraph from Henry. It was Henry's invention of the Relay that made the Telegraph possible. Henry was appointed the first Secretary of the Smithsonian Institution in 1846, and served in this capacity until 1878. He did early pioneering work into the nature of sunspots. From 1832 to 1846, Henry served as the first Chair of Natural History at the

College of New Jersey (now Princeton University). While in Princeton, he taught a wide range of courses including natural history, chemistry, and architecture, and ran a laboratory on campus. Decades later, Henry wrote that he made several thousand original investigations on electricity, magnetism, and electro-magnetism while at the Princeton faculty.

15 - Meters

Most radio theory exams will not ask you to describe the operation of a moving coil meter movement. I do believe it is a good idea to include them as it will reinforce much of the material already covered. We do need to know about using moving coil meters to build ammeters, voltmeters and ohmmeters.

A pictorial diagram of the moving coil meter is shown in figure 15-1. The moving coil is wound on an aluminium former. The coil is free to move clockwise and anticlockwise through about 130 degrees, this motion in turn moves the pointer on the scale from left to right. Without any current flowing through the moving coil, the pointer will be towards the left of the scale, pushed there by a small coil return spring. The pointer will not go past the left end of the scale as there is a small pointer stop. When current is passed through the moving coil, a small magnetic field is created around it which interacts with the field created by the permanent magnet in such a way as to cause the moving coil and the pointer along with it to rotate clockwise. So we have a simple but very effective method of detecting current flow with this instrument. Importantly, the degree of deflection from left to right by the pointer is directly proportional to the current. If a certain current causes the pointer to move to 1/4 scale, then twice that current will cause the pointer to move to 1/2 scale - this is a direct proportion.

The other important feature of the moving coil meter is that it is extremely sensitive to very small currents, typically in the order of microamperes and therefore does not consume much power from the circuit in which it is placed. The moving coil meter is a microammeter. Typical current to enable full-scale deflection ranges from 1μA to 30mA. The moving coil does have some resistance of course. A movement with a smaller full-scale deflection current has a higher coil resistance, as more turns of fine wire are needed to obtain that deflection.

We can make use of this meter by calibrating and using it to measure current, voltage and resistance. From now on I will draw the moving coil meter as a circle, but it does help to remember what is inside.

The other point I would like to make is that many modern meters are digital. They do not use a moving coil. The digital circuitry performs an analogue to digital conversion of the applied current or voltage and displays the amount as a numerical readout. These meters are very accurate. However, the moving coil meter (called an analogue meter) has advantages that will see it in use for a long time to come. The greatest advantage of the analogue meter is its ability to show changes in voltage or current. For example, if an analogue meter is placed across a charging capacitor, the pointer will slowly rise up the scale as the capacitor charges. I have an all bells and whistles digital meter. When I place it across a charging capacitor, because the voltage is changing, the digital display just "blinks" as it is unable to show a varying voltage adequately.

MEASUREMENT OF CURRENT 

Whether we are measuring amperes, milliamperes or microamperes, two important facts to remember are:

1. The current meter (ammeter) must be in series with the circuit in which the current is to be measured. The amount of deflection depends on the current through the meter. In a series circuit, the current is the same in all parts of the circuit. Therefore, the current to be measured must be made to flow through the meter as a series component in the circuit.

2. A DC meter must be connected with the correct polarity for the meter to read upscale. Reversed polarity would make the meter read down-scale, forcing the meter pointer hard against the left-hand stop.

An ammeter should have a very low resistance when compared to the circuit in which it is placed. An arbitrary figure is 1/100th of the resistance of the circuit in which the ammeter is placed.

AMMETER SHUNTS

A meter shunt is a precision resistor connected across the meter movement for the purposes of shunting or bypassing, a specific fraction of the circuit current around the meter movement. Shunts are usually inside the meter case. The schematic symbol for an ammeter does not show the shunt.

While shunts are called resistors, they are extremely low-value resistors. A high current shunt may be a brass bar and measure in the order of milli-ohms or less. Figure 15-2 shows a typical high current range shunt.

One way of adjusting precisely the resistance of a high current shunt is to make small cuts in it using a very fine metal saw.

For example, we may have a 25mA meter movement with a moving coil resistance of 1.2 ohms. We want the meter to be able to read 50mA full scale. In other words, to double the range of the meter from 0-25mA to 0-50mA.

To achieve this, a shunt resistance of 1.2 ohms (equal to the resistance of the moving coil) would suffice.

With a 1.2-ohm shunt, half of the total current will flow through the meter and half through the shunt since both form a parallel circuit consisting of two 1.2 ohms resistances. The use of the shunt in this instance has extended the full-scale deflection (FSD) of the meter from 0-25mA to 0-50mA.

With a correct shunt, a moving coil meter can be used to measure any amount of current (FSD). The shunt is a low value resistor. In typical ammeters, the shunt is often a solid copper bar with a resistance in milli-ohms, particularly for high current ranges on the meter.

It is common to hear a current meter called an 'ampmeter' - this is wrong; the correct name for a current meter is an ammeter with no 'p'.

CALCULATING ANOTHER SHUNT 

Figure 15-4 shows an ammeter. The moving coil has a resistance of 2000 ohms and is deflected full scale with 50 microamperes. We wish to modify the meter to measure  1 ampere full-scale deflection. Calculate the value of the shunt resistor that would extend the range of the ammeter to 0-1 amperes.

This is just an Ohm's law problem. Assume that one ampere is flowing in the circuit. You know there is 50uA flowing through the meter movement. The current through the shunt is then:

lshunt = 1 amp - 50µA = 0.99995 amperes.

We now know the current through the shunt. What is the voltage across it? We know the resistance of the meter and the current through it. Since the meter and the shunt are in parallel, they will have the same voltage. So, if we calculate the voltage across the meter we will know the voltage across the shunt:

Eshunt = Im x Rm= 50µA x 2000 ohms= 0.1 volts.

Now calculate the resistance of the shunt:

Rshunt = Eshunt / lshunt = 0.1 / 0.99995 = 0.100005 ohms.

This shunt, which is just over 1/10th of an ohm, would be a solid bar inside the meter. The manufacturer (or the builder) would use a reference current and adjust the resistance of the shunt accurately.

VOLTMETER 

Although a meter movement responds only to current moving in the coil, it is commonly used for measuring voltage by the addition of a high resistance in series with the movement. Such a high series resistance is called a multiplier.

The multiplier must be higher than the coil resistance in order to limit the current flow through the coil. The combination of a meter movement with its added multiplier then forms a voltmeter.

Since a voltmeter has a high resistance, it must be connected in parallel to measure the potential difference between any two points in a circuit. Otherwise, the high

resistance multiplier would add so much series resistance to the circuit the current would be reduced to a very low value.

The circuit is not opened when you connect a voltmeter in parallel. Because of this convenience (not having to break the circuit), it is common to make voltmeter tests when troubleshooting rather than ammeter tests. If you need to know the current through a resistor, it is far easier to measure the voltage across it and then work out the current using Ohm's law.

Figure 15-5 shows how a 1mA meter movement is connected with a multiplier to enable it to be used as a voltmeter with an FSD of 10 volts. In other words, a voltmeter with a 10V range.

With the 10V applied by the battery, there must be a total of 10,000 ohms of resistance to limit the current to 1mA for full-scale deflection (FSD) of the meter movement. Since the movement has a resistance of 50 ohms, 9950 is added in series, resulting in a total resistance of 10kΩ. Current through the meter is then: I=10/10,000 =1mA.

With 1mA in the movement, the FSD can be calibrated as 10V on the meter scale. Of course, since deflection is directly proportional to current the meter can be calibrated proportionately from 0-10 volts. For example, half scale would be 5 volts, 1/4 scale 2.5 volts, etc.

With the battery removed the circuit now consists of the meter movement and the multiplier. This is our 0-10V voltmeter. Different multipliers can be switched in for other voltage ranges.

Let's calculate another multiplier to make sure we understand this.

The circuit of figure 15-6 is a voltmeter. It has a very sensitive meter movement (50µA). What is the value of the multiplier resistor required to allow this meter to measure from 0 to 10 volts?

We know that at full-scale deflection (FSD) the current in the circuit and through the multiplier will be 50µA. We can work out the voltage across the meter movement and subtract this from the applied voltage (10V) to get the voltage across the multiplier.

voltage across meter= I meter x Rmeter = 50uA x 2000 ohms= 0.1 volts

Rmultiplier = Emultiplier / I multiplier

Rmultiplier = (10-0.1 volts)/ 50µA = 9.9 volts/ 50uA = 198,000Ω

VOLTMETER RESISTANCE 

The high resistance of a voltmeter with a multiplier is essentially the value of the multiplier resistance. Since the multiplier is changed for each range, the voltmeter resistance changes. Most moving coil voltmeters are rated in ohms of resistance needed for 1V of deflection. This value is the Ohms-Per-Volt rating of the voltmeter.

Figure 15-7 is a circuit of a multi-range voltmeter. Why don't you check this circuit yourself by calculating two or three of the multipliers?

The leads on the voltmeter are shown by the+ and - signs. When this voltmeter is switched to the 2.5 volt scale, can you see that the only multiplier resistance used is the 48kΩ. So the total resistance of the voltmeter is 48kΩ + 2000 ohms =50kΩ.

The total resistance of this voltmeter on the 2.5 volt scale is 50kΩ.

If we divide the total resistance of the voltmeter by the scale to which it is switched, we get the sensitivity of the voltmeter in ohms-per-volt:

ohms-per-volt=total resistance/ scale= 50kΩ / 2.5 = 20,000 ohms-per-volt.

This sensitivity works for all other scales as well. If we want to know the total resistance of the voltmeter on any scale, just multiply the sensitivity by that scale.

Example: What is the total resistance of this voltmeter if it is switched to the 10 volt scale?

Total resistance of voltmeter= ohms-per-volt x scale.

Total resistance of voltmeter= 20,000 x 10 = 200,000 ohms.

Is this right?

Check it in the circuit. On the 10 volts scale the voltmeter's resistance consists of: 150kΩ+ 48kΩ+ 2000Ω= 200,000 ohms.

Using this method, you can work out quickly the total resistance of any voltmeter on any scale - provided you know the ohms-per-volt.

A QUICK WAY TO WORK OUT SENSITIVITY 

A quick way of working out the ohms-per-volt or sensitivity of any voltmeter is to take the reciprocal of the full-scale deflection current of the movement. In the last example, current FSD is 50uA and so the reciprocal of 50uA is 1/50 x 10-6 which gives 20,000 ohms-per-volt.

We need to know the sensitivity of a voltmeter so that we can determine if it is going to affect significantly the circuit in which it is placed.

Suppose we were using a 20,000 ohms-per-volt voltmeter on a 10 volt range. The voltmeter's resistance would be 20,000 x 10 = 200kΩ. So our voltmeter has a resistance of 200,000 ohms when switched to the 10 volt range. When we place our voltmeter in parallel with a component to measure the voltage across that component, the voltmeter is adding 200,000 ohms of resistance across the circuit.

Now, if the component we are measuring the voltage across is a 1000Ω resistor, placing the voltmeter resistance of 200kΩ in parallel with 1000Ω is not going to disturb the resistance of the circuit much at all. However, if we were to use the same voltmeter across a 200kΩ resistor, we would be reducing the resistance of the 200kΩ resistor to 100kΩ. 200kΩ in parallel with 200kΩ is 100kΩ.

This does not always matter as long as you know what effect the voltmeter is having

on the circuit. In some cases, though, the interaction of the voltmeter with the circuit may cause the circuit to stop operating, particularly in high resistance radio frequency circuits.

Very good voltmeters have a very high resistance in the vicinity of 10MΩ-per-volt. Whether or not you have to be concerned about the interaction of the voltmeter and the circuit still depends on the circuit from which you are taking the measurement.

Most digital meters have an input resistance which is not scale dependent. So you may see a digital voltmeter with 10MΩ resistance irrespective of the voltage scale used.

OHMMETERS 

An ohmmeter consists of an internal battery, the meter movement and a current limiting resistance. When measuring resistance, the ohmmeter leads are connected across the resistance to be measured. The circuit power is turned off. Only with the power off can you be sure that it is only the ohmmeter's battery that is producing current and deflecting the meter movement. Since the amount of current through the meter depends on the external resistance, the scale can be calibrated in ohms.

The amount of deflection on the 'ohms' scale indicates the measured resistance directly. The ohmmeter reads up-scale regardless of the polarity of the leads because the polarity of the internal battery determines the direction of current through the meter movement.

The leads of a meter are normally coloured 'black' for negative and 'red' for positive. It is important to remember that a multi-function meter, when switched to ohms, may have the output polarity reversed, because of the internal battery or cell, supply a positive voltage to the negative lead and vice-versa for the other lead. This can be of particular importance when testing semiconductors.

The ohmmeter circuit shown in figure 15-8 has 1500 ohms of resistance. The 1.5 volt cell will then produce 1mA if the leads are shorted and the pointer will go to full scale. In a practical ohmmeter, a small variable resistor would be in series to 'zero' the meter exactly.

When the ohmmeter leads are short-circuited the meter will show full scale or zero resistance. With the ohmmeter leads open (not touching), the current is zero and the ohmmeter indicates infinite resistance.

Therefore, the meter face can be marked zero ohms at the right for full-scale deflection and infinite ohms on the left for no deflection. The in between values can be marked in ohms by calibrating the meter against known resistances.

Notice with an ohmmeter the red lead is negative and the black positive. When this meter is switched to volts or amps, the lead colours are correct as voltage or current is coming from outside the meter and going in. With an ohmmeter, the current and voltage is coming out of the meter. This is handy to know when testing semiconductors in the circuit as the polarity of the leads can be used to reverse or forward bias PN-junctions.

MULTIMETERS

All of the above meters can be built into the one box. Shunts, multipliers and the battery can be switched in and out of the circuit as required to perform the various functions. Multimeters can be digital or analogue. There are advantages and disadvantages to each. Digital meters make static (non-changing) readings clear. Analogue meters make changing voltages and currents easy to read. Any good digital meter will have auto ranging and over volt and current protection. For an investment of a few dollars, you can buy a cheap multimeter and just do some measurements around the workshop or the house - you will learn a lot.

A word of caution, though; cheap meters like the one shown in 15-9 are great to learn on and you really do not care if you destroy if for the price - but - be very careful using such meters on high voltages. They tend to have cheap probes and a brittle plastic case. As long as you are careful, you can learn a lot from the meter and when you graduate to a better one it can be used on your car electrics.

Great for learning with but be careful of high voltages; these cheap meters are not safe on mains electricity regardless of what the manufacturer says.

When an analogue moving coil meter is not in use it is good practice to short circuit the terminals and put the meter on a low current scale. This has the affect of physically dampening the meter from being jostled around. The meter is a coil on a pivot in a magnetic field, in effect a simple motor. If the meter is bumped the needle with the coil will attempt to deflect. However, in doing so there will be a counter emf induced into the coil that opposes this motion. A backward torque is electrically produced that

causes the meter movement to be damped.

Moving coil meters often have a mirrored scale. When reading the meter look over the top of it straight down so that you line up the pointer with its reflection in the mirrored scale. This helps you to avoid parallax error.

DIGITAL MULTIMETER (DMM) 

Digital multimeters range in price from a few tens of dollars to hundreds of dollars. Modern meters have many functions other than volts, amps and ohms. Some can measure capacitance, frequency and temperature. There are auto ranging meters. You just have to switch to volts or whatever you want and the meter will look after the range.

Good meters have a large backlit display and update the display very quickly. Most DMMs have a bargraph in the digital readout to simulate an analogue display. Nearly all have a continuity test that makes an audible alarm when the circuit is complete.

A meter marked TRUE RMS will read the true RMS value of a voltage or current irrespective of wave shape being measured.

Electrical measuring instruments are assigned a CAT number. For example CATI, CATII and CATIII. These categories tell you about the safe working voltage and insulation of the meter. Caution needs to be exercised as some imported meters can be falsely labelled.

The DMM shown in figure 15-10 is CATIII Measurement Category Ill:

This category refers to measurements on hard-wired equipment in fixed installations, distribution boards, and circuit breakers. Other examples are wiring, including cables, bus bars, junction boxes, switches, socket outlets in the fixed installation, and stationary motors with permanent connections to fixed installations.

Safety when working on high voltages is paramount. A CATIII meter should be used with the correct leads and probes. (figure 15-10)

16 - Electric Cells & Batteries

There are many different types of batteries. The basic principles of operation are all the same. There is much material here that you do not need to know for examination. It might seem a bit strange, but let's start off our discussion about batteries by starting with corrosion. The two topics are related chemically and knowledge of corrosion is useful particularly when it comes to antennas.

CORROSION 

Corrosion is a chemical reaction. Corrosion involves removal of metallic electrons from metals and the formation of more stable compounds such as iron oxide (rust), in which the free electrons are usually less numerous. In nature, only rather chemically inactive metals such as gold and platinum are found in pure or nearly pure form; most others are mined as ores that must be refined to obtain the metal. Corrosion simply reverses the refining process, returning the metal to its natural state. Corrosion compounds form on the surface of a solid material. If the compounds are hard and impenetrable and if they adhere well to the parent material, the progress of corrosion is arrested. If the compound is loose and porous, however, corrosion may proceed swiftly and continuously.

Aluminium is a good example. When aluminium corrodes, it becomes covered with aluminium oxide. Aluminium oxide adheres well to aluminium and prevents further corrosion. This makes aluminium an excellent choice for antennas. An added bonus is its light weight and strength.

HOW THINGS CORRODE 

If two different metals are placed together in a solution (electrolyte), one metal will give up ions to the solution more readily than the other. This difference in behaviour will bring about a difference in electrical voltage between the two metals. If the metals are in electrical contact with each other, electrons will flow between them and they will corrode; this is the principle of the galvanic cell or battery. Though useful in a battery, this reaction causes problems in a structure. For example, steel bolts in an aluminium framework may, in the presence of rain or fog, form multiple galvanic cells at the point of contact between the two metals, corroding one or both them.

An electrolyte is any liquid that conducts electricity. With corrosion, the electric cell effect of dissimilar metals in the presence of an electrolyte is undesirable. Nevertheless this is what we desire in an electric cell. Although the term battery, in strict usage, designates an assembly of two or more voltaic cells capable of such energy conversion, it is commonly applied to a single cell of this kind.

THE VOLTAIC CELL

When two different electrodes are immersed in an electrolyte, the chemical reaction which takes place results in a separation of charges. The arrangement required to convert chemical energy into electrical energy is called the voltaic cell.

The charged conductors are the electrodes, serving as the connection of the cell to an external circuit. The potential difference resulting from the separated charges enables the cell to function as the source of applied voltage.

Electrons from the negative terminal of the cell flow through the external circuit and return to the positive terminal. The chemical action in the cell continuously separates charges to maintain the terminal voltage that produces the current in the circuit.

AN EXPERIMENT 

If you have a voltmeter with a low DC volts scale, you can easily demonstrate the action of a Voltaic cell. All you need are two different conductors and some type of electrolyte. I have had great success using a lemon or an orange. Just take the lemon and push two electrodes into it. I have used different nails, paper clips; almost anything will work. Place your voltmeter across the conductors and you will measure a potential difference, usually a significant fraction of a volt. You could find out if two coins are made of the same alloys or not! The amount of voltage developed by two coins you can tell (roughly) how dissimilar they are. No doubt this technique has an application in metallurgy.

SEPARATION OF CHARGES 

When metals dissolve in an electrolyte, the chemical action causes separation or disassociation of the molecules, which results in charged ions. Figure 16-1 shows a generic cell with two electrodes immersed in an electrolyte which could be liquid or paste. A chemical reaction with the electrodes causes a flow of ions through the electrolyte. This flow of ions to the two electrodes causes one to become negatively charged and the other to be positively charged.

As long as the reaction continues and the external circuit can be connected between the negative and positive terminals an electron flow will occur between them and do work for us. In this case, the electron flow is lighting (by current causing heat) a light bulb. The actual chemistry is not important to us as cells use many different types of electrodes and electrolytes. It is the principle of the disassociation of charge due to ionic movement in the electrolyte that makes one electrode negative and the other positive.

The ionic current flow in the electrolyte is an "electric current". Electric current is not "just" the flow of electrons. Electric current is the ordered flow of any charge. One of the first practical batteries developed used zinc and copper electrodes immersed in ammonium chloride. These early cells were assembled using glass jars. To obtain the required output voltage, the cells (jars), were connected in series. These banks of cells connected together were called a Voltaic pile; we call it a battery today.

PRIMARY CELLS

In a primary cell, the chemical action of forming the solution is not reversible. For instance, zinc can dissolve in ammonium chloride, but the process cannot be reversed to form the zinc electrode from the solution.

SECONDARY CELLS 

In secondary cells, the chemical action occurring in the electrolyte can be reversed. The electrodes can dissolve in the solution when the cell provides current to the external circuit. In this case, the cell is discharging. When an external voltage is applied to the cell to make current flow in the reverse direction, the metal comes out of the solution and is deposited back onto the electrodes, recharging the cell. Since a secondary cell can be recharged, it is also called a storage cell.

The carbon-zinc dry cell is a modern day version of the Leclanche cell. See figure 16-2. We will look at this cell with a view to understanding how most cells work in general. You do need to know a couple of things specific to other cells and these will be covered in this chapter

The Leclanche cell is a zinc-carbon cell. The carbon rod in the centre is the positive electrode and the zinc case is the negative electrode but also the housing for the entire cell. The electrolyte in the cell is ammonium chloride. The cell is a primary cell in that it cannot be recharged. The Eveready-Red is a common zinc-carbon cell.

As the cell discharges, the zinc electrode becomes dissolved in the ammonium chloride

electrolyte. The electrolyte is in the form of a paste. The cell is completely discharged when the electrolyte is converted to zinc ammonium chloride, which usually corresponds with the zinc, in the zinc case almost being depleted. Early carbon-zinc cells would often leak electrolyte into equipment when they were discharged, as the zinc case would get holes in it.

Construction of Zinc-Carbon cell (Leclanche)

POLARISATION

Now, if you're old enough, you might remember when the zinc-carbon battery would no longer work. It could be heated by placing it in or near an oven for a few minutes and it would come to life again, for a while at least.

Well, one of the problems with the zinc-carbon cell is that as the chemical reaction takes place to charge both of the electrodes, hydrogen gas forms around the carbon rod in the form of small bubbles. This build up of hydrogen gas around the carbon rod will begin to insulate the carbon rod from the electrolyte. Since the surface area of the carbon rod in contact with the electrolyte is reduced, the terminal voltage of the cell will drop dramatically and the cell(s) will no longer operate the equipment. This unwanted build up of hydrogen gas (and other gases in other cells) is called polarisation.

Placing the dry cell in the oven would drive the hydrogen gas from the carbon rod bringing it back to life for a while. The higher temperature would also increase the rate of chemical reaction between the electrodes and the electrolyte.

A chemical called manganese dioxide is mixed in with the electrolyte. Manganese dioxide absorbs the hydrogen gas and prevents the gas from building up on the carbon rod. Manganese dioxide is rich in oxygen and this oxygen combines with the hydrogen to form water. Manganese dioxide in the zinc-carbon cell is called the depolariser, as removing hydrogen from the carbon rod is called depolarisation.

LOCAL ACTION 

If the zinc electrode (the case) contains impurities, small voltaic cells are formed

which do not contribute to the output voltage of the cell. Also, these unwanted cells caused by impurities in the zinc, consume chemicals and dissolve the zinc. This is called local action. To minimise local action, the zinc electrode is coated with mercury by a process called amalgamation.

ALKALINE CELL

The carbon-zinc cell is now largely being superseded by the alkaline cell, which has better discharge characteristics and will retain more capacity at low temperatures. The alkaline cell typically has an ampere-hour capacity of about twice that of the carbon zinc cell. Its nominal voltage is also 1.5V.

The negative electrode is manganese dioxide and the positive electrode is zinc. The electrolyte is potassium hydroxide or sodium hydroxide. High conductivity (low resistance) of the electrolyte results in higher current ratings than the carbon-zinc cell. The alkaline cell is supposed to be a primary cell. However, I have been recharging them for years after finding out by experiment that it could be done. I charge these cells at 50mA constant current overnight. I first placed them inside a plastic garbage bin in case they exploded, but I have never had a misadventure with one yet. I have found that over the last few years, chargers have become available to recharge them! I guess they just did not want the public to know about it! These are the Copper Top and Energizer type batteries.

All chemical reactions are slowed by reduced temperature. Even at zero degrees centigrade, some cells give up the ghost. Alkaline cells have superior low-temperature characteristics compared to the older carbon zinc cell.

LEAD-ACID STORAGE BATTERY 

The most widely used high capacity rechargeable battery is the lead-acid type. In automotive service, the battery is usually expected to discharge partially at a very high rate and then to be recharged promptly while the alternator is also carrying the electrical load. If the conventional car battery is allowed to discharge fully from its nominal 2.2 V per cell to 1. 75 V per cell, fewer than 50 charge-discharge cycles may be expected, with reduced storage capacity. The typical lead-acid car battery consists of 6 cells connected in series.

Many older car batteries could be physically sliced into six individual 2.2V cells. The plates in a lead-acid battery are lead peroxide for the positive and spongy lead for the negative. The electrolyte is dilute sulphuric acid.

SULPHATION

As a lead-acid cell discharges, lead sulphate is deposited onto the plates. This is commonly referred to as sulphation. Lead sulphate is a white powder often seen on the outside of old batteries or on the terminals. If lead-acid batteries are allowed to remain discharged for very long the plates will be covered in lead sulphate and the

capacity of the battery greatly reduced as the lead sulphate insulates the plates from having contact with the electrolyte.

For radio use, lead-acid batteries make a very cheap alternative to an expensive power supply. They are cheap to buy and can be trickle charged with an inexpensive charger.

Lead-acid batteries are also available with gelled electrolyte. Commonly called gel cells, these may be mounted in any position if sealed, but some vented types are position sensitive.

Lead-acid batteries with liquid electrolyte usually fall into one of three classes:

1. Conventional, with filling holes and vents to permit the addition of distilled water lost from evaporation or during high-rate charge or discharge.

2. Maintenance-free, from which gas may escape, but water cannot be added.

3. Sealed.

SPECIFIC GRAVITY

Specific gravity is the weight of a substance compared to the weight of water. An hydrometer (figure 16-3) can be used to draw some electrolyte from a lead-acid cell into a reservoir tube; a weighted float can be used to measure the specific gravity of the electrolyte. This reading gives a very good indication of the state of charge of a cell. In a fully charged cell, the specific gravity is in the vicinity of 1.280 (which means the density of the electrolyte is 1.280 times that of water). When the specific gravity is down to about 1.150, the cell is fully discharged. Water has a specific gravity of 1.0 so at an electrolyte level of 1.15, means we almost have water for an electrolyte.

As you can imagine, when a lead-acid cell discharges, its electrolyte becomes weaker in sulphuric acid and approaches water. As a lead-acid cell discharges, the specific gravity or density of its electrolyte decreases (it turns more towards water).

WARNING

Lead-acid cells produce hydrogen and oxygen when being charged, these are highly flammable gases in combination with air. The bubbles in a liquid electrolyte are hydrogen. The oxygen remains mostly locked in the cell due to other chemical reactions. It is the combination of liberated hydrogen with air that is hazardous.

I have seen a telephone exchange levelled to the ground by the ignition of hydrogen gas from the charging cells. Neither hydrogen nor oxygen is flammable independently, but they are flammable when found in combination with air. Pure hydrogen will not burn by itself nor will oxygen. A spark in a container of hydrogen won't cause an explosion. Likewise, a spark in a container of pure oxygen may only form a bit of ozone. But when oxygen and hydrogen are combined, a vigorous reaction takes place when the mixture is ignited.

It is dangerous to allow salt water to get into lead acid cells; though it is a bit hard to avoid this in a sinking boat. Salt water in combination with sulphuric acid releases huge amounts of chlorine gas, a very heavy green gas which if inhaled causes severe burning of the respiratory system.

If a lead-acid cell is short circuited, enormous current will be drawn from the battery. It will overheat in seconds and explode spraying sulphuric acid everywhere. This sometimes unfortunately happens in car accidents.

NICKEL-CADMIUM BATTERY (NiCd) 

NiCd batteries held the top spot as the battery of choice for use in portable equipment for decades. Today the NiCd has been displaced as best choice by the Lithium battery. The nickel-cadmium (NiCd), has a nominal voltage of 1.2 - 1.25 V per cell.

The NiCd cell has a positive electrode made of nickel and a cadmium negative electrode. The electrolyte is potassium hydroxide.

Carefully used, these are capable of 500 or more charge and discharge cycles. To ensure longer life, the NiCd battery should not be fully discharged. Where there is more than one cell in the battery, the most discharged cell may suffer polarity reversal, resulting in a short circuit, or seal rupture. All storage batteries have discharge limits and NiCd types should not be discharged to less than 1.0 V per cell.

Nickel cadmium cells are not limited to "D" cells and smaller sizes. They also are available in larger varieties ranging to mammoth 1000Ah units having carrying handles on the sides and caps on the top for adding water, similar to lead-acid types. These large cells are sold to the aircraft industry to start jet engines and to railroads for starting locomotive diesel engines. They also are used extensively for uninterruptible power supplies. Although expensive, they have very long life. Surplus cells are often available through surplus electronics dealers and these cells often have close to their full rated capacity.

Advantages for radio use is that these vented-cell batteries are the availability of high discharge current to the point of full discharge. Also, cell reversal is not the problem that it is in the sealed cell since water lost through gas evolution can easily be

replaced. Simply remove the cap and add distilled water. By the way, tap water should never be added to either nickel-cadmium or lead-acid cells, since dissolved minerals in the water can hasten self-discharge and interfere with the electrochemical process.

NiCd batteries must be charged with a constant current source. A constant current source is one where the current through the cell does not change as the battery is charged. The rule of thumb is 1/10th the milliamp hour rating for 15 hours. So if a NiCd battery is rated at 500mA/hours, then it should be charged for about 15 hours at 50mA constant current if it is fully discharged. If the NiCd is only, 1/3 discharged then it should be charged for 5 hours.

LITHIUM CELLS 

Like any other battery, a rechargeable lithium-ion battery is made of one or more power-generating compartments called cells. Each cell has essentially three components as all other chemical cells: a positive electrode, a negative electrode and an electrolyte in between them.

The positive electrode is typically made from a chemical compound called lithium cobalt oxide (LiCoO2) or, in newer batteries, from lithium iron phosphate (LiFePO4). The negative electrode is generally made from carbon (graphite).

The electrolyte varies quite a lot with many options available. Electrolytes comprise of lithium salts or organic solvents, such as ethylene-carbonate, dimethyl-carbonate and diethyl-carbonate.

All lithium-ion batteries work in broadly the same way. When the cell is charging up, the lithium-cobalt oxide, the positive electrode gives up some of its lithium ions, which move through the electrolyte to the negative graphite electrode and remain there. The battery takes in and stores energy during this process. When the battery is discharging, the lithium ions move back across the electrolyte to the positive electrode, producing the energy that powers the battery. In both cases, electrons flow in the opposite direction to the ions around the outer circuit. Electrons do not flow through the electrolyte: it's effectively an insulating barrier, so far as electrons are concerned.

The movement of ions (through the electrolyte) and electrons (around the external circuit, in the opposite direction) are interconnected processes and if either stops so does the other. If ions stop moving through the electrolyte because the battery completely discharges, electrons can't move through the outer circuit either-so you lose your power.

Lithium cells if overcharged or short circuited can cause an explosion. Large batteries usually have some electronic control and safety protection. Generally, lithium-ion batteries are more reliable than older technologies such as nickel-cadmium (NiCd) and don't suffer from a problem known as the "memory effect" (where NiCd batteries appear to become harder to charge unless they're discharged fully first). Since lithium-

ion batteries don't contain cadmium (a toxic, heavy metal), they are also (in theory, at least) better for the environment-although dumping any batteries (full of metals, plastics and other assorted chemicals) into landfills is never a good thing. Compared to heavy-duty rechargeable batteries (such as the lead-acid ones used to start cars), lithium-ion batteries are relatively light for the amount of energy they store.

CHARGING CELLS AND BATTERIES

A charger for a lithium battery can output a constant voltage of 4.2V per cell in series. If a lithium cell does not receive more than 4.2V it can remain connected to the charger and will not over-charge.

CELLS IN SERIES AND PARALLEL 

Cells can be connected in series, positive to negative to increase the output voltage. This method is common to all batteries. The small 9 volt transistor battery is 6 cells connected in series. The 6V lantern battery has 4 completely separate cells inside the case. If you get the opportunity, I suggest you break an old one open and have a look. It isn't too messy and you will find what looks like 4 oversized 'D' cells inside.

Batteries or cells can be connected in parallel to increase the current capacity. The batteries must be identical. A more desirable way to get greater capacity is to use a bigger battery in the first place.

It is very rare indeed to have batteries connected in a combination of series-parallel. This would only be done in specialist applications and is not recommended.

TESTING BATTERIES 

The best way to test a lead-acid cell is by measuring the specific gravity of the electrolyte as already discussed. Smaller batteries and cells must be tested on a load. This means the equipment in which the battery is installed should be turned on and then the terminal voltage of the cell or battery measured. A fully discharged battery will still show its correct terminal voltage if it is not under load. It is important you

understand this and the reasons why. As a battery ages its internal resistance increases.

A new battery will have an internal resistance, which is a small fraction of an ohm. The electrolyte between the plates forms part of the total circuit. If the battery is supplying 1A and the internal resistance of the battery is 0.1 ohms then a mere 0.1 volts will be dropped across the internal resistance, which is insignificant. As the battery discharges, the internal resistance will increase. However, no voltage is lost across the internal resistance unless the battery or cell is placed on a load. The load should be the nominal load that the battery is expected to deliver.

ELECTROLYTIC CORROSION 

The use of dissimilar metals in engineering (say when building an antenna) is likely to cause considerable trouble due to electrolytic corrosion. Every metal has its own electro-potential and unless metals of similar potential are used the difference will cause corrosion at the point of contact even when dry. When moisture is present, this effect will be even more severe. If for any reason, dissimilar metals must be used then considerable care should be taken to exclude moisture, the corrosive effects of which will vary with atmospheric pollution.

Metals can be arranged in what is called the electrochemical series, as follows:

Metals from within the same group may be used together with little corrosion, but metals used from across the groups will suffer greatly from the voltaic corrosion effects. Also, since the above groups are arranged in order, the greater the spacing in the list, the greater will be the corrosion.

The metals of the lower group will corrode those in the upper portion. For example, brass or copper screws in aluminium will corrode the aluminium considerably, whereas with cadmium plated brass or copper screws there will be much less corrosion of the aluminium.

17 - Microphones

SOUND

Sound consists of small fluctuations in air pressure. We hear sound because these changes in air pressure produce fluctuating forces on our eardrums. You only have to place your hand in the front of your mouth while you are talking, or in front of a sound system, to feel the pressure waves.

Similarly, microphones respond to the changing forces on their components and produce electric currents that are effectively proportional to those pressure waves.

The best way of detecting sound is with a diaphragm ('dia'-'fram'). Our eardrums have a diaphragm. Just like the skin or membrane covering of a musical drum. When sound waves enter the ear, the force of the sound waves causes the eardrum to vibrate. Vibrations from the eardrum are transmitted by various structures in the ear to our brain for processing.

All microphones have a diaphragm, which usually consists of some type of taut material like plastic, paper, or even very thin aluminium. With all microphones, sound waves strike a diaphragm and cause it to vibrate. This vibration is then, by the mechanism of the microphone, made to make a voltage or current vary in sympathy with the sound waves. The voltage or current thus produced can be made to travel long distances (if necessary) along conductors and then we can recover the sound by converting current variations back into sound wave pressure variations.

THE CARBON MICROPHONE

Carbon microphones are no longer used, as they are low quality. However, a short discussion of the carbon microphone is a good introduction to all microphones. The carbon microphone was for many decades the only type of microphone used in telephones and two-way radios.

The principle of operation was both simple and ingenious. Sound waves strike the diaphragm and move it. The movement of the diaphragm causes a plunger or piston to move with it.

The plunger compresses and decompresses a chamber filled with carbon granules.

Now, carbon granules will conduct electric current. If a battery is connected to the microphone terminals, a current will flow.

How much current flows will depend on the degree of compression of the carbon granules. If the sound waves force the diaphragm inwards, then the granules are compressed and their resistance decreases and the current increases. Similarly, if the sound amplitude (loudness) decreases, the tension of the diaphragm allows it to move outwards, the carbon granules decompress, the resistance increases and so the current decreases.

In other words, the resistance of the carbon microphone varies in sympathy with the sound waves that strike the diaphragm and this, in turn, causes a varying current in the circuit which is a good representation of the original sound wave.

Carbon microphones were used for many years. You may have seen people bang an older type telephone handset against something to get rid of the noise. This is because the carbon granules would cling together in older microphones and make a noise called 'frying' because the noise sounded like something frying in a pan.

THE DYNAMIC OR MOVING COIL MICROPHONE 

In the dynamic microphone, the diaphragm is connected to a lightweight coil. Inside the coil is a permanent magnet. When sound strikes the diaphragm, the coil will move back and forth in the magnetic field of the permanent magnet. We have relative motion between a conductor and a magnetic field (Faraday's Law), so an emf or voltage is induced into the coil. This induced emf is a very good electrical representation of the original sound wave. A dynamic microphone produces its own output voltage and does not need a battery like the carbon microphone.

Dynamic microphones can be made in various impedances. (Impedance is the total opposition to current flow in an AC circuit). The dynamic microphone or some variation of it is widely used in telephones, radiocommunications and quality sound recording.

The speaker is essentially the same as the dynamic microphone, except the current carrying the sound to be recovered is fed through the coil, which creates a moving magnetic field around the coil. The interaction between the magnetic field of the coil and the field of the permanent magnet cause the diaphragm to move back and forth. The motion of the diaphragm recreates the original sound wave.

A SIMPLE TELEPHONE (FAR SOUND)

You do not need to know how a telephone works, however, looking at a simple telephone circuit will help to consolidate what you do need to know. In figure 17-3, we have a carbon microphone and a receiver in each handset.

A speaker is called a 'receiver' in telephony. A source of DC is applied to each microphone. The carbon microphones are coupled to the receiver and telephone line via a transformer. Sound on either carbon microphone will be converted to varying DC in the handset. The transformer will convert varying DC to AC and sound will be heard in both receivers.

The current contains all of the information present in the original sound wave (amplitude and frequency). Since the current flows through the receiver (most likely a moving coil), the diaphragm (cone) of both receivers will move back and forth with the same frequency and relative amplitude of the original sound wave and therefore recreate it.

The distance between the microphone and the speaker can be a long way apart enabling voice communications over a long distance through wires. The modern landline telephone is really not much more than this in principle.

The carbon microphone that was used in telephones for many decades has been replaced by a variant of the moving coil type called a 'rocking-armature'. The rocking armature microphone is just a moving coil microphone with an inbuilt mechanical advantage between the diaphragm and the coil.

It seems simple does it not? Yet the impact of the telephone when it was first invented had a profound effect on the world. Of course, the telegraph came first. However, imagine how mysterious and wonderful it must have been for the first telephone users to hear and talk to someone thousands of miles away.

The word telephone comes from the Greek roots 'tele' ("far") and 'phone' ("sound"). Alexander Graham Bell invented the telephone (disputed), though many others improved on the invention. The U.S. patent granted to Bell in March 1876 (No. 174,465) for the development of a device to transmit speech sounds over electric wires, is often said to be the most valuable patent ever issued.

CONDENSER (CAPACITOR) MICROPHONE

When we learned about capacitance, we found that the capacitance of a capacitor was determined by the area of the plates, the type of dielectric and the distance between the plates.

Now, suppose a capacitor is connected to a source of emf and allowed to charge fully (at least 5-time constants). What would happen if we left the capacitor in the circuit and somehow altered its capacitance?

If we increased the capacitance of the capacitor in the circuit, it would be able to hold more charge. So increasing the capacitance would cause the capacitor to charge further and current would flow while the charging process was taking place. If we then decreased the capacitance, the capacitor would no longer be able to hold as much charge and it would discharge back into the source of the applied emf.

While it is discharging, current would again flow in the circuit.

In the capacitor microphone, that is what happens. One of the plates of the capacitor is made of very light material and is the diaphragm of the microphone. Sound waves striking the diaphragm (one plate) will cause it to vibrate in sympathy with the sound waves. The moving diaphragm (plate) will cause the capacitance to change. As the diaphragm moves in, the capacitance will increase and a charge current will occur. As the diaphragm moves out, the capacitance decreases and a discharge current occurs. Since the motion of the diaphragm and the capacitance are in sympathy with the sound waves, the charge and discharge currents are once again an electrical representation of the original sound wave.

The diaphragm of the microphone can be one of the plates of the capacitor microphone, or a diaphragm can be connected mechanically to make a capacitor plate move.

Like a carbon microphone, the capacitor microphone needs a source of emf, as it does not generate any of its own.

The term 'condenser' is an old term for 'capacitor'. When you see these microphones referred to, the words 'condenser' and 'capacitor' are often used interchangeably. I prefer 'capacitor microphone' but it seems for many the term 'condenser' has stuck from tradition. Capacitor microphones have the advantage of being very small, which makes them attractive for use in small equipment, such as handheld two-way radios (transceivers), small voice recorders and the like.

There is an another type of capacitor microphone called the 'electret microphone.' The principle of operation of these microphones is identical to that of a capacitor microphone. However, a special electret material is used as the dielectric in the capacitor. The electret microphone does not require a bias battery. An electret material is one that holds a charge for many years similar to the way a magnetic material can hold a magnetic field for a long time.

For exam purposes, you need only remember that an electret is the same as an ordinary capacitor microphone. However, it can be used without a bias voltage.

The dynamic and capacitor microphones are the most popular microphones in use today for radiocommunications.

CRYSTAL MICROPHONE 

The Piezoelectric Effect (pee-zo-electric) microphone.

If a piece of quartz crystal is held between two flat metal plates and the plates are pressed together, a small emf will be developed between the plates as if the crystal became a small battery for an instant. How much emf is produced is proportional to the pressure applied. When the pressure on the plates is released the crystal springs back and an opposite polarity emf is produced on the plates. In this way, mechanical energy is converted into electrical energy by the crystal. Piezoelectricity means "pressure-electricity".

If an emf is applied to the plates of a crystal, the physical shape of the crystal will distort. If an opposite polarity emf is applied, the crystal will reverse its physical distortion. In this way, a quartz crystal converts electrical energy into mechanical energy and vice versa.

Some ceramic materials also exhibit a piezoelectric effect. These two reciprocity qualities of a quartz crystal and ceramics are known as the piezoelectric effect.

Well, if you are thinking ahead of me, here we have another way to make a microphone. After all, the function of a microphone is to convert mechanical energy (sound waves) into electrical energy and the piezoelectric effect does just this.

Sound waves striking the diaphragm cause varying pressure to be applied to the crystal, which in turn causes the microphone to produce an output voltage in sympathy with the sound waves. A crystal microphone does not require a battery. Like the dynamic microphone, it directly converts mechanical energy into electrical energy.

The crystal earpiece is the same principle used in reverse. Crystal microphones are not high quality, but they have the advantage of being small and inexpensive. The quartz crystal is not used in the form you may have seen them in nature. They are cut into thin slices and ground, like a gemstone is ground, to the exact size.

Well, that's about it for microphones. Microphones used for radio communications are not high fidelity (high quality audio reproduction). Talk to a recording or sound engineer about microphones and they can go on about all of the different types used in their field. For example, special microphones that pick up sound from some directions and not others, etc. However, for us radio communication people, a simple dynamic or capacitor microphone does the job nicely.

MICROPHONE AMPLIFICATION

Because the output of a microphone is very low in electrical terms, in almost all applications, an amplifier called a microphone amplifier or pre-amplifier, is connected to the microphone to increase the level of the output signal. Many microphones come with a built in amplifier in the microphone housing.

Many radio operators add microphone amplification to their transceiver. This is fine, however adding too much amplification may cause distortion to the transmitted signal that does not sound good (though many think it does). This can cause interference to other radiocommunications users. We will be discussing this in depth later; it is called 'overmodulation.'

Alexander Graham Bell (born March 3, 1847, Edinburgh. Died, August 2, 1922, Beinn Bhreagh, Cape Breton Island, Nova Scotia, Canada). Scottish-born American audiologist best known as the inventor of the telephone (1876). For two generations his family had been recognised as leading authorities in elocution and speech correction, with Alexander Melville Bell's Standard Elocutionist passing through nearly 200 editions in English. Young Bell and his two brothers were trained to continue the family profession. His early achievements on behalf of the deaf and his invention of the telephone before his 30th birthday,

bear testimony to the thoroughness of his training.

Antonio Meucci. There is much controversy over who really invented the telephone. There is strong evidence that an Italian immigrant to the United States by the name of Antonio Meucci invented the telephone before Bell and that his apparatus was misplaced or stolen. The evidence is so strong the US Congress passed a Bill naming Meucci as the inventor of the Telephone. A copy of this Bill can be easily found with an Internet search.

18 - Transformers

One of the most common devices used in electricity, electronics and radio, is the transformer. The name itself indicates that the device is used to transform, or change, something. The transformer may be used to step up or step down AC voltages, to change low voltage high current AC to high voltage low current AC, or vice versa, or to change the impedance of a circuit to some other impedance in order to transfer energy more efficiently from a source to a load.

A BUZZER

A buzzer has nothing to do with transformers. However, I am going to describe how a buzzer works as this will lead nicely to transformers.

Take a close look at the pictorial diagram of a buzzer in figure 18-1. It is so easy to make one of these on a piece of board. No need for you to make one but it would be good if you can picture how it is made and how it works. The electromagnet is just a soft iron bolt (any bolt would do) about 75mm long. Wind as many turns of thin single strand insulated wire on the bolt as you can get. The armature is just a strip of tin about 5mm wide and 75mm long. A nail holds it on the board on the left hand side. The contact on the right hand side is just another nail.

The strip of tin (the armature) forms part of the circuit for current flow. The circuit as it is now in figure 18-1 can conduct current. When the battery has been connected for a fraction of a second the magnetic field builds up around the electromagnet and the electromagnet pulls the armature towards it. When the armature moves towards the electromagnet, the circuit is broken and the current stops.

The magnetic field about the electromagnet collapses and the armature springs back to the contact. Current can now flow again. This cycle is repeated over and over. The result is that the motion of the armature hitting the electromagnet makes a buzzing sound. We have a buzzer! If the armature was extended with a rod and on the end of that rod we had a small weight (hammer) that could strike a gong; we would have an electric bell. What type of current flows in this circuit?

I hope you agree it is pulsating DC, or DC which is being turned ON and OFF rapidly. Now think about the magnetic field around the electromagnet. It is a pulsating magnetic field, or perhaps more importantly, it is a magnetic field which is continually varying. It never stays still as it is either expanding when the current is ON or collapsing when the current is OFF.

Let's make a modification to our simple buzzer circuit to demonstrate the action of a transformer. Refer to figure 18-2.

All we have done is wind a second coil of wire, either on top of or next to, the electromagnet using insulated wire and connected it to a voltmeter. The two coils (inductors) are insulated from each other.

Now, do you remember when we discussed inductance and alternating current? We talked about Faraday's law of magnetic induction.

Faraday's law states: When relative motion exists between a conductor and a magnetic field an emf is induced into the conductor.

Is there relative motion between the conductors on the second coil and a magnetic field? Yes, there is. An emf (voltage) is induced into the second conductor and this will be shown on the voltmeter. We have created a simple, though very inefficient transformer. Generally, a transformer has two windings. The primary winding is supplied with some type of current that will cause the magnetic field around it to vary. In our experiment, the primary winding is the coil of wire around the electromagnet. The other winding of a transformer is called the secondary winding.

A transformer is basically two or more windings (coils, inductors) wound on a common core or former. The primary winding is fed with some type of varying current so that a moving magnetic field is created around it. The moving magnetic field created by the primary winding causes an induced emf into the secondary winding.

For a transformer to work the primary winding must have a current through it that produces a varying magnetic field. This is virtually any current other than DC, such as AC, pulsating DC, varying DC and the like. The secondary voltage (type) will always be AC.

What we need to learn are the uses for a transformer and how we can determine the amount of induced voltage into the secondary.

Obviously, we could reason that the amount of induced voltage into the secondary would have something to do with the voltage on the primary and the ratio of the number of turns on the primary and secondary. We will discuss this relationship in more detail shortly.

Transformers do not have to have a magnetic material such as iron for a core. The core can be air. The basic function of a transformer is to step voltage up or to step voltage down, which is also a way of matching unequal impedances.

The schematic symbol for a transformer is shown in figure 18-3 (excluding the writing which I have added). The two vertical lines between the two windings indicate that this transformer has a laminated iron core. If no lines were shown, it would be an air core transformer. You do not know what the number of conductor turns are on the primary or secondary from the symbol. More important is the ratio of the number of turns on the primary to the secondary. This ratio is called the turns ratio. If there are more turns on the secondary than the primary, then voltages are stepped up. Conversely, fewer turns on the secondary and voltage is stepped down. The symbol may show you if the transformer is step up or step down but it will not give the turns ratio. The voltage ratio is the same as the turns ratio. If voltages for primary and secondary are given, then you know the turns ratio since voltage and turns ratio are the same.

TRANSFORMER CONSTRUCTION

Figure 18-4 shows one construction method for a laminated iron core transformer. Here the primary and secondary are wound separately around a laminated iron core.

LAMINATED IRON CORE

Winding the primary and secondary on an iron core improves the efficiency of the transformer since the iron core concentrates the magnetic lines of force.

The problem with iron cores is that the core is also a conductor. Think back to Faraday's law again. The core of a transformer (iron) is in a moving magnetic field. This means that small currents will be induced into the core. These unwanted core currents are called Eddy Currents.

These currents are given this name because they flow in circles in the iron core much like eddies of water around a propeller.

Eddy currents are undesirable because of P=l2R losses. What this means is that current flowing through any resistance produces heat. This is fine if you want to make heat. However, the function of a transformer is not to make heat but to transform from one voltage to another. By the way, you may hear the term "I squared R losses" used. This means the same thing, though "I squared R losses" can occur other ways besides eddy currents.

What is the product of the current and voltage in a circuit? Power= E x I. A transformer should ideally have no losses. This means the power in the primary circuit should be equal to the power in the secondary circuit. The power in each circuit is the product of the voltage and current in the respective circuit.

In practical transformers, particularly iron core ones, the major form of loss of power is due to eddy currents, also known as I squared R losses.

If we could increase the electrical resistance of the core without changing its magnetic properties, we would reduce the magnitude of the eddy currents. When we discussed the properties that determine the resistance of a conductor, one of these properties was the cross-sectional area. The smaller the cross sectional area the greater the resistance. This is what we are doing when we laminate the iron core.

Imagine taking a solid iron core and slicing it into lots of thin sheets. Each sheet (lamination) will have a higher resistance to current flow than the solid iron core. We now spray each sheet with an insulating lacquer and bolt or glue the entire iron core back together again. We now have a laminated iron core, which will have less power lost in it due to eddy currents.

Eddy currents are not a problem if the core of a transformer is made of air or some other non-conductive material.

Another construction method for a transformer is shown in the diagram of figure 18-5. Eddy currents are reduced in amplitude by laminating the core. I have shown one E-lamination and one I-lamination. Imagine 50 or more of such laminations. Insulated from each other, then bolted together to form a solid laminated iron core.

The type of transformer shown in figure 18-6 is used at high frequencies. Iron core transformers are not used at radio frequencies, as the eddy current losses become too great.

HYSTERESIS - LOSSES

If iron is in an unmagnetised state, its magnetic domains are not arranged in any particular manner. The domains are randomly oriented. When a magnetising force is applied to them, the domains rotate into a position in line with the magnetising force. If the magnetising force is reversed, the domains must rotate to the opposite position. In rotating from one alignment to the opposite, the domains must overcome a frictional hysteresis, or a resisting effect, in the core. In some materials the resisting effect is small, in others it is appreciable. Due to this effect, we lose some energy as heat. Heat is nearly always lost energy. This loss is called hysteresis loss.

Hysteresis occurs in iron cores of transformers. As frequency is increased, the alternating magnetising force will no longer be able to magnetise the core completely in either direction. Before the core becomes fully magnetised in one direction, the opposite magnetising force will begin to be applied and start to reverse the rotation of the domains. The higher the frequency, the less fully the core magnetises.

Transformers operated on low-frequency AC may not have much hysteresis loss, but the same cores used with a higher frequency have more hysteresis and are less efficient.

COPPER LOSS 

Iron core transformers are subject not only to eddy current and hysteresis losses in the core but also to a copper loss which occurs as heat lost in the resistance of the copper wire making up the windings. The current flowing through whatever resistance exists in these windings produces heat. The heat in either winding, in watts, can be found by the power formula P = I2R. For this reason, the copper loss is also known as the I2R loss. The heavier the load on the transformer (the more current that is made to flow through the primary and secondary), the greater the copper loss.

With one layer of wire wound over another in a transformer, there is a greater tendency for the heat to remain in the wires than if the wires were separated and air cooled. Increased temperature causes increased resistance of a copper wire. As a result, it becomes necessary to use heavier wire to reduce resistance and heat loss in transformers than would be required for an equivalent current value if the wire was exposed to air during operation.

EXTERNAL INDUCTION LOSS

Another loss in a transformer is due to external induction. Lines of force expanding outward from the transformer core may induce voltages and therefore currents into outside conducting bodies. These currents flowing through any resistance in an

outside body will produce a heating of the external resistance. The power lost in heating these outside circuits represents a power loss to the transformer, since the power is not delivered to the transformer's secondary circuit. In a well designed transformer, the amount of power lost in this fashion is usually small. The efficiency of a well designed transformer is around 98%.

THE VOLTAGE RATIO OF TRANSFORMERS

One of the main uses of transformers is to step up a low voltage AC to a higher voltage. This can be accomplished by having more turns on the secondary than on the primary.

The turns ratio of a transformer is the ratio of the number of turns on the primary to the number of turns on the secondary.

If a transformer has an equal number of turns on the primary and secondary (it happens), then the turns ratio is 1:1.

If a transformer has 100 turns on the primary and 10 turns on the secondary, then the turns ratio is 100:10 which is the same as 10:1.

If a transformer has 300 turns on the primary and 900 turns on the secondary, then the turns ratio is 300:900 which is the same as 1:3.

The shorthand for primary turns is usually Np and for secondary turns Ns. The voltage of the primary is usually designated Ep and for the secondary Es.

The turns ratio of a transformer is the same as the voltage ratio. In other words:

Np/Ns = Ep/Es

A Worked Example.

A transformer has 100 turns on the primary and 10 turns on the secondary. If 500 volts AC is applied to the primary what will be the secondary voltage?

Np/Ns = Ep/Es

We could transpose this equation for Es but for exam purposes an easier approach is to see that the turns ratio of the transformer Np/Ns is 100/10 or 10:1. For every 10 volts on the primary, there will be 1 volt on the secondary. Therefore, the secondary voltage will be 500/10 or 50 volts.

This is a step-down transformer because the secondary voltage is lower than the primary voltage. A step up transformer is where the secondary voltage is higher than the primary voltage

The turns ratio is the same as the voltage ratio.

A lot of learners get confused, especially with the step up transformers. You can make a transformer to convert 10 volts AC to 10,000 volts AC. At first sight, it may appear that you are getting something for nothing - no such luck.

The power in the primary circuit is equal to the power in the secondary circuit (disregarding losses).

No power is gained in a transformer. If a transformer steps the voltage up, there is a corresponding decrease in secondary current. So we may get more secondary voltage, but at the sacrifice of the secondary current.

Take an arc welder. This is basically a huge step-down transformer. 240 volts AC to the primary and only a few volts on the secondary, but a huge amount of current (60-100 amps or more) for melting metals is available in the secondary circuit.

TRANSFORMER ISOLATION 

One major advantage of transformers is the safety isolation they can provide. Small battery eliminators are really just small transformers. The primary connects to 240 VAC and the secondary may be 12 VAC (or converted to DC).

Because there is no metallic contact between the secondary and the primary, it means the user of the low voltage equipment is isolated from the mains power, providing a significant safety advantage.

If you build an interface between your radio transceiver and your computer for using digital modes, you will most likely use some form of isolation. There are several methods, but one method is to use an audio isolation transformer. This will prevent DC levels in your transceiver affecting DC levels in the computer sound card.

AUTO TRANSFORMERS 

An auto transformer consists of a single winding with one or more taps on it, as shown in figure 18-7.

Auto transformers are not "automatic". The name "auto" comes from their use as a car (auto) ignition coil.

Everything we have discussed about other transformers (mutually coupled transformers) applies to autotransformers.

Auto transformers used on high voltages are dangerous, as they provide no electrical isolation between the user and the supply. These transformers are not commonly used in radio and communications anymore. Auto transformers have the advantage of requiring less copper, therefore less weight and cost. However, in nearly all applications today better options are available than using auto transformers. An exception in radio is where RF auto transformers are used as an antenna matching device in vehicle installations.

We have not discussed the purpose of impedance matching yet and I am not going to now. Suffice to say, in electronics; it is important to connect components together which are of the same impedance (impedance is the total opposition to current flow in an AC circuit).

For example, your sound system may specify that you use 8 ohm speakers. If you use speakers other than 8 ohms on your sound system, you may damage the sound system or at least get reduced quality sound.

A transformer could be used to connect any impedance speaker to a sound system. The impedance ratio of a transformer is related to the turns ratio. The relationship between turns ratio and impedance ratio is given by the equation:

This equation "says" the turns ratio is equal to the square root of the impedance ratio and the impedance ratio is equal to the square of the turns ratio.

Example.

A 100Ω source is connected to a 25Ω load using a transformer. What is the turns ratio of the transformer? Well, the impedance ratio is given as 100:25 which is 4:1 - this is the impedance ratio. Look at the equation at the bottom of page 161. The turns ratio is on the left and the impedance ratio on the right so one equals the other except there is a squareroot sign on the right-hand side. So turns ratio Np/Ns equals the square root of the impedance ratio. The square root of 4:1 (just take the square root of each number 4 and 1) is 2:1.

So to match a 100Ω source to a 25Ω load we would use a transformer with a 2:1 turns ratio.

How is a transformer able to match impedance?

Suppose we had a transformer with 2400 turns on its primary and 150 turns on its secondary. The turns ratio of this transformer is 2400 / 150 or 16:1.

The turns ratio is 16:1. Let's see if we can work out what the impedance ratio would be.

For the sake of this exercise let's apply a primary voltage of 240 volts. Since the voltage ratio is equal to the turns ratio, the secondary voltage must be 15 volts.

The turns ratio is 16:1 and this gives us the same voltage ratio, that is, 240/15 = 16:1.

Now for calculation purposes, I have to nominate a maximum secondary current that the transformer can handle. This value is arbitrary and any value can be chosen for our purposes. The maximum secondary current I will choose is 1 ampere.

This transformer is shown in figure 18-8.

Since we know the secondary current and voltage (for full load) we can work out the secondary power:

Psecondary = Esecondary X Isecondary = 15 X 1 = 15 watts.

Since the power in the primary is equal to the power in the secondary (neglecting losses) we can, knowing the primary power is 15 watts, work out the primary current:

Iprimary= Pprimary/ Eprimary = 15/240 = 62.5 mA.

Where is all this taking us? Well, impedance is the ratio of voltage to current:

Z = E/I.

We know what the current and voltage is in the primary and secondary circuit, what is the primary and secondary impedance?

Impedance of the primary= Eprimary /Iprimary= 240volts / 62.5mA = 3840Ω.

 Impedance of the secondary= Esecondary/Isecondary= 15/1 = 15Ω.

In other words, the impedance ratio of this transformer is 3840:15 or 256:1. I have gone about it the long way just to show you how it works.

The rules you need to remember:

(a) The turns ratio is equal to the square root of the impedance ratio.

(b) The impedance ratio is equal to the square of the turns ratio. Np/ Ns = Square root of (Zp/Zs)

USING THE FORMULA

Let's work out the impedance ratio from the formula. From the last example, we know the voltage ratio is 240:15 which is the same as the turns ratio Np/Ns.

Np/ Ns = square root of (Zp/Zs) (remember Zp/Zs is the impedance ratio)

240 / 15 = square root of (Zp/Zs)

16 = square root of (Zp/Zs)

We do need to get rid of the "square root" on the right-hand side. To do this we "square" both sides and we are left with:

16 x 16 = Zp/Zs

or

Impedance ratio= Zp/Zs = 16 x 16 or 256 : 1

This agrees with our earlier calculation.

If you have trouble using this equation, ask your trainer for help. Many people do have some trouble, so don't be afraid to ask.

The type of question you need to answer in Advanced exams is something like this. What is the turns ratio of a transformer that is required to match a 600Ω source to a 50 ohm load?

Zp = 600Ω;  Zs = 50Ω

Turns ratio= Np/ Ns = square root of (600/50) = 3.464:1.

For every turn on the secondary, there will be 3.464 turns on the primary.

Another.

A transformer is used to match a 300Ω source to a 50Ω load. What is the turns ratio of the transformer?

The turns ratio (Np/Ns) equals the square root of the impedance ratio. Square root of (300/50) = 2.45:1

and·

The impedance ratio of a transformer is 10:1 what is the turns ratio?

The turns ratio is the square of the impedance ratio 102 = 100:1

The type of transformer that we have been discussing here is the mutually (magnetic) coupled transformer and can be used for impedance matching, however, their bandwidth is very narrow. A good example might be an RF auto transformer in the boot of a car to match a mobile vertical whip. This will work fine but because such a transformer will have a narrow bandwidth the usual thing is to have many tappings on it and when changing frequency even slightly on a short whip you might have to readjust the impedance match.

A better broad impedance match is the transmission line balun (to be discussed in transmission lines). You should know that while these may look similar to mutually coupled transformers, they have nothing in common at all. Transmission line baluns have no turns ratio, no primary or secondary, they do not work on the principle of Faraday's Law. Apply nothing you have learned in this chapter to transmission line baluns.

19 - Resistive, Inductive & Capacitive Circuits

The purpose of this chapter is to understand the combination of resistive, inductive and capacitive circuits and the concepts of impedance, quality factor or 'Q' and resonant circuits.

Impedance (symbol [Z])

Impedance is the opposition to current flow in an AC circuit, measured in ohms. There is no inductive or capacitive reactance in a DC circuit. However, in an AC circuit, there is resistance, inductive and capacitive reactance. All of these oppose current flow and it is this combined opposition that we call impedance.

Since impedance includes capacitive and inductive reactance it is frequency dependent. Resistance is not frequency dependent.

Impedance cannot, except in the case where reactances are equal and opposite, be expressed as a single number. There are two standard methods of expressing impedance.

1. The rectangular form and;

2. The polar form 

The rectangular form is more often used in radio. Modern impedance meters display both forms. The rectangular form is favoured by radio experimenters as they are usually concerned about the amount of unwanted inductance or capacitance in antennas.

RECTANGULAR FORM 

When we discussed capacitive and inductive reactance, we talked about how the current leads voltage in a capacitive circuit, and current lags voltage in an inductive circuit.

When the reactances are equal (XL=XC) then there is no lead or lag. The lead effect of XC and the lag effect of XL cancels. We have no lead or lag even though we still have XL and XC in the circuit.

When the reactances are equal we have a special case called resonance and the circuit is resistive. There is no lead or lag. The current and voltage are in phase just as if we had a purely resistive circuit.

Notice how we show resistance as starting from an origin and moving horizontally to the right. In a purely inductive circuit the current lags the voltage and we show this as an upward vector from the origin. Similarly a capacitive circuit causes the current to lead the voltage so we show this as a downward vector from the origin.

The reactance vectors are opposed at 180 degree so that the larger one (if there is a larger one) cancels the smaller one. If they are equal there is complete cancellation and the net reactance is zero. Suppose we had a RLC circuit comprising of 100Ω of R and 100Ω of XC and 100Ω of XL. We could plot these opposition vectors as shown in figure 19-2.

Since the XL and XC vectors are opposed to each other and the same length (100Ω) they will cancel and the net reactance is zero and the only opposition left is the resistance (R).

If we did have a RLC circuit comprising of R, XL and XC equal to 100Ω each then the impedance of that circuit would be 100Ω. However just saying the impedance is 100Ω does not really describe the circuit in full. There are two reactances there that are left out if we just say the impedance is 100Ω.

In mathematics R is said to be on the number line just like any real number. The reactances are ninety degrees off the number line and opposing. For naming sake we call the inductive reactance number line +j and the capacitive number line -j. In mathematics anything on the -j and +j number line are called IMAGINARY numbers! The resistive number line is called REAL.

These terms REAL and IMAGINARY just describe to us the way impedance is plotted in figure 19-2. Impedance written in the form R+/-JΩ is called the rectangular form. This will become more obvious shortly.

The impedance shown on figure 19-2 would be written down as 100j0Ω. This tells us the circuit is equal to 100Ω of resistance and the reactances cancel to give j0Ω.

Suppose we had the RLC circuit shown in figure 19-4.

The capacitive reactance uses 50 of its ohms to fully cancel the inductive reactance of 50 ohms leaving a net capacitive reactance of 50 ohms. In rectangular form the net impedance is written as 100-j50Ω 

In figure 19-5 the inductive reactance is now 150Ω and the capacitive reactance 100Ω. Now the inductive effects over power the capacitive reactance. The net reactance (XL-XC ) is 50Ω of XL and the impedance of the series RLC circuit is now 100j50Ω. By convention we do not write +j50. We drop the"+" and just write "j".

I think by now you have a good understanding of using rectangular notation for describing an impedance. As radio experimenters this is important to use as our antennas are series RLC circuits. We will cover antennas later but for now consider our antennas are RLC circuits and when they are resonant  XL=XC and they are resistive. When you measure the impedance of an antenna it is usually in rectangular form R+/jXΩ. If the antenna has net capacitive reactance it is too short (relative to the nearest multiple of a quarter wave) and if it is inductive it is too long.

POLAR FORM 

Take a look at figure 19-6. Here we have a resistance of 150Ω and our net reactance is equal to 150Ω and is inductive. In rectangular form we would say this is 150j150Ω

The other method of describing impedance is the polar form. In figure 19-6 notice we have drawn a right angle triangle the base of which is R and the height is XL. The length of the hypotenuse is not known and neither is the angle θ. In polar form "Z" is called the magnitude of the impedance and θ  the (phase) angle. What we need to do is use trigonometry to calculate Z and the angle θ. You probably can guess that the angle θ will be 45 degrees.

We can use Pythagoras to find Z and angle θ will be given by the trigonometric function Tangent.

A series circuit comprising of 150Ω of "R" and 150Ω of "XL" has an impedance in rectangular form of 150J150Ω and in polar form 212Ω/45 degrees.

In rectangular form R+/-JX R is called the real and X the imaginary. In polar form the impedance is referred to as magnitude and angle.

Let's do one more with some not so predictable figures.

With reference to figure 19-7 express the impedance of the circuit in both rectangular and polar forms.

Rectangular:

The resistance is 115Ω and the net reactance (XL-XC) is 130Ω so the impedance of this circuit is 115-J130Ω.

Polar:

The magnitude of the impedance is; square root (1152 + 1302) = 173.5Ω.

The phase angle is arctan (XC/R) = arctan(130/115) = 48.5 degrees.

The impedance in polar then is 173.5Ω angle 48.5 degrees.

Numbers expressed in polar or rectangular form are called "Complex Numbers". For finding the impedance of more complex circuits with series and parallel combinations the same rules apply as with resistors. However adding, subtracting, multiplying and dividing complex numbers has specific rules.

THE IMPEDANCE OF A PARALLEL LR CIRCUIT 

A parallel circuit comprises of a 30Ω inductor in parallel with a 50Ω resistor. What is the impedance and phase angle of the circuit in polar form.

The equation and working out to find the impedance of a reactance in parallel with a resistance is:

This same method can be used for a parallel RC circuit. If a parallel circuit contains many LCR branches then these can be simplified to a single resistor and reactance. Susceptance is the reciprocal of reactance in siemens. Admittance is the reciprocal of impedance in siemens. Conductance is the reciprocal of resistance in siemens.

Recall when we found the resistance of a number of resistors in parallel? We used this equation:

This equation says that the total resistance of resistors in parallel is the reciprocal of the sum of their reciprocals. You may not have realised it at the time but what you are doing here is converting the resistances to conductance. Adding the conductances and then finding the reciprocal of the sum to convert your answer from conductance back to resistance.

This same method can be used for any parallel circuit with any combination of reactances. The reactances must be treated as complex numbers and the rules for complex operations must be applied. Many scientific calculators will perform complex number operations and there are also many online calculators available.

RESONANCE.

Resonant circuits have some very useful properties in electronics and radiocommunications, however, let's talk a bit about what resonance is.

Electrical and mechanical resonance are very similar. A taut string, like that on a guitar, if plucked, will resonate at a particular frequency. The length of the string determines the frequency of resonance.

A metal tuning fork is designed to resonate at a particular frequency. When you strike a tuning fork, it will vibrate at the same single frequency every time, because the tuning fork is resonant at that frequency.

If you hit the rim of a wineglass with a hard object it will "ring" and it will always ring at the same frequency because it is resonant at that frequency.

In all the cases above, we had to deliver some energy to the object (guitar string, tuning fork or wineglass) to get it to resonate.

Have you ever been listening to loud music and at certain times the window may rattle, or an object on a table may start to move (vibrate with the music)? The window will start to vibrate if sound waves at its resonant frequency strike it. Since music contains many frequencies, the window will only vibrate when its resonant frequency is present in the music.

HOW DOES A SINGER BREAK A GLASS?

It is true that a singer provided they can reach the right note can break a wine glass. A wine glass has a frequency at which it will resonate. Making a loud noise will not break a wine glass. However, if a singer reaches and sustains a note which is equal to the resonant frequency of the wine glass, then the wine glass will absorb energy from the sound wave and it will begin to resonate (vibrate) and if the amplitude (loudness) is enough, it will shatter.

The wineglass absorbs energy on its resonant frequency. All objects, even electrical circuits, will absorb energy at their resonant frequency.

TUNING FORK EXAMPLE

Suppose we had two tuning forks designed to create the same note (frequency) and we struck one fork to make it resonate. Then place the two tuning forks say 50mm apart, the tuning fork that you did not strike would begin to resonate. The second tuning fork has absorbed sound wave energy from the first tuning fork and starts to vibrate in sympathy.

In electronics, we don't say something vibrates. We say it oscillates. A mechanic might say that guitar string, when plucked, vibrates at 800 times per second. A musician would say it makes such and such a note. An electronics person will say it oscillates at 800 hertz.

DAMPED OSCILLATIONS

If a guitar string or tuning fork is given energy, we have learned that it will oscillate at its resonant frequency. All things being perfect, the wave produced will be the shape of a sinewave. Now what happens to the sound wave emitted from a guitar string or whatever, after the initial pulse of energy is given to it?

The guitar string will oscillate vigorously at first and then slowly decrease in amplitude until it no longer makes any sound. Importantly - the frequency stays the same, but the amplitude dies down to nothing. This is a damped oscillation.

CONTINUOUS OSCILLATION 

A swing (perhaps with a child on it, though the child is not an essential ingredient) will oscillate as it is a pendulum. We know that a pendulum will move back and forth at the same frequency (or period) every time. That is a fact because we use pendulums to create clocks. The amplitude of the swing of the pendulum will slowly dampen, but the frequency will remain the same.

Back to the child on the swing. How do we keep the rhythm going (oscillating)? Well, we have to keep giving it energy. When do you give it energy? Well if you are a good swing pusher, you know to give the extra push to sustain the motion of the swing when it is at the top of its cycle (about to change direction). You do not have to push hard to sustain the swing's oscillations. Once the swing is going, you only need to keep supplying enough energy to overcome the losses in the swing system. It is the losses in the swing, which slow it down. The losses in a swing are from friction.

Everything we have just discussed about resonance in mechanical systems (swings, guitars and the like) are equally applicable to resonant electronic circuits.

LC RESONANT CIRCUITS

Not every LC (inductive and capacitive) circuit is resonant. A resonant circuit is only resonant if we use it as a resonant circuit. Though every LC circuit will have a resonant frequency, we don't have to use it as a resonant circuit. We are going to talk about LC circuits that we want to resonate.

If we connect a capacitor and an inductor in parallel as shown in figure 19-11, nothing happens, as there is no energy in the circuit. This is just like the child's swing before we push it.

Now suppose we give the parallel LC circuit some energy. There are many ways we can give this circuit a pulse of energy. One way would be to expose the inductor to a moving magnetic field (Faraday's Law of Induction). We could disconnect the capacitor, charge it then connect it back to the inductor.

The latter is what I have done in figure 19-11. I have charged the capacitor and then connected it back in parallel with the inductor. What happens?

Look at 19-11A. We have given the capacitor some energy and all of that energy is stored in the electric field of the capacitor. The capacitor will begin to discharge through the inductor. As it does so, a magnetic field will be created around the inductor; 19-11B. Eventually, the capacitor will be discharged; 19-11C.

Now the energy has moved from the electric field of the capacitor into the magnetic field of the inductor. When the capacitor stops creating current in the circuit the magnetic field around the inductor cannot stay there, as it has no current to support it.

The magnetic field about the inductor will now begin to collapse into the inductor. In doing so, there will be relative motion between the inductor and the magnetic field and an emf will be induced into the inductor.

This emf will cause a current to flow in the opposite direction and will cause the capacitor to charge; 19-11D. Eventually, all the energy from the magnetic field will have returned to the circuit and the capacitor will be charged (storing energy in its electric field) 19-11E.

The capacitor will begin to discharge through the inductor again and so on.

This circuit is oscillating. The shape of the voltage produced is a sinewave. These oscillations would go on forever except, just like the swing, there are losses in the circuit, which dissipate energy. The losses are the resistance in the wire of the inductor, the circuit and the plates of the capacitor. There is also a little energy lost in the dielectric of the capacitor. The oscillation of this circuit then is a damped oscillation.

If we wanted a continuous oscillation, we would have to supply the circuit above with energy to overcome the losses. Such a circuit is called an oscillator.

We know what moves with mechanical resonance as we can see or feel it. The guitar string vibrates, the tuning fork vibrates back and forth. What does the moving with electrical resonance? It is the electric and magnetic fields that move. The capacitor dumps its electric field energy into the magnetic field of the inductor; then the inductor dumps its magnetic field energy back into the electric field of the capacitor. This happens at a certain rate and that rate is known as the resonant frequency of the circuit.

It should be intuitively obvious that if we had small Ls and Cs that could not hold much energy that the rate of dumping to each other would be faster - a higher resonant frequency. If we had large Ls and Cs then they could hold a significant amount of energy; then the rate of dumping would be much slower - a lower resonant frequency.

RESONANT FREQUENCY 

If you thought about the circuit we have just described, you could probably guess what determines the resonant frequency or frequency of oscillation. Imagine if the capacitor was huge and took ages to discharge through the inductor. Likewise, if the inductor is large. You would expect the oscillations or resonant frequency to be low. You would be right. Large values of Land C resonate at a low frequency whereas small values of L and C resonate at a higher frequency.

To work out the exact resonant frequency (fr) of a tuned circuit we can use the following important equation:

The resonant frequency of a tuned circuit is inversely proportional to the square root of the product of the inductance and capacitance. The equation gives the resonant frequency in Hertz and L and C must be entered in Henrys and Farads.

You may have to use this equation in an Advanced exam. You may be asked to identify the equation from among others. You must know how to increase or decrease the resonant frequency of a tuned circuit.

The same equation is also used to find the resonant frequency of a series LC circuit. The resonance equation is probably the most important fundamental equation in radio. Now you might be wondering just how this equation is derived. Recall we said resonance occurs when XL=XC? This is equivalent to saying resonance happens when: -

USING THE RESONANCE EQUATION: 

A tuned circuit (series or parallel) consists of an inductor of 100 microhenries and a capacitor of 250 picofarads. On what frequency will it resonate?

100 microhenries = 100 x 10-6 henries

250 picofarads= 250 x 10-12 farads

Inserting these values into the equation we get:

Resonant frequency (fr) = 1 / (2 x π x square root (100 x 10-6 X 250 x 10-12))

Resonant frequency= 1.007 megahertz.

It was not by accident that I chose the values of L and C used in this example. The resonant frequency is close to 1MHz, which is roughly the centre of the AM radio broadcast band. You would need approximately these values of L and C to make a broadcast band radio receiver or a 'crystal set'.

THE 'Q' OF A RESONANT CIRCUIT 

The "Q" is a term used for the 'quality' of a tuned circuit. We want as high a Q as possible. The more losses a tuned circuit has, the lower the Q. The fewer losses a tuned circuit has, the higher the Q. The equation below defines what Q is:

You can see that Q is a measure of the losses in a tuned circuit or a lone inductor or capacitor. If a tuned circuit had no losses the Q would be infinite. There are many equations for calculating Q. However the one that is the most practical is:

This is the equation you would use for an RLC circuit. You might think "what about capacitor losses?" The equation does not seem to take that into account. You would be right - it doesn't. In practice we can ignore the losses in the capacitor because the losses in the inductor swamp the losses in the capacitor. The losses of the capacitor are so small compared to those of the inductor we can ignore the capacitor and just calculate Q using the inductor.

We use tuned circuits and inductors and capacitors to make filters. A filter is a device that responds differently to different frequencies. For example a bandpass filter

passes a narrow band of frequencies in and blocks all others. How "sharp" or "selective" a bandpass filter is at doing this is very much to do with its Q.

Suppose we made a bandpass filter to pass 10.7MHz plus and minus 300kHz. This filter passes a band of frequencies centred on 10.7MHz with a bandwidth of 600kHz. If we did a graph of the filter's frequency response we would get this diagram shown in figure 19-13.

In figure 19-13a we have a filter circuit that has no losses or an infinite Q. Notice the sharpness of the filter. It passes exactly 600kHz with no losses and is centred on 10.7MHz. Of course such a filter is not possible. There are always some losses and the Q is not infinite. Figure 19-13b shows a more realistic but nevertheless high Q bandpass filter. We call this sharpness of a filter its "selectivity". The width of the signal that is passed by filter is called its "bandwidth". Bandwidth is related to the Q and frequency of the filter.

There are times when we want to increase the bandwidth of a filter or tuned circuit. We want to make it broader or decrease the selectivity. One of the ways to do this is to reduce the Q. We can reduce the Q by introducing a loss to the circuit in the form of a resistor. Adding a resistor in series or parallel will dissipate heat, increase the losses , lower the Q and broaden the bandwidth.

IMPEDANCE OF TUNED CIRCUITS 

When you read 'tuned circuits,' you can also think of resonant circuits as we are discussing one and the same thing. Parallel and series tuned circuits have different properties which allow us to use them in electronics for different purposes.

If there were no losses in tuned circuits (never possible) the following would be true:

Parallel resonant circuits have infinite impedance.

Series resonant circuits have zero impedance.

In the real world though resonant circuits have some losses and so we have to say:

Parallel resonant circuits have a maximum impedance at resonance.

Series resonant circuits have a minimum impedance at resonance.

The impedance type for both series and parallel LC circuits at resonance is resistive. The impedance of a series resonant LC circuit is minimum and resistive. The impedance of a parallel LC circuit at resonance is maximum and resistive.

There is no net reactance at resonance since XL=XC. That is why we say that resonant circuits are resistive.

IMPEDANCE TYPE ABOVE AND BELOW RESONANCE 

First, what do we mean by impedance type?

Impedance is made up of three oppositions:

1. Resistance (not affected by frequency).

2. Inductive reactance - increases with frequency.

3. Capacitive reactance - decreases with frequency.

All of these oppositions are measured in ohms. All oppose current flow. The total combined effect on a circuit of all of these oppositions is called impedance and it too is measured in ohms.

Now think of a circuit at resonance. At resonance XL=XC. So at resonance the only opposition is resistance, or a better way of putting it, the impedance type of a resonant circuit is resistive. The impedance type of both series and parallel circuits at resonance is resistive because XL=XC - Anything which is resonant has no reactance, only resistance.

Impedance type of a series LC circuit - off resonance

A simple way to work out what the impedance type of a series circuit used above or below its resonant frequency, is to think, which reactance (L or C), has the largest voltage drop.

Above resonance XC will decrease and XL will increase. Therefore, XL has the largest voltage drop and the impedance type is inductive. Below resonance the XC is greater than XL. The capacitance will have the greater voltage drop and the circuits impedance type is capacitive.

Impedance type of a parallel LC circuit - off resonance

With parallel LC circuits, the largest branch current determines the impedance type. Say to yourself, which branch will have the least reactance and therefore draw the most current. Above resonance XL increases and XC decreases and the capacitive branch will draw the most current. Above resonance a parallel circuit is capacitive. Below resonance then, it has to be inductive.

Summary- Impedance Type (i.e. L or C)

Parallel LC circuits: 

1. Above their resonant frequency are capacitive.

2. Below their resonant frequency are inductive.

Series LC circuits: 

1. Above resonance are inductive.

2. Below resonance are capacitive.

Understanding the impedance type off resonance is very useful. This especially so for series circuits because our antennas are series circuits. If you measure the impedance of your antenna with an impedance meter and it is inductive, then it is too long. If it is capacitive then it is too short.

IMPEDANCE OF LC CIRCUITS VERSUS FREQUENCY

A parallel LC circuit has a maximum impedance at resonance. At resonance, the impedance is maximum and resistive. Either side of resonance the impedance will be less. An LC circuit with no losses has an infinite impedance at resonance. If there was a resistance in parallel with a parallel resonant circuit, then the impedance of the circuit would be equal to the parallel 'R'. For example, an infinite impedance (which is the same as an open circuit) in parallel with a 100kΩ resistor would give a total impedance at resonance of 100kΩ. (Figure 19-14)

A series LC circuit has a minimum impedance at resonance. At resonance, the impedance is minimum and resistive. Either side of resonance the impedance will be greater. A series LC circuit with no losses has zero impedance at resonance. If there was a resistance in series with a series resonant circuit, then the impedance of the circuit would be equal to the series 'R'. For example, a zero impedance (which is the same as a short circuit) in series with a 100kΩ resistor would give a total impedance at resonance of 100kΩ. (Figure 19-15)

.THE EFFECT OF LOSSES ON THE 'Q' OF TUNED CIRCUITS 

We know that, in the real world, we cannot have parallel or series tuned circuits with no losses at all. The effect of losses on a tuned circuit is to flatten out the impedance curves shown in figure 19-16. The higher the Q the sharper the curve. Tuned circuits can be used to make filters and select radio stations. Sometimes we want the curve (often referred to as the selectivity curve) to be sharp or a high 'Q'. Other times we want it to be flat and not as selective so we may add losses in the form of resistance to flatten the curve out. (Figure 19.16)

Figure 19-16 shows the curves of a parallel tuned circuit with three values of 'Q'. For a series resonant circuit, the graph would be inverted.

What is a flywheel? In mechanics, a flywheel is a wheel with a large mass (weight). If you get the flywheel turning, it will continue to turn for a long time because of its mass. A flywheel is a means of storing energy and releasing it later.

The science fiction writer Isaac Asimov predicted that one day electric power stations would use gigantic flywheels weighing hundreds of thousands of tonnes. Perhaps floating on mercury or using magnetic levitation. Power stations have a demand on the generators that varies enormously. They cannot, particularly with fossil fuel plants, turn the furnaces up and down at a whim. Imagine though if you had a gigantic flywheel, perhaps floating on mercury or on a magnetic field to avoid friction. All of the energy created by the power station is used to make the enormous flywheel move. You would be storing a huge amount of energy in this flywheel. It is so massive that it would continue to rotate for months left untouched. When we wanted energy from the flywheel, we could make contact with it and have it drive a generator for us. So, even though the output of the power station may be irregular, the power available from the flywheel would be regular because of the massive amount of stored energy.

Now a resonant circuit exhibits the same properties of a flywheel. This effect of resonant circuits is called the flywheel effect.

Suppose we want a sinewave to be produced. We know that a resonant circuit will generate a sinewave if it is given energy. We know that the sinewave output from a resonant circuit will dampen if we don't keep on providing it with energy.

Suppose we have pulses of energy, very short pulses and assume we have 1 million of them per second. Let's use these pulses to start a resonant circuit oscillating. Let's make the resonant frequency of the tuned circuit 3 megahertz. This means that the resonant circuit would get a pulse of energy and produce 3 cycles of sinewave output. Now a tuned circuit of reasonable Q will be able to run fine for 3 cycles. Then our next pulse comes along and away the tuned circuit goes again for another three cycles. The output of the resonant circuit is a sinewave at 3MHz. The input is some 'cruddy' pulses at 1MHz.

So, the resonant circuit is producing a 'flywheel effect' for us.

There are many situations in electronics where we want to convert pulses to sinewaves or double or triple the frequency of a signal. One way of doing this is the flywheel effect of a resonant circuit.

APPLICATIONS OF RESONANT CIRCUITS 

The diagram of figure 19-18 shows an antenna connected to a simple "crystal-set" radio receiver. The first stage of this receiver is L1 and C1 which form a parallel tuned circuit. The parallel tuned circuit is connected between antenna and ground.

Now, remember a parallel tuned circuit has a very high impedance at one frequency only, its resonant frequency.

All of the radio waves passing by the antenna will induce a minuscule voltage into the antenna. Let's say our resonant circuit is tuned to 1000kHz. That is the radio signal that we want to select and reject all others.

A radio wave on 1000kHz passing by the antenna will induce a voltage into it. This voltage will cause a current to flow down the antenna cable and through the tuned circuit to earth. At 1100kHz, the inductor and capacitor are not resonant and the impedance of the parallel circuit will be very low. E=IR or if you like E=IZ (Z=impedance). The voltage created across the LC parallel circuit will be very low as its impedance is low. The same story applies to all other radio signals that induce a voltage into the antenna except at 1000kHz. At 1000kHz, the LC circuit is parallel resonant and will be a very high impedance. The small current through the parallel resonant circuit will produce a significant voltage across it compared to all the other radio signals.

A voltage will appear at the output terminals of the signal that the parallel tuned circuit is tuned to. So here we have the basic method of selecting the desired radio signal from the many that are present at the antenna.

An application for a series resonant circuit:

Recall that at resonance a series tuned circuit has extremely low impedance. If you like, you can think of it as zero impedance or even a short circuit. Zero impedance is like a piece of conductor. If you place a conductor across the back of your TV on the terminals where the signal comes into the set, do you think you would get much of a television picture?

Suppose this TV is getting interference from an amateur radio transmission on 29MHz. If we place a series resonant LC circuit across (in shunt) the TV feedline then anything on 29MHz will see a short circuit at the back of the TV and be stopped in its tracks.

The TV signal, which is well above 29MHz will be unaffected. Depending on the Q of the series LC circuit we could expect an attenuation on 29MHz of 100 times or 20dB.

This is an example only and it would work. However when we come to do transmission lines we will find that instead of an LC circuit we can do this with even less effort with a transmission line stub.

A final word on Q and something to remember because it seems to puzzle many; in radio circuits:

Low Q means broad bandwidth or poorer selectivity.

High Q means narrow bandwidth or better selectivity.

Adding losses to any antenna, or tuned circuit causes its Q to decrease. These losses are always through 'resistance' of some sort. The resistance of the wire used in a helically wound vertical, ground losses under an antenna and the resistance of the wire used for an inductor in a tuned circuit are good examples. If the wrong core material is used for an RF inductor or a balun, then the losses can be very high and the Q low. Resistance is sometimes deliberately added to tuned circuits to lower their Q and increase their bandwidth.

DESCRIBING A SELECTIVITY CURVE

It is somewhat difficult to describe an entire selectivity curve using words. One way that is used is to state the curves bandwidth at the 6dB and 60dB points. This method is used to describe the selectivity of a receiver or a filter. Figure 19-20 shows a bandpass on a spectrum analyser. The bandwidth at 6dB is 5.6kHz and at 60dB it is 13.6kHz. This looks like a good double sideband filter or receiver front end selectivity to me.

20 - Power Supplies

THE RECTIFIER DIODE

A rectifier is another name for a diode. I am not going to explain the internal operation of a rectifier now as we will be covering that in full later. I will explain what a rectifier diode does and ask you to accept the internal operation for now.

The schematic symbol of a rectifier is shown in figure 20-1. A rectifier (diode) has two terminals, a cathode and an anode as shown. If a negative voltage is applied to the cathode and a positive to the anode, the diode is said to be forward biased and it will conduct. If it is reverse biased, it will not conduct. So a diode will only conduct current in one direction i.e. from the cathode to anode.

PEAK INVERSE VOLTAGE (PIV)

Though we say a diode will not conduct in the reverse direction, there are limits to the reverse electrical pressure that you can apply. Manufacturers of diodes specify a 'peak inverse voltage' (PIV) for each particular diode. The PIV is the maximum reverse bias voltage that the manufacturer guarantees that the diode will withstand. In practice, the PIV is well below the pressure that will cause the diode to breakdown and conduct. However, except in special circumstances, the PIV should never be exceeded.

ELECTRON FLOW VERSUS CONVENTIONAL CURRENT FLOW

Some textbooks show current flow from anode to the cathode. This is called the conventional direction of current flow and is a hangover from the days when the current was thought to flow from positive to negative. Blame Benjamin Franklin, he arbitrarily set the flow of an electric current from positive to negative. That was before J.J. Thompson discovered the electron. Electrical engineers and electricians seem to hang on to this conventional direction of current flow. Electrons flow from negative to positive, from the cathode to the anode. In radio, electronics and communications, 'electron flow' is almost universally used. Electron flow is of course from negative to positive.

The vast majority of 'modern' references agree on the direction of current flow. Even textbooks that use conventional flow acknowledge that this direction (positive to negative) is just a convention. There is no harm in using conventional flow if this is what you prefer. However, for circuit descriptions in this book, electron flow is used.

To help remember which way current flows through a diode look at the symbol - it has an arrow and current flows against the arrow. This will help you not only with the diode but other semiconductor devices to be discussed later.

Let's have a look at the operation of a single diode rectifier if we apply an alternating voltage source to it. Since the diode will only conduct when the potential on the cathode is negative with respect to the anode, only half of the sinewave of alternating voltage will cause current to flow in the circuit of figure 20-2.

The current flow in the circuit of figure 20-2 is DC, but it is pulsating DC. The diode refuses to conduct for a complete half cycle of input voltage. The diode conducts (is forward biased) during the half cycle where the cathode is negative and the anode is positive.

This is called halfwave rectification. This terminology rectification has always intrigued me a little. To rectify something means to 'make it right,' to 'fix it up!' This is the origin of this term. The radio pioneers considered converting AC to DC as fixing up the AC voltage, hence the term rectification. I often wonder if Edison had anything to do with the terminology. Edison was strongly opposed to AC power distribution. Tesla and Edison were bitter rivals. It was Tesla who invented and implemented the AC power and distribution system we use today. Edison even electrocuted animals in public performances to demonstrate the dangers of AC. As it turned out, Tesla's AC system was more efficient and therefore adopted. The first power generating plant was constructed at Niagara Falls. Let me make the point that AC does not need 'fixing up', but we are left with this term 'rectification', which I find rather amusing. In many cases, we need to convert DC to AC, so I suppose we should call this un-rectification!

So, in trying to convert AC to DC, all we have managed to do so far is convert AC to half-wave pulsating DC (PDC).

Diodes make it very easy to produce full wave rectification. I am going to start with the most common method, the bridge rectifier. A bridge rectifier has four diodes as shown in figure 20-3. Rather than apply an AC voltage source, I have shown how the bridge network will operate when the two different polarities are applied to it, which in essence is simulating AC.

As you can see from figure 20-3, two of the bridge diodes will always conduct because they have a negative voltage applied to their cathodes with respect to their anodes. Notice how current flows against the arrow. More importantly, notice how current always flows through the load resistor in the same direction, regardless of the polarity applied to the bridge.

We have created full wave rectification.

You simply must commit the diagram of a bridge rectifier to memory, but be careful, the diodes can all be reversed and you still have a working bridge. I like to think of the four diodes as positions on a clock face. So, we have diodes at 2, 4, 8 and 10 o'clock. The diodes at 2 and 8 o'clock can be reversed, provided the diodes at 10 and 4 o'clock are reversed. You also need to be able to determine the polarity of the output, or the direction of the current through the load. A way to do this easily is to pretend you are an electron out for a stroll. You can go wherever you want provided you go into a cathode and you will seek to get to the positive terminal of the battery or supply. You can then trace out the current flow mentally or on paper and determine if the bridge is drawn correctly.

The bridge I have drawn is a diamond or kite shape, but it can also be drawn as a square. Tracing the current to determine if current will flow through the load in the same direction regardless of polarity, as I have done, is your surest way of determining if the bridge circuit is drawn correctly.

Using a centre tapped transformer for full wave rectification.

A less conventional method (today) of obtaining full wave rectification is to use a centre tapped transformer and only two diodes. I have added some extra detail to the schematic in figure 20-4, which I will fully explain as we go along. A bridge rectifier would not use a centre tapped transformer as shown.

I have shown the polarities on the transformer for one-half cycle of AC input from the mains supply. As you can see, the top diode has a negative potential on its cathode so it will conduct with the path of the current as shown. During the next half cycle, all of the polarities will be the opposite of that shown and the bottom diode will conduct. In either case, the current will be the same through the load. So, full wave rectification is achieved again.

Can you see that this circuit is two half wave rectifiers? Each diode rectifies half of the AC sinewave giving full wave rectification. For this reason, the secondary winding has twice the turns compared to a transformer used for a full wave bridge rectifier. Twice as many turns means twice the copper on the secondary, more cost and more weight.

This circuit was once very popular, as it only required two rectifier diodes, and is just as effective as the bridge rectifier. Which one to use comes down to cost and convenience. A centre tapped transformer is more expensive than one without a centre tap. Electron tubes (to be discussed) can also be used as diodes. Electron tubes are relatively expensive compared to semiconductor diodes. So if the power supply was using vacuum tubes, this approach would be the most cost effective, as it requires only two diodes and that outweighs the cost of the centre tapped transformer.

Except in very high voltage applications, the modern trend is to use semiconductor diodes, so this circuit (figure 20-4) is not often used today. Still, you are expected to know it and it does have a useful purpose when using junk box parts. Note also that the total secondary voltage is double that required for the bridge rectifier circuit, as only one half of the secondary is being used on alternate half cycles.

CAPACITIVE FILTERING - WITH A HALF-WAVE RECTIFIER

So far the output of the power supplies has not been smooth DC, which, perhaps with the exception of a simple car battery charger, is our requirement. Adding a capacitor to the output of the power supply will smooth the pulsating DC a great deal. The circuit of figure 20-5 shows half-wave rectified DC fed to a capacitor.

If pulsating DC is fed to a capacitor as shown, the capacitor will charge to the peak value of the pulses. Without any load, the capacitor will charge to the peak value and stay there. I have shown the effects of a load. Between the pulses, the capacitor will discharge through the load and the voltage will drop a little. I have left the pulses under the DC output for illustration purposes only. The capacitor is a high value electrolytic - more on this shortly.

The DC output, in this case, is not pure. Pure DC would be a flat line indicating no voltage variation. The DC rises and falls a little, the rate of rise and fall being related to the frequency of the DC pulses. The frequency of the AC from the mains is 50Hz. For every cycle of AC rectified by a half-wave rectifier we get one pulse of DC, so the pulses have a frequency of 50Hz as well. We can, therefore, conclude that the ripple frequency of a half-wave rectifier is the same as the mains frequency i.e. 50Hz.

Just to emphasise that a little, the DC output is not flat, it has a ripple on it. A ripple is a periodic rise and fall of voltage. The rate of rise and fall of the DC output is called the ripple frequency and is equal to the mains frequency, which in Australia is 50Hz.

CAPACITIVE FILTERING - WITH A FULL-WAVE RECTIFIER

The ripple frequency of a full wave rectifier is 100Hz. Full-wave rectification with filtering is much better than a half-wave. However, with capacitive filtering alone there is still some ripple. The frequency of the ripple will always be equal to the mains frequency for half-wave rectification and twice the mains frequency for fullwave rectification.

A COMPLETE CIRCUIT OF A PRACTICAL POWER SUPPLY. 

Figure 20-7 is the circuit of a full-wave bridge rectifier showing the transformer, the mains connection, a switch, fuse(s) and a capacitor for a filter.

Most of this circuit has been explained. I will point out some important features, as such knowledge applies to subjects other than power supplies.

Notice how the secondary voltage Es is shown as 10 volts. This is the RMS value. The output of the power supply is the peak value, RMS x 1.414, or near enough to 12 volts. There will be a small voltage drop across the two conducting diodes. A silicon rectifier diode will have a forward voltage drop of 600-700mV. The negative side (also called the negative rail) of the power supply shows a chassis connection. This just means that if the power supply is in a metal box, the negative terminal is connected to the box. This is not done for safety purposes but for ease of construction, just in the same way that the negative terminal of a car battery is connected to the chassis (body) of the car. Of course, the positive output could be connected to the chassis. This is a construction issue and will depend on the type of semiconductor devices used. However, it is more common for the negative to be connected to the chassis.

I have shown a switch in the active lead of the mains. The switch must always be in the active lead. The earth lead from the mains or power point is connected to the chassis of the power supply. We will have much more to do with safety issues later.

I have shown two fuses. There really only needs to be one. The important thing about fuses is to remember that a fuse operates on current. Should something go wrong in the power supply (or outside the power supply) excessive current will be drawn and the fuse will melt, opening the circuit.

What may not be obvious to you is the difference in choice of fuses - in the primary of the transformer and the output of the power supply. Remember the power in a transformer is the same in the primary and secondary, disregarding losses. However, the voltage and current are not the same. Their product (the power) is the same. Fuses work on current. Say this power supply is 12 volts at 2 amps maximum. The fuse in the secondary circuit will be around 2 amps. It will melt if more than 2 amps are drawn from the supply and stop the supply or the load from being damaged further by excessive current.

Think about the fuse in the primary circuit. It would not be anything like 2 amps. If it was 2 amps, then 480 watts would have to be drawn from the mains before it would melt. I will leave the calculation of the primary fuse to you. As a hint how much power can be drawn from a 12 volt 2 amp power supply?

Let's get a bit more serious about power supply filtering. What you are about to read may go beyond what is required for the examination on power supplies. Though, where concepts are needed to be known, perhaps not in power supplies but in other subjects, I have included the information pertinent to power supplies knowing that this is required knowledge elsewhere.

CAPACITIVE INPUT FILTERING

Capacitance is that property of an AC circuit which opposes changes of voltage. If a large value capacitor is connected across the output of the rectifier circuit, i.e. in parallel with the load, the capacitor will smooth out the pulsating DC to DC with a small ripple voltage. The filter capacitor does this by taking energy from the circuit and storing this energy in its electric field. If the voltage across the load tends to fall, the capacitor will discharge some of its energy back into the circuit, which smooths out the voltage. Because a high value of capacitance is required (1000µF to 10,000µF or more), the capacitor has to be an electrolytic type, as this is the only type of capacitor which can provide such a high value of capacitance. Capacitive filtering alone can be used for power supplies which need to deliver only a few amperes of current.

One disadvantage of capacitive input filtering is that of surge current. When the power supply is turned off the capacitor is discharged. When the power supply is first turned on, the capacitor will charge rapidly and draw a large current from the transformer and rectifier circuit. This surge current can be so high that it may exceed the current rating of the rectifiers and damage it, or blow the fuse, whichever comes first. This is not so much an operational problem of the power supply, but a design problem.

To ensure the filter capacitor(s) in a power supply discharges when a power supply is turned off, a high value resistor is often connected across the filter capacitor. A high resistance, say 10kΩ, in parallel with the filter capacitor will have no effect on the operation of the power supply and provide a path for the capacitor to discharge through.

This resistance is known as a bleeder resistor. You may have noticed on some power supplies that have a light to indicate that the supply is turned on, that this light will slowly dim and eventually go out some time after the supply is turned off. This is the filter capacitor discharging. Sometimes the "ON indicator lamp" acts as a bleeder resistor and discharges the filter capacitor.

Best is a high value bleeder resistor connected across the output of the power supply to discharge the filter capacitor(s) when the supply is switched OFF.

INDUCTIVE INPUT FILTERING

Inductance is that property of an AC circuit which opposes changes of current. If we are trying to reduce ripple from a power supply, it should be no surprise then, that an inductance can be used to filter the DC output.

When an inductance is connected in series with a rectifier, a filtering or smoothing action results. An inductor used in this manner is always iron core to obtain the high level of inductance required. Inductors used in power supplies for filtering (and some other applications) are referred to as chokes.

Pulses of current through the choke build up a magnetic field around it, taking energy from the circuit to produce the field. As a pulse of current tries to decrease in amplitude, the magnetic field collapses and returns energy to the circuit, thereby tending to hold the current constant. If the inductance is the first component in the circuit after the rectifiers, then this type of filtering circuit is called inductive input filtering. It is not practical to use inductive input filtering alone in a power supply. Inductive filtering is always used in conjunction with capacitive filtering. A disadvantage of inductive input filtering is that there is voltage dropped across the internal resistance of the choke (the resistance of the wire making up the choke). The voltage dropped across the choke reduces the output voltage of the power supply. In practical terms, this means that the secondary voltage of the transformer has to be a little higher in voltage output to compensate.

SWINGING CHOKES 

You will recall from our study of inductance that the purpose of the iron core is to increase the value of the inductance. The magnetic iron core does this by concentrating the magnetic lines of force. Usually, the magnetic iron core of a choke has no air gap to prevent the core from magnetically saturating. In the swinging choke, the magnetic iron core has little or no air gap. This means that the magnetic iron core will begin to saturate at average current values for the power supply. When low current flows through a swinging choke, it has a high inductance and filters effectively. With high current the magnetic core saturates and has less choking effect. Thus, with a light load and little current, the swinging choke has a high reactance and develops a significant voltage drop across it. When the load increases, the choke saturates and has less reactance and consequently less voltage drop across it. This means the voltage output from the power supply tends to remain constant under varying loads, improving its regulation. Typically, a swinging choke will change (swing) from 5H for a heavy load (high current) to 20H for a light load.

COMBINATIONS OF CAPACITANCE AND INDUCTANCE 

For better regulation, combinations of chokes and filter capacitors are used. It is not necessary for you to remember these combinations (for exam purposes). It is important to bear in mind that whatever filter type is used, it will get its name from the first component seen, looking from the rectifier towards the filter.

If the first component is an inductor(s), then it is an inductive input filter. Likewise, if the first component is a capacitor, it is called a capacitive input filter. You may be asked the advantages and disadvantages of each type.

(1)   Pi - Capacitive input filter.  

(2)   Capacitive input filter.  

(3)   Capacitive input filter.  

(4)   Inductive input filter.  

(5)   Inductive input filter.  

(6)   Capacitive input filter.  

(7)   Capacitive input filter.  

All of the power supply filter circuits shown in figure 20-8 use the principles we have discussed (except for circuit 20-8(7)). The purpose of a power supply is to provide smooth DC output, that is, a constant voltage with varying load conditions. In all circuits, each parallel capacitor has a capacitance that opposes change in voltage and the inductance of the inductors oppose change in current.

Figure 20-8(7) uses another principle, which you don't often see in power supplies. However I will discuss it as the principle is one we need to know for other purposes. In circuit 20-8(7) the parallel inductor and capacitor are resonant at the ripple frequency. A parallel tuned circuit has very high impedance only at its resonant frequency. The parallel LC is resonant at the ripple frequency. Any 100Hz ripple (assuming full-wave rectification) will be blocked significantly from passing through this LC combination. An ingenious technique.

THE VOLTAGE DOUBLER (FULLWAVE) 

The diagram in figure 20-9 is that of a full-wave voltage doubler. With a standard fullwave power supply (e.g. bridge) the output voltage is approximately the peak value of the RMS secondary voltage, or RMS x 1.414.

When lines are crossed without a dot as shown, it means the wires are not connected. When the AC voltage makes point 'A' negative and 'B' positive, D1 will conduct and charge C2. When the AC voltage makes 'B' negative and 'A' positive, then D2 will conduct and charge C1. The capacitors C1 and C2 are in series and so the voltage at the output is the sum of the voltage on C1 and C2, or 2.82 times the RMS secondary voltage.

The voltage doubler can't deliver very high currents. However, it is an excellent method of obtaining the higher voltages required for an electron tube.

EQUALISING RESISTORS AND TRANSIENT PROTECTION CAPACITORS 

In very high voltage power supply circuits, many rectifier diodes are often connected in series to increase the peak inverse voltage (PIV) rating. If a rectifier has a PIV of 400 volts, then 'theoretically' two such rectifiers connected in series should have a PIV of 800 volts. More diodes can be added in series for even higher PIV. However, for proper series rectifier operation it is important that the PIV be divided equally amongst the individual diodes. If it is not done, one or more diodes in the string may be subjected to a greater PIV than its maximum rating and as a result may be destroyed. As most failures of this type lead to the diode junction going short circuit, the PIV of the remaining diodes in the string is raised, making each diode subject to a greater value of PIV. Failure of a single diode in the series (stack) can, therefore, lead to a 'domino effect', which will destroy the remaining diodes.

Forced voltage distribution in the stack is necessary when the diodes vary appreciably in their reverse resistance.

The resistors in figure 20-10 provide PIV equalisation across the two diodes.

The reverse resistance of the diodes will be very high, in the order of megohms. Now, 470kΩ in parallel with megohms is roughly still 470kΩ. So irrespective of the diode's reverse resistance the PIV is distributed roughly equally across each diode.

TRANSIENT PROTECTION CAPACITORS 

Power supplies, high voltage ones in particular, are prone to producing high voltage spikes called transients. These transients are caused primarily because of inductive effects of the circuit (the secondary of the transformer). These are very short duration high voltage transients which can destroy the rectifier diodes. The capacitors shown across the diode in figure 20-10 above will absorb or smooth out any transients. Recall that capacitance is that property that opposes voltage change.

In summary, equalising resistors distribute the applied voltage almost equally across a string of diodes when they are reverse biased. This ensures that each diode, irrespective of its reverse resistance, will share the same amount of reverse voltage drop. Transient protection capacitors absorb short duration high voltage transients caused by inductive effects in the circuit.

ELECTRONIC POWER SUPPLY REGULATION

For power supplies that require excellent regulation, electronic regulation can be added to the filter network. This consists of either an electronic circuit comprised of discrete components or, far more commonly these days, an integrated circuit that contains all the necessary electronics.

There are three basic types of regulation:

Series Regulation - where the regulator is in series with the current path.

Shunt Regulation - where the regulator is placed in parallel or 'shunted' across the power supply output.

Switching regulators -these are the most efficient - that is they dissipate the least amount of wasted power.

These days series regulation is almost always used. The disadvantage with the shunt regulator is that the power dissipated by the regulator circuit is much higher. This translates to lower power supply efficiency and more heat to get rid of in the regulator circuit.

Figure 20-11 is a schematic diagram of a power supply that uses a three-terminal integrated voltage regulator; this is a series regulator. More efficient than a shunt regulator.

The 7805 voltage regulator is just one of many off the shelf integrated voltage regulators.

The IC 7805 is a 5V voltage regulator that regulates the voltage output to 5V. It comes with a provision to add a heatsink. The maximum value for input to the voltage regulator is 35V. It can provide a constant steady voltage level of 5V for higher voltage input to the threshold limit of 35V. If the voltage is near to 7.5V, then it does not produce any heat and hence no need for a heatsink. If the voltage is too high, then excessive power is dissipated as heat from the 7805.

IC 7805 is a series of 78XX voltage regulators. It's a standard, from the name the last two digits '05' denotes the amount of voltage that it regulates. Hence, a 7805 would regulate 5v and 7806 would regulate 6V and so on.

The shunt regulator method shown in figure 20-13 is only used for very low power circuits as shunt regulation is the least efficient of all types of regulation.

A good practical example of a shunt regulator and the only one you need to know is that of a zener diode along with its current limiting resistance.

We have not discussed the operation of a zener diode yet - we will do so in the semiconductors chapter. For now, a zener diode is one that is meant to be operated with reverse bias and beyond its PIV or breakdown voltage. Usually, a diode would be destroyed if operated beyond breakdown. The series resistance R1 (refer to figure 20- 13) limits the reverse current so that the zener diode is not destroyed.

Under such conditions, the zener diode will have a constant voltage drop across it. Zeners come in a range of voltages sometimes a bit odd like 9.1 volts. Zener regulators are used a lot inside transceivers to regulate the voltage to the active devices. A typical example is an oscillator which is low power consumption and must have a stable voltage.

Assuming this zener is 9.1V then as the unregulated input voltage varies from say 10 to 15 volts, the voltage across the zener will remain (almost) constant at 9.1 volts. However, the voltage across R1 will vary. The sum of the zener voltage (9.1 V) and the voltage across R1 will equal the unregulated input voltage as this is a series circuit.

The zener circuit draws maximum current when there is no load as shown now in figure 20-13. This is why shunt regulators are so inefficient. They are dissipating maximum power when doing no work. When a load is applied some of the current going through the zener will now go through the load reducing the heat dissipated by the zener. The sum of the currents through the load and the zener is constant. A zener shunt regulator circuit can be converted into a series regulator circuit by the addition of pass transistors.

A CONSTANT CURRENT SOURCE

This simple circuit (figure 20-14) is a favourite of mine, as I have found so many uses for it. First, allow me to explain what constant current means. The purpose of most power supplies is to maintain a constant regulated DC voltage output. For example, a radio transceiver may require around 13.8 volts DC. The transceiver, when in use, will

draw whatever current it requires from the power supply, so the current varies. The purpose of the power supply is to maintain the constant voltage output of 13.8 volts, regardless of the changing current demands of the transceiver.

Now, there are situations where you don't care about the voltage output of a power supply. What you care about is current. This may seem a little strange because usually, we apply a voltage to a load and the load determines the current. Suppose we want to force a particular current through the load irrespective of what the load wants.

A classic example is charging slow charging lithium batteries. These are very common in portable radio communications equipment. Lithium cells can be slow charged at one tenth of their amp-hour rating for 14 hours (if fully discharged). So a 500mA hour cell or battery should be charged at 500/10 = 50mA for 14 hours. This cannot be done with a constant voltage output power supply. We need a constant current supply. A three terminal regulator can be used to do this for a cost of less than $2. Commercial devices for charging lithium cells (including cell phone batteries) are mostly constant current chargers. You can charge Lithium cells at a much higher rate but in this case the temperature and cell voltage should be monitored.

The resistor is in series with the load and the three terminal regulator is producing a constant voltage across it. The resistor will, therefore, have a constant current through it. Since it is in series with the load, the load will have the same current as the resistor.

All you need to do is buy a regulator, which will handle the current you want and calculate the value of the resistor and its minimum wattage.

POWER SUPPLIES - PASS TRANSISTORS 

The zener diode cannot handle a significant amount of current, usually no more than a few hundred milliamps. Also, a zener diode is not a perfect regulator. There is a way of improving the current handling capabilities of a zener regulator circuit and improve regulation at the same time. This is done by adding a pass transistor.

Figure 20-15 is the schematic diagram of a zener regulator with a pass transistor added. You will recognise Rs as the usual current limiting resistance that prevents the zener from being destroyed. The zener is reverse biased, with a positive voltage applied to its cathode.

The zener regulated voltage drives the base of a transistor connected as an emitter follower (common collector). The output of the emitter follower goes to the load. Because of the current gain (Greek letter beta; β) of the emitter follower, any change in load current is reduced by a factor of β, This means voltage regulation is improved by a factor of β and that is a significant improvement.

Use of the pass transistor increases the maximum load current the regulator can handle. You need to be able to identify this circuit as a zener regulator with a pass transistor. The purpose again - to improve regulation and the current handling capabilities of the zener.

A pass transistor can be added to a three terminal voltage regulator in much the same way and for the same reasons. We will be discussing β and transistors more deeply in the chapter on semiconductors and amplifiers.

THE DARLINGTON PAIR

Two transistors can be connected in a configuration known as a Darlington Pair. As far as I am aware, you do not even have to know what a darlington pair is. We are jumping ahead of ourselves, but it is best, like the series pass transistor to mention them now. The darlington pair is an improvement on the single pass transistor.

The higher the β; the higher the input impedance of an emitter follower. One way to increase current gain or β is with a darlington pair, two transistors of the one type connected as shown in figure 20-16.

The overall current gain is equal to the product of the two individual beta. Transistor manufacturers can put a darlington pair inside a single transistor package.

Notice how the external connections to the two transistors are a base, emitter and collector.

A traditional application of a darlington pair is a 'pass transistor' in a power supply. A darlington pair can also be created with two PNP transistors.

A POWER SUPPLY WITH PASS TRANSISTORS (Darlington Pair) 

All of the regulator circuits we have looked at are series regulators. The pass transistors are in series with the load. Series regulators are more efficient than the shunt type. The shunt type regulator (which is in shunt or parallel with the load) is rarely used, except in low power circuits, as they dissipate too much power.

Figure 20-17 is a full-wave power supply. It uses two diodes. Therefore, it must have a centre tapped transformer. C1 and C2 are both filter capacitors, probably around 1000 microfarads and therefore electrolytic. R1 is the current limiting resistor for the zener regulator D3.

The zener regulator has a darlington pair as the pass transistors. The darlington pair does a superior job compared to a single transistor, improving the regulation and the current handling abilities of this power supply significantly. Read the section on pass transistors and the darlington pair again if you need to.

R2 supplies a light load on the power supply should the 'real' load not be connected. Its value would be about 1kΩ. C3 is an RF bypass capacitor about 0.01µF.

Is the zener diode reverse biased? Yes, the positive rail (line) is at the top of the circuit. See if you can deduce this from the power supply diodes and how they would conduct and charge C1. R1 is a current limiting resistor for the zener diode.

SWITCHING REGULATORS (BUCK CONVERTERS) 

As the name infers switching regulators regulate voltage by some form of switching. The best way to understanding this type of regulator is to start from the beginning and develop the principles involved. The type of regulator we will develop is the buck converter. This type of converter is the most commonly used in radio communications as it converts a high voltage to a low voltage. One way we could control the voltage to a load could be with a resistor as shown in figure 20-18.

The problem with this method of voltage regulation is very poor efficiency. Resistors dissipate energy in the form of heat and this energy is lost. A controlled variable resistance is essentially how series linear regulators work. With switching regulators we are endeavouring to take as much resistance out of the regulator circuit as possible between the source and the load.

When the switch in figure 20-19 is open the load receives 0V. When the switch is closed the load receives 10V. The switch can be operated continuously and quickly if we wanted at high frequency. What would be the average voltage across the load? The average load voltage would be 5V. However this is not a good voltage output as there are deviations in voltage between 0 and 10V. We have achieved something. The switch does not dissipate any power as the resistor did in figure 20-18. Perhaps we could smooth the voltage out across the load by adding a capacitor as in figure 20-20.

Figure 20-20 certainly looks like a step forward. Capacitance is the electric property that opposes changes of voltage. Since the capacitor is connected across the load it should oppose changes to load voltage. We still have not used resistance so our circuit efficiency is high. The problem with this circuit is when the switch is turned ON there is a rush of high current into the capacitor. The time constant of the capacitor is short and we do not want to lengthen it by added resistance that we are trying to avoid. The capacitor is smoothing out the load voltage but we need to stop the excessive surge current when the switch is closed.

We could do this by adding a series inductor as shown in figure 20-21. Inductance is the electric property that opposes changes of current. The inductor will then control the surge current by storing energy in its magnetic field.

Now when the switch is closed (figure 20-21) current flows as shown. There is no capacitive surge current as the inductor opposes this rapid change of current. The load is supplied power from the source. The capacitor is charged and stores energy. The magnetic field about the inductor expands and stores energy. All is looking better. What happens when we open the switch?

Inductance is the electric property that opposes changes of current. We have just opened the switch and demanded that the current stop. The inductor will create a back emf that will oppose our attempt to change current. The polarity of that back emf will be to keep the current going in the direction it was before the switch was opened. A very large voltage will be developed across the inductor. How large? As large as it takes to get rid of the stored energy. The switch will most likely arc across. If a semiconductor switch is used it could be destroyed. The solution is to give the energy of the inductor somewhere to go.

With a diode connected as in figure 20-23 there is now a discharge path for both the inductor and the capacitor through the diode and the load when the switch is in the OFF position. We need to look at what the diode does when the switch is in the ON position.

When the switch is closed the diode is reverse biased. The diode is then an open switch and is essentially out of circuit.

Recapping, during the ON phases the load, capacitor and inductor are supplied energy from the source and the diode is out of circuit. During the OFF phases the diode is forward biased and conducts now providing a path for the inductor and capacitor to dump their energy by allowing a current path through the load. We now have all the essential topology of a buck converter.

The output voltage depends on the percentage of time the switch is ON. In a practical buck converter we would use a BJT transistor or a MOSFET as the switch. We control the ON/OFF ratio of the switch by a pulse width modulation (PWM) on the control of the switch (gate or base). The switch will operate at anywhere from 60 to 200kHz. The diode would be a schottky type for fast switch and low forward voltage drop.

We would also want to monitor or sense the output voltage and have that control the ON/OFF switching ratio of the semiconductor switch.

It would not be difficult to build a buck converter. We do not have to go to component level as there are many off the shelf switch mode converter integrated circuits and they are inexpensive.

DIAGRAM - BUCK CONVERTER

The only difference here compared to what we have just discussed is that now we have a voltage divider on the output which is fed back to an operational amplifier and a reference voltage. The oscillator provides the switching square wave and the operational amplifier turns on the square in bursts to the NPN transistor. This transistor would be a darlington pair - see figure 20-16. The diode is a schottky.

A Switch Mode Power Supply (SMPS) that converts to a lower voltage than the input is a buck converter as discussed here. An SMPS using a boost converter outputs a higher voltage than the input. Boost converters operate in a similar way to buck converters. They use the same components organised in a slightly different way. Many off the shelf integrated circuits can be operated in buck or boost mode.

SMPS are more efficient than their linear counterparts. Efficiencies exceeding 90% are possible. SMPS are smaller and much lighter than linear power supplies. They are also less expensive to build. The cost and weight saving is primarily due to the SMPS not requiring a mains transformer and large heat-sinks.

The mains is usually connected directly to the SMPS where there is a bridge rectifier but no transformer. This means the danger of electric shock is higher. Unless you are experienced in working on high voltages an SMPS should always have the power removed when fault finding.

When purchasing an SMPS for radio use, choose one designed for radio applications. Some SMPS can produce significant amounts of radio noise.

THE MAINS SUPPLY

We have covered in earlier chapters the frequency, voltage relationships, RMS, peak, and the wave shape of the mains. What we have not covered is the wiring of the mains.

Household wiring is a parallel connection. If it were not, when we switch an extra light on, all other lights would dim a bit (series circuit).

The three wires in the (Australian) mains circuit are:

The Active - Colour Brown (old red).

The Neutral - Colour Blue (old black).

The Earth - Colour Green/Yellow (old green).

These names are a little confusing. First of all, active and neutral deliver the 240 volts AC throughout your home. There are 240 volts AC RMS between active and neutral. The standard for the mains voltage in Australia is really 230V AC RMS but this varies a lot with load and still referred to as the 240V AC Mains.

The earth is not ground in the sense that radio operators call ground. Earth is just that, EARTH, dirt if you like. The earth connection is usually somewhere near your power box and is a copper rod going into the ground.

Also, one side of the mains is connected to the earth as well. This earthed side of the mains is called neutral. The neutral is connected to the 'neutral bar' in the switchboard and the neutral bar to the electrical ground. This means that there must be 240 volts AC RMS between active and earth. The potential difference between neutral and earth should be zero volts, but they may be a few volts (up to 5-6) due to capacitive coupling.

The locations of these wires are shown for a power point (socket) in figure 20-26. The active is on the left on a power point (socket). The active is on the right looking at a plug and on the left looking at the wall socket.

The photo in figure 20-27 shows the connections for both a plug and a socket (extension lead).

Should the active wire come adrift and contact the metal chassis of any appliance a fuse will blow. The metal (conductive) parts of appliances are connected to earth, as is the neutral. Should an active touch a metal part and therefore potentially 'you', the active and neutral are effectively short circuited and a fuse will blow.

All being well since there is no potential difference between neutral and earth you should be able to touch the neutral wire in your house and nothing will happen - never put this to the test, though by all means, use a voltmeter to check.

Every power switch in your house should be in the active wire. 

It is extremely dangerous to assume that the wiring in your home is correct. If someone has wired a switch into the neutral wire instead of the active, then the appliance will still work. However, the active will still be going to it when it is switched off. For example, if someone has placed the switch in the neutral wire of a light, the light will still work as it should (as will all other appliances). If you turn the light switch OFF and it is wired incorrectly like this, the active is still present at the light socket. If you touch the active terminal in the light socket, you will receive an electric shock that could be fatal.

How easy it is for someone to reverse the active and neutral accidentally or carelessly on the plug or socket of an extension lead. Doing so could be fatal. In passing, electrocution is death by electric shock. You cannot be electrocuted and survive.

You need to know the potential difference between each wire in your household mains. This is not so you can work on your house mains. It is necessary for you to know this if you build equipment that you connect to the mains. You need to know how to test a power point with a voltmeter. This is safe provided you do not contact the metal parts of your multimeter leads. If you measure less than 240V between active to earth and active to neutral, it may mean you have a problem. Any voltage above a few volts between earth and neutral indicates a problem.

If you are in a new home, you will have an earth leakage detector fitted. Older homes may not have them, so it is your choice to have one fitted by an electrician.

Only qualified electricians should work on the household wiring. Being a licensed radio operator or a professor of physics does not qualify you to tamper with house electrical wiring. This part of the chapter is not a definitive explanation of safety procedures. The best procedure is to remove equipment from the mains before working on it. However, as a licensed radio operator, you are qualified to build equipment which you can connect to the mains. Be aware when purchasing home brew equipment which is to be connected to the mains. Perform an electrical safety check if you are competent to do so. If you are not competent then have someone who is test the equipment for you.

Different countries will have specific Federal, State, or Local government laws. You need to know your local requirements regarding electrical safety.

21 - Electron Tubes

One of the most significant developments of the early twentieth century was the invention of the electron tube. The British call it a valve. In the USA it is referred to as the "tube". Thomas Edison, the inventor of the electric light bulb (among other things), came extremely close to inventing the electron tube. When Edison was trying to develop a light bulb his most significant problem was to find a filament that did not burn out. He concluded early in his experiments that a filament would last longer if it was placed in a vacuum. Edison, being the entrepreneur that he was, would be kicking himself today if he knew just how close he had come to the discovery of the electron tube.

Edison tried hundreds of different types of filaments, without using true scientific method (Edison did not like scientists), more like a laborious trial and error approach. One of the things that frustrated Edison was that some of his filaments were giving off material which was deposited on the inside of the glass bulb causing the light to dim and overheat. He even inserted a metal electrode into some of his light bulbs and found this prevented these deposits from occurring. We now call that additional electrode an anode. It worked, but he dismissed the idea as impractical for a light bulb.

In radiocommunications, electron tubes are not used as much as they once were. One exception is very high power radio transmitters and amplifiers. Electron tubes are extensively used in industry and commercial radio communications.

Also, many of the principles of amplification, oscillation, rectification and the like, are the same with modern semiconductor devices as they are with electron tubes. It is somewhat beneficial to understand these principles with electron tubes first.

THERMIONIC EMISSION

When metals are heated to very high temperatures electrons are boiled off. These boiled off electrons have left the metal and formed a cloud called a space charge. Since electrons have left the metal, it becomes positive. The space charge, consisting of electrons, is negative. As long as the metal remains heated the space charge will exist, as it requires energy to keep the negative electrons away from the positive metal. Metals that are designed to enhance their ability to create a space charge are called cathodes. Since electrons have left the heated cathode, the cathode will be positive

with respect to the space charge. The cathode will continually attract electrons back. However, electrons will be continuously ejected by the thermionic emission.

CATHODES

A cathode is something capable of emitting electrons. For example, in a light bulb, a piece of wire carrying an electric current becomes hot. If sufficient current flows, the wire becomes white-hot. Heat is 'really' the measure of the internal kinetic (moving) energy of atoms or molecules. Electrons in the outer orbits of the atoms move so rapidly due to increased temperature that some of the less tightly bound ones fly outward and away from the wire into the surrounding space. This creates a cloud of free electrons around the wire, as long as it is hot enough. The wire has become a cathode. When the atoms in the filament wire lose electrons, the filament is left with a positive charge. The electrons expelled outwards are then attracted back toward these positively charged atoms in the filament (cathode); some do make it back, only to be expelled again. This results in a constant in and out, back and forth movement of electrons, in the area directly surrounding the cathode. This creation of the space charge around a hot filament is called the Edison effect or thermionic emission.

The space charge has no practical use in a light bulb. Filaments designed for creating a space charge are called cathodes. There are a number of materials used for cathodes, however, by far the most popular is thoriated tungsten. Thorium is an excellent electron emitter, but this material is not strong enough for practical use. Mixing thorium with the more rugged tungsten produces a thoriated-tungsten cathode that will permit many electrons to be emitted at a relatively low temperature (1600 degrees centigrade). Cathodes of this type are used as radio transmitting tubes.

To enhance the space charge creating properties of the cathode, it is placed in a glass envelope and the air is pumped out. To improve the vacuum further, the entire assembly is heated to force out any additional gas molecules in the metal electrodes. Then a small amount of magnesium (called the getter) placed inside the envelope

during manufacture, is ignited. The resultant chemical action of the vaporising magnesium with the gases released from the metal removes the final traces of gas in the tube. The by-products of the vaporising magnesium condense on the inside of the electron tube forming the silvery coating commonly seen on electron tubes.

THE DIODE

The cathode of an electron tube can be heated by a separate filament, in which case the filament is called a heater. Such an arrangement is known as an indirectly heated cathode. Alternatively, the heater itself can be treated with thorium to act as a cathode. This method is referred to as a directly heated cathode.

Figure 21-2 shows an indirectly heated cathode, the heater is a third element connected to its own power supply.

It should now be obvious that electric current does not have to occur in a conductor. In the last chapter, we discussed power supplies and rectification. The diode electron tube just described can be used in any of those power supply circuits. A diode electron tube will always conduct if its anode (also called a plate) is positive with respect to the cathode and a space charge exists. Electron flow from anode to cathode is not possible.

THE TRIODE

A circuit schematic of a Triode (tri=3) appears in figure 21-3. In a diode, a cathode and anode are required to enable electrons to flow. Also, a triode has a third electrode called the control grid. The grid is a fine metal wire, usually nickel, molybdenum, or iron. The anode and cathode are both solid electrodes. The control grid of the triode is a fine spiral wire placed between the cathode and the anode. All electrons attracted to the plate from the cathode go through the openings in the control grid. The grid is connected to the base of the electrode so that voltage can be applied to it. Imagine if you will a triode operating without voltage applied to its grid, it will act just like a diode.

If we make the grid slightly negative with respect to the cathode, the negative grid will inhibit (restrict) the flow of electrons from the cathode to anode (like charges repel). The voltage between cathode and anode may be hundreds of volts. On the other hand, a small negative voltage on the control grid will have a substantial effect on the flow of current from the cathode to the anode. The significance of this is that we can control a large cathode-anode current with a very small negative grid voltage. Making the grid more negative will decrease the anode current; making the grid less negative will increase the anode current.

A pictorial diagram of the construction of an electron tube is shown in figure 21-4. The electrodes and grids are in cylinders surrounding each other. All of the electrodes are usually connected to pins out of the bottom of the electron tube.

Why is the electron tube called by some a valve? Think about how a water valve works. A minor input of energy from your hand can control a huge pressure of water. Likewise, a small voltage on the control grid can control a large anode/plate current.

Under normal circumstances the control grid is negative. Because of this, it does not draw any electrons from the cathode. It is the negative voltage alone on the control grid that can control what can be a substantially large current from the cathode to anode (voltage without current is no power P=EI).

The control grid is placed closer to the negatively charged cathode and further from the highly positively charged anode. This placement allows it to function more effectively than if it were simply midway between the cathode and anode.

The cathode-anode circuit of the electron tube is the output circuit. The control grid cathode circuit of the electron tube is the input circuit. No current flows in the control grid-to-cathode of the electron tube. There are special cases where current does flow, but it is still very small; see grid-leak bias. On the other hand, the voltage and current in the output circuit of the electron tube is substantial. And as we learned, the product of current and voltage is power (watts). Therefore, with the triode, we have the means to control significant amounts of power by simply applying a small negative voltage to the control grid.

We could, for example, connect a microphone to the control grid of an electron tube and use the very small voltage from this microphone to change the negative potential on the control grid, that in turn would control the cathode-anode current. The microphone produces small voltages corresponding to sound waves striking its diaphragm. These small voltages are then applied to the control grid, which in turn controls the larger cathode-anode current. The cathode-anode current will contain all of the information (intelligence) that was initially fed into the microphone.

What we have just described is amplification. The triode was the first electronic device ever to be able to produce amplification.

THE TRIODE AS AN AMPLIFIER

The triode amplifier in figure 21-5 has an audio input that could be from the microphone. It has an output transformer to match the output impedance of the triode to the impedance of the speaker. The small battery on the left makes the control grid negative at all times - this is called negative bias. The audio signal will cause the control grid to become more or less negative. In practice, the battery or power supply voltage sources would be bypassed with a capacitor. In a practical amplifier, batteries would not be used. Negative variations on the control grid cause the much larger cathode-anode current to vary and an amplified sound comes out of the speaker.

DISADVANTAGE OF THE TRIODE 

When we discussed capacitance earlier in this book, we found that any two conductors separated by an insulator have capacitance. The problem with the triode is the capacitance between the control grid and anode. (more on why this capacitance is bad shortly). We also learned in our study of capacitance that capacitors in series decrease the overall circuit capacitance. Inserting another grid called the screen grid between the control grid and the anode, reduces the capacitance between the control grid and the anode.

Why is the control grid to anode capacitance bad?

The anode is in the output circuit of the triode. The control grid is in the input circuit of the triode. The unwanted capacitance we're talking about is between the control grid and anode. This unwanted capacitance is inside the electron tube. However, it may as well be a physical capacitor connected externally from the anode to the control grid. This means that there is a connection through this capacitance from the output of the triode to the input of the triode, this is undesirable. This unwanted capacitance can cause positive feedback.

You will be well aware of the problems with feedback from a public address system. If the sound from the speakers in a public address system gets into the microphone of the same system, you will have feedback and it will oscillate (squeal).

If we wanted the triode to oscillate that would be just fine. However, if we want it to amplify, then this oscillation (because of feedback) is a problem. The inclusion of a screen grid between the control grid and anode reduces the control grid to anode capacitance and improves the stability of the triode as an amplifier. A triode with a screen grid is no longer a triode; it is called a Tetrode.

TETRODES

The screen grid of tetrodes (tetra=four) is not used to control the plate current but has a steady positive DC voltage on it to help accelerate electrons to be collected by the anode. The path for current inside a tetrode is from the cathode through the control grid and through the spaces in the screen grid, to the anode.

Since the screen grid is positive, it will collect some electrons. Most of the electrons arriving at the screen grid have enough momentum to continue to the anode. Electrons arriving at the screen grid pass through it, attracted by the much higher positive potential on the anode. The screen grid current is wasted current since it is not used in the output circuit. The benefits of the screen grid (reduced control grid to anode capacitance) outweigh this disadvantage.

More about the triode and feedback

Even though we are talking about electron tubes in this chapter, all that you learn here can be carried over to other devices that amplify, such as transistors. The diagram in figure 21-7 shows a generic amplifier. The signal to be amplified is applied to the input and a larger signal appears at the output.

All amplifiers work this way regardless of what the amplifying device is. The power for the amplified output is provided by the power supply.

Figure 21-8 shows a little more detail of a generic amplifier. Most amplifiers have, as a natural consequence of their construction, a small amount of unwanted capacitance between their output and their input. I have shown this unwanted capacitance on the amplifier below. Remember, this capacitance is not an external physical capacitor, rather an unwanted capacitance inside the amplifying device.

The consequence of this unwanted capacitance in any amplifier, between output and input, is that some of the output signal can return to the input. If you like, some of the output signal 'leaks' back to the input. This is called feedback. In the case of unwanted capacitance between output and input, as shown, the feedback is called positive feedback.

Positive feedback means the output signal is fed back to the input in such a way that it adds to, or is in phase with, the input signal. I have shown the feedback signal as a small sinewave. Can you see how this sinewave is in phase with the input signal? Positive feedback adds to the input signal - so it's like taking some of the output and amplifying it all over again. This is called regeneration. The terms regeneration and positive feedback can be used interchangeably.

If there is enough positive feedback the amplifier will stop being an amplifier and it will oscillate. Like a public address system where the microphone is placed too close to the speaker and it howls. An amplifier with too much positive feedback will oscillate (like the howl of a public address) but you may not hear it at all - it could oscillate on a radio frequency above human hearing. It certainly won't be amplifying as it should. The amplifier is said to be self-oscillating and amplifiers are supposed to amplify not self-oscillate. We will cover more of this in detail later. The point I am trying to make here is that unwanted positive feedback is a bad thing and we must prevent it from happening.

THE TRIODE AMPLIFIER

Just to recap for a moment look at a basic triode circuit in figure 21-9. The input signal is applied to the control grid and cathode. The output signal is taken from the anode and the cathode. (The cathode is common to both input and output). If any of the output signal in the anode was able to get back to the control grid, then this would be undesirable positive feedback.

UNWANTED CAPACITANCE IN THE TRIODE 

We have an unwanted capacitance formed in a triode between the control grid and the anode. It is there because everything is in place to form a capacitor. The control grid and the anode are the two plates and the vacuum between them is the dielectric. There are other unwanted capacitances in the triode. Between the cathode and the control grid for example and many others. However, it is the capacitance between the anode and the control grid that will allow positive feedback to occur.

The reactance of a capacitor decreases with increasing frequency. The higher the frequency a triode (or any amplifying device) is operated at, the more positive feedback there is because of this lower reactance. Remember, enough positive feedback will cause the amplifier to oscillate and prevent it from its proper job of amplifying. This is where the tetrode comes in.

How the tetrode helps 

The tetrode breaks the capacitance between the control grid and the anode into two capacitors in series. This is shown in the diagram of figure 21-11. What happens when you connect capacitors in series? Does the total capacitance increase or decrease?

I hope you said the total capacitance decreases. This is the primary function of the screen grid. The insertion of the screen grid reduces the unwanted interelectrode capacitance between the control grid and the anode and in doing so reduces the likelihood of unwanted positive feedback, enabling the electron tube (or any other amplifying device) to be used at higher frequencies.

The unwanted capacitance is not a real physical capacitor that anyone has deliberately added to the electron tube - it is the nature of the electron tube's construction to have this unwanted capacitance.

When we have done all we can with the amplifying device and we still have positive feedback the only thing we can now do is introduce an equal amount of negative feedback. Negative feedback is out-of-phase feedback. Negative feedback is also called degeneration. The process of deliberately applying negative feedback to cancel out unwanted positive feedback is called neutralisation. We will talk more about neutralisation as it is an important concept of amplifiers used at radio frequencies.

PENTODES

Fast moving electrons (relatively speaking), in an electron tube, may strike the anode with considerable force. Some of the electrons striking the anode will collide with electrons in the anode material and bounce back, or electrons arriving at the anode may dislodge electrons in the anode material and cause them to be emitted from the anode. This phenomenon is called secondary emission. Secondary emission is undesirable. Electrons participating in secondary emission are not performing any useful function and can build up a small cloud of electrons somewhat similar to the space charge around the cathode, though nowhere near the same size.

This secondary space charge around the anode will inhibit or restrict the flow of electrons from cathode to anode.

Pentodes (pent = 5) have the same construction as tetrodes but with the addition of another grid, called the suppressor grid, in the space between the screen grid and anode. The suppressor grid has a negative voltage placed on it with respect to the cathode. Now you might think that a negative voltage on the suppressor grid would also inhibit cathode-to-anode current. In fact, it does, but not to the extent of secondary emission. The negative voltage on the suppressor grid does not appreciably reduce the cathode-anode current. Also, by the time electrons come close to the anode they have built up a significant amount of momentum that will carry them through the negative electric field of the suppressor grid.

The secondary electrons, the ones created by secondary emission, do not have a large amount of energy and are repelled back to the anode by the negative potential on the suppressor grid. The pentode has the additional advantage of having still less capacitance between the control grid and the anode. The suppressor grid, like the screen grid, acts like another series capacitor between the control grid and anode reducing the unwanted capacitance even further.

X-RAYS 

As a matter of interest, if the cathode/anode current is made very high by an extremely large voltage on the anode relative to the cathode and if secondary emission is encouraged, a by-product of this is that x-ray radiation will be emitted from the anode. Secondary electrons that are ejected from the anode are at a higher energy level. When they get pushed back to the anode or just fallback, they discard their excess energy as a photon in the x-ray band. This was how the x-ray machine was developed. In an x-ray machine, the anode is specially shaped at an angle of 45 degrees to the approaching electron stream to deflect the x-ray emission sideways out of the electron tube.

I am amused that x-rays are still called "X" for unknown. Rontgen discovered them. Perhaps 'Rontgen waves' was too hard to pronounce but R-Rays would be cool. x-rays are electromagnetic waves.

We have described all the basic types of electron tubes. There are others, but these are only modifications of the types we have just discussed. An electron tube may have two diodes within one envelope. The two diodes may share one cathode, or they may have separate cathodes - this is called a duo-diode. Other types are duo-triodes and triode-pentodes.

SOFT TUBE 

An electron tube can become faulty and have unwanted "gas" or "air" in its vacuum. This means the vacuum is not as "hard" as it should be. Such a fault with electrons tubes is called a gassy or soft tube. The terms 'hard' and 'soft' refer to the integrity of a vacuum.

MICROPHONICS

Another problem which can occur with electron tubes is microphonics. An electron tube is a mechanical as well as an electronic device and if it is tapped with a screwdriver, or flicked with a finger, it will vibrate. The vibration of the grid will modify the cathode-to-anode current and this vibration will 'modulate' the output.

Modulation means imposing the information of something onto something else. In the discussion above the vibrating grids would transfer this vibration 'message' to the output current.

If an audio (sound) system was constructed from electron tubes and some of the audio output sound wave energy from that system was able to reach the electron tubes and caused them to vibrate, then the system would produce microphonics, or perhaps even feedback. In some old 'wireless' sets, if you hit them on the cabinet, you would hear a 'thud' sound from the speaker.

More on Feedback

Feedback is not a problem particular to electron tubes. Feedback is a sub-topic of its own. However, since we have mentioned it in this chapter, we may as well discuss it a little further.

Feedback is only a problem if you don't want it. If you want an electron tube to oscillate, then you may take advantage of the capacitance between the control grid and the anode. Alternatively, you may use external components, usually a capacitor, to take some of the electron tube's output and feed-it-back to its input.

An oscillator is a device for producing electronically, AC or VDC. The frequency of the voltage may be from audio to microwave and beyond.

We have discussed the two types of feedback, called positive and negative. Nothing to do with polarity. When some of the output of an amplifier is fed back to its input, in such a way that the voltage is in phase with the input voltage, this is called positive feedback. This is the type of feedback we require if we want oscillation to take place.

If some of the output of an amplifier is fed back to its input so that it is out of phase with the input, this is called negative feedback. Negative feedback reduces the amplification (gain) of an amplifier. However, it also has benefit such as improving the linearity. A perfect amplifier (no such thing) would do nothing to the input signal except increase its amplitude. In practice, all amplifiers produce some distortion. The distortion just means that what we are getting out of the amplifier is something we did not put into it. However, there is always unwanted information in the output created non-linearity in the amplifier. Negative feedback can reduce the distortion of an amplifier. The ability of an amplifier to amplify with minimum distortion is called linearity. Negative feedback does improve the linearity of an amplifier.

Remember our old friend direct proportion? If an amplifier's output is directly proportional to its input, it is linear. That is the output signal varies in direct proportion to the input signal.

THINGS TO DO 

It is not very hard to get your hands on an old electron tube. If you can, please do so. Place it in a cloth bag or towel and smash it and have a look at the construction. You will see that the heater is in the centre with a cylindrical cathode around it; cylindrical spirals around the cathode for the various grids and finally a cylindrical anode.

Lee De Forest (August 26, 1873 to June 30, 1961) was an American inventor. Although he held over 180 patents he is best known for his invention of the Audion (Triode) vacuum tube. His invention made live broadcasting possible and was critical to radio, television, radar and telephone systems prior to the development of the transistor.

There is some evidence to indicate that Lee De Forest did not know what could be done with his audion valve. It was Edwin Armstrong who first used the audion to produce amplification and regeneration (oscillation).

De Forest and Armstrong were locked in a bitter legal dispute for two decades. Many times the court found in favour of Armstrong. Then one final court battle was won by De Forest. Armstrong was shattered by the result and committed suicide. In 1910 he broadcast a live performance from the Metropolitan Opera in New York to advertise his new invention.

He also discovered that he could cause a self generating oscillation that could be fed through an antenna to strengthen the signal further.

In 1920 he developed a sound-on-film optical recording system that was demonstrated between 1923 and 1927 but the poor quality of the system made it technically impractical.

During the 1930s he invented audion-diathermy machines for medical use. He lacked business skills and, after he was defrauded several times by his partners, he sold most of his patents cheaply to the American Telephone and Telegraph Company.

Edwin Howard Armstrong (December 18, 1890 - February 1, 1954) was an American electrical engineer and inventor, best known for developing FM (frequency modulation) radio and the superheterodyne receiver system. He held 42 patents and received numerous awards, including the first Medal of Honour awarded by the Institute of Radio Engineers (now IEEE), the French Legion of Honour, the 1941 Franklin Medal

and the 1942 Edison Medal. He was inducted into the National Inventors Hall of Fame and included in the International Telecommunication Union's roster of great inventors. Armstrong was an engineering genius. He invented, Regeneration, Oscillation, Frequency Modulation and the Superheterodyne system. All of which are still in use today and most likely always will be. His genius of electrical and electronic invention is unmatched. After decades of legal battles with Lee De Forest over the audion tube all of which he won until one last one that he lost and was devastated. It was said by his friends that he was too principled. After the last lost legal challenge Armstrong felt so disgraced that he returned an award (The Medal of Honour) endowed upon him by the Institute of Radio Engineers (IRE) The board of the IRE refused to accept it back. On the night of January 31-February 1, 1954, with his wife in Connecticut and three servants having left for the day, Armstrong removed the air conditioner from a window in his twelve-room apartment on the thirteenth-floor of River House in Manhattan, New York City, and jumped to his death.

22 - Decibels

For some reason, decibels are disliked and misunderstood by many radio experimenters, engineers, technicians and the like. The decibel is used in equipment handbooks and specification sheets so we really do need to understand them. Not just understand, but appreciate the advantages of the decibel and want to use them.

Human senses of sight, touch, hearing and others are all logarithmic. Our human senses are not linear. Decibels are also logarithmic and as such more closely match changes that affect our senses.

Early man tiptoed through the jungle listening for:

Sounds indicating something to eat.

Sounds indicating something was going to eat him!

His ears would pick out quite faint sounds. They had to, or he would starve. He also heard some very loud noises from animals bellowing, trees falling, landslides and the like. For shelter, early man lived in caves; yet he had to be able to distinguish members of his family from the noises of predators. And at the same time, he had to handle the harsh bright sunlight when he was out hunting for food. To avoid overloading the information processing centre in his brain, his various sensing mechanisms accommodated the signals from almost all his senses into a compressed range. Twice as much energy in a sound does not seem twice as loud. There is a lot less energy involved in a leaf rustling, compared to a tree falling. Having two candles lit in the cave is quite a significant change from just one; but lighting a candle at the mouth of the cave, even on a dull day would hardly register on his visual cortex.

If our ears interpreted noises as a direct proportion, then to be able to hear very weak sounds, strong sounds would be more than deafening! They would be painful, perhaps lethal. Apart from heat and pressure or touch, most of our senses respond to increments in the signal rather than to its absolute level, i.e. the amount of the change divided by the level already there.

Very early in the development of amplifiers, it was realised that the units for comparing output powers must match the hearing of the operator or listener. These early amplifiers were used for the long distance telephone lines that were starting to criss-cross all the continents and oceans of the world.

There were also economic factors to consider. If one amplifier could increase the signal level so that communication could be heard 1000 miles away, that would be better than one that only carried 100 miles before it required boosting again. Why? Because one tenth the number of booster amplifiers would be required. However, if the 1000-mile amplifier was used, then some of the signal would be heard in adjoining lines, by capacitive and inductive transfer - the crosstalk effect. Also, if all amplifiers were designed for 1000 miles, there would need to be some means of attenuating the signal for nearby connections - or people would have their hearing damaged by the use of the telephone. But how much signal was required for normal hearing, how much could the signal fall or increase before customers complain? For a sound to be perceived as twice as loud, it seemed that an increase of about 10 times the power at the source was required.

For sound to seem twice as loud, increase the power about 10 times.

For sound to seem twice as loud again, increase the power about another 10 times. The total increase so far is about 100 times.

To seem twice as loud once more, increase the power by about 10 times again. The total power increase is now about 1000 times.

You can see that this system of describing the power of a sound is very cumbersome. This could be written much more conveniently:

To seem twice as loud - increase the power by approximately 101.

To seem twice as loud again - increase the power by approximately 102•

To seem twice as loud once more - increase the power by approximately 103•

(101 = 10, 102=100, 103=1000)

We can see that a convenient unit to use is the index of 10. Because the Bell Telephone Company was at the forefront in researching long distance telephonic communications, this unit is called the Bel, after Alexander Graham Bell. The Bel is a unit of comparison. We use it, just like with sound levels, to compare current, voltage and power levels.

In mathematical terms the Bel is:

Where Pl and P2 are the two power levels to be compared.

The logarithm [or 'log'] of a number is the power, or index, that 10 must be raised to get that number.

LOGARITHMS 

The mathematical shorthand to indicate that the log of a number is to be found is log(N), where 'N' is the number whose logarithm is to be found. The base of the logarithm used with the Bel is 10. Other bases can be used, but we are not interested in these in this course. If there is any possibility of confusion in texts about which base is being used, the shorthand is written as log10(N) and log(N) for common (base 10) and natural logarithms respectively.

Common logarithms which express a number as a power of the base 10, are the ones that interest us. Natural logarithms express a number as a power of the base 'e' where 'e' equals 2.71828. For the Advanced exams, you need only concern yourself with the use of common logarithms (base 10). Throughout the rest of this chapter, you can consider log(N) to mean log10(N).

The laws of indices [plural of 'index'] are:

• to multiply numbers, add their indices

• to divide by a number, subtract their indices

From the laws of indices, it follows that we can say:

102 =100 so log(100) is 2 (10 x 10 = 100)

103 =1000 so log(1000) is 3 (10 x 10 x 10 = 1000)

10-1 =1/10th so log(0.1) is -1

10-2 =1/100th so log(0.01) is -2

What is the logarithm of 10,000? In other words, to what power must 10 be raised to give 10 000? The answer is 4 since 104 is 10 x 10 x 10 x 10 = 10,000.

The common log of a number between 1 and 10 lies somewhere between 0 and 1. The common log of a number between 10 and 100 lies between 1 and 2. The common log of a number between 100 and 1000 lies between 2 and 3. You can see that using logs simplifies the expression of very large numbers and ratios.

To find out these 'in between' logarithms it was once necessary to look up large tables (books actually) of logarithms. Fortunately, most calculators have a 'log' key. Try the following numbers on your calculator:

log(10)=1:

Enter 10 into the display and press 'log' and you should get 1.

On some calculators you have to enter 'log' then the number you want the log of and press'='.

log(50)=1.698

Enter 50 into the display and press 'log' and you should get 1.698. log(250)=2.3979

Try the next for yourself:-

Finding the antilog of a number [i.e., an index], converts it back to the original number. On most calculators, an antilog is found by:

1. entering the number [index] into the keypad;

2. pressing 'INV'; (this can be "shift" or 2nd on some calculators)

3. pressing 'log'; and

4. the antilog displays, i.e., the original number.

Try the following yourself:

• antilog of 2 = 102 = 100

• antilog of 3 = 103 = 1000

• antilog of 1.5 = 101.5 = 31.622

• antilog of 0.5 = 100.5 = 3.1622

For example, to find the antilog of 2: (on some calculators the order is 2,3,1,4)

1. enter 2 into the display;

2. press 'INV';

3. press 'log'; and

4. your display should read 100.

Logarithms are very useful in radio work. Many test and measuring instruments have their scales calibrated logarithmically to enable a greater dynamic range of measurement to be displayed on one scale. On some meter scales, you will find two sets of numbers - one set going from 0 to 10 and the other set going from 0 to 3.16. Why? [Hint: (3.1622)2=10]

Dynamic range means the range between the lowest (weakest) and highest (strongest) level. The dynamic range of receivers and other equipment is expressed in decibels.

BACK TO THE BEL

If P1 is 30 watts and P2 is 2 watts (this is a change in power from 2W to 30W which is a numerical increase of 15 times; 30 divided by 2 is 15 ) then this change represents log(30/2) = log(15) = l.1761Bel (try it).

The Bel as a unit is too large for our purposes. It is more convenient to use one tenth of a Bel and call it a decibel or just dB. 10dB = 1Bel.

The formula you will always use for calculating the difference in power levels in decibels is:

An increase in power level of 15 times is a change of 11.76dB (as we just calculated but multiplied by ten to convert it to decibels).

So, a change of 11.76dB is an increase of 15 times. For example:

From 2 watts to 30 watts - is 11.76dB.

From 2 milliwatt to 30 milliwatt - is 11.76dB. From 10 kilowatts to 150 kilowatts - is 11.76dB.

The 'S' meter on a receiver has (or should have) a logarithmic response. Most radio manufacturers use 6dB as the step between 'S' units.

The IARU Region 1 Technical Recommendation R.1 defines S9 (see top scale in figure 22-1) as 50µV at the receiver terminals assuming the input impedance is 50Ω. On the VHF bands the same recommendation defines S9 as 5µV across 50Ω. One 'S' unit as 6dB; a voltage ratio of 2 and a power ratio of 4.

A decrease in decibels, rather than an increase, is shown by adding a minus sign. A decrease from 15 watts to 1 watt (a decrease of 15 times) is a change of -11.76dB. To put it another way, 1 watt is 11.76dB below 15 watts.

Using decibels with current and voltage

We know that power is E2/R or 12R, so provided the input and output impedances are the same (and they normally are and will be for exam purposes - just remember for the future, that this explanation assumes the above) then:

P1/P2 = E12/E22 = (E1/E2)2 = I12/I22 = (I1/I2)2 

What this means is that to express a change between two voltages or two currents, the log formula must be modified to have a 20 in it rather than a 10.

E1 and E2 are the two voltages that we want to express as a change in decibels.

11 and 12 are the two currents that we want to express as a change in decibels.

As an example, suppose a signal going into the input of an amplifier has a level of 2 volts. At the output of the amplifier, the signal has a level of 50 volts. What is the voltage gain of the amplifier in decibels?

dB= 20Iog(E2/E2)

dB= 20Iog(50/2)

dB= 20Iog(25)

dB= 20 x 1.3979

dB= 27.95

The amplifier has a voltage gain of approximately 28dB.

Remember to use '20' in the formula for voltage and current and '10' for power.

Suppose a radio station has an output power of 25 watts. The operator connects a power amplifier to the transmitter to amplify the power to the antenna from 25 watts to 200 watts. What is the gain of the amplifier in dB?

dB= 10Iog(P1/P2)

dB= 10Iog(200/25)

dB= 10Iog(8)

dB= 10 x 0.903089

dB= 9.03

The amplifier connected to the transmitter has a power gain of approximately 9dB. The decibel does not measure an absolute value. The decibel is a measure of the ratio of two levels. It is ridiculous to say that power or voltage (or anything else) is so many decibels. Such a statement is meaningless unless there is a reference level given.

Amplifiers increase power levels, so we can say an amplifier has a gain of n decibels. Attenuators reduce power so we can say they have a loss of n decibels. Antennas can increase transmitter power by focusing the radiation into a narrow beam - much like you can increase the water pressure on a hose by placing a nozzle on it. So antennas have a gain expressed in decibels. You may be interested to know that organ pipes are attenuators. Organ tuners go around the pipes adjusting the air flow to each pipe to regulate the sound levels so that all pipes in a 'register' have the same attenuation.

ABSOLUTE MEASUREMENT USING DECIBELS

Measurements such as volts, amps and watts are absolute measurements.

So far we have dealt with dB as a method of comparing two values. However, there are some related units which can be used with the dB to refer to absolute values. To do this, a reference point must be given, such as 1 watt.

If the reference level is 1 watt, the unit is called the dBW. So 3dBW is 3dB above 1 watt and -3dBW is 3dB below 1 watt.

You do not need to know this for assessment purposes. However you will come across it and it is worthwhile to know this for a complete understanding of decibels.

By far the most common absolute and useful unit used in radio and communications is the dBm, which is the number of decibels above or below one milliwatt.

For example, what is the power of a 50 watt radio transmitter expressed in dBm? To express 50 watts in dBm we use the equation above:

dBm = 10Log(50W/1mW)

= 101og(50,000)

= 10 X 4.698

= 46.989dBm (usually rounded to and written as +47dBm).

This is a good figure to remember as many transmitters are 50 watts. Now, a doubling of power is an increase of 3dB, which means 50dBm is 100 watts, or 44dBm is 25 watts. Remember, if you increase power by 3dB, you double the power. If you decrease power by 3dB, you halve the power.

You don't have to be able to recall the following numbers in the exam, but after some experience, you will find these numbers to be quite useful.

-120dBm = typical VHF receiver sensitivity 0.22µV across 500

-30dBm  = 1 microwatt

0dBm     = 1 milliwatt

30dBm   = 1 watt

47dBm   = 50 watts

50dBm   = 100 watts

60ddBm = 1000 watts

70dBm   = 10 kilowatts

Do you see how much easier it is to use the decibel relative to a milliwatt than it is to use absolute measures?

Another commonly used unit is decibels relative to a volt or to a microvolt. By now you should have the idea. To express something in decibels relative to a volt [dBV], you place 1 volt in the denominator. To express decibels relative to a microvolt [dBµV], you place 1µV in the denominator of the equation.

Below is the formula for expressing something in decibels relative to a volt.

The symbol E here is used for the voltage in the numerator of the equation -you can use V if you prefer it.

Remember, if you are using voltage or current multiply the log by 20, for power multiply the log by 10.

A decibel is a ratio unless it is relative to something. Radio communications experimenters will often use decibels without a reference, which is fine as it is meant to be used either way. Just remember that you can't say, for example, the transmitter power is 30dB - this is a nonsense statement. You should say 30dB higher or lower than what it was, or 'by comparison with', or 'by reference to.' You could say, I am going to decrease the transmitter's power by 3dB (-3dB). Shortly, I will give you an example of a radio system using decibels and I am sure you will then see the advantages.

For your assessment, you will need to know the basic equations to express either a voltage ratio or a power ratio in decibels. You may be asked what an increase or decrease of ndB means.

For example, we have said that an increase in power by a factor of 2 is 3dB, so how do we convert 3dB back to a ratio, i.e., 2.

dB= 10Iog(ratio)

This formula can be transposed in terms of the ratio P1/P2 (ratio) = antilog(dB/10)

Let's try it for 3 dB:

(ratio) = antilog (3/10)

(ratio)= antilog (0.3)

1. enter 0.3 into your calculator's keypad;

2. press 'INV';

3. press 'log'; and

4. you get 2. [on some calculators you may get 1.9952623 - but for our purposes, this is close enough to 2]

Reminder; on some calculators you have to press INV (or Shift) log and then enter your number (0.3)

We have worked backward to show that 3dB is an increase of 2 (two times) while -3dB is a halving.

Do remember for voltage or current use 20 and not 10 - I know I harp on this but it is a very common mistake made by many students.

Your examiner may not expect you to do this calculation. Though it is in my view the easiest way. What the examiner will expect is that you know some common power and voltage/current ratios expressed in dB.

This table is power ratios (for voltage or current - See table 22-2.). So what is an increase in power of 5 times?

We can look at the table and see that 10 times is +10 and halve it (-3dB); or 5 times is 10dB - 3dB = 7dB.

I would much prefer if you could remember the two basic equations for power and voltage/current. I think it is easier to convert 5 times as a power ratio to dB by doing:

10 log(5) = 6.989 dB

More simpler I think, than remembering tables.

A voltage is increased from 1 volt to 100 volt, what is the change expressed in decibels?

20 log(100) = 40dB

Table 22-2 has the most important current and voltage ratios expressed in decibels

By now you are probably wondering why bother with all this decibel stuff? Well, it's sort of like metric and imperial - once you get used to it, it is just so much easier. Test equipment is frequently calibrated in decibels. How do you measure antenna gain (or loss)? In decibels of course. A filter connected to your transmitter has a loss expressed in decibels. The list goes on and on. For me, saying my transmitter power is +50dBm is just the same as saying 100 watts but decibels are more useful.

Skilled people, with their unaided senses, can just about detect a 1dB change. Most of us require 2 to 3dB change before we notice. A 6dB change is quite clear to even the most untrained. So, you can see that unless a new antenna or the tuning an amplifier is going to increase the signal strength at the other end by at least 2dB, nobody will notice.

You may find this strange, but increasing a transmitter's power from 100 watts to 130 watts is insignificant. It only sounds significant because 130 sounds like a lot more than 100, after all, it is 30 watts more! It is not significant at all, but for some it gives them a warm, fuzzy feeling!

Is it really worth boosting a transmitter from a nominal 100 watts to 130 watts? Assuming the signal path is unchanged, the increase in power output is only 1.14dB. This would not register on most S meters. To what level would you need to increase the power to achieve 2dB?* [see the end of chapter for the answer]

Here is an example of the use of decibels. Refer to the block diagram in figure 22-2, of a transmitter and receiver system.

The diagram shows an entire transmitter-receiver system. The path loss block represents the radio propagation path loss. Line loss (coax or whatever) is shown for the receiver and transmitter. Filter losses in dB (it's written on them) are also shown. The receiver has a 6dB gain pre-amplifier in it. The antenna gains are shown. The transmitter power is shown in dBm (100 watts). Now, without working in decibels, if I were to ask you what the received power was, this would be a nightmare.

What is the power after the 6dB amplifier in the receiver?

Just add and subtract.

50-3-5+4-100+6-2-1+6=-45dBm

Was that easy? -36dBm is a strong signal while -120dBm is verging on a noisy signal.

If you are lost with math and using the calculator, please speak to your Facilitator or Elmer for help. RES has a maths video tutorials available on DVD or direct download.

* Answer: 2dB = 1.58

So, you would need to increase the power output from 100 watts to 158 watts. Before embarking on such a step, you might want to consider the rating of the power output device and what safety factors you are willing to sacrifice. Most solid state devices wouldn't like such an increase.

23 - Electromagnetic Radiation

THE MECHANISM OF RADIATION 

The purpose of this chapter is to describe electromagnetic radiation and how it radiates. We also cover the concept of wavelength, frequency and period. We look at an overview of the electromagnetic spectrum.

Again I am faced with the dilemma of providing some information that you most likely will not be examined on. However, such information provides useful insights on the topic, which I believe makes it more interesting.

Though radio waves can have different wave shapes, I would like you to think of them as sinewaves for this exercise. Many are just that, sinewaves. We have already looked at alternating current and voltage at lower frequencies, for example, the mains, which is 50 hertz. AC produces radio waves. Yes, the AC we have already learned about. The difference is that the frequency of oscillation is much higher than 50Hz.

We have also learned that current, either alternating or direct (or any other), has associated with it electric and magnetic fields. We refer to these combined fields as 'electromagnetic fields'.

It was discovered that high-frequency electromagnetic currents in a wire (antenna), which in turn result in a high-frequency electromagnetic field around an antenna, will result in electromagnetic radiation which will move away from the antenna into free space at the velocity of light (approx. 300,000,000 metres per second).

Firstly, for electromagnetic radiation to occur the frequency must be reasonably high - I will explain this. Also, because the drawing of both electric and magnetic fields around a wire in three dimensions is difficult, I will stick to just two dimensions.

All we need to create an electromagnetic wave is to accelerate any charge. The obvious choice of the particle to accelerate is the electron because of its low mass. However, any charge would do.

The simplest way to do this is to get a high frequency generator (transmitter) and connect it to a dipole antenna. When we do this; electrons will flow in the same

direction in each leg of the dipole. When the RF driving force changes polarity then the electrons will flow in each leg of the dipole in the same but opposite to the previous direction. That flow of electrons will not be immediate in all parts of the dipole.

The charge movement will begin at the feedpoint (presume the centre) and move in one direction. By this I mean charge will propagate along the length of the antenna and this takes time, it is not instant, even if the electrons had no mass and moved as fast as photons ('c'; 300,000,000m/s) they would still take time to propagate down the antenna.

When electrons are accelerated, they create both magnetic and electric fields. These fields move with the accelerating electrons. The result is an electromagnetic field that forms around the antenna.

When the RF generator changes polarity , you might expect this field to collapse back into the antenna. The field does not have time to collapse. Another set of fields; electric and magnetic; called the E and H fields respectively is created around the antenna and the direction of the lines of force of this second field is the opposite of the first; and the first field is propelled away at the velocity "c."

If we could see this, it would look like figure 23.1

There are two fundamental fields associated with every antenna, an induction field and a radiation field. The field associated with energy stored in the antenna, is the induction field. This field provides no part in the transmission of electromagnetic energy through free space. However, without the presence of the induction field, there would be no energy radiated.

To understand the manner in which the induction field is produced, a low frequency generator will be connected to an antenna, and one cycle of operation explained.

Assume as in 23-2(A) that the generator produces a slight potential and having the instantaneous polarity as shown. With the initial application of the generator potential, the antenna capacitance acts as a short circuit, allowing a large flow in antenna current in the direction indicated. This, in turn produces a large magnetic field about the antenna. Since the current is minimum at the ends of the antenna the corresponding magnetic field at the ends will also be minimum. As time passes, charges accumulate at the ends of the antenna, which opposes the antenna current and produces an electric field. Eventually, the antenna capacitance becomes fully charged and stops the antenna current flow. Under this condition, the electric field is maximum, and the magnetic field is fully collapsed, as shown in figure 23-2(B).

As the generator potential decreases back to zero, discharging of the antenna potential occurs. During the charging process, the electric field collapses and current flows in the manner shown in figure 23-2(C). With the flow of current an associated magnetic field is produced. Eventually, the electric field completely collapses, the generator potential reverses and current is maximum, as shown in figure 23-2(D). As charges accumulate at the ends of the antenna, an electric field is produced and current flow decreases. This causes the magnetic field to begin collapsing, producing more current flow, with a greater accumulated charge and electric field. Eventually, the condition shown in figure 23-2(E) occurs, where the current is zero and the accumulated charges are maximum.

As the generator potential decreases toward zero, the antenna begins to discharge and the electric field collapses. When the instantaneous generator potential becomes zero, discharge current is maximum, and the associated magnetic field is maximum. Shortly thereafter, the generator potential reverses and the condition shown in figure 23-2(A) occurs. If fields in the vicinity of the antenna were plotted against time, a graph as shown in figure 23-4 would result.

Notice that the two fields are 90° out of phase with each other. Figure 23-4 shows that the two fields are displaced by 90° from each other in space (the H field exists in a plane perpendicular to the antenna, while the E field exists in a plane parallel to the antenna).

Since no energy was radiated from the antenna, all of the energy supplied to the induction field, was returned to the antenna by the collapsing E and H fields. The intensity of the induction field decreases, as the square of the distance from the antenna. For all practical purposes the induction field is considered to be a local field.

If the frequency of the antenna generator is increased, a radiation field as well as an induction field is produced. To understand the manner in which radiation occurs, it must be kept in mind, that the collapse of the E and H fields involved in the induction field requires time.

Though we have not discussed antennas yet, it is convenient here to use this antenna in describing the mechanism of radiation. A half wave antenna is one which is a half wave long at the operating frequency. When power is delivered to such an antenna, two fields are set up by the fluctuating energy. One, the induction field, is associated

with the stored energy, and the other, a radiation field which moves out into space at the speed of light.

At the antenna the intensity of these fields is proportional to the amount of power delivered to the antenna. A short distance from the antenna and beyond, only the radiation field exists. This radiation field is made up of an electric and magnetic component at right angles to each other in space and varying together in intensity.

Figure 23-5 shows the manner in which the radiation field is propagated away from the antenna. The electric and magnetic field components are represented here by separate sets of flux lines, which are at right angles to each other and to the radial direction of propagation.

The magnetic flux lines are shown as circular lines, having the axis of the antenna as their axis, so that they appear in the illustration as dots and crosses. The electric flux lines are closed or endless. The electric flux lines reverse direction, at precisely the places where the magnetic flux lines reverse. Their density varies along the radial direction in the way that the magnetic flux density varies. In fact, the electric flux density is everywhere, proportional to the magnetic flux density.

As time passes, these flux lines expand radially with the velocity of light, and new flux lines are created at the antenna to replace those that travel outward.

With a high frequency generator connected to the antenna, the induction field is created in the same manner as previously discussed. However, the generator polarity reverses before the electric field has had time to completely collapse. The reversed generator potential neutralises the remaining antenna charges, leaving a resultant E field stranded in space.

Since each new E field is generated with a polarity opposite to that of the preceding E field, an oscillating electric field is produced along the path of travel.

When an electric field oscillates a magnetic field is produced, having an intensity which varies directly with that of the E field. The variations in the E field intensity are equivalent to a current, even though they are is not associated with a charge. This is called a displacement current, and it produces a magnetic field in the same way as a conduction current. The variations in magnetic field intensity, in turn, produce an E field.

The two varying fields sustain each other, thereby resulting in electromagnetic propagation. Radio waves do not need a medium to travel along as the two fields of an electromagnetic waves support each other. A varying magnetic field produces a varying electric field and vice versa. Each field supports the other.

The action occurring at the antenna during radiation is similar to snapping a whip, in that the radiation components are snapped off and projected into space. The waves propagate from the antenna at the speed of light because light is also an electromagnetic wave.

It is the same with electromagnetic waves. The electric and magnetic fields propagate at right angles to each other and as one field collapses it generates the other. A collapsing electric field recreates the magnetic field, then when done, the collapsing magnetic field recreates the electric field. An electromagnetic wave is self supporting.

A WAVE GETS WEAKER 

There is attenuation in any medium, even a vacuum. Also, as the wave propagates it spreads out in all directions - the same energy in a greater volume means less field strength as we move away from the antenna. The wave attenuates at the wavefront in accordance with the inverse square law. If you double the distance from the source the wave intensity decreases by (1/2)2 or 1/4 which is a fourth. At three times the distance the wave intensity is now (1/3)2 or 1/9 or one ninth.

Why does an electromagnetic wave travel at the speed of light?

Well, I will give you the simple answer. Light is an EM wave. All waves travel at the same maximum velocity in free space and that velocity is denoted by little 'c' and is equal to approximately 300,000,000 metres/second.

A clue to why EM waves travel at 'c' is that they slow down when not going through free space. Why do they slow down?

EM waves propagating through a cable either RF or optical slow down. Why? Well, it must have something to do with the medium through which they are propagating. This is indeed the case. The velocity of an EM wave in a cable is determined by the permittivity and the permeability of that medium.

To remind you;

Permittivity is the ability of any material to concentrate electric lines of force.

Permeability is the ability of any material to concentrate magnetic lines of force.

We are inclined to think of free space or just 'space' as having no properties. However, this is not the case. Space has properties and is certainly never empty. It was James Clerk Maxwell who worked out the theory of electromagnetism or the combining of electric and magnetic fields into electromagnetic waves and describing their behaviour. Maxwell was the first to calculate 'mathematically' the velocity of c. He did this more accurately than anyone before him.

The permeability µo and permittivity εo can be just measured. These properties were known to Maxwell.

Maxwell discovered that these properties of free space determined the maximum velocity of an EM wave in free space just as they determine the velocity of an EM wave through any other medium. The values for µo and  εo for free space are given below, without units, as we do not need them. We just need Maxwell's equation for determining the velocity of c.

Permeability and Permittivity of free space. 

Now have we responded to the question posed at the beginning of the section?

Our eyes are biological receivers that can detect EM waves in the region of 400-700 nanometres. We generally call that the visible light spectrum. I often think that it is advantageous that our eyes only detect such a narrow bandwidth of EM radiation. If that were not the case, we would see the world awash with the light of colours yet to be determined. Even your cell phone would glow with light.

USES OF ELECTROMAGNETIC RADIATION

Naturally, since the electromagnetic radiation travels so fast (300,000,000 m/s), we can use it to transfer information from one place to another. In most cases because the velocity is so fast, it appears to be instant, though it is important to realise that it is not instant. The process of impressing intelligence or information onto an electromagnetic wave is called modulation.

In radio transmission, a radiating antenna is used to convert a time varying electric current into an electromagnetic wave, which freely propagates through a nonconducting medium such as air or space. In a broadcast radio channel, an omnidirectional antenna radiates a transmitted signal over a wide service area. In a point-to-point communication channel, a directional transmitting antenna is used to focus the wave into a narrow beam, which is directed toward a single receiver site. In either case, the transmitted electromagnetic wave is picked up by a remote receiving antenna and reconverted to an electric current.

Radio wave propagation is not constrained by any physical conductor or waveguide. Radio is ideal for mobile communications, satellite and deep space communications, broadcast communications and other applications in which the laying of physical connections may be impossible or very costly. The medium through which radio waves propagate is highly variable, being subject to diurnal, annual and solar changes in the ionosphere, variations in the density of water droplets in the troposphere, varying moisture gradients and diverse sources of reflection and diffraction.

Of course with the world communicating so much and using electromagnetic radiation, steps must be taken to have different users share different frequencies so that communications do not interfere with each other. The range of useful frequencies is a finite resource which many governments including ours (Australian) has capitalised on by selling parts of it very much like real estate even to the point of Spectrum Auctions.

THE ELECTROMAGNETIC SPECTRUM 

Refer to figure 23-7 showing the electromagnetic spectrum from low frequency long wave radio, to the exceedingly high frequency of gamma rays. Going from the values of radio waves to those of visible light is like comparing the thickness of a piece of paper with the distance of the Earth from the Sun, which represents an increase by a factor of a million billion. Similarly, going from the (frequency) values of visible light to the very much larger ones of gamma rays represents an increase in frequency by a factor of a million billion.

This enormous range of values is called the electromagnetic spectrum, together with the common names used for its various parts, or regions.

As frequency increases, it becomes increasingly dangerous to humans. Frequency up to about the top end of ultraviolet are non-ionising. From X-rays and up, EM waves are ionising and in this range all exposure should be avoided where possible. Of course, you cannot avoid it all. The Sun drenches the Earth in ionising and non-ionising radiation. However, to a degree, we have evolved to live in such environments. Additional exposure from X-rays and above are dangerous. EM waves below X-rays may also be dangerous. They may or may not be but below X-rays, we have safety limits on power, distance from the source and duration (duty cycle) of the source.

Frequency and Wavelength

This conversion must be known for examinations. The relationship between frequency and wavelength is:

Wavelength (λ) = c/f  Equation 23-2

Where 'c' is 299,792,458 metres per second. In radiocommunications, it is nearly always rounded to 300,000,000 metres per second.

A more useful form and easier to memorise is:

λ= 300 / F(MHz)

Calculating wavelength

For example, what is the wavelength of 146MHz, which just happens to be the middle of the 2-metre amateur band?

λ= 300 /146 = 2.0547 metres.

When describing this 'band', the wavelength is rounded to '2' metres. More often, accurate measurements of wavelength are required, such as cable lengths and antennas dimensions. Where more accuracy is needed, the wavelength as calculated from the above equation must be expressed using the appropriate number of decimal places.

Frequency bands have the following common names:

POLARISATION

The electric and magnetic fields of an electromagnetic wave are perpendicular (at right angles) to each other.

The polarisation of an electromagnetic wave is always described with regard to the direction of the electric field relative to the earth. If the electric field is vertical, relative to the earth, the wave is said to be vertically polarised. If the electric field is horizontal relative to the surface of the earth, then the wave is said to be horizontally polarised.

If the antenna is horizontal with respect to the earth, the wave is horizontally polarised. If the antenna is vertical with respect to the earth, the wave is said to be vertically polarised. The important factor is that the direction of the electric field is what determines whether a wave is called vertically or horizontally polarised. When there is propagation via the ionosphere, it is possible for a wave radiated from a vertical antenna to have its polarisation twisted - this is called Faraday Rotation. So even though a wave may be radiated from a vertical antenna it can have its polarisation rotated by the ionosphere and become horizontal. For this reason, we do not define the polarisation of a wave by the type of antenna which is radiating it. We always define polarisation by the direction of the electric field. Never assume that radiation from a horizontal or vertical antenna will be received at a remote location by ionospheric propagation in the same polarisation that it left the antenna.

Radiation and Reception

How much electromagnetic energy can leave an antenna depends on the relationship of its length to the wavelength of the current.

Just as electric and magnetic fields surround a wire or antenna carrying an RF current, so a wire placed in an electromagnetic field will have a current induced in it. As far as antennas are concerned, transmitting and receiving antennas are basically interchangeable, apart from power handling considerations. In fact, a so called principle of reciprocity exists, which states that the characteristics of antennas, such as impedance and radiation pattern, are identical regardless of their use for transmission or reception.

To receive a vertically polarised wave (electric field vertical), a vertically polarised antenna should be used.

However as explained earlier Faraday rotation over a high frequency (HF) circuit can modify the polarisation. Propagation effects such as diffraction, refraction and reflection can alter the polarisation of VHF waves and above.

A different way of looking at impedance

We have talked about impedance in the past as belonging to something, i.e. resistors, capacitance and inductance. Impedance is the total opposition to current flow in an AC circuit. When we talk about electromagnetic waves our concept of impedance needs to be broadened. This applies in particular to transmission lines (e.g. coaxial cable) and antennas. Impedance should not be thought of as belonging to a thing but as the ratio of voltage over current.

From Ohm's law R=E/I and we can extend that to impedance with Z=E/I. Frequently we have been talking about the voltage across something and the current through the same thing, to calculate the impedance. This might appear a bit of a leap, but when talking about electromagnetic waves, we need to take the concept of the impedance belonging to a component(s) away and think of the impedance as the ratio E/I.

This is particularly true of antennas and transmission lines. I am just preparing you for that here. For example, free space has impedance! When an electromagnetic wave travels through free space its electric and magnetic components settle into a particular ratio that just happens to be 120πΩ or 377Ω - so we say the impedance of free space is 377Ω.

Similarly, an electromagnetic wave travelling down a transmission line will cause particular voltage and current ratios to exist at different points. We then have to think beyond the transmission line and reflect on the ratio of voltage and current at various points on it to understand or define the impedance at those points.

In other words, electromagnetic waves can be impedance up-setters. A wave travelling down a cable may determine the impedance of the cable. This will become clearer as we go (I hope). For now, impedance is the total opposition to current flow in an AC circuit. Introduce electromagnetic waves into transmission lines and antennas and the wave and its behaviour will be what determines the impedance at any given point. Impedance is always the ratio provided by Ohm's Law E/I.

We will also be discussing the propagation of waves. It will help if you think about light waves. We are all very familiar with the behaviour of visible light. Whatever we can imagine visible light doing, the same can happen with invisible, electromagnetic waves. The reason for this is that they are one and the same thing, it is just the frequency

that is different. Reflection, refraction, absorption and anything else you can think of pertaining to visible light, applies equally to all electromagnetic waves.

DOPPLER SHIFT 

When a car blowing its horn approaches you the pitch (frequency) of the horn sounds higher. As it immediately passes, you hear the actual pitch of the horn. As it moves away from you, you hear a lower pitch. This effect is called Doppler Shift.

The same happens to electromagnetic waves which are being radiated or received from a moving source. Doppler shift is most noticeable when communicating through satellites. When the satellite is moving at high velocity towards you, the frequency of your receiver has to be tuned a little higher than the actual frequency. When the satellite moves away from the receiver has to be tuned to a lower frequency.

Stars give off visible light. Red light is a lower frequency than blue light. Scientists are able to tell if stars are moving towards us (or us towards it), by the blue shift (increase in frequency) of the light reaching us. If the star is moving away, then there will be a red shift.

This is also precisely how police Doppler Radar works. An electromagnetic wave pulse is sent to the target (the vehicle). If the reflected wave is echoed on the same frequency, the vehicle is not moving. If the car is moving, there will be a down shift or an upward shift in the frequency of the echo. How much shift there is can be used to compute exactly how fast the vehicle is moving.

Doppler shift only plays a part in radiocommunications when the relative velocity between the receiver and transmitter is high. An example is communication with or through a satellite. When communicating through satellite, the Doppler correction is done manually by the operator or under computer control. We never really have to calculate the actual frequency shift.

The relationship between the observed frequency f and the emitted frequency f0 is given by:

James Clerk Maxwell (13 June 1831 - 5 November 1879) James Maxwell was a real polymath. As well as his scientific discoveries, he loved poetry and enjoyed drawing. Though befitting of his image as eccentric, many contemporaries mentioned he lacked grace and confidence in social situations. Maxwell's greatest contribution to science included:

The observation electromagnetic fields travel at the speed of light showing the connection between light and electro- magnetism. Prediction of waves and oscillating electric and magnetic fields.

Writing equations for electromagnetism, later known as Maxwell's equations. The concept of the electromagnetic field, which was later worked on by Albert Einstein, leading to his theory of special relativity.

James Maxwell is considered by many to be the one of the three greatest ever scientists. On a par with Isaac Newton and Albert Einstein.

Einstein himself once described Maxwell's work as the: "most profound and the most fruitful that physics has experienced since the time of Newton."

24 - Semiconductors I

The objective of this chapter is to cover how semiconductors work. Discuss the operation of bipolar junction transistors (BJTs), FETs MOSFETs and SCRs, as well as a few of the characteristic circuits in which they are employed.

Solid state devices

Solid state devices are much smaller physically, more rugged and lighter than vacuum types, but cannot withstand heat as well, changing their characteristics as they warm. However, many newer special solid state devices will operate at much higher frequencies than any vacuum device.

SEMICONDUCTORS

The outer orbit, or valence electrons of some atoms, such as metals (conductors), can be detached with relative ease at almost any temperature and may be called free electrons. This is why metals are good conductors. These valence electrons can move outward from a standard outer orbit level into a conduction level or band, from which they can be easily dislodged. Such materials make good electrical conductors. Other substances such as glass, rubber and plastics, have no free valence electrons in their outer conduction bands at room temperatures and are therefore good insulators.

A few materials have a limited number of electrons (4) in the conduction level (outer orbit or valence band) at room temperatures and are called semiconductors. Applying energy in the form of photons (small packets of light or heat energy) to the valence electrons moves some of them up into the conduction band and the semiconductors then become better electrical conductors. Energy of some form is required to raise semiconductor electrons to a conduction level. Conversely, if an electron drops to the valence level from a higher conduction level, it will radiate energy in some high frequency form such as heat, light, infrared, ultraviolet and, if the fall is significant enough, X-rays.

The semiconductors, germanium and silicon have four outer valence electrons. Semiconductors can be laboratory grown, this makes mass production of them easy.

COVALENT BONDING

In nature atoms are more stable and 'like' to have eight valence (outer) electrons called an octet. Chlorine has seven valence electrons. If two Chlorine atoms are brought near each other, they will snap together and form a Chlorine molecule. Each atom is sharing one of its valence electrons with the other. This covalent bonding makes the Chlorine molecule more stable.

Noble gases have eight valence electrons called an octet, this is what makes noble gases so stable.

In the case of germanium and silicon which only have four valence electrons. A special arrangement occurs when they rub shoulders. Germanium or silicon in pure form creates what is called a crystal lattice structure. The four valence electrons of each atom in a crystal lattice structure share themselves with the adjacent orbits of all other electrons in the crystal lattice structure. In this way by borrowing electrons from neighbouring atoms a type of shared valency of eight is created. Consequently, the valence electron arrangement is very stable and it is difficult to make these electrons participate in current flow. The great breakthrough in physics (electronics) was the discovery of how the characteristics of pure germanium or silicon could be changed dramatically by adding impurities (other atoms) to the crystal. Adding impurities disturbs or upsets the crystal lattice structure.

INTRINSIC SEMICONDUCTOR LATTICE

A perfectly formed intrinsic semiconductor crystal lattice is illustrated in figure 24-1. Such a crystal acts more like an insulator than a conductor at room temperature. I have drawn the crystal in only two dimensions (not being much of an artist). Shown are the valence band ( the outer orbit of each atom) and the four valence electrons. The valence electrons are of course not stationary, but orbiting around the atom as if on the surface of a sphere. The sharing of valence electrons is called covalent bonding. This arrangement is very stable electrically.

Electrons are locked into the crystal lattice and at normal temperatures the crystal is neither a good insulator nor conductor.

DOPING (N-type)

Doping is the process of deliberately adding impurities to the crystal during manufacture. Say we added some arsenic, which has five valence electrons to a pure semiconductor crystal. The ratio of germanium to arsenic is about a million to one.

Arsenic is pentavalent (five outer electrons) and cannot fit into the crystal lattice structure. What happens is four of the arsenic electrons participate in the sharing (covalent bonding) and one is left out!

The crystal lattice shown in figure 24-2 has one atom in a million with an excess outer ring electron not being tightly held. This type of doped semiconductor is called N-type.

It should be understood that 'N1 type semiconductor does not have extra electrons electrically. N-type semiconductor does not have a negative charge. What is 'extra' in N-type material is electrons which do not fit into the crystal lattice structure. These extra electrons are not locked into the crystal lattice structure, so they are much easier to move.

When an electrostatic field (by application of an emf) is developed across such arsenic-doped germanium, a current will flow. The N-type semiconductor is about 1,000 times better as a conductor than the intrinsic semiconductor. Doped germanium with such relatively free electrons is known as N germanium and is a reasonably good conductor. To form N-silicon, phosphorus can be used as the dopant - you do not need to remember the dopant. Merely by adding a small amount of impure pentavalent atoms to a pure crystal, we convert it into a conductor by disrupting the harmony of the crystal lattice structure.

DOPING (P-Type)

When germanium is doped with gallium, which has three valence electrons (tri-valent), the crystal lattice is again disrupted. This time, there is an area, or hole, in the crystal lattice structure, a region that apparently lacks an electron. While the hole may not actually be positive, at least it is an area in which electrons might be repelled to by a negative charge. This positive appearing semiconductor material is called P-germanium or just P-type.

When an electrostatic field is impressed across a P-type semiconductor, the hole areas act as stepping stones for electron travel through the material. It can be said that hole current flows in a direction opposite to the electron flow. Note that both N-germanium and P-germanium have zero electric charge because both have an equal number of electrons and protons in all of their atoms. One dopant used to produce P silicon is boron.

HOLES

I am going to talk about holes for a bit, as it seems to be a stumbling block for many. I have drawn the hole as a gap in figure 24-3. The hole is a missing electron in the crystal lattice structure which destroys the crystals insulating properties. It is very easy with N-type material to visualise that electron flow can take place. With a hole, it is a little harder and I find some textbooks a little confusing on this issue. A hole is a hole in the crystal lattice structure. Because the lattice is not complete in the location where a hole is, electrons can move into the hole and in doing so, they create a hole from whence they came.

SOME FOOD FOR THOUGHT

A hole is a missing electron in the crystal lattice structure. A hole is not a positive charge.

A hole like any hole can be filled.

A hole can be filled with an electron.

When an electron does fill a hole - then the filled hole disappears, but where the electron came from there is now a hole.

A hole can be thought of as positive for behavioural description purposes.

An electric current is an ordered movement of electrons.

Holes allow electrons to move in the crystal by giving them somewhere to go i.e. filling a hole.

When an electron moves to fill a hole it leaves a hole from whence it came.

I think most of us have seen the toy shown in figure 24-4. A flat panel of plastic squares with pictures or numbers on them and the objective is to move the squares around into some order, either to get the numbers in order or to make a picture. Would you be able to slide the squares around if the game was made without a missing square? No, of course not. By leaving a square out, leaving a hole in the puzzle, it makes it possible to slide the squares around by moving them into a hole. In moving a square into a hole you create a hole, making it possible to slide other squares into that hole. Think of the squares as electrons and their ability to move is made possible by the presence of the hole (missing square).

Slide 14 (figure 24-4) could be moved straight up. That would leave a hole where slide 14 was. Now, if you were to put this puzzle on autopilot and sit back and watch it, what would you notice about the way the hole moves? It moves in the opposite direction to the slides. So if the numbered squares are electrons the hole is behaving like a positive charge in that it moves in the opposite direction to electrons. Some references do not explain this very well and go on to talk about "hole current" moving from positive to negative, I believe this to be confusing. Electrons are the only current. Though I will be talking shortly about holes moving, holes do really move when you fill them. However, all of the real moving is done by electrons falling into holes in a P-type semiconductor.

The P-type semiconductor material is a conductor because of the presence of holes in

the crystal lattice structure. Doped silicon has considerably more resistance than germanium and finds its uses in higher voltage and current applications. Also, it does not change its resistance when heated and it can withstand greater temperatures without its crystalline structure being destroyed.

So what?

Well, we have not seemed to have achieved much have we? We have taken a perfectly good semi-insulator (semiconductor) and turned it into a conductor by adding pentavalent impurities (N-type) or trivalent impurities (P-type). The magic starts when we combine the two, that is, we make one side of the crystal N-type and the other P-type. They are not made separately and then stuck together; crystals are grown and doped on different sides of the same crystal in the laboratory.

SOLID-STATE DIODES

Before we start, the term solid state is only used because the alternative devices before them were the electron tube devices.

Let's take a piece of N type and P type semiconductors and join them together. The area in which the N and P substances join is called the junction. We don't really take one of each and physically put them together. It is achieved by doping different sections of the same piece of intrinsic semiconductor.

Some of the relatively free electrons in the N-type material at the junction fall into some of the holes in the P-type material at the junction. So, right at the junction, there are no free electrons (in the crystal lattice structure) and no holes, as free electrons from the N material have filled some of the holes in the P material. This creates a region at the junction, which has neither free electrons nor holes and it is called the depletion zone.

This develops an area at the junction that is actually slightly negative on the P side (because electrons have filled holes) of the junction and slightly positive on the N side (because electrons have left to go and fill holes). This produces a barrier to any further electron flow of about 0.2 V with germanium and 0.6-0.7 V with silicon diodes. This small potential is called the barrier potential.

We have created a semiconductor diode (PN junction). In figure 24-5 the depletion zone is shown at the junction drawn as a small band.

The whole (no pun intended) diagram is exaggerated greatly as the depletion zone is extremely narrow and there are many more holes and electrons in a real PN junction. Don't forget the diode in figure 24-5 right now has a very small potential across it called the barrier potential. We can't do any work with that voltage. It is not a small battery; it is a weak electrical pressure, created by hole and electrons recombining at the junction. However, this barrier voltage is real and affects how the PN junction diode operates.

Applying a voltage to a PN-Junction diode

The diode of figure 24-6 has the polarity applied to it as shown, The N; end of the diode is called the cathode (K) and the P; the end is called the anode. Remembering electron tubes, if we applied negative to an anode and positive to a cathode would we get conduction? No, we would not. This is called reverse bias.

REVERSE BIAS

In figure 24-6, we have applied an external electrical pressure. Electrons are attracted toward the positive terminal whilst holes, thinking of them as if they were positive charges, are attracted to the negative terminal.

No current flows through the PN junction, which from now on, we will call a diode. The depletion zone is widened as electrons and holes are moving away from the junction. The diode is said to be reverse biased. I have drawn the schematic symbol of a diode, so you can see that for reverse bias, positive is connected to the cathode and negative to the anode. The left-hand side of the diode shown is the cathode.

Recall when we discussed power supplies without really describing how a diode worked. I suggested you look at the diode schematic symbol as an arrow. In figure 24- 6, the arrow is pointing to the left. I asked you to remember that conduction was only possible in the opposite direction of the arrow. Electrons can only flow in the direction cathode-to-anode, against the arrow.

We have said that no current flows through the diode when it is reverse biased. There is an extremely low leakage current which for most practical purposes can be considered to be zero. Also, if you increase the reverse bias voltage high enough you will force breakdown conduction an damage the diode. This reverse breakdown voltage is called peak inverse voltage (PIV).

The reason why you do get a reverse leakage current in a diode is that some of the N material will have just a few holes in it and some of the P material will have some electrons in it. These are due to extremely small amounts of contaminants. So there is a minor 'ghost' diode the opposite way around to the 'real' diode. These contaminants are called minority current carriers. The real holes and electrons are called the majority current carriers. If you like, you have a majority diode one way and a minority diode the other way. When the majority diode is reversed biased the minority diode is forward biased and this accounts for the small leakage current.

The reverse leakage current of a PN junction increases with temperature. Reverse biased PN junctions can be used to measure temperature, by amplifying and measuring the reverse leakage current.

FORWARD BIAS 

Now let's reverse the polarity. I know you are aware that the diode is going to conduct but let's look at exactly what goes on. We are going to think of the holes as positive charges when we really know they aren't - we covered that issue with the 'puzzle' example earlier.

We have now applied a negative potential to the N material (cathode) and positive to the P material (anode). Provided this potential is greater than the barrier potential (0.2V germanium, 0.6V silicon) the depletion zone will be flooded with electrons and the diode will conduct as shown in figure 24-7.

You may well ask, "why don't all the electrons move across the junction and fill up all the holes." We all know that current flow is electrons. In figure 24-7 the right-hand side is P-type (holes) and electrons leave the P-type anode and flow to the positive terminal of the battery. Every electron that leaves the anode creates a hole. The holes move toward the junction to be filled by more electrons.

Such a diode could be used in a rectifier circuit. All diodes have a maximum current rating as well as a peak inverse voltage rating (PIV). A diode, for example, may be rated at 1 amp 400V PIV. Diodes come in many shapes, sizes and package types. All of them more or less work on the principles we have described here. Even LED's (light emitting diodes) are just special PN junction diodes.

Figure 24-8 is a typical rectifier diode that could be used as part of a power supply. The band around one end marks the cathode. A group of four such diodes could be packaged into a bridge rectifier.

CHARACTERISTIC CURVE OF A DIODE 

The graph in figure 24-9 shows the operating characteristics of a diode. The forward voltage is the voltage that biases the diode 'on' and it conducts. The reverse voltage causes the diode not to conduct or block current. However, if the reverse voltage is made high enough, the diode will breakdown and conduct in the reverse direction.

This (break down) is either the Zener effect if the emf value at breakdown is less than about 5V, or Avalanche effect if it is more than about 5V. This is not a normal operating condition for most semiconductor diodes and may cause lattice damage, ruining the diode.

ZENER DIODES

The reverse voltage breakdown effect, however, is used in special zener diodes. These diodes are deliberately operated under enough voltage to cause them to conduct in the reverse direction. A resistor must be connected in series with a zener diode to prevent the junction from being destroyed. The circuit across which the diode is

connected will not increase in voltage over the zener breakdown voltage. For this reason, zener diodes are used as shunt (parallel) voltage regulating devices. Zener diodes are used to provide a regulated DC voltage in low power applications. So if some part of a 12 volt DC circuit required 5V DC at low power, then a zener diode with an appropriate series resistor could be used to provide a regulated 5 volt DC output in spite of variations in the 12 volt DC input voltage. A good way to remember the symbol of a zener diode, as shown in figure 24-10, is to note the shape of the cathode line on the diode as representing the forward and reverse current characteristics of a diode shown earlier in figure 24-9.

THE CIRCUIT OF A ZENER VOLTAGE REGULATOR

The circuit diagram of a zener used as a voltage regulator is shown in figure 24-11. The unregulated DC to the circuit varies from 8 to 12 volts. Rs is a current limiting resistance to prevent the zener from being destroyed.

Remember, a zener regulator is operated with reverse bias and to the point where it breaks down and conducts in the reverse direction. For some, the term 'breakdown' is confusing. Breakdown does not mean the zener is destroyed or busted! Break down means it is forced to conduct in the opposite direction (from the anode to cathode). Normally a diode operated beyond breakdown is destroyed. However, zener diodes are designed to operate in the breakdown region with a small breakdown current. A zener would be destroyed just like any other diode except for the current limiting resistance Rs. Under these conditions the voltage across the zener is constant. In figure 24-11 the voltage across the zener will be 5.6 volts (it is a 5.6 volt zener - you buy them with a voltage rating). Irrespective of input voltage fluctuations, the voltage across the zener will be a very constant 5.6 volts.

Rs and the zener form a series circuit. The sum of the voltage across the zener (5.6V) and across Rs is equal to the input voltage. Suppose the unregulated input voltage was at a maximum (12V), then the voltage across Rs would be 12-5.6 = 6.4 volts.

As an important rule-of-thumb, the reverse zener current is about 1/10th of the maximum current drawn by the load - the load draws 100mA so one could expect the reverse current of the zener to be 10mA. The zener and the load form a parallel circuit - so the sum of the branch currents is equal to the current through Rs. The current through Rs must then be 100+10=110mA. So we know the maximum current through Rs is 110mA. What is the maximum voltage across Rs? The maximum input voltage is 12V, so the maximum voltage across Rs will be 12-5.6 = 6.4 volts. We can now calculate the resistance of Rs from Ohm's Law:

Rs= E(across Rs)/ I(through Rs)= 6.4 volts/ 110 mA = 58Ω.

Just as important is the power rating of Rs:

Power (of Rs)= E(across Rs) x I(through Rs)= 6.4 volts x 110 mA = 0.704 watt.

EFFICIENCY OF SHUNT REGULATORS 

Shunt regulation of voltage is the most inefficient. Look at the circuit of figure 24-11. The current through the zener plus the current through the load is constant. This is because the voltage across the zener and the load is more or less constant at 5.6V. When the load is removed all of the current flows through the zener. So with no load (meaning the regulator is doing nothing for us) maximum current flows through the zener. The zener is then creating maximum heat (losses) when no load is connected.

For this reason shunt regulators are only used in low power applications. For higher power, pass transistors or a darlington pair would be used in conjunction with the shunt regulator. For even higher efficiencies an electronic regulator circuit would be used. For still high efficiencies a Switch Mode Regulator is used. See the discussion of these in the chapter on power supplies.

VARACTOR OR VARICAP

A reverse biased diode (or PN junction) does not conduct. If you refer to when we applied a reverse bias to a PN junction, we saw the width of the depletion zone increased. If we increase the amount of reverse bias further (without reaching breakdown), the width of the depletion zone would widen even more. If we reduce the reverse bias, the depletion zone will narrow. Now, if we continually varied the amount of reverse bias, the width of the depletion zone would also continuously vary. Each time the depletion zone changes in size there must be some movement of electrons in the circuit. However, electrons never move across the junction. The junction, under reverse bias, is an insulator.

Does this movement of current on each side of an insulator remind you of capacitance? It should because a reversed biased diode will act just like a small capacitor whose capacitance can be changed by altering the amount of reverse bias. If you like to think of it another way, the depletion zone is the dielectric, which can be made to change in thickness or width by the amount of reverse bias.

So a reverse biased diode can be used to create a voltage variable capacitor, the symbol of which is shown in figure 24-12. There are purpose made diodes for use as varactors, though in practice almost any diode can be used for this effect. This ability of a diode to behave as a variable capacitance is extremely useful. The frequency of a tuned circuit or a quartz crystal can be made to vary by using a varactor diode. By using a variable resistor to adjust the reverse bias, the capacitance of the diode can be made to vary, which in turn will affect the frequency of the tuned circuit.

Though we have not discussed single sideband (SSB) reception yet, many readers will know that with an SSB receiver you have to tune the radio finely to the received stations with a control most often called a BFO (Beat Frequency Oscillator) or clarifier. The BFO is usually a variable resistor in combination with a varactor to make small changes to the receiver's frequency. On amateur transceivers, the 'clarifier' is called the 'RIT' (Receiver Incremental Tune).

LIGHT EMITTING DIODES

In any forward biased diode, free electrons cross the junction and fall into holes. When electrons recombine with holes, they radiate energy. In the rectifier diode, the energy is given off as heat. In the light emitting diode (LED), this energy radiates as light.

It takes energy from the source to move an electron from the valence level to the conduction level. When electrons drop back to the valence level, they will emit this extra energy in the form of photons (light).

An electron moving across the PN junction moves to a hole area. This can allow a nearby conduction electron to fall to its valence level, radiating energy. In common diodes and transistors made from germanium, silicon, or gallium arsenide, this electromagnetic radiation is usually at a heat frequency, which is lower than visible light frequencies. With gallium arsenide phosphide the radiation occurs at red light frequencies. Gallium phosphides produce still higher frequency (yellow through to green) radiations. Gallium nitride radiates blue light.

Light emitting diodes come in many colours. The short leg on the diode identifies the cathode so if you want the diode to make light it needs negative on the cathode for forward bias. Typical forward current for the conventional LED is 10-20mA.

There are several photodiodes and photosensitive devices. The photodiodes convert photons to electric emf. There are also a number of other specialist diodes. For examination purposes, we have more than covered enough material here. Also, the depth of the material is more than adequate. You will not be asked to describe the operation of a diode at the electron/hole level, although you should remember the terms used thus far and what they mean.

AN APPLICATION FOR A DIODE

Power diodes are made from silicon. Besides being used as rectifiers, one very useful application for a single power diode is reverse voltage protection in radio.

All mobile (used in vehicles) radio equipment is very much prone to being connected to the source of power the wrong way. I have first hand experience of doing this myself. Connecting the power supply or battery to a mobile radio (or any radio) the

wrong way around would be devastating to the radio if some sort of reverse polarity protection did not exist. All mobile radio equipment has an inline fuse. Where the negative and positive leads of the power supply enter the equipment, there is a reverse biased silicon diode. When the power supply polarity is connected the correct way, this diode is reverse biased and acts as an open circuit. If the user accidentally connects the radio to the wrong polarity, the diode becomes forward biased and conducts heavily, blowing the fuse.

Most times when this happens, the diode is destroyed and remains as a short circuit across positive and negative. Backyard technicians will often fix the problem by just cutting one lead of the diode removing it from the circuit and replacing the fuse. Of course, they will charge you too many dollars for this two-minute job! With the diode out of the circuit, the next time the radio is connected to reverse polarity you can say goodbye to the radio for good.

DIODE CLAMPING

A diode will not conduct when forward biased if the amount of forward bias does not exceed the barrier potential. The barrier potential for silicon diodes is approximately 0.6V or 600mV. Suppose we had an application where we had signals that are normally below 600mV but if something was to go wrong and the signal went over 600mV we want some sort of over volt protection.

One such application is a landline telephone receiver. Landline telephones are subject to all sorts of static and other unwanted induced line voltages. The normal operating voltage for a telephone receiver (the bit you put against your ear) is less the 600mV. So if we connect two back to back silicon diodes across the receiver they will have no effect on the receiver's normal operation. Should there be a large static crash or anything else that induces more than 600mV on the telephone line then one or both of the silicon diodes will conduct, effectively short circuiting the telephone earpiece, and saving the user's eardrum.

This is just one of many applications for diode clamping. It can be used in a receiver or transmitter to clamp a signal path from becoming too high a level. It could be used as the limiter in an FM receiver. Diodes can be configured to clamp either the positive or negative side of a signal. The clamping diodes can be biased to permit a wide range of clamping voltages other than 600mV.

TRANSISTORS

The basic transistor can be thought of as two diode junctions constructed in series. From the bottom, there is a contact against an N-type emitter element. Next to this is a thin P-type base element, with a metal electrode connected to it, forming the first PN junction. A second N-type collector element is added, with a contact on it, forming the second PN junction. This produces an NPN transistor.

This type of transistor is called a bipolar junction transistor (BJT). The important characteristics of construction are:

The base region is very thin and lightly doped.

The emitter region is heavily doped.

The collector is large and usually connected to the case as a heat sink, so that heat can be removed from the transistor.

With just the collector supply connected, no current will flow in the collector circuit as the top PN junction - the one between collector and base - is reverse biased.

Consider when the base-emitter junction is forward biased as shown in figure 24-17. The heavily doped emitter region floods the thin base region with charge carriers (electrons). The base region is lightly doped compared to the emitter. All of the electrons passing across the forward biased base-emitter junction are looking for a hole to fall into. There are more electrons crossing the lower junction than there are holes available on the other side (in the base) to meet them. I like to think of the base region as becoming saturated with charge carriers (which are electrons for an NPN transistor). The excess of electrons come under the influence of the collector voltage (which is higher than the base voltage) and consequently electrons flow in the collector circuit.

The important aspect of the transistor is that small amounts of base-emitter current can control large amounts of collector current. If the base current was made to vary, say by the insertion of a carbon microphone (which is a sound dependent resistor), then the collector current will be an amplified representation of the base current. The transistor is an amplifier. Since the BJT transistor uses a small base input current to control a larger output collector current, it is called a current amplifier. Where there is current, there is voltage. Z=E/I and because the current is significant, the BJT transistor is a low input impedance device.

The symbol for a PNP transistor (figure 24-18) is the same as the NPN except the arrow is pointing IN rather than OUT and all the polarities would be reversed.

It is interesting to note that the name transistor comes from "transfer resistor." Another way of looking at the operation is that without the base-emitter junction being forward biased there is no collector current.

When the base-emitter junction is forward biased the resistance between collector and emitter decreases from infinity (or some very high value) and current flows in the emitter circuit. Small variations in the amount of base-emitter current cause the resistance between collector and emitter to vary greatly, but in proportion. Therefore, the collector current faithfully follows the base current but is much larger and supplied with a higher voltage. The collector current is greater than the base current, so the transistor has amplified.

The amount by which an amplifier amplifies is called the gain. The amount by which a transistor amplifies is called Beta and has the Greek symbol β. The beta of a transistor is calculated from:

The triangle symbol 11 is the Greek letter delta and is the mathematical shorthand for 'change in'. Thus, ΔIc and ΔIb are the change in collector and base currents respectively.

So the Beta (β) or gain of a transistor, is the change in collector current divided by the change in base current. 

A small variation of base current can control 50 to 150 times as much collector current. Thus, the transistor is an ideal control and amplifying device. A junction transistor of this type can be called a bipolar junction transistor (BJT) to differentiate it from a field effect transistor (FET) discussed later.

If a junction transistor has its base-emitter current changed from 10 to 30 milliamps and this causes the collector current to change from 50 to 250 milliamps, what is the current gain or Beta of the transistor? The change in base-emitter current is from 10mA to 30mA = 20 mA. The change in collector current is from 50mA to 250mA = 200 mA. The Beta is therefore 200/20 = 10. The transistor has a current gain of 10.

Comparing a triode and BJT

A triode electron tube is also an amplifier as we have learned. There is one significant difference between a triode and the BJT. Firstly, just to refresh your memory, a triode amplifies by adjusting the negative voltage on the control grid, which in turn can control the large cathode to plate current, resulting in amplification.

A triode is often called a voltage amplifier because it is voltage on the control grid which controls the anode current. Also, because there is no input current to a triode's control grid (Z=E/I), the input impedance of any electron tube is high. A BJT is called a current amplifier because it is base current which controls the much larger collector current. A BJT is a low input impedance amplifier.

The control-grid cathode circuit of a triode does not have any current flowing in it (there are exceptions). This is important. Since a triode can amplify with voltage alone, a triode consumes no power from the input source. From P=EI, if you have no 'I' you have no 'P'. A triode is a high input impedance amplifier, whereas a BJT is a low input impedance amplifier.

Whether a device is a voltage amplifier or current amplifier is irrelevant to the final amplification, though sometimes the input impedance is important. The triode has a significant advantage in being able to amplify a weak signal from a low power source without taking any power from it.

The advantages of the BJT though, are enormous: size, low heat, low power consumption, lower voltages, easier construction and much more.

Amplifier Input Impedance

What is the big deal about input impedance of an amplifier? Take a high input impedance like the electron tube. Only voltage is used on the control grid to control the output current. There is no input current. P=EI; without I there is no P. Suppose an antenna was connected to the control grid. There is only a very small amount of power arriving at the input of a receiver. You cannot cook potatoes with the power

coming off an antenna. The power from an antenna is measured in femto-watts. Femto means 10-15. So an amplifying device that does not need power (high input impedance) is the best to use. If you do take power from an antenna, remembering that it is a resonant circuit, you would drastically lower the Q of the antenna. BJT's are low input impedance; so we have to do tricks with transformers to make them look like a higher input impedance.

Memory Jogger: 

Always remember, if you are trying to work out, or asked to work out if a transistor has the correct polarity voltages to operate:

The base-emitter must have forward bias.

The collector-base is reverse biased.

If the bias voltage is correct, current will flow against the arrow in the symbol.

The collector voltage must also permit current flow against the arrow.

A LITTLE ABOUT NOISE 

We tend to think of electricity (electron flow) as being fluidic or smooth. This is not correct; electricity is made up of lumps - very small lumps called electrons. Noise is produced whenever an electron does not do what it is supposed to do when it is supposed to do it. In the Electron tube, electrons might collide with secondary electrons emitted from the anode. Imagine a situation in a PN junction where an electron is ready to fall into a hole, but no hole is to be found! For that very small instant that electron represents noise. Any random or unwanted electron motion, or lack of motion, in semiconductor devices, is noise.

Don't get the wrong idea - PN junctions in transistors are wonderful low noise amplifiers, however when it comes to super sensitive receivers like those used for radio astronomy, PN junctions and hole-electron recombination is just too noisy. We shall see later that there are semiconductor devices that amplify and don't have a hole-electron recombination, making them lower noise devices.

POINT CONTACT DIODE

A point-contact germanium (figure 24-19) or silicon diode is a semiconductor pellet (of germanium or silicon) with fine gold-plated tungsten wire with a diameter of about 80 to 400 microns (millionths of a metre) a sharp point, makes contact with the polished top of the semiconductor pellet and is pressed down on it slightly from a spring contact. This cat's whisker, as it is known, is connected on the right hand side to a brass plate which is the cathode. The semiconductor injects electrons into the metal. The energy level between the valence electrons in the semiconductor pellet and the tip of the wire produces a diode action. The contact area exhibits extremely low capacitance.

Because of the low capacitance, point contact diodes can be used for applications at extremely high frequencies. Ordinary PN-junction diodes have too much junction capacitance for use at these high frequencies.

SCHOTTKY DIODE 

The Schottky diode (named after the inventor) uses a metal such as gold, silver, or platinum on one side of the junction and doped silicon (usually N-type) on the other side. When the Schottky diode is unbiased, free electrons on the N side are in smaller orbits than the free electrons in the metal. This difference in orbit size is called the Schottky Barrier.

When the diode is forward biased, free electrons on the N side gain enough energy to travel to larger orbits (it takes energy to make an electron move to a larger orbit). Because of this, free electrons can cross the junction and enter the metal, producing a large current. Because the metal has no holes, there is no depletion zone. In an ordinary diode, the depletion zone must be overcome before a diode can conduct - this takes time - a very short time, but time nonetheless. The Schottky diode can switch on and off faster than an ordinary PN junction. In fact, a Schottky diode easily rectifies frequencies above 300MHz. The Schottky is also called the hot-carrier diode. The current carriers are 'hot to trot' as it were and conduction (unlike a conventional diode) takes very little electric pressure (voltage) in the forward direction to conduct. This is an advantage with very weak signals.

The schematic symbol of a Schottky diode:

John Bardeen, William Shockley and Walter Brattain in 1948

The first amplifying devices were the electron tubes, They were large in size, consumed a lot of power, produced a lot of heat and were very unreliable. Large equipment using all electron tubes and running all the time required technicians to be on hand at all times just to replace faulty electron tubes.

1930s engineers at American Telephone and Telegraph knew that vacuum-tube circuits would not meet the company's rapidly growing demand for increased phone call capacity. Bell Laboratories' director of research Mervin J. Kelly assigned William Shockley to investigate the possibility of using semiconductor technology to replace tubes.

On December 16, 1947, their research culminated in a successful semiconductor amplifier. Bardeen and Brattain applied two closely-spaced gold contacts held in place by a plastic wedge to the surface of a small slab of high-purity germanium. On December 23 they demonstrated their device to lab officials and in June 1948, Bell Labs publicly announced the revolutionary solid-state device they called a "transistor."

Continuous improvement to the transistor occurred through the 1950s. An important advance in 1954 was the silicon transistor, first from Morris Tanenbaum at Bell Labs and shortly after by a team led by chemist Willis Adcock at Texas Instruments. By the end of the 1950s, silicon had become the industry's preferred material and Tl the dominant semiconductor vendor.

in 1959 when, working for Egyptian engineer Martin M. (John) Atalla on the study of semiconductor surfaces at Bell Labs, Korean electrical engineer Dawon Kahng built the first successful field-effect transistor (FET) comprising a sandwich of layers of metal (M - gate), oxide (O - insulation), and silicon (S - semiconductor). The MOSFET, popularly shortened to MOS, promised a significantly smaller, cheaper, and lower power transistor.

25 - Semiconductors II

TRANSISTOR CONFIGURATIONS

There are different ways of connecting a transistor so that it will amplify. The principle of small changes in base current controlling larger changes in collector current remains the same. The configurations we are going to discuss cause the amplifier to have different characteristics.

I am not going to go very deep into this subject, as there is no need to for examination purposes. For the exam, all you really need to be able to do is identify which configuration is illustrated and remember some basic characteristics of each configuration.

The three configurations are:

Common-emitter

Common-base and

Common-collector (also called emitter-follower)

I will give you the basic circuits of each. For the exam, you need to identify which circuit is which and that is all. Please do remember that with all transistor amplifier configurations, it is still the small base current controlling the larger collector current which results in amplification. At the end of this section, I will also provide a table of the different characteristics of each configuration. A detailed description is not necessary as this would be rather lengthy and contain much information which is not required.

COMMON-EMITTER CONFIGURATION

The basic transistor amplifier circuit is the common-emitter. It is also the most common configuration you will see and is easy to remember. The circuit shown in figure 25-1 is a basic common-emitter amplifier using an NPN transistor.

If a PNP transistor was to be used, the polarity of the batteries would be reversed.

This amplifier circuit uses transformer coupling at both the input and output. The transformers are air cores, so this indicates that the circuit is used at radio frequencies, as iron core transformers have too much loss in the laminated iron core at radio frequencies. The type of coupling does not determine the configuration.

The reason the configuration of figure 25-1 is called common-emitter is because the emitter is the common leg (or lead) between input and output. This is how you will identify the common-emitter circuit.

The identifying feature of this circuit as common-emitter is the emitter leg being common to input and output. One thing worth noting is that the signal being amplified undergoes an 180° phase change. Mutually coupled transformers create a 180° phase change. Notice how the input signal in figure 25-1 goes through a 180° phase change through the input transformer. Common-emitter configuration also causes another 180° phase change as shown at the output of the transistor. Once more the signal passing through the output transformer produces yet again another 180° phase shift.

COMMON-BASE CONFIGURATION

The common-base circuit is identified by the common base leg between input and output. In this circuit transformer coupling is once again used.

Transformer coupling in these two circuits is for impedance matching. We have learned that one of the functions of a transformer, if required, is to match two unequal impedances. For example, if you had an audio amplifier with an output impedance of 1000Ω, it would not work well if connected to an 8Ω speaker. An audio output transformer could be used to perform an impedance conversion from 1000Ω to 8Ω.

Just a note, in all the transistor circuits we have seen so far the bias voltage (between base and emitter) and the collector voltage (between collector and emitter) has used separate batteries. In practical circuits, one source of supply is used for base bias and collector voltage. The input signal for both circuits so far is AC. BJT's do not work on AC. However, the base-emitter battery bias not only turns the base-emitter junction on; it converts the incoming AC to VDC (varying DC).

EMITTER-FOLLOWER or COMMON-COLLECTOR 

Figure 25-3 shows an emitter-follower, also called a common-collector configuration. I have shown how one source of supply can be used for both base-emitter forward bias and collector voltage. Unlike the previous two circuits, this one is a little different. The key to the identification of the common-collector (emitter-follower) is that the output is taken from across a load or resistor in the emitter circuit. The output of this amplifier and all amplifiers of this configuration is taken from across the emitter load RL 

The only reason the different configurations are used is that the amplifiers provide different characteristics, a summary of which I will provide in table form shortly. They are all just amplifiers, relying on small changes in base current to control larger changes in collector current.

The coupling between the input and output of the circuit in figure 25-3 is called capacitive coupling. Coupling is the method by which signal is fed into and the output is taken away from a transistor amplifier. There will be more on coupling later.

Notice also how a single resistor Rb is used to forward bias the base-emitter junction of the transistor, doing away with having to use two power sources. The resistance of Rb determines the amount of bias current that flows from the negative ground up into the emitter and out of the base, through Rb and back to the positive supply. This bias arrangement is called fixed-bias. I would also like to point out that a number of transistors could be connected via coupling to produce a multistage amplifier.

There you have it. The three basic transistor configurations and an illustration on biasing with a single voltage in the last circuit. We have been using BJTs here. We will be talking about other types of transistors soon and we have already spoken about the electron tube. All of these active devices can be connected in the above configurations.

Summary of the characteristics of each configuration:

A common-emitter has a low input impedance and a high output impedance and inverts the phase of the incoming signal.

A common-base also has a low input impedance and has a high output impedance but does not create a phase inversion between input and output.

A common-collector has high input impedance and a low output impedance and provides no phase change. A common-collector could drive a low impedance load such as a 50Ω antenna or an 8Ω speaker. The pass-transistors in a low voltage high current power supply are common-collector, as the impedance of most things (like a transceiver) connected to a power supply are low impedance. Think about it 13.8V at 20A for a typical transceiver means a low input impedance R=E/I.

BIASING TRANSISTORS

Biasing transistors is another broad topic that much could be written about. However I am again going to confine this chapter to what I think is the 'need to know' even that may extend further than necessary.

Biasing a transistor means applying a fixed DC voltage between the base and emitter. By varying the amount of bias current, we can make the transistor amplify in the required class of operation i.e. A, B, AB or C.

If you have trouble understanding the need for bias (and many students do) imagine using a transistor without any bias and feeding an AC signal to it to be amplified. Half of the AC signal would not forward bias the base-emitter junction and there would be no output from the transistor during this half cycle. Transistors (including FETs) and electron tubes are not AC devices - they work on varying DC. When we bias the input of an active device at a DC potential, we can then feed an AC signal to that input. The combination of the AC superimposed on top of the DC bias produces varying DC at the input of the transistor or other active device.

We have already seen one method of biasing using a single resistor (Rb) in the emitter follower circuit shown earlier. This type of biasing is called fixed-bias. I suggest you go back and have a look at it now.

Fixed bias is simple. However, it is quite unstable thermally. If the transistor warms for any reason, due to a rise in ambient (surrounding) temperature or due to current flow through it, the collector current increases. The higher the current gain of the transistor the greater the instability of the circuit.

A far superior and the most common biasing arrangement for BJTs, is shown in the schematic circuit of figure 25-4 and is called voltage-divider bias. I have shown typical values for a practical audio amplifier. You will not have to perform any calculations on the circuit, but you may need to identify the circuit, not as a whole but in separate parts so we will have a look at it for the necessary detail.

The common-emitter circuit with voltage divider bias. 

The purpose of bias in any BJT (transistor) circuit is to forward bias the base-emitter junction of the transistor. In the circuit of figure 25-4, this is achieved primarily by the series circuit consisting of R1 and R2 in series with the supply voltage (in this case 20 volts) The transistor is an NPN type which requires the base to be positive with respect to the emitter for forward bias. R1 and R2 in series are across the 20 volt supply which is positive at the top (collector) and negative at the earth symbol. Now you could use Ohm's law to approximate the voltage across R1 and R2 knowing they are across a 20 volt supply and have the values shown. Their total resistance is 50kΩ. We get 40/50 (four-fifths) of 20 volts dropped across R1 and 10/50 (one-fifth) of the voltage will be dropped across R2. One fifth of 20 volts is 4 volts. So the approximate voltage across R2 is 4 volts. The top of R2 is positive and the bottom negative. So neglecting RE, there are about 4 volts applied between the base and the emitter of the transistor, positive at the base and negative at the emitter. The polarity is correct, so we have a forward biased base-emitter junction. This is how voltage divider bias works. R1 and R2 form the voltage divider.

Let's just have a look at some of the other components in the circuit and what they do. Resistor RE you will notice a relatively low value (500 ohms) and is connected between the emitter and ground. RE provides thermal stability to the circuit. An increase in DC voltage through RE caused by a reduction in the transistor collector-emitter resistance will cause an increase in voltage across RE. The voltage across RE is in opposition to the bias voltage. If the voltage across RE was 1 volt, then this opposes the voltage across R2 and so the effective bias voltage is only 3 volts. The voltage across RE will only increase if the transistor heats up and as a consequence its collector-emitter resistance decreases. Without RE the transistor could go into thermal runaway.

Let's look at the situation without RE. The transistor is operating. It heats up due to the current through it or an increase in the ambient (room or surrounding) temperature. If the transistor heats up, its emitter-collector current increases which causes it to heat up more, which causes its resistance to decrease more, which increase the current more, which causes it to heat up more, etc. - this is a thermal runaway and results in the transistor being destroyed.

RE provides what is called degeneration. Degeneration is a single word, which explains the operation in the second last paragraph. The degeneration used here is also known as inverse current feedback. If the current increases through RE (due to the transistor heating up for whatever reason) the voltage across RE reduces the bias voltage, that decreases the emitter-collector current, allowing the transistor to cool and not go into thermal runaway.

Now, it is the DC current flowing through RE that we are using to provide thermal stabilisation and prevent thermal runaway. There is an AC component in the circuit. This AC component is the signal we are trying to amplify. An AC voltage is applied to the input of the transistor via capacitive coupling and that AC signal will appear in the emitter-collector circuit, amplified. We do not want the AC signal to flow through RE. If the AC component (the signal to be amplified) did flow through RE, it would affect the bias of the transistor. So the simple approach is to provide an AC path around RE for the AC component. This is accomplished by adding the parallel capacitor across RE (CE). So, the signal which is being amplified flows through CE and does not affect the biasing of the transistor, while the DC current, which is what affects the operating characteristic of the transistor and can cause thermal runaway, is allowed to flow through RE.

If this is difficult to see, let me add the following points to refresh your memory. The circuit of the transistor has a current, this current without any input signal is just DC. When an AC (or varying DC) signal is applied to the transistor, the current through the transistor now has two components (or parts): a DC component, which is responsible for bias; and an AC current which is the signal being amplified. The DC component is used to bias the transistor and prevent thermal runaway - the degenerative voltage across RE must be treated differently by the transistor than the AC component, which is the signal we are trying to amplify.

If we were to allow the AC component of the current to flow through RE, then any increase in the signal to be amplified would reduce the gain (amplification) of the transistor, defeating the whole purpose of amplification.

A capacitance will pass an AC current, but block a DC current. So the bias current flows through RE (DC), while the signal to be amplified passes through CE. For this to work effectively the capacitive reactance of CE must, as a rule of thumb, be about 1/10th the value of RE. So in the circuit of figure 25-4, the XC of CE would be about 50 ohms.

Since CE bypasses the AC component of the emitter-collector current around RE, CE is called an emitter bypass capacitor, or just a bypass capacitor. RE is referred to as the emitter stabilisation resistor.

You do not have to explain how this works as I have done. But you do need to know the purpose of R1, R2, RE and CE (which may be labelled differently).

R1 and R2 provide voltage divider bias. RE provides thermal stability.

CE bypasses the AC component (i.e. the signal to be amplified around RE).

RL is just a load resistor. If it were not there, the output would be connected to the +20 DC rail and there would be no output other than +20DC - hardly a useful amplifier.

JUNCTION FIELD EFFECT TRANSISTOR (JFET)

Field effect and bipolar junction transistors are entirely different devices. FETs are solid-state amplifying devices that have operating characteristics very similar to those of triode electron tubes. There are three types of FETs, the junction (JFET) and two metal oxide semiconductor types known as MOSFETs. One is the depletion MOSFET; the other is an enhancement MOSFET.

The essential construction of a JFET is shown in figure 25-5. A block of P-material

called the substrate has an N-type channel running through it. The figure shows a cross section. Think of the N-channel as a wormhole in the P-substrate. As with any PN junction, electrons fall into holes at the barrier and a depletion zone is created. You can see the N-channel running through the P-substrate. The connections are made as shown in figure 25-5. The drain can be thought of as similar to the anode, the source similar to the cathode and the gate similar to the control grid of a triode valve. Though this device is fully manufactured from semiconductors, the purpose of the JFET is to amplify, as is the purpose of the BJT and the triode. If a supply voltage is connected between drain and source, there will be a current flow as there is no PN-junction either forward or reverse biased.

So we have connected a supply voltage between drain and source and you can imagine a current flowing from source to drain through the N-channel.

Notice also that the depletion zone occupies part of the channel.

To refresh your memory. A depletion zone is called a depletion zone because it is depleted of charge carriers. A charge carrier is either an electron or a hole. A PN junction can be reverse biased increasing the size of the depletion zone and how much voltage is applied to a PN junction in the reverse bias condition will determine the size of the depletion zone.

If we wanted to reverse bias the JFET in the previous diagram, we would apply a negative potential to the substrate that would attract the holes and a positive potential to the channel that would attract electrons.

If we reverse bias the PN junctions on each side of the channel, we will increase the width of the depletion zone. Since the depletion zone would widen, it would occupy more of the channel. In fact, if we applied enough reverse bias the depletion zone could be made to occupy the entire channel and no current would flow from source to drain. This is called pinch-off.

We have a way of controlling the amount of current that flows in the channel by changing the amount of reverse bias between the gate connection and the channel (the substrate and the gate are connected together).

The gate is always biased negative in the JFET (N-channel), then the signal to be amplified can be applied to the gate. The signal to be amplified would change the reverse bias and hence the size of the depletion zone. Since the depletion zone occupies part of the channel, the resistance of the channel will alter in sympathy with the input signal and in doing so, control the source-drain current.

So the JFET is an amplifier. Since the gate connection is always reverse biased (no current), the input impedance is very high. It is the changes in the negative potential on the gate that controls the width and conductivity of the depletion zone and that in turn controls the much larger drain current.

This is, in essence, exactly how a triode works - by changing the negative potential of the control-grid of a triode we can control the much larger anode current. If the control-grid of a triode is made negative enough, no electrons will flow from the cathode to the anode. This is called cut-off.

Similarly, if the negative potential of the gate of an N-channel JFET is large enough, the depletion zone will occupy the entire channel and there will be no source-drain current. This is called pinch-off.

To run through the operation of an N-channel JEFT one more time, the gate is biased negative with respect to the source, causing the depletion zone to occupy part of the channel. The width of the depletion zone in the channel controls the channel's resistance. If a signal is applied between the gate and the source, it will control proportionately a much larger drain current. The drain current will be an amplified version of the signal applied to the gate.

The JFET is a voltage amplifier like a triode. By this, we mean that changes of voltage only on the gate are required to control the drain current. Since voltage alone is needed to control the JFET, the input signal does not have to deliver any power. You can have all the voltage in the world, but without any current you have no power (P=EI). This is very different to the BJT, which is a current amplifier. You can have voltage without current, but not current without voltage - think about that. The JFET and all FETs are then high input impedance devices.

You could also have a P-channel JFET that would have an N-substrate. The operation would be the same except you would have to bias the gate positive.

Important points to remember: Symbol; arrow in for N-channel; arrow out for P-channel; high input impedance; voltage Amplifier; the semiconductor version of a triode valve; why high input impedance can be an advantage. There are no forward biased PN junctions in a FET; therefore, no electron-hole recombination and therefore less noise.

MOSFETS

Metal Oxide Semiconductor Field Effect Transistors.

When a FET is constructed as shown in figure 25-7 with the gate insulated (silicon dioxide) from the very narrow N-channel, it is called an insulated gate FET, IGFET, or MOSFET, the latter being the most common term. Combinations of these transistors as a single unit are referred to as CMOS, MOS, VMOS.

When a voltage is applied, with negative to the gate and positive to the source, its electrostatic field extends into the N-channel. This reduces its ability to carry current by repelling channel electrons, depleting the channel of its carriers.

This is a depletion mode MOSFET. Sufficient reverse bias can pinch off the drain current completely. Conversely, a forward bias can increase drain current up to a certain point. As a result, this device can operate with no bias at all, which simplifies circuitry. The depletion mode MOSFET is ON without bias. An enhancement mode MOSFET requires a bias to induce a channel and is normally OFF.

The more common enhancement-mode MOSFET or eMOSFET, is the reverse of the depletion-mode type. Here the conducting channel is lightly doped or even undoped making it non-conductive. This results in the device being normally "OFF" (nonconducting) when the gate bias voltage is equal to zero. The circuit symbol shown in figure 25-8 for an enhancement MOSFET transistor uses a broken channel line to signify a normally open non-conducting channel.

The application of a positive gate voltage to an n-type eMOSFET attracts more electrons towards the oxide layer around the gate thereby increasing or enhancing the thickness of the channel allowing more current to flow. This is why this kind of transistor is called an enhancement mode device as the application of a gate voltage enhances the channel.

MOSFETs do not produce any input circuit current due to the insulation between gate and channel. MOSFETs have an extremely high input impedance in the order of 10 megohm. This extremely high input impedance is the MOSFET's great advantage apart from being less noisy than a BJT, this extremely high input impedance means virtually zero drive power. So the source (such as an antenna) does not have to deliver power to a MOSFET to have that signal amplified.

The input impedance of MOSFETs (as much as 40 megohm) and similar devices are so high that they require special handling, as normal handling can result in a static charge being created which can destroy the device. You may find some wrapped in metal foil to protect them from static voltages.

The MOSFET was a significant breakthrough for semiconductor technology and led to combinations of them being fabricated within a single package called an integrated circuit. Of course, even BJTs and JFETs can be fabricated in conjunction with MOSFETs into a single package. It is a simple matter to create resistors in an integrated circuit by controlling the width and doping level of semiconductor strips.

Capacitance in an integrated circuit can make use of the fact that a reverse biased PN junction acts as a capacitor. For your radio assessment you should remember the symbols; identify P-channel (arrow out); and N-channel (arrow in); and that these devices are very high input impedance (2MΩ for the JFET and 10MΩ for the MOSFET). Figure 25-8 shows the symbols for JFETs and MOSFETs for both P and N channel. MOSFETs can have more than one gate. These are called dual-gate MOSFETs. These are ideal for use as mixers where two signals are mixed (with the MOSFET being nonlinear) to produce new frequencies - covered later when we look at mixers.

PROTECTED GATE MOSFETS

MOSFETs have very high input impedance of 10 Megohms or higher. Because of this high input impedance, even static electricity from handling them can build up a high voltage on the gate (or gates) and rupture the metal oxide insulator. Some MOSFETs are made with internal zener diodes connected in parallel and in opposite directions between the gate and the substrate. Under normal operation, neither of these zeners will conduct. However, if a high static voltage is created on the gate, one of the zeners will conduct and discharge the voltage. These are called protected gate MOSFETs. The symbol is that of an ordinary MOSFET, but within the symbol, you will see one or more zener diodes.

SILICON CONTROLLED RECTIFIERS (SCRs)

The SCR construction shown in figure 25-10 illustrates one of the many NPNP or multilayer semiconductor devices. SCRs are also referred to as Thyristors. The layer structure could also be PNPN. This one is called an SCR. "A" is the anode, "K" is the cathode and "G" the gate. If a voltage, even a large one, is placed across the anode and cathode (of any polarity), this device will not conduct because at least one junction will be reverse biased. The main current path of an SCR is between cathode and anode.

Switch SW1 is normally open (NO). When SW1 is closed, the first P-Type region, acting as the base of an NPN BJT, is forward biased through RG and "load" which allows current to flow through J2. Since J3 is forward biased already, current flows through the whole device from K to A and the load.

The gate switch SW1 can now be opened and current will continue to flow because J2 loses control of its current carriers. Even reverse biasing the gate will not stop the cathode-anode current. It is necessary to reduce the applied voltage (Vaa) to almost zero or open SW2 to stop current flow. No current will flow if the source potential (Vaa) is reversed, even with SW1 closed.

Therefore, with an AC source rather than Vaa, which is DC, the SCR acts like a rectifier in that it allows current to flow in one direction only. The SCR is a unidirectional switch.

An SCR acts like an ordinary rectifier except that it can be switched ON and OFF. When OFF it is an open circuit and does nothing. When ON it acts like any rectifier would. The switching ON can only be done by the gate; the switching OFF can only be done by removing the supply voltage. If the supply voltage is the mains, then on the change of the half cycle on the sinewave the SCR will automatically switch OFF.

SCRs can be made to handle medium to very high currents. A typical application could be a light dimmer or motor speed control circuit (though a TRIAC is better for the latter). The gate of the SCR is not switched (usually) with a mechanical switch instead, some of the mains AC that the SCR is going to control is used to switch or 'fire' the SCR's gate.

An SCR is still a rectifier like any other rectifier, though when it starts to behave as a rectifier depends on the voltage applied to its gate. If you want to control both halves of an AC waveform you could use two SCRs. A device in one package which does this and which has mostly replaced the SCR is called a Triac. Triacs are not in the current (Australian) syllabus.

Triacs can be considered as back-to-back SCRs and perform as a full wave SCR for alternating current. An SCR is a unidirectional switch and a TRIAC is a bidirectional switch. The gate control voltage of a TRIAC, unlike the SCR, can either be positive or negative in polarity. Figure 25-12 is the schematic symbol of a triac.

OVER-VOLT PROTECTION

One failure mode for many analogue regulated supplies is that the series pass transistor can fail with a short circuit appearing between the collector and emitter. If this happens the full unregulated voltage can appear at the output, and this would place an excess high voltage on the supply output and significant catastrophic damage to the load may occur.

By looking at the voltages involved, it is very easy to see why the inclusion of overvoltage protection is so important. A typical supply may provide 13.8 volts stabilised to logic circuitry. To provide sufficient input voltage to give adequate stabilisation, ripple rejection and the like, the input to the power supply regulator may be in the region of 16 to 20 volts. Even 16 volts would be enough to destroy equipment connected to the load.

SCR/Thyristor over voltage crowbar circuit

The thyristor crowbar circuit shown figure 25-13 is very simple, using only a few components. It can be used within many power supplies, and could even be retrofitted in situations where no over-voltage protection may be incorporated.

The SCR over voltage crowbar or protection circuit is connected between the output of the power supply and ground. The zener diode voltage is chosen to be slightly above that of the output rail. Typically, a 13.8V volt rail may run with a 15-16 volt zener diode. When the zener diode voltage is reached, current will flow through the zener and trigger the silicon-controlled rectifier or thyristor. This will then provide a short circuit to ground, thereby protecting the circuitry that is being supplied from any damage and also blowing the fuse that will then remove the voltage from the series regulator. Zener diodes can be connected in series to achieve the 1-2 volts above rail voltage of 13.8V.

As a silicon-controlled rectifier, SCR, or thyristor is able to carry a relatively high current - even quite average devices can conduct five amps and short current peaks of 50 or more amps, cheap devices can provide a very good level of protection for small cost. Also, voltage across the SCR will be low, typically only a volt when it has fired and as a result the heat sinking is not a problem.

The small resistor, often around 100 ohms from the gate of the thyristor or SCR to ground is required so that the zener can supply a reasonable current when it turns on. It also clamps the gate voltage at ground potential until the zener turns on. The capacitor C1 is present to ensure that short spikes do not trigger the circuit. Some optimisation may be required in choosing the correct value although 0.1 microfarads is a good starting point.

If the power supply is to be used with radio transmitters, the filtering on the input to the gate may need to be a little more sophisticated, otherwise RF from the transmitter may get onto the gate and cause false triggering. The capacitor C1 will need to be present, but a small amount of inductance may also help. A ferrite bead may even be sufficient. Experimentation to ensure that the time delay for the thyristor to trigger is not too long against removing the RF. Filtering on the power line to the transmitter can also help.

26 - Amplifiers

The basic purpose of an amplifier is to do just that, to amplify (a signal). However, the way different types of amplifiers do this can vary greatly and an amplifier can do other tasks besides amplifying. When we speak of amplifying, we mean, to increase the amplitude of a signal. We are starting to get into the building blocks that make up a radio system.

Signals that we amplify in radio and communications are very often complex waves and sometimes they are a sinewaves. For our discussion, we will consider that we are amplifying a sinewave(s) of alternating voltage or current.

DEGREES

When discussing alternating signals, it is usual to speak of a full cycle as being equivalent to 360 degrees. Fractions of a full cycle can then be more easily described. As an illustration, if a full 360 degree sinewave of alternating current is sent to a rectifier, only 180 degrees of current will appear at the output. A halfwave rectifier or diode could be said to have an operating angle of 180 degrees. Similarly, different types of amplifier will provide at their output all or only a portion of the amplified input signal. An amplifier with an operating angle of 180 degrees will behave similarly to a halfwave rectifier except that the output is amplified.

This is usually the hardest concept about amplifiers to grasp. It is incorrect to make the assumption: "what goes into an amplifier is the same as what comes out amplified". It is correct that much of the time that is all we want. We just want the amplifier to amplify and make a signal stronger. In radio circuits, there are all sorts of other considerations. One of the main ones is the efficiency of the amplifier. A number of techniques are used to improve the efficiency. There are situations where we do not care about distortion and what comes out of the amplifier. These are some of the things we will discuss in detail in this chapter.

We have covered the actual principle of amplification in the last two chapters. A smaller voltage or current is used to control a much larger voltage or current. Most of the time this is done using one of the active devices such as a BJT, JFET, or Electron tube.

Now we cannot get power for nothing. The power supplied to the amplifier comes

from the power supply, so if an amplifier has an efficiency of only 25%, that means for 25 watts of usable signal output we have to provide it with 100 watts of power from the power supply. So efficiency, particularly at radio frequencies where the power tends to be high, perhaps 100,000 watts for a TV station, becomes important. Efficiency is not just important in terms of say running down batteries in portable equipment, but also heat. If a power supply is only 25% efficient, then 75% of the power is being converted into heat and this heat brings with it all sorts of other problems, particularly with semiconductors and keeping them cool.

A little more on efficiency. An active device say a BJT, may be forward biased, turned ON and yet not amplifying. Even with no input signal there is still emitter-collector current. So even though we are not doing any amplifying, the active device may be consuming power from the power supply.

Accept just for now, that not all amplifiers amplify the entire input signal fed to them. Like the example given above, if an amplifier only amplified half of one cycle it would have an operating angle of 360/2 = 180 degrees. It may seem that if an amplifier does not have an operating angle of 360 degrees then what we put in (the input signal) will not be what we get out. An amplifier that does not have an operating angle of 360 degrees distorts, or is non-linear. Sometimes non-linearity is very undesirable. With some type of radio modes non-linearity is desirable.

Amplifiers fall into four basic categories called Classes and you need to remember them. It is important you remember the classes and their approximate efficiency and the basic principles and in a couple of cases, you will need to identify a circuit. This does not mean you need to know the complete circuit operation.

CLASSES OF AMPLIFIER AND THEIR OPERATING ANGLES

Class A   360 degrees  

Class B   180 degrees  

Class AB   270 degrees  

Class C   90-120 degrees  

At the outset you should see that a Class A amplifier with an operating angle of 360 degrees amplifies all of the input signal - this is the basic definition of a linear amplifier. Class A operation, while being linear, is the least efficient. Class A is used for small signal applications because of its poor efficiency, but nevertheless, it is a quality amplifier. However, we can do tricks with the other non-linear amplifiers to make linear amplification possible. In some cases, we don't care if we have non-linear amplification.

A LOOK AT HOW THE CLASSES DIFFER

Take an active device such as an electron tube. If the control grid is made negative enough, the anode current will fall to zero. This point is called cutoff. Decreasing the negative bias applied to the control grid increases the anode current linearly, until at zero bias the anode current is almost at maximum. Making the control grid positive will increase anode current slightly, but the electron tube quickly saturates. Saturation is when an active device is conducting its maximum current.

A fixed DC voltage applied to the control grid (bias) determines the class of operation. That's so important I will say it again - bias determines the class of operation. For Class A operation, the electron tube (or any active device) is biased at the centre of the linear portion (straight-line section) of the operating curve. Class B is biased at, or near, cutoff. In Class C operation the bias is about twice cutoff, though it can be higher. For Class AB, bias is about halfway between cutoff and the centre of the linear portion of the operating curve.  

Radio experimenters frequently use the term "linear amplifier" as a synonym for "power amplifier". Such usage is incorrect as power amplifiers can be linear or nonlinear, depending on their application. For audio, Class A operation is the only single ended amplifier that provides linear amplification. Single ended means only one active device employed. Linear amplifiers do not distort the amplitude of the signal being amplified within specified practical limits. It is possible to use Class AB and B as linear radio frequency (RF) amplifiers for amplitude modulated signals since the output power is proportional to the input power. The missing cycle can be restored in the tank circuit (flywheel effect).

Amplitude modulated signals are those which contain intelligence (or information) in their amplitude. Since a Class B amplifier has an operating angle of 180 degrees, it is possible by using a pair of active devices and to arrange for each device to amplify half of the sinewave and to combine the two amplified halves in the output to achieve linear amplification. Such an arrangement is called a class B push-pull and is most useful for audio and RF amplifiers.

Class B is non-linear and has an operating angle of 180 degrees. However, we can arrange two such amplifiers to look after each half of the input and combine them after amplification in the output, to obtain the full signal with linear amplification

Why bother? Well we discussed that Class B was biased at or near cutoff, so with no input signal (the signal to be amplified), little or no current flows in the anode, collector or drain circuit - no power taken from the supply when no amplification is taking place means higher efficiency

AMPLIFIER EFFICIENCY 

CLASS A 25-30%

Use: Audio - low distortion RF: Very inefficient

CLASS B 30-35%

Use:

Audio Power (push-pull)

RF power - all modes - linear with two active devices

CLASS AB 50-60%

Use:

RF Power Amplifiers all AM modes - linear with two active devices

CLASS C 60-80%

Use:

RF power, frequency modulation

We have not covered transmission modes. Most will be familiar with AM and FM radio stations. AM is amplitude modulation, the information, music, intelligence, is in the amplitude of the signal. FM is frequency modulation, the information, music; intelligence is in the frequency of the wave. Remember, a sinewave has two fundamental characteristics - think back to your basic sinewave. These characteristics are amplitude and frequency. Either can be modified to carry information (modulated), the amplitude or the frequency and we can disregard one or the other without losing any information.

INPUT-OUTPUT CURVES

CLASS A- OPERATING CURVE

The characteristic curve diagram of figure 26-1 is that of an electron tube Class A amplifier. It could just as easily be for a FET or BJT. In an electron tube, a negative bias is applied to the grid. In the diagram, I have labelled the grid bias (above zero) as shown. The actual value in volts of the grid bias is of no significance, as it will vary from device to device.

The graph is a plot of grid bias versus plate (anode) current. It is important to understand this graph. Forget the waveforms for a moment and just concentrate on the lines on the graph, which are a plot of grid bias verses plate current. The plate (anode) current is on the vertical axis while the negative grid volts are on the horizontal axis. You can see from the graph that there is a point where the grid bias is so negative that no plate current will flow and this point is labelled cutoff. Further along the curve is a spot marked operating point. This operating point is the amount of bias required for Class A operation.

Note that the characteristic curve is really a curve, for if I had extended the curve a bit further upward it would have quickly flattened out, this is called saturation. Importantly, notice that a portion of the characteristic curve is a straight line. If the active device (here an electron tube) is operated on the straight line portion of its characteristic curve, then variations to the bias by the input signal superimposed on it will cause proportional variations in the larger anode current.

Operating an amplifier on the linear portion (straight-line portion) means the amplifier will be linear and faithfully reproduce the output signal the same as the input signal.

If the input signal drives the bias point into cutoff or saturation, then the amplifier will produce distortion and the output anode current will not be an exact representation of the input signal.

As an example, audio amplifiers often operate in Class A. Think of your TV or stereo system. If you turn the volume control up too high, the music will be louder, but it will begin to sound distorted.

The volume control adjusts the level of the input signal into the audio amplifier. When you turn it up too high, you overdrive the amplifier causing it to go into the cutoff and saturation regions of the curve and you hear this as distortion.

So figure 26-1 demonstrates Class A operation. The active devices are operated on the linear portion of the operating curve. Since all of the input signal is amplified in a Class A amplifier, it is said to have an operating angle of 360 degrees.

Notice in the diagram, (26-1) if the input signal was to be removed then there would still be significant plate current. Without an input signal the Class A amplifier is still dissipating power. This is why the Class A has such low efficiency.

CLASS B - OPERATING CURVE

Have a look at the operating curve of a Class B amplifier in figure 26-2. Notice the operating point is now at, or near, cutoff.

Cutoff is when the grid voltage is so negative that it prevents any electrons from flowing from cathode to anode. If the input signal is negative going, it takes the electron tube beyond cutoff and no anode (plate) current flows. If the input signal goes positive it will take the electron tube out of cutoff (to the right on the horizontal axis) and current will flow in the output and be amplified. As you can see by the diagram, only one-half cycle of the input signal is amplified. A Class B amplifier is therefore not a linear amplifier. However, unlike a Class A, with no input signal, there is no anode current in a Class B, so it is a more efficient amplifier. A Class B amplifier has an operating angle of 180 degrees. A combination of two Class B amplifiers configured correctly, one to amplify one-half cycle and the other the other half cycle, can be used to produce linear amplification.

CLASS C - OPERATING CURVE 

Have a look at the operating curve of a Class C amplifier in figure 26-3. Notice the operating point is well beyond cutoff.

Not even one-half cycle of the input signal is amplified (180°). About 90° to 120° of the input signal is amplified. A Class C amplifier causes massive distortion to the amplitude of the input signal. Don't be confused by the size of the input signal and the output signal (plate current) shown on any of these curves, their physical size on the curves does not represent their power levels. On all the curves, plate current is much larger and at a much higher voltage than the input signal.

If there is information in the amplitude of the input signal it will be severely distorted. If there is information in the frequency of the input signal, there is no distortion to frequency, as the frequency of the signal that goes in, is the same as that which comes out. So if we have coded some information into the frequency (frequency modulation), the Class C amplifier is the only way to go, as it is the most efficient amplifier of all. A Class C amplifier can only be used at radio frequencies (RF).

We can restore the full cycle in the output of a Class C amplifier by using a tuned circuit in the plate of the electron tube. Such a circuit is called a tank circuit and it will restore the other half cycle by utilising the flywheel effect.

CLASS AB

I will just mention that there is another Class of amplifier called Class AB - it is not in the syllabus. It is an improvement of the Class B. For linear amplification, two active devices like a Class B amplifier, are required. One problem with the Class B is that the operating curve is not quite straight for a little bit near cutoff. Even if you use two Class B amplifiers, one for each half cycle, you get some distortion when one amplifier turns off (after one-half cycle) and the other Class B amplifier turns on. This is due to

the non-linear part of the operating curve near cutoff. The distortion that results is called crossover distortion. The Class AB is a minor modification of the Class B to overcome this problem. The Class AB in push-pull is an excellent practical RF Linear amplifier.

ACTIVE DEVICES 

I have used graphs of an electron tube to illustrate the operation of Class A, Band C, as I think it is easier to visualise. Any active device can be used for all of the classes of amplifier. For a FET we would have to speak of gate bias instead of grid bias and drain current instead of plate current. The polarity of the bias voltage will be different depending on the type of active device used. Polarities are not important for this chapter; I just used them because I was explaining the operation of the curves using an electron tube.

You may be presented with a circuit diagram of different amplifiers in the exam and basically have to identify them. Most exams are multiple choice, so you are presented with a circuit (schematic) diagram and asked to pick one of four choices of what it is. I have seen dozens of actual exam papers, so I will show you a couple of schematics of amplifiers and give you the clues to identification. I may cover some of the operation only for the purpose of reinforcing some earlier material.

CLASS A, B and C on one graph 

Figure 26-4 shows the three main classes of amplifier and their operating curves on the one graph. This very useful diagram that shows in an easy way how the main three classes differ.

PUSH-PULL AMPLIFIERS

We spoke of a Class B amplifier as having an operating angle of 180°. To obtain linear amplification we could use two Class B amplifiers, one to look after and amplify each half cycle. This type of amplifier is called a push-pull. For Class B operation the bias is about 0.95 of the cutoff voltage.

Following is a brief description of the operation that will give you a bit more of an idea of how push-pull works.

Refer to the vacuum (electron) tube circuit of figure 26-5. Both tubes are biased at or near cutoff. Without any input signal the plate current shown on meters 11 and 12 is very small or even zero.

Now suppose an input signal is applied via T1, which makes the top of the secondary 5 volts positive with respect to the centre tap and the bottom five volts negative with respect to the centre tap.

In other words, the grid voltage on V1 will be 5V less negative while on V2 the grid voltage becomes 5V more negative. Assume that the reduced negative bias on V1's grid causes V1's anode current to increase. V2 will be driven further into cutoff so meter 12 will not register current.

V1 will amplify a half cycle of input. V2 does not amplify as it just stays in cutoff. Meter I3 will read the same current as I1.

On the next half cycle of input V1 will be driven into cutoff and V2 will amplify the half cycle that drives V2 out of cutoff and into conduction.

V1 and V2 amplify one half of the input signal. The two Class B waveforms are combined in the output transformer to give us a complete amplified cycle.

The operation of the (BJT) transistor circuit in figure 26-6 is the same, except that voltage divider bias is shown.

In figure 26-6 Q1 and Q2 operate as did V1 and V2 in figure 26-5. Q1 and Q2 are both PNP transistors. Forward bias is (electron flow) from base to emitter (against the direction of the arrow in the symbol). When Q1's base is made negative by the input signal, Q1 will conduct while Q2 remains dormant. On the next half cycle of input Q2 will conduct while Q1 remains dormant. The two half cycles amplified by Q1 and Q2 produce the full amplified waveform at the output.

R1 and R2 provide for voltage divider bias for Q1 and Q2.

A disadvantage of the last two push-pull circuits is that they are both using transformers. The transformers are controlling the phase relationships in these circuits. However transformers are expensive and we will discuss a method of doing away with them shortly.

An important advantage of push-pull operation over the single-ended circuit is the cancellation of even order harmonics. Such even order (i.e. 2nd, 4th, 6th ) harmonics are 180° out of phase in the output and completely cancel.

HARMONICS

Harmonics are distortion products (signals) produced on multiples of the operating frequency. So a radio frequency amplifier operating say on 10MHz will produce some output on 20, 30, 40MHz etc. It is a fact that harmonics always exist, are caused by non-linearity in an amplifier and that every amplifier has some non-linearity. The big advantage of the push-pull circuit is that even order, 2nd, 4th, 6th, etc. harmonics are cancelled in the output.

COMPLEMENTARY SYMMETRY AMPLIFIER

The schematic of a transistor complementary symmetry amplifier is shown in figure 26-7.

This amplifier takes advantage of semiconductor devices that are fabricated as the complement of each other and a matched pair in terms of characteristics. An NPN transistor is the complement of a PNP transistor. A push-pull amplifier normally has an input transformer to provide out-of-phase signals to the input elements of two active devices. With complementary symmetry, transformer phase inversion is unnecessary.

In the figure 26-7 notice that the base connections of the two transistors are connected directly together. If the input goes negative, the PNP transistor (Q1) will be biased harder and its collector current will increase. A negative-going input signal will reduce the bias current of the NPN transistor (Q2) causing its collector current to decrease by the same amount.

When the input signal swings positive, Q1's base and collector current is decreased, while Q2's base and collector currents undergo a corresponding increase.

The resistor networks on each transistor look complicated, but close inspection shows that R1 and R3 provide voltage divider bias for Q1, while R2 and R4 provide the same function for Q2.

AN INTERMEDIATE FREQUENCY AMPLIFIER

When we come to cover receivers and transmitters, we will come across a stage called the intermediate frequency amplifier. The intermediate frequency or IF amplifiers are a little different from other amplifiers, in that they are designed to operate on one narrow band of frequencies. Typical intermediate frequency amplifiers operate on 10.7MHz and 455kHz.

There are many intermediate frequencies and they are all reserved by international convention. We can't have transmitters operating on specified intermediate frequencies unless the purpose was to jam or interfere with communications.

Because this amplifier operates only on one frequency, it can be designed with tuned circuits only to pass that frequency, actually a narrow band of frequencies. An intermediate frequency amplifier is just like any other amplifier. However, you may need to identify a circuit similar to this in an Advanced assessment. See figure 26-8.

The clue to the identification of the circuit is the use of the transformers (radio frequency transformers) T1 and T2. They are ferrite slug tuned (indicating radio frequencies) and shielded (the dashed box). This is a circuit of a fixed tuned radio frequency amplifier, or an intermediate frequency amplifier. The tuned transformer coupling provides greater selectivity. The transformer primaries form part of a parallel tuned circuit and their bandwidth determined by their Q.

This circuit of an IF amplifier has shielded loosely coupled LC circuits to provide the bandpass filtering. If more selectivity was required then crystal or ceramic filters would be added or switched in as required.

The IF amplifier in figure 26-8 would be selective enough for a broadcast band receiver. With narrow band radio transceivers, we need bandwidths as narrow as 2-300Hz for CW, for SSB 2.8KHz and DSB 6kHz. Such high selectivity can only be achieved by the use of crystal or ceramic filters that are switched in when the mode switch is operated.

Out of interest and for some reinforcement, notice how the collectors are connected to a tapping on the transformer primaries. This is to prevent the low impedance of the transistors loading the tuned circuits and reducing Q and hence the selectivity. The turns ratio of T1 and T2 also serve to match the output and input impedances of each stage. R2 and R3 provide voltage divider bias for Q2. R4 is the emitter stabilisation resistor and C4 is the emitter bypass capacitor.

PUSH-PULL RF POWER AMPLIFIER

Figure 26-9 shows an RF power amplifier using two enhancement mode (protected) MOSFETs in push-pull configuration. No input transformer is necessary as each MOSFET will only respond to one half of the input cycle. Simple amplifiers like this can provide up to several hundred watts of output power. Power amplifiers require a lot of cooling using heatsinks and fans, In very high power applications refrigerated cooling may be used. For MOSFETs the maximum amount of heat that can be dissipated by the device is called the drain dissipation in watts. For BJTs this is referred to as maximum collector dissipation. The amount of output power an amplifier can produce depends on the Class of operation, the amount of cooling employed and the mode of operation.

FREQUENCY MULTIPLIER 

While frequency multipliers are not amplifiers, it seems like an appropriate place to discuss them. The purpose of a frequency multiplier is to do just that, multiply frequency. A 1MHz signal can be converted to a 2MHz signal using a frequency multiplier, or to any multiple of 1MHz. See figure 26-10.

Frequency multipliers should not be confused with mixers, which is a method of converting a signal from one frequency to another.

Frequency multipliers can only convert to integer multiples of the input signal.

If you remember (if not go back and have a look at the chapter on tuned circuits) that a parallel tuned circuit has a property called the flywheel effect. A parallel tuned circuit in the output of an amplifier is commonly referred to as a tank circuit. Frequency multipliers are designed with output tuned circuits (tanks) that are resonant on either the second, third and less frequently the fourth, harmonic of the input frequency.

The output waveform of a multiplier is a sinewave produced by the " flywheel effect" of the output tank. Multipliers are also referred to more specifically as doublers, triplers and quadruplers. Class C operation is essential, as current pulses into the output tank are required to keep the tank oscillating. In a doubler, the output tank is tuned to twice the input frequency and will receive one input current pulse and then go through two complete oscillations before the next current pulse arrives just in time to overcome the lost energy (remember damping). Output tanks in quadruplers require a much higher Q since they must sustain four full cycles of oscillation without appreciable attenuation or damping, before receiving a new current pulse.

Multipliers can only be used to multiply signals that have no intelligence in their amplitude, as the stage is nonlinear. I emphasise again that multipliers operate in Class C, which is nonlinear.

BUFFER AMPLIFIER

An oscillator is a circuit (to be discussed) which provides weak low power signals on a certain frequency. The power output of an oscillator is very low. If we were to connect something like a BJT amplifier after an oscillator, the oscillator would probably cease to function as a BJT requires current from the source being amplified.

A buffer amplifier is any amplifier (typically after an oscillator) designed to amplify the input signal, without placing any great demands, power-wise, on the stage supplying that signal. A buffer would normally be a high input impedance device like a FET.

In other words, a buffer amplifier requires very little or no power to drive it and it prevents excessive loading of the previous stage.

Some microphones have a small pre-amplifier actually built into them, as the microphone insert (crystal, dynamic, etc.) cannot provide much power out. A preamplifier after a microphone is never called a buffer, but in effect, it is doing the same job as a buffer amplifier.

OTHER CLASSES OF AMPLIFIER

There are many other classes of amplifier. Probably the one you might come across is the Class D, though at the time of writing it is not part of the syllabus. If and when it is; it will be added. These classes are not a knowledge requirement.

• Class D Amplifier - A Class D audio amplifier is basically a non-linear switching amplifier or pulse width modulated (PWM) amplifier. Class D amplifiers theoretically can reach 100% efficiency as there is no period during a cycle where the voltage and current waveforms overlap as current is drawn only through the transistor that is on.

• Class F Amplifier - Class F amplifiers boost both efficiency and output by using harmonic resonators in the output network to shape the output waveform into a square wave. Class-F amplifiers are capable of high efficiencies of more than 90% if infinite harmonic tuning is used.

• Class G Amplifier - Class G offers enhancements to the basic class AB amplifier design. Class G uses multiple power supply rails of various voltages and automatically switches between these supply rails as the input signal changes. This constant switching reduces the average power consumption and therefore power loss caused by wasted heat.

• Class I Amplifier - The class I amplifier has two sets of complementary output switching devices arranged in a parallel push-pull configuration with both sets of switching devices sampling the same input waveform. One device switches the positive half of the waveform, while the other switches the negative half similar to a class B amplifier. With no input signal applied, or when a signal reaches the zero crossing point, the switching devices are both turned ON and OFF simultaneously with a 50% (Pulse Width Modulation) PWM duty cycle cancelling out any high-frequency signals.

To produce the positive half of the output signal, the output of the positive switching device is increased in duty cycle while the negative switching device is decreased by the same and vice versa. The two switching signal currents are said to be interleaved at the output, giving the class I amplifier the named of: "interleaved PWM amplifier" operating at switching frequencies in excess of 250kHz.

• Class S Amplifier - A class S power amplifier is a non-linear switching mode amplifier similar in operation to the class D amplifier. The class S amplifier converts analogue input signals into digital square wave pulses by a delta-sigma modulator and amplifies them to increase the output power before finally being demodulated by a band pass filter. As the digital signal of this switching amplifier is always either fully "ON" or "OFF" (theoretically zero power dissipation), efficiencies reaching 100% are possible.

• Class T Amplifier - The class T amplifier is another type of digital switching amplifier design. Class T amplifiers are starting to become more popular these days as an audio amplifier design due to the existence of digital signal processing (DSP) chips and multichannel surround sound amplifiers as it converts analogue signals into a digital pulse width modulated (PWM) signals for amplification increasing the amplifiers efficiency. Class T amplifier designs combine both the low distortion signal levels of class AB amplifier and the power efficiency of a class D amplifier.

27 - Oscillators

WHAT IS AN OSCILLATOR?

Oscillators are used in radio circuits to produce radio and audio frequency energy, generally with a sinewave output, though the waveform can be many shapes such as a square wave or saw tooth. The sinusoidal waveform may be AC or VDC. Oscillators used in radio frequency circuits are always very low power devices, in contrast to AC generators in a power station. Nevertheless, the AC power generator and the electronic oscillator are related, in that they both produce sinusoidal electrical energy. Unlike the AC generator, though, the electronic oscillator can produce output on frequencies measured in tens of megahertz. Special oscillators can produce output at microwave frequencies.

An oscillator producing a radio frequency output is actually a low power transmitter in its most basic form. In a radio transmitter and receiver, up to several or more oscillators may be employed.

We are going to look at a number of different types of oscillators and their circuits in this chapter. Don't be put off by the number of circuits as you don't have to remember them in detail. You do need to learn the identifying features of each oscillator circuit. In the assessment, you will be asked to name the type of oscillator shown in the circuit. The fundamental principles of oscillator operation will be explained for each of the types. You will find a repeating theme across all of the oscillator types.

REQUIREMENTS FOR OSCILLATION

If any circuit has the following properties in the required amount, then the circuit will oscillate whether it is supposed to or not: -

a) Amplification.

b) A frequency determining device.

c) Positive feedback (regeneration).

In oscillators, the factors above are designed into the circuit intentionally. The requirements (a) and (c) also occur in many amplifiers. For this reason, care must be taken with amplifiers to prevent or control, in particular, the third requirement for

oscillation, positive feedback. Any amplifier provided with sufficient positive feedback will begin to self-oscillate. Amplifiers are not supposed to oscillate, they are meant to amplify, though many amplifiers can easily become undesirable oscillators.

An amplifier which gets sufficient unwanted positive feedback will become an oscillator and potentially cause interference. Amplifiers that oscillate generate a signal, rather than amplify one. Such unwanted signal generation can cause interference.

A generic-oscillator (figure 27-1) is any amplifier with positive feedback. When an amplifier has enough positive feedback it takes off and oscillates - not a good thing if this is not was intended.

Example: When sound from the speaker of a public address system gets back into the microphone(s) of that system, oscillation will occur. In audio circles, it is called feedback. The amplifier squeals. When this happens at a radio frequency, you can't hear it. The oscillation is well beyond human hearing, but the effect is the same.

FREQUENCY DETERMINING DEVICE

The frequency determining device is usually a resonant LC circuit or a quartz crystal. Slices taken from quartz crystals make the most stable oscillators.

STABILITY

To ensure good stability, an LC oscillator should:

a) Have a high C-to-L ratio.

b) Have a well regulated power supply.

c) Have good isolation between the oscillator and its load.

b) Employ components which have low temperature coefficients.

e) Not be exposed to large changes in temperature.

f) Have all components mechanically rigid.

DRIFT

Drift is an unwanted slow change in the frequency output of an oscillator.

One of the main causes of drift in LC oscillators is unwanted capacitance changes in the circuit. These capacitance changes are mostly due to temperature effects. If the tuning capacitance is made high compared to the inductance in the frequency determining-circuit, then such unwanted capacitance changes will cause a smaller percentage change than if the tuning capacitance was smaller. Simply having a large capacitance compared to inductance produces a more stable oscillator. We say the stability is better with a higher C-to-L ratio; this means a high value of capacitance compared to inductance in the resonance equation.

BUFFER AMPLIFIER 

A buffer amplifier improves the frequency stability of the oscillator by isolating it from the load. An oscillator is not able to deliver much, if any, power to other circuits. If too much power is taken from an oscillator, then it may be 'pulled' off frequency, or even damped so badly that it fails to oscillate. The buffer amplifier is placed immediately after the oscillator. The buffer amplifier has high input impedance and as such draws little or no power from the oscillator. The buffer has just enough gain to supply the following stage with usable power without loading the oscillator.

CHIRPING

In a telegraphy (Morse code) transmitter, the stage which is being keyed (by the Morse key) should never be too close to the oscillator as this can result in oscillator chirping. Chirping sounds like rapid short changes in frequency, very much like a canary chirping. What is happening is that sudden changes of load on an oscillator are occurring when the telegraphy key is closed, pulling the oscillator and hence the output of the transmitter off frequency. The chirp is the oscillator stabilising to the new frequency.

As we go through some different types of oscillator circuits, you will notice a common theme. I would like you to take notice of the:

(a) Type of active device employed (however the type of oscillator is not

      determined by the active device used.)

(b) The polarity of the power supply and whether it is correct!

(c) How feedback (regeneration) is achieved.

(d) What is the frequency-determining device?

(e) The bias arrangement of the active device.

THE ARMSTRONG OSCILLATOR 

In figure 27-2 an NPN BJT is used as the active device. L2 is called the tickler coil and is the distinguishing feature of an Armstrong oscillator. L2 provides regeneration to the input of the BJT. L2 does this by being inductively coupled to L1. Some of the signal in the output circuit is inductively coupled back to the input circuit by L2. The base circuit of the transistor contains a parallel tuned circuit consisting of L1 and C1. This circuit determines the frequency of operation. C1 is variable to change the frequency of oscillation.

Provided the connections to the tickler are the right way around, then feedback is positive (regenerative) and oscillation will be sustained. Connecting the tickler coil the wrong way would produce negative feedback (degeneration) and the circuit would not operate. RB provides for the correct amount of bias current. DC bias flows from earth (or negative) through RE, into the emitter, out of the base, through RB and then back to positive. The value of RB and to a lesser extent RE determines the amount of DC bias current.

RE provides emitter stabilisation to prevent thermal runaway and CE is the emitter bypass capacitor. We do not want the oscillating signal to flow through RE, as any signal current that flows through RE will produce negative feedback. The operation of RE and CE was discussed in an earlier chapter.

The figure 27-3 schematic shows where the DC bias current flows in our Armstrong oscillator. This is fairly straightforward. The amount of DC bias current is primarily determined by the value of the resistor RB.

The capacitor in series with the base is a DC blocking capacitor. This capacitor is also known as a coupling capacitor as it couples signals into the active device and prevents the DC bias from being affected. For example, L1 would short circuit the base to ground if this capacitor were not present. This capacitor will block the DC bias current from flowing into L1 but allow the signal coming from L1-C1 to pass to the base.

The figure 27-4 circuit shows the DC output circuit of the transistor (dashed lines). Because the transistor is forward biased in its base-emitter circuit, then, emitter collector current will flow. This circuit shows the DC emitter-collector current.

A much larger current than the base current flows from the negative terminal of the battery - up through RE, into the emitter out of the collector and back to the positive terminal of the battery.

The figure 27-5 circuit shows where the signals would flow in this oscillator. Assume that the oscillator is meant to produce a sinewave on 1MHz. This will be a sinewave of varying DC, not AC. Most active devices do not work on AC.

When the oscillator is turned on, L1 and C1 start producing an oscillation on 1MHz. This oscillation would normally die down due to losses in the components of the resonant circuit.

The oscillating voltage across L1 and C1 is superimposed on top of the DC bias current in the base circuit. So a 1MHz signal current flows in the base circuit as shown as a dashed line. Notice how the signal flows through CE and not RE. (A little bit of signal current does really flow through RE but not enough to be significant). The capacitive reactance of CE at 1MHz would be 1/10th the value of RE.

Now this 1MHz signal in the base circuit causes a 1MHz signal in the collector circuit. The signal in the collector circuit is much stronger and flows as shown with a different dashed line. The capacitor across the battery bypasses the signal around the supply. We never want signal currents to flow through a battery or power supply. For one reason, the power supply is common to all stages.

If we allow signals from any stage into a power supply, they (the signals) can affect the operation of other stages via the power supply. You will nearly always see a power supply bypass capacitor and often an RFC (radio frequency choke) in series with the power supply just to make it all that much harder for signal currents to get into the power supply.

Notice that the amplified signal flows in the tickler coil. The tickler coil (L2) is inductively coupled to L1. If you like, think of the tickler coil as the primary of a transformer and L1 as the secondary. We have positive feedback from the tickler coil into L1 - so the oscillations are sustained.

L1 is also inductively coupled to L3, so we can take some of the signal current away from the circuit for use elsewhere. An oscillator would not be of much use if it did not provide us with output - L3 is the output. We will discuss what we can do with oscillators in a future chapter.

AN ELECTRON TUBE ARMSTRONG OSCILLATOR

As with the BJT circuit, the tickler coil provides feedback. The tickler coil is the most identifying feature of the Armstrong oscillator.

L1 and C1 determine the frequency of oscillation. The output is taken across L3, which is inductively coupled to L1.

The oscillator is operating at a high frequency (radio frequencies). The one stage that is common to all other stages in a radio system is the power supply. Therefore, the power supply is a potential path for each stage to interfere with the other stages. C2

and the RFC (radio frequency choke), either alone or together, will be seen in many RF signals and be choked by the RFC and bypassed by C2. Because of the high frequency of the oscillator, C2 has a low reactance to RF energy created by the oscillator and bypasses this energy around the power supply. The power supply is only shown as a battery for simplification.

On the other hand, the RFC has a high reactance to high frequencies and blocks radio frequencies from entering the power supply. C2 and the RFC have no effect on the DC from the power supply getting to the oscillator. Looking at it another way, C2 and the RFC form a low-pass filter, allowing DC to pass from the supply to power the oscillator, but blocking RF from getting from the oscillator into the supply.

GRID LEAK BIAS

Bias for the electron tube is obtained by Cg and Rg. I have not discussed this bias arrangement before. In the case of an electron tube, it is called grid leak bias. This type of bias will also be found on a FET, in which case it is called gate leak bias.

By now you should well and truly know that the purpose of bias on any active device is to place the correct DC operating potential onto the input element of the active device, to set the correct operating point and class of operation. However, in the case of BJTs it is bias current rather than voltage.

With grid or gate leak bias, you will always see the same configuration of Rg and Cg at the input of the device (the control-grid or gate). When the oscillator is first turned on, it will have no bias.

Oscillations in the parallel LC circuit (L1 and C1) will place an AC voltage on the grid. When the grid is positive, it will draw current from the cathode (space charge) and Cg will be charged negative on the right and positive on the left. After a few cycles, the negative voltage on the right will remain constant and provide the required negative bias.

The circuit of figure 27-8 shows how grid leak bias works. L1 and C1 are replaced with a source of AC. A diode rectifier is formed by the control-grid and the cathode. I have just shown a semiconductor diode here.

When the oscillator first starts up (when it is turned on), for a while, positive half cycles will cause current to flow in the circuit as shown and Cg will charge negative on the right-hand side. It is this negative voltage that biases the control grid.

THE HARTLEY OSCILLATOR

The Hartley is a simple extension of the Armstrong. I suspect it came about because Hartley was lazy (not really) and worked out a way to make the Armstrong work without having to wind a separate tickler coil.

The tickler coil is now incorporated into part of the resonant tank inductor L1. The output in either circuit flows through a portion of L1 providing the necessary regeneration.

The tapped inductance most easily identifies the Hartley oscillator. The tap position is adjusted to control the amount of feedback - it is not a centre tap as some diagrams suggest.

There is no difference between an Armstrong and a Hartley except the tickler coil is made part of L1. Instead of being a mutually coupled pair of coils, L1 is an autotransformer, the primary of which is the tickler coil. All other operations of this circuit are the same.

A BJT HARTLEY OSCILLATOR

Another Hartley oscillator (tapped inductance doing away with the tickler). L1 and C1 determine the frequency of oscillation. Re and Ce are for emitter stabilisation and bypassing. See figure 27-10.

The input signal from the oscillatory circuit is taken from between the tapping and the top of L1. Feedback is injected back into the circuit because the output flows between the bottom of L1 and the tapping.

About the only other difference with this circuit is that bias is now determined by R1 and R2. This is called voltage divider bias.

C2 is a DC blocking capacitor and C3 is a power supply bypass.

Disconnecting the power supply from the 'signal' using RFCs and a bypass capacitor like C3 is sometimes referred to as power supply decoupling. So, you may see C3 and the RFC described as 'power supply decoupling components.' This is just a fancy way of saying that the RFCs and bypass capacitors 'decouple' or disconnect the power supply from the point of view of the signal.

THE COLPITTS OSCILLATOR 

The configuration of the Colpitts oscillator resembles that of a Hartley in operation and appearance. The difference is that the tapping to the resonant circuit is now made with a capacitive voltage-divider rather than with a tapped inductance. The output voltage is applied to the input via the voltage divider. The ratio of C1 and C2 controls the amount of feedback, a lot easier than fiddling with an inductance.

Sometimes C1 and C2 are ganged to provide a fairly constant amount of feedback over a wide range of operating frequencies.

Ganged capacitors are two or more variable capacitors on the one shaft, with their movable plates connected to that shaft.

A good feature of the Colpitts oscillator is its comparatively good wave purity. This is because C1 and C2 provide a low impedance path for harmonics, effectively shorting them to the emitter. The Colpitts is an exceptionally fine high-frequency oscillator and has been used as the VFO (variable frequency oscillator) in many radio experimenter's transceivers.

The Colpitts and the Hartley are the same - except the Colpitts uses a tapped capacitance rather than a tapped inductance to provide feedback.

The inductor L1 in figure 27-11 can be replaced with a crystal - in which case the circuit becomes a Crystal Colpitts Oscillator.

THE CLAPP OSCILLATOR

All of the oscillators we have discussed up to now, have contained a parallel LC circuit at the input of the active device to determine the frequency of operation. The Clapp oscillator uses a series LC circuit.

In figure 27-12, L1 and C1 form a series resonant circuit to determine the frequency of operation.

The voltage-divider capacitors C2 and C3 perform the same function as in the Colpitts oscillator. The frequency of oscillation is slightly higher than the series-resonant frequency. Because a series circuit has low impedance, the Clapp oscillator is less affected by variations in load conditions. The Clapp oscillator has excellent frequency stability and has frequently found applications in electronics and radio.

Gate leak bias is provided by Cg and Rg. The purpose if Rg is to discharge Cg.

You have to be a little careful not to confuse a Clapp and a Colpitts. The Clapp has a series LC circuit as shown by L1 and C1 in figure 27-12. If C1 was removed in this circuit, then it would be a Colpitts.

QUARTZ CRYSTALS

Quartz crystals or better put, thin slices of quartz cut from a larger crystal, exhibit the piezoelectric effect. They will oscillate just like a tuned circuit. The accuracy of the frequency of oscillation is extremely stable. Hence, quartz is used in watches and many other timing devices.

FREQUENCY OF A QUARTZ CRYSTAL

The physical dimensions primarily determine the resonant frequency of a quartz crystal. However, cuts (the plane or angle of the slice through the main crystal) from the natural crystal will provide different frequency ranges and characteristics.

By proper selection of the type of cut, dimensions of the plate (the plates are the electrical contacts to the crystal) and mode of vibration, it is possible to obtain crystals with resonant frequencies from as low as 6kHz and as high as 75MHz. For higher frequencies, the slice of crystal becomes too thin and fragile and is more susceptible to frequency changes with temperature.

MORE THAN ONE RESONANT FREQUENCY

A quartz crystal actually has two resonant frequencies, a series resonant frequency and a parallel resonant frequency.

A quartz crystal is capable of acting as a parallel resonant circuit or a series resonant circuit. The electrical equivalent circuit of a quartz crystal along with its two resonant frequencies is shown in figure 27-14.

The equivalent circuit is a combination of a series and parallel-tuned network. It is not possible to construct the electrical equivalent circuit of a crystal as any man-made inductor of the magnitude shown would have very large losses indeed. If a quartz crystal is placed in series with a signal path, then signals on the series resonant frequency will be passed easily through the low impedance offered by the crystal. That is, it behaves like an LC series circuit.

TEMPERATURE COEFFICIENT 

The term temperature coefficient defines the way in which the crystal frequency will vary with temperature change. Crystals are usually rated in hertz-per-megahertz-per-temperature change in degrees celsius.

A crystal might have a positive, negative, or zero temperature coefficient.

If a crystal has a negative temperature coefficient (NTC) a temperature increase results in a frequency decrease. A positive temperature coefficient indicates that a temperature increase results in a frequency increase. A crystal with zero temperature coefficient will maintain a relatively constant frequency within the manufacturer's stated frequency limits.

Temperature coefficients are usually expressed in hertz per megahertz per degree celsius (or centigrade), or more simply, in parts per million, with the degrees celsius understood.

When crystal stability is of paramount importance, the crystal is enclosed in a temperature controlled 'oven'. The crystal is then kept at a constant temperature via heating and a feedback mechanism to maintain the constant temperature. Crystal ovens were once used even in standard communications equipment. In modern times, crystal stability has been much improved and ovens are not as common. However, they are still used where equipment is likely to be exposed to great temperature extremes (space, polar environments and the like).

OVERTONES

An overtone crystal is specially ground to obtain enhanced oscillation on odd harmonics of its fundamental frequency. A crystal cut with a fundamental frequency of 10MHz can be cut so as to enable oscillation on 30 and 50MHz, which are the third and fifth overtones respectively. The use of a crystal on overtone frequencies makes stable oscillator operation possible up into the VHF range. In many VHF/UHF transceivers, the conversion of the incoming signal to the first intermediate frequency (IF) is accomplished by a local overtone oscillator.

Crystals that are to be used on overtone frequencies are always connected in series with a signal path because, for overtone operation, the crystal must operate on its series resonant frequency. For this reason, an overtone is more accurately defined as an odd multiple of the series resonant frequency. Most ordinary crystals can be used on the third or fifth overtone. When a crystal is used on an overtone, the crystal vibrates at the overtone frequency. Many things can vibrate (oscillate) in different planes. Take a wobble board. It can vibrate long ways, cross ways and from corner to corner all at different frequencies. Similarly, overtone crystals are cut to enhance vibration in various planes.

CIRCUIT OF AN OVERTONE OSCILLATOR 

In the circuit of an overtone oscillator shown in figure 27-15. The crystal frequency is shown as 43MHz - this is very high for a crystal frequency. The fundamental frequency of the crystal would really be much lower for stability. The crystal is operating on an overtone frequency. The actual fundamental frequency of the crystal could be 14.333MHz. However, the crystal has been cut in such a way that it will physically vibrate on an overtone. In this case 43MHz, which is an odd multiple of the series resonant frequency of the crystal.

You can tell the circuit is not that of a harmonic oscillator, because the crystal is labelled with the same frequency as the output.

The variable capacitor at the output of the JFET would be used to tune the primary of the RF transformer to 43MHz. The 100 ohm resistor and the 0.01µF capacitor provide power supply decoupling. That is, they form a simple, low-pass filter to prevent RF from getting into the power supply.

THE HARMONIC CRYSTAL OSCILLATOR

A crystal oscillator with its output circuit tuned to any harmonic of the fundamental frequency of the crystal is called a harmonic oscillator. The harmonic oscillator takes advantage of the flywheel effect of the output stage to maintain oscillation in the same way as a frequency multiplier.

The harmonic oscillator operates on an entirely different principle to that of the overtone oscillator. In the harmonic oscillator, the crystal is physically vibrating on its fundamental frequency. In the overtone oscillator, no fundamental vibration or frequency is present anywhere in the circuit.

THE PIERCE CRYSTAL OSCILLATOR

The Pierce crystal oscillator has no resonant tank circuit. The crystal is connected directly between the output and input of the active device used. The crystal operates on its series resonant frequency.

The Pierce oscillator is a crystal oscillator. It must have a crystal. An interesting thing about the Pierce is that the crystal provides the feedback path. The crystal shown is connected between drain and gate. The crystal is series resonant meaning the crystal is operating on its series resonant frequency and has a low impedance. Any signal that can travel from the drain to the gate is positive feedback.

The resistor between gate and source provides the small bias voltage for the JFET.

THE COLPITTS QUARTZ CRYSTAL OSCILLATOR

The Colpitts crystal oscillator is like any other Colpitts except a crystal is installed in place of the LC tank. As with a normal Colpitts, feedback is provided by the capacitive voltage divider. The operation of the circuit is the same except that the crystal now determines the frequency of oscillation. The crystal operates on its parallel resonant frequency. Since the Q of the circuit is high, the feedback required is considerably less than with standard LC Colpitts.

A small 'trimmer' capacitor may be placed in series with the crystal to enable small adjustments to the crystal frequency (doing this is not a unique feature of the Colpitts). This capacitor would typically be 30 to 100 picofarads and one should not expect to vary the frequency by more than +/- a few kilohertz if predictable operation is to be maintained. Adjusting a crystal frequency in this way is called pulling the crystal. Try to change the frequency too much using this method and you may find that the crystal will jump to some unpredictable frequency and operation becomes unreliable and unstable.

This excessive pulling is sometimes done illegally on 'pirate' radio. Often referred by the users as a slider control since you can slide-off-channel between channels. It is a bad engineering practice and illegal as it can cause the transmitter to operate on unauthorised channels (which is the intention). However, more important than the legalities is the interference to other radio services, which has the potential to endanger life.

There is nothing new in the circuit of figure 27-17 The LC circuit has been replaced by the crystal. There is a variable capacitor in series with the crystal to enable small frequency adjustment.

A VOLTAGE CONTROLLED OSCILLATOR

Figure 27-18 shows one method of adjusting a crystal oscillator's frequency with a varactor diode.

This technique is frequently employed in the BFO/clarifier (single sideband is to be discussed) circuits of transceivers. The crystal would form part of a standard crystal oscillator. The reverse-biased varactor diode is connected in series with the crystal and the reverse bias voltage (and hence the junction capacitance) is adjusted by the potentiometer (variable resistor) R2. RS, D1, C1 and R2 provide an adjustable and regulated reverse voltage for D2.

You might ask why bother with such an arrangement? The alternative would be to have a variable capacitor in place of D2. In addition, this capacitance will, by necessity, have to be mounted on the front panel of the radio. This creates all sorts of engineering difficulties. The wiring between the variable capacitor and the crystal all

form part of the total capacitance in the oscillator circuit. However, with the varactor method just described, the variable capacitance is right at the crystal and R2 can be mounted in any convenient position on the front panel, as the wiring between R2 and D2 has no appreciable effect on the operation of the oscillator. This is an excellent method to overcome the unwanted stray capacitance effects of wiring.

THE PIEZOELECTRIC EFFECT

Piezoelectricity is a complex subject, involving the advanced concepts of both electricity and mechanics. The word piezo-electricity takes its name from the Greek piezein "to press", which means pressure-electricity. Certain classes of piezoelectric materials will, in general, react to any mechanical stresses by producing an electrical charge. In a piezoelectric medium, the strain or the displacement depends linearly on both the stress and the field. The converse effect also exists, whereby a mechanical strain is produced in the crystal by a polarising electric field. This is the basic effect that produces the vibration of a quartz crystal.

Quartz resonators consist of a piece of piezoelectric material precisely dimensioned and oriented with respect to the crystallographic axes. This wafer has one or more pairs of conductive electrodes, formed by vacuum evaporation. When an electric field is applied between the electrodes, the piezoelectric effect excites the wafer into mechanical vibration. Many different substances have been investigated as possible resonators, but for many years quartz has been the preferred medium for satisfying the needs for precise frequency generation. Compared to other resonators e.g. LC circuits, mechanical resonators, ceramic resonators and single crystal materials, the quartz resonator has proved to be superior by having a unique combination of properties. The material properties of quartz crystal are both extremely stable and highly repeatable. The acoustic loss or internal fraction of quartz is particularly low, which results in a quartz resonator having an extremely high Q-factor. The intrinsic Q of quartz is 107 at 1MHz. Mounted resonators typically have Q factors ranging from tens of thousands to several hundred orders of magnitude better than the best LC circuits. The second key property is its frequency stability with temperature variations.

PHASED LOCKED LOOP FREQUENCY SYNTHESIS

The Phased Locked Loop (PLL) method of frequency synthesis is now the most commonly used method of producing high-frequency oscillations in modern communications equipment. There would not be an amateur or commercial transceiver of any worth today that does not employ at least one if not several, phase locked loop systems, to generate stable high frequency oscillations.

PLL circuits are now frequently being used to demodulate FM signals, making obsolete the Foster-Seeley and ratio detectors of early years. Other applications for PLL circuits include AM modulators, FSK decoders, two-tone decoders and motor speed controls.

The PLL technique has, surprisingly, been around for a long time. In the 1930s, the superheterodyne receiver was in its heyday (and it's still going strong today). However, attempts were made to simplify the number of tuned stages in the superheterodyne.

THE HOMODYNE RECEIVER

Around 1932, British radio engineers developed a new type of receiver to challenge the superheterodyne - it was called the Homodyne or Synchrodyne. The idea was simple: the receiver consisted of a mixer and a local oscillator, followed immediately by an audio amplifier!

When the input signal and local oscillator are mixed at the same phase and frequency, the output is an exact audio representation of the modulated carrier.

Problems, however, occurred in trying to keep the local oscillator on the same phase and frequency as the input signal. To counteract local oscillator drift, the output of the local oscillator was fed together with a sample of the input signal to a phase detector. The output of the phase detector was a correction voltage which was then applied to the local oscillator to keep it on frequency.

It was this type of feedback circuit, which led to the evolution of the phase locked loop. The homodyne receiver was superior to the superheterodyne, but the cost of the PLL circuit outweighed its advantages, so the idea did not take off.

In the late 80s some single-chip receivers were developed using the homodyne principle. Such receivers are referred to by some manufacturers as zero intermediate frequency receivers since there is a direct conversion from RF to audio.

DEVELOPING A PLL

Let's have a look at how we can develop our own PLL system, step by step from scratch and also look at a practical application.

About 120 years ago, Pierre Curie, along with his brother Jacques, discovered the effect that an electric field has on certain crystals. The Curies discovered that when physical pressure was applied to certain crystals, electric charges were produced on the opposite faces. Conversely, if an electric field was applied, the crystal structure itself would distort. We know this phenomenon today as the piezoelectric effect.

With the invention of wireless, there came a need for an accurate frequency determining device. So evolved the crystal oscillator with its excellent frequency stability.

The crystal oscillator had one major limitation; it could only be used for a narrow range of frequencies. The crystal frequency can only be varied slightly by use of a variable capacitor or the use of circuits designed to respond to harmonics of the crystal's fundamental frequency, as is done with frequency multipliers or overtone oscillators.

For a larger range of frequencies, these methods are not very practical. To obtain a larger frequency range and maintain essential stability, two crystal oscillators could have their outputs heterodyned (mixed) to produce two new frequencies - i.e. the sum and the difference of the two original frequencies.

Master /Slave System

As a practical example: a 24-channel system could use four master crystals, heterodyned one at a time with each of six other slave crystals, to give us four times six or 24 output frequencies.

So, with the use of only 10 crystals, we can obtain 24 frequencies. This appears okay, but the inhibiting factor in such a system is the cost of the crystals. Imagine the cost of a 400-channel system using crystals!

For those of you who were around at the time of the 23 channel CB radio this master/slave technique was used to generate the 23 channels, though some enterprising operators worked out they could get an additional channel by switching in the last master/slave combination.

Doing more with a VCO

Voltage controlled oscillators allow us to tune easily to a large range of frequencies. The big problem is the VCOs are nowhere as stable as a crystal oscillator. Any slight voltage variation in the circuit will cause the frequency to shift. If there was some way we could combine the flexibility of the VCO with the stability of a crystal oscillator; we would have the ideal frequency synthesis system.

Let's try something. Suppose we feed the output of a VCO and a Crystal Oscillator into a phase detector. What's a phase detector? Well, it is similar to a discriminator or ratio detector used in frequency demodulation, or it could be a digital device (an exclusive or gate).

If two signals are fed into a phase detector and these signals are equal in phase and frequency, there will be no output from the detector. On the other hand, if the signals are not in phase, the difference is converted to a DC output voltage. The greater the frequency/phase difference between the two signals, the larger the output voltage.

Now, where were we? Right, take a look at figure 27-20. The outputs of the VCO and the crystal oscillator are combined with a phase detector and any difference will result in a DC voltage output. Now, suppose this DC voltage is coupled back to the VCO in such a manner that it drives the output of the VCO towards the crystal oscillator frequency - eventually, the VCO will LOCK onto the crystal oscillator frequency. This is a PHASE LOCKED LOOP in its most basic form. Only part of the VCO output need be sent to the phase detector. The rest can be usable output.

Further Development 

Wait a minute! The VCO is locked onto the crystal oscillator and is, therefore, behaving as if it was a fixed frequency oscillator. This gives us the stability of a crystal oscillator, but we have lost the flexibility we were trying to achieve. We may just as well use the crystal oscillator alone for all the good this arrangement has done us. It certainly doesn't appear as if we have accomplished anything at all.

Okay, let's investigate how this problem may be overcome. Suppose our crystal frequency was 10MHz, but we wanted the VCO to operate on 20MHz. The phase detector will, of course, detect a frequency difference and pull the VCO down to 10MHz, but what if we could fool the phase detector into 'thinking' the VCO was really only operating on 10MHz when in reality it is operating on 20MHz. Take a look at figure 27-21.

For example, suppose in figure 27-21 we used a divide-by-four instead of the divide-by-two. Then, at lock, the VCO would be oscillating at 40MHz yet will still be as stable as the crystal reference frequency.

Counters/Dividers

If we could design a divider that would enable us to change the 'divide by' figure at will, we would certainly have a very versatile frequency generating system.

Such frequency dividers are available and are known as programmable frequency dividers. The internal operation of such circuits is not within the scope of this book, but let's have a look at the basic principle involved.

Programmable dividers are digital circuits in that they operate with two voltage levels, a low-level (O) and a high level (1). Ordinary circuits which operate on all voltages are called analogue. As the VCO is an analogue device, the sinewaves that it outputs to the frequency divider need to be converted into square waves. This changes the wave shape, but not the frequency.

The divider is really a pulse counter. It can be programmed to count to two and then reset, count to two again and reset and so on. At each reset, one pulse is output from the divider - this is a divide-by-two action. This divider would be suitable for our circuit of figure 27-21.

More elaborate counter/dividers can be designed to count to different amounts before resetting - e.g. a count-to-four divider would be a divide-by-four; a count-to-35 would be a divide-by-35; and so on. Remember that no matter what the reset level is, we only get one output pulse from each reset. The counter/divider may have several inputs which can be programmed in binary or some other digital code to determine its divide-by number. For example, if the divider had four inputs to be coded in binary and we applied a high level on inputs 1 and 3, a binary code of 1010 (which is the equivalent of decimal 10), we would have a divide-by-10 action. More specialised programmable dividers provide for a large range of frequency divisions.

A PRACTICAL PLL 

Now we have assembled all the necessary components for a workable PLL system: A voltage controlled oscillator, a crystal oscillator, a programmable divider and a phase detector.

One of the most versatile PLL systems, seen particularly in Citizens Band transceivers, is the UNIDEN 858. Figure 27-22 shows a block diagram of the system. Let's work through it step by step and see what we can discover.

The reference crystal, in this case, is 10.24MHz but note that in this instance the reference crystal is not oscillating at the reference frequency - its signal is passed through a 1024 divider to give us a reference frequency of 10kHz. This 10kHz reference signal is passed to the phase detector.

Now we know that the signal coming from the VCO must be divided to 10kHz before being applied to the phase detector - but notice one thing: in this system, our VCO must oscillate at around 36MHz to give us the correct output frequency. This frequency is going to take a lot of dividing to get it down to the 10kHz reference frequency.

So here a cunning method has been used to convert the VCO frequency to a workable value before division. This is where the 11.2858MHz crystal oscillator comes into play. It's an overtone oscillator producing an output on the third overtone of the crystal's fundamental frequency - i.e., 33.8575MHz. This signal is then mixed with the VCO output, the difference frequency being around 2 to 3MHz. This signal can then be divided to 10kHz quite simply and applied to the phase detector.

Before we get too involved in some actual circuit frequencies, let's look more closely at the frequency divider.

We see that it is a programmable divider; it can be set to divide by any amount from 1 to 399. The input data to the divider is binary coded decimal (BCD) and is applied to pins 13 through to 22 on the actual integrated circuit.

What's BCD? It's a method of expressing a decimal value as a four-bit binary number. The units in the decimal number are expressed as a four-bit binary number, as are the tens, then the hundreds, etc. For example, decimal 251 would require three four-bit conversions: 1 is expressed as 0001; 5 becomes 0101 and 2 equals 0010. The final figure is the chain of the three four-bit numbers: 251 equals 0010 0101 0001 in BCD.

The divider has 10 inputs. These inputs can be set with a BCD code in the range 0 to 399 which equates to 400 channels. For channel 399 the four bit BCD code would be 0011 1001-1001 (3-9-9).

So there are a total of 400 possible input combinations to the programmable divider, which theoretically means 400 operating frequencies, provided the radio frequency stages of the transceiver remain in tune or are tuned accordingly.

A logic (1) is represented by a +5V input level and a logic (0) by zero volts. If the input to the divider is supplied with the BCD code for 146 (0001 0100 0110), then the input signal will appear at the output divided by 146.

Another point worth mentioning is that the VCO signal is not the final transmit frequency. All necessary processing of the signal to be transmitted is performed before the PLL stage is reached. The output of the VCO is then mixed with the intermediate frequency (IF) and the difference frequency produced is the actual transmit frequency.

Conversely, during receive operation, the VCO and the incoming signal are heterodyned to produce the IF.

A WORKED EXAMPLE

Let's take a desired output of 28.505MHz and develop the conditions which would need to exist around the circuit. Since the output is 28.505MHz, the VCO will be 7.8025MHz higher (the IF). The VCO is therefore 36.3075MHz. This is fed to the mixer along with a 33.8575MHz signal derived from the third overtone of the 11.2858MHz crystal oscillator.

The 36.3075MHz and 33.8575MHz signals mix to produce a difference frequency of 2.45MHz. Now the divider must be set to divide the 2.45MHz frequency down to 10kHz. This requires a BCD code on the data inputs equivalent to 245 decimal (divide by 245). The logic levels applied to the 10 BCD inputs would be 10 0100 0101

The 10kHz signal produced by the divider is phase detected with the stable 10kHz reference frequency from the crystal oscillator and a control voltage applied back to the VCO. After a very brief period, the circuit will establish a lock.

Changing the divide-by number will change the output frequency in 10kHz steps over a maximum frequency range of 400 x 10kHz = 4MHz. Incrementing or decrementing the divider will alter the VCO frequency by 10kHz. So the channel spacing, in this case, is 10kHz.

If you think there is some relationship between the 10kHz reference frequency and the 10kHz channel steps, then you're right! If 5kHz channel spacing was required, all that would be necessary is to change the 1024 divider to a 2048 divider. The 858 chip has a provision on board for this - pin 7 can be toggled between high and low to change from 1024 to 2048.

A microprocessor can be added to the PLL circuit to control the logic fed to the programmable divider. Such systems are common in modern communications receivers/transmitters. See figure 27-24. Now a whole new scope of functionality is available. The microprocessor can be told what to do from a keypad - and its internal program can do things like change frequency, memorise frequencies, scan a range of frequencies, or operate between different programmable transmit and receive frequencies and much more. The microprocessor can even re-tune the VCO and other parts of the transceiver to give good broadband coverage. An alternative to re-tuning the VCO is to have several VCOs and have the microprocessor switch the appropriate one into the circuit for the desired frequency range.

You now should have a very good idea of the way PLL frequency synthesis systems work. More complex systems do exist, but they are merely extensions of what has been described. Some modern communications equipment may use not one, but several PLLs and even PLLs within PLLs.

DIRECT DIGITAL SYNTHESES (DDS) 

There is currently no assessment requirement on DDS (in Australia) apart from the general concept of that DDS is a method of digitally synthesising signals.

We are used to digital signals. Many things today are digital such as DTV, mobile phones, broadcast radio and many others. We are not digital so there has to be a digital analogue conversion (DAC) so we can hear it. The types of information encoded into digital are usually complex. A TV signal contains an enormous amount of data, but vision and sound can be encoded to digital and transmitted and decoded into sound and picture at the receiver, though the picture can remain digital. It is the TV screen that produces light output that we perceive as analogue.

So what if we were to store just one sinewave only - one cycle in digital format. We could do this easily with just a small amount of memory. Then if we were to read that memory and perform a digital to analogue conversion we would get one cycle of the sinewave.

Not that interesting really. What if we used a clock to access the stored digital data for a sinewave repeatedly? Read that data and do a DAC and repeat endlessly. If we did this, we would have a continuous sinewave - we would have a signal that could be an audio or RF signal of almost any frequency. We would have created a continuous sinewave signal using only one digitally stored single cycle. We would need a DAC and some analogue filtering after it. The point is though we have created an RF signal without tuned circuits. We would need a stable frequency source for the clock reading the data. This would be a crystal. However, using some tricks we can not only produce one frequency from the digitally stored single cycle, we can produce a very wide range of frequencies. This is the essence of direct digital syntheses.

From the start, unlike PLL, DDS has been integrated into specialised integrated circuits. The same as PLL has today - so there is no need to build discrete component circuits for DDS or PLL.

What is Direct Digital Synthesis?

Direct digital synthesis (DDS) is a method of producing an analogue waveform, usually a sinewave, by generating a time-varying signal in digital form and then performing a digital-to-analogue conversion. Because operations within a DDS device are primarily digital, it can offer fast switching between output frequencies, fine frequency resolution and operation over a broad spectrum of frequencies. With advances in design and process technology, today's DDS devices are very compact and draw little power.

The ability to accurately produce and control waveforms of various frequencies and profiles has become a key requirement common to a number of industries. Whether providing agile sources of low-phase-noise variable-frequencies with a good spurious performance for communications, or simply generating a frequency stimulus in industrial or biomedical test equipment applications, convenience, compactness and low cost are important design considerations.

Many possibilities for frequency generation are open to a designer, ranging from phase-locked-loop (PLL)-based techniques for very high-frequency synthesis to dynamic programming of the digital-to-analogue converter (DAC) outputs to generate arbitrary waveforms at lower frequencies. But the DDS technique is rapidly gaining popularity for solving frequency (or waveform) generation requirements in both communications and industrial applications because single-chip IC devices can generate programmable analogue output waveforms simply and with high resolution and accuracy.

Furthermore, the continual improvements in both process technology and design have resulted in cost and power consumption levels that were previously unthinkable. For example, the AD9850 a DDS-based programmable waveform generator (figure 27-25), operating at 5.5 V with a 25-MHz clock, consumes a maximum power of 30 milliwatts

How does a DDS device create a sinewave?

Here's a breakdown of the internal circuitry of a DDS device: its main components are a phase accumulator, a means of phase-to-amplitude conversion (often a sine look-up table) and a DAC. These blocks are represented in figure 27-26.

DDS produces a sinewave (or any other wave shape) at a given frequency. The frequency depends on two variables, the reference-clock frequency and the binary number programmed into the frequency register (tuning word).

The binary number in the frequency register provides the main input to the phase accumulator. If a sine look-up table is used, the phase accumulator computes a phase (angle) address for the look-up table, which outputs the digital value of amplitude, corresponding to the sine of that phase angle, to the DAC. The DAC, in turn, converts that number to a corresponding value of analogue voltage or current.

To generate a fixed-frequency sinewave, a constant value (the phase increment-which is determined by the binary number) is added to the phase accumulator with each clock cycle. If the phase increment is large, the phase accumulator will step quickly through the sine look-up table and thus generate a high frequency sinewave. If the phase increment is small, the phase accumulator will take many more steps, accordingly generating a slower waveform.

Continuous-time sinusoidal signals have a repetitive angular phase range of 0 to 2π. The digital implementation is no different. The counter's carry function allows the phase accumulator to act as a phase wheel in the DDS implementation.

To understand this basic function, visualise the sinewave oscillation as a vector rotating around a phase circle (figure 27-27). Each designated point on the phase wheel corresponds to the equivalent point on a cycle of a sinewave. As the vector rotates around the wheel, visualise that the sine of the angle generates a corresponding output sinewave. One revolution of the vector around the phase wheel, at a constant speed, results in one complete cycle of the output sinewave. The phase accumulator provides the equally spaced angular values accompanying the vector's linear rotation around the phase wheel. The contents of the phase accumulator correspond to the points on the cycle of the output sinewave.

The phase accumulator is a modulo-M counter that increments its stored number each time it receives a clock pulse. The magnitude of the increment is determined by the binary-coded input word (M). This word forms the phase step size between reference clock updates; it effectively sets how many points to skip around the phase wheel. The larger the jump size, the faster the phase accumulator overflows and completes its equivalent of a sinewave cycle. The number of discrete phase points contained in the wheel is determined by the resolution of the phase accumulator (n), which determines the tuning resolution of the DDS.

Creating the analogue sinewave

A phase-to-amplitude lookup table is used to convert the phase accumulator's instantaneous output value (28 bits for AD9850)-with unneeded less significant bits eliminated by truncation-into the sinewave amplitude information that is presented to the (10-bit) D/ A converter. The DDS architecture exploits the symmetrical nature of a sinewave and utilises mapping logic to synthesise a complete sinewave from one quarter-cycle of data from the phase accumulator. The phase-to-amplitude look-up table generates the remaining data by reading forward then back through the look-up table. This is shown pictorially in figure 27-28.

28 - Propagation

THE IONOSPHERE

The ionosphere is a region of the upper atmosphere extending from a height of about 50 km to greater than 500 km. Within this region, some molecules of air become ionised by ultraviolet radiation from the sun. The ionised gas within the ionosphere is called plasma.

Ionisation is a process by which electrons, having a negative charge, are stripped from neutral atoms or molecules to form positively charged ions. It is these ions that give their name to the ionosphere. The electrons that have been stripped off are light and free to move. These electrons under the influence of an electromagnetic wave will absorb and re-radiate energy and modify the direction of an electromagnetic wave front. If the electron density is sufficient and the frequency of the electromagnetic wave is neither too high nor low, then total wave refraction will occur.

There are four regions of the ionosphere called layers.

D 50- 90 km

E 90-140 km

Fl 140 - 210 km

F2 > 210 km

The regions of the ionosphere are not sharply defined and merge smoothly from one into the other, each region containing similar chemical and physical properties. Ionisation of the D region is weak because it is low down in the atmosphere. The D region can refract signals at low frequencies (less than 5MHz). High frequencies pass right through it with only partial attenuation. After sunset the D region disappears rapidly due to recombination of its ions.

The E region is also known as the Kennelly-Heaviside layer. The rate of ionic recombination is rapid after sunset and the region has usually disappeared by midnight. The E region can refract higher frequency signals than the D region. In fact, the E region can refract signals as high as 20MHz. The ionospheric layers during the day and the night are shown in figure 28-1.

During daylight hours, the F, region separates into two distinct regions called the Fl and F2. The ionisation levels in these regions can be quite high and varies greatly depending upon the degree of ultraviolet radiation from the sun, which in turn is primarily determined by the altitude of the sun (i.e. time of day). At the height of the F region the density of the atmosphere is low and because of this, recombination of ions occurs slowly after sunset. The F2 region will remain throughout the night at a fairly constant ionisation level. The F regions are responsible for long-distance communications due to their ability to refract signals up to 30MHz and also due to the long skip distance provided by refraction from such a high elevation.

CAUSES OF IONISATION

Two kinds of solar radiation cause ionisation in the ionosphere, namely X-rays and extreme ultraviolet (EUV). The X-ray output from the sun is irregular, increasing greatly during large solar flares. However, by far, the most important ionisation radiation is EUV. It is generated by the chromosphere in hot plage regions that overlie sunspot groups. Figure 28-2, EUV and X-rays primary cause of ionisation.

Meteor storms occur often and are predictable. They can cause considerable ionisation and are used for long distance HF communication.

A plage is a bright region in the chromosphere of the sun, typically found in regions of the chromosphere near sunspots. The term itself is poetically taken from the French word for "beach".

At any time, the EUV output from the sun is approximately constant, but varies from month to month and year to year, as the number of sunspots vary.

11 VEAR SUNSPOT CYCLE

The most important slow changing factor in high frequency (HF) propagation prediction is the 11-year sunspot cycle. Solar activity follows a cycle, which has a period of 11 years. The best indication of solar activity is the sunspot number. Sunspots are always accompanied by plage areas, which are the source of extreme ultraviolet radiation. It has been found that the solar radio flux at a wavelength of 10.7cm (10cm flux) is closely related to the sunspot number and is more easily measured. The sunspot number and the 10cm flux may vary greatly from day to day so that monthly or yearly averages are usually employed to show the progress of the solar cycle.

Figure 28-3 shows all the sunspot cycles since accurate recording began. Sunspot cycles have been traced further back by means other than direct solar radiation. There is some evidence that the 11-year sunspot cycle is not set in stone. Earth's cycles take centuries to be completely mapped and established. For all we know there may be cycles within cycles. It would be naive of us to assume that after just 110 years of direct solar observation that solar cycles are firmly established.

SPORADIC-E

Sporadic-E layers are only a few kilometres thick and can have peak electron density comparable to the F regions maximum density. Sporadic-E layers, like the higher F-layer, are very efficient reflectors of HF signals. Sporadic-E is formed mainly by the concentration of winds of ions and electrons into a thin layer. At mid-latitudes, sporadic-E is most prevalent during summer and at midday. In the equatorial zone, it is nearly always present at midday.

Communication distances of 800-2200 km can occur using a single sporadic E region. This variability in distance depends on a number of factors, including ion cloud height and density. MUF also varies widely, but most commonly falls in the 25 - 150MHz range, which includes the FM broadcast band (87.5-108MHz), band 1 VHF television (American channels 2-6, Russian channels 1-3, and European channels 2-4, the latter no longer used in Western Europe), CB radio (27MHz) and the amateur radio 2-meter, 4-meter, 6-meter, and 10-meter bands. Strong events have allowed propagation at frequencies as high as 250MHz.

As its name suggests, sporadic E is an abnormal event, but can happen at almost any time; it does, however, display seasonal patterns. Sporadic E activity peaks predictably in the summertime in both hemispheres. In North America, the peak is most noticeable in mid-to-late June, trailing off through July and into August. A much smaller peak is seen around the winter solstice. Activity usually begins in mid-December in the southern hemisphere, with the days immediately after Christmas being the most active period.

CRITICAL FREQUENCY - MAXIMUM USABLE FREQUENCY - ABSORPTION LIMITING FREQUENCY 

At vertical incidence (straight-up), the highest frequency which an ionospheric layer will reflect is called the critical frequency (fc).

The highest frequency which is returned to earth at a given angle of radiation is referred to as the maximum usable frequency (MUF).

The absorption limiting frequency is the lowest frequency for reliable radio communication via the ionosphere.

Operating a radio transmitter right on the MUF will not produce the most reliable communications, as the precise MUF does fluctuate somewhat. The optimum working frequency (OWF) is the one that provides the most consistent communications. For transmission using the F2 region, the optimum working frequency is about 85% of the MUF. However, when the E layer is used, propagation is quite consistent if a frequency very near but less than the MUF is used. Since ionospheric attenuation of radio waves is inversely proportional to frequency, using a frequency as close to the MUF as possible results in the maximum signal strength.

VIRTUAL HEIGHT

The virtual height is the height of the ionosphere when regarded as a flat plane surface reflector such as a mirror.

Until it reaches the ionosphere, a radio wave propagates in a straight line. Once in the ionosphere, it may be refracted back to earth. Refraction is a process whereby the wave front is slowly bent downward toward the earth. Although a wave is actually refracted in the ionosphere, it is permissible to substitute a simple triangular path for the real ray path, as if the ray was mirror-reflected.

Radio waves are often spoken of as being reflected from the ionosphere when in fact they are refracted by the ionosphere and reflected by the earth.

CRITICAL ANGLE

The critical angle is the angle measured between the wavefront incident on the ionosphere and a line extended to the centre of the earth. For each frequency, there is a critical angle and if the wavefront arriving at the ionosphere is less than the critical angle then wave refraction will not occur.

The shortest distance through an ionospheric region is when the wavefront strikes the region at vertical incidence. The critical frequency is the highest frequency returned to earth when the wave is transmitted at vertical incidence. However, if the wavefront strikes the ionosphere obliquely then the apparent depth of the region is greater and frequencies higher than the critical frequency will be returned to the earth. For any particular frequency higher than the critical frequency there will be a minimum critical angle if refraction is to take place. A critical angle of zero corresponds to vertical incidence.

GROUND WAVE 

Ground wave is the wavefront, which upon leaving the antenna, propagates close to the earth's surface. Severe signal losses due to ground conductivity limits the range of ground waves to about 100 km overland and 300 km over water for the lowest HF frequencies.

The higher the frequency, the shorter the ground wave coverage of the transmitter. Ground wave distance drops off very quickly with increasing frequency. Long ground wave is best under 5MHz. Even on the 80M band (3.5MHz) when communication over a short distance, say across town, you may very well be communicating using skywave.

SKIP DISTANCE

The skip distance is the distance from the transmitter to where the skywave first returns to the earth. Within the skip distance, only ground wave communication is possible. The skip distance is shorter for lower operating frequencies. Between the point where the ground wave ends and the point where the skywave first returns to earth, no signals will be heard. This area is called the skip zone. The skip zone is a no signal area.

FACTORS DETERMINING SKIP DISTANCE 

The main factors affecting range are frequency, radiation angle and the height of the reflecting region.

If the height of the reflecting region is increased, then the skip distance will increase. As the frequency of the transmission is increased the skip distance will increase until the frequency exceeds the MUF, above which the signal is not refracted back to earth.

If the angle of radiation above the earth's surface is increased, then the skip distance is decreased. If the transmission frequency is greater than the critical frequency, then making the angle of radiation too high will cause the wave front to penetrate the refracting region.

LONG-DISTANCE COMMUNICATIONS ABOVE THE HF

Temperature inversions in the earth's troposphere make it possible for radio waves to be ducted or guided over large distances. This mode of propagation is called tropospheric ducting. This propagation mode occurs only on VHF frequencies and above.

The troposphere is the layer of the atmosphere that lies directly above the surface of the earth; it extends to a height of about 10.5km. Under normal conditions, the density of the troposphere is higher near the surface of the earth and becomes progressively lower at higher altitudes. A temperature inversion occurs when a pocket of warm air is trapped above cool air. Instead of a gradual changing density, abrupt changes occur, making complete refraction possible. The refracted wave does not travel back to earth; it is refracted back and forth by both boundaries on each side of the layer of warm air. The trapping medium is called a tropospheric duct. In order to use the duct, both transmitting and receiving antennas must be within the duct.

FADING

Fading can be broken down into two main categories: multiple path reception and selective fading. Multiple path reception occurs when signals arrive at the receiving antenna by more than one path. No path length is exactly the same from one moment to the next due to the dynamic nature of the ionosphere.

Multi-path signals may arrive in-phase one moment and produce signal enhancement and the next moment may arrive out-of-phase and produce, at times, total cancellation. Under such conditions, the received signal may fluctuate wildly. Selective fading occurs when individual frequency components undergo different amounts of refraction at the ionosphere to such an extent that some of the frequency components may not arrive at the receiving antenna.

Multiple path reception occurs when the skywave returns to the earth within the ground wave region of the transmitter. Since ground wave coverage does not extend far, this type of fading only occurs when the skip distance is short. This effect is most noticeable in the 160-metre amateur band. AM broadcast stations frequently employ 5/9 wavelength antennas. Antennas of this wavelength have a radiation angle which provides a skip distance that falls outside the ground wave coverage area, thus avoiding fade at the ground wave-skywave boundary.

Fading due to multiple path reception can occur when the signals arriving at the receiving antenna travel by different ionospheric regions, or when signal reflection from a large object such as a man-made structure or a mountain range is involved.

Because a single radio transmission consists of a band of frequencies, then it is possible for a group of frequencies within the signal bandwidth to be refracted by a greater or lesser amount. This can result in some signal components not arriving at the receiving antenna - this phenomenon is called selective fading. Expectedly, the signals of wider bandwidths are more susceptible to selective fading. A double sideband signal (AM) is more likely to suffer selective fading than a single side band signal (SSB) due to its wider bandwidth. A telegraphy signal will not experience any selective fading. One classic example of this phenomenon is the well known high school physics experiment using a light beam from a torch and a prism. The different colours (frequencies) are seen to be refracted by different amounts. Sunlight through water droplets undergoes selective refraction and creates a rainbow.

HF (ionospheric) propagation is crucial and will always be so. In the event of war, communication satellites and submarine cables would be among the first things to go, leaving nothing but HF radio communications.

29 - Amplitude Modulation

This is the first time we will be discussing how radio is used to transfer information across a long distance in virtually no time at all. Therefore, it is my intention to cover the concepts completely without the use of unnecessary mathematics. Please do not think that without all of the mathematics we are short changing the subject. I have worked with many trainees, who have come straight out of university and when I have asked them about amplitude modulation they reel off a whole set of mathematical equations in an attempt to explain it. However, when I have asked, "What really is AM"? I have often received a blank look. Mathematics alone does not always explain everything in such a way that you really get a feel for the subject. I hope that during this chapter you will gain an understanding of what radio transmission and amplitude modulation is about. This and the next two chapters may be verbose and sometimes repetitive, but this is done to help you understand the important real concepts of AM transmission and reception.

Firstly, let's have a look at what radio transmission is really all about. It's fine to have a microphone to speak into and expect to be heard somewhere else in the world. What are the real principles involved? This does not apply just to amplitude modulation but to all types of modulation.

Modulation - in radio communications means combining signals, one of which is normally the information we want to transmit (which is usually a low frequency such as audio or voice), with a radio frequency.

Radio communication uses the ability of an electromagnetic wave to transfer information from one point to another. It is very easy to create an electromagnetic wave, send this wave to an antenna and have this wave propagate over a long distance at the speed of light. It's another matter to have the electromagnetic wave contain useful information such as voice, or some other form of intelligence, which after all is the main objective of radio communication.

Remember that electromagnetic radiation takes many forms. Light is electromagnetic radiation. The infrared signal from your TV remote control is electromagnetic radiation. The heat given off by a bar radiator is electromagnetic radiation. The whole secret of radio communication is to place information onto the signal, to convey intelligence or a message from one point to another.

Amplitude modulation (AM) is just one method of doing this and is the first method ever used to transfer voice information from one place to another. There are many misconceptions about how this is done and what AM really is. The first thing that should be understood is that voice frequencies range from about 50Hz to about 3000Hz. Would it be more simple if we could just talk into a microphone, convert the sounds from our voice to electrical energy, feed it to an antenna and have it transmitted to anywhere we wanted?

The problem is that voice frequencies are not high enough in frequency to be radiated by an antenna efficiently. You can put voice frequencies right into an antenna. However, when you work out the length of antenna needed from the wavelength equation, it is many thousands of kilometres long. We have a name for such an antenna it is called a telephone line! For a more practical antenna, the basic principle involves converting voice frequencies, without losing any intelligence, to a higher frequency, radiating them via an antenna and at the other end converting the electromagnetic radiation back to voice frequencies so that they can be heard.

Again, the basic principle is to move voice frequencies to radio frequencies, radiate them from an antenna, have them propagate at light speed and at the other end recover those voice frequencies.

The basic principle of amplitude modulation is to take voice frequencies and mix (or modulate) them with a radio frequency signal so that they are converted to radio frequencies which will radiate or propagate through free space.

It is very easy to convert low frequencies to high frequencies so that they will radiate. All we need to do is take our voice frequencies (say from a microphone), then mix them with a radio frequency carrier and convert them to radio frequencies. The term carrier is very misleading; it is simply a sinusoidal high-frequency radio signal which we use to convert voice frequencies to radio frequencies for the purpose of radiation. I have often heard and read that the carrier 'carry's the voice frequencies' - this is a misconception.

Rather than talk about the whole range of voice frequencies from 50Hz to 3000Hz, we will look at the subject of amplitude modulation as if we were trying to transmit a single audio frequency of say, 1000 Hz, to a distant location. Using one audio frequency rather than the entire voice frequency range just simplifies our explanation.

FREQUENCY CONVERSION

The method used to convert one frequency to another is quite simple. You take the signal that you want to convert (in our case a 1000Hz audio frequency) and a radio frequency signal and we are going to use a radio frequency of 1MHz to illustrate how 1000Hz can be converted to a radio frequency for transmission. All that is required to do this is to feed the 1000Hz signal and the 1MHz signal into a non-linear device. The

output of that non-linear device will contain our converted frequencies, some of which we want and some of which we don't. In radio transmission, the non-linear device is called a modulator, in radio reception the non-linear device is referred to as a demodulator or detector.

The apparatus we need is an oscillator for the radio frequency source, a mixer (modulator) and our audio to be frequency converted. The old name for this combination (mixer and oscillator) was called more clearly a frequency changer.

Remember, we are using a 1000Hz audio frequency for the purposes of simplification. In practice, we would be using the whole range of audio frequencies from 50Hz to 3000Hz and the same principles would apply.

Now then, we want to transmit a 1000Hz audio frequency using radio frequency transmission.

We take the 1000Hz audio frequency from the microphone and the radio frequency (poorly called the carrier) and inject them into a mixer or a modulator (which are just non-linear devices) - the output of the non-linear device will contain our wanted frequencies. The output of the non-linear device will contain the original frequency that is 1000Hz audio, the 1MHz radio frequency and also the sum and difference of these two frequencies. The output of the non-linear device will contain a 1MHz radio frequency signal, a 1.001MHz signal (i.e. sum) and a 0.999MHz signal (i.e. difference). There will be other mixing products produced as well, but these will be eliminated in the following stages by filters. The 1.001MHz signal is called the upper side frequency. The 0.999MHz signal is known as the lower side frequency. If we were using the whole range of audio frequencies from 50 Hz to 3000 hertz, then we would have an upper sideband (USB) and a lower side band (LSB) of frequencies.

WHAT IS AMPLITUDE MODULATION?

In amplitude modulated (AM) systems, the modulating audio is applied to the radio frequency carrier in such a way that the total power of the transmitted wave is made to vary in amplitude, in accordance or in sympathy with the power of the modulating audio.

It is a popular misconception that in an amplitude modulated system the carrier power (in our case the 1MHz signal) is made to vary with the application of the modulated audio. Contrary to this, it is, in fact, the total wave power which varies in amplitude and not the carrier power. The carrier power in an amplitude modulated system remains constant.

You might ask, "Why modulate the audio frequency at all" (yes, I know I am repeating myself). If audio signals are fed to an antenna, radiation will not occur, because the frequencies are too low to radiate. When an alternating current is made to flow in an antenna, a system of alternating electric and magnetic fields is developed in the vicinity of the antenna. With each 180 degrees of alternation, these fields will return the energy to the antenna by collapsing into it. At high frequencies, the fields do not have time to collapse into the antenna and are left stranded in the space about it. This is called a free space field. Successive free space fields exhibit a repulsive force on their predecessors causing the fields to move out from the antenna at the velocity of light. This mechanism of radiation begins to occur at around 10kHz.

The function of the carrier in amplitude modulation is simply to provide a signal to heterodyne (mix) with the modulated audio, to convert all the audio frequency components to a higher frequency so that the mechanism of radiation will occur. The carrier contains no intelligence. The carrier can be removed before transmission, as is the case with single side band (SSB).

One possibility for the misconception of the modulated audio riding on top of the carrier may have arisen from the pattern that an AM signal produces on the screen of a cathode-ray oscilloscope (the oscilloscope is to be discussed). The pattern produced does appear to support the fallacy. The oscilloscope is limited in its operation by the fact that it can only display the resultant instantaneous voltage amplitude of all the signals present on its deflection plates.

When discussing AM, it is important to realise that the term refers to several modes of transmission wherein the total wave power transmitted is made to vary in accordance with the applied modulating audio. Double sideband (DSB), single sideband (SSB), vestigial sideband (VSB), are common modes used on all amateur and commercial bands. All of these are correctly referred to as amplitude modulation. The reference to double sideband as AM and single sideband as SSB on some amateur transceivers gives credence to the misconception that SSB is not an amplitude modulated wave when in fact it is.

HOW IS DOUBLE SIDE BAND PRODUCED?

Regardless of the type of AM system, the principle is the same. The radio frequency carrier is combined with the modulated audio in a non-linear device. The output of the non-linear device will contain the sum and difference frequencies of the original signals (with the exception of balanced mixers used for SSB).

WHAT DETERMINES THE BANDWIDTH OF AN AM (DSB) SIGNAL?

Bandwidth means the signal width in hertz, kilohertz and in some cases megahertz. The bandwidth of an AM signal is equal to twice the highest modulating audio frequency.

As the highest voice frequency that needs to the transmitted (for acceptable intelligibility) is 3kHz and the bandwidth of a double sideband signal is twice the highest modulating frequency, a double sideband transmission must, therefore, have a bandwidth of 2 x 3kHz = 6kHz.

Many modern transmitters have audio filters that slice off some of the voice frequencies above 2.8kHz making the bandwidth even narrower. The bandwidth is not dependent upon the power of the modulating audio (provided the transmitter is not overmodulated). In commercial AM broadcast transmitters, the frequency of the modulating audio is permitted to be as high as 4.5kHz and since a double side band system is used, commercial stations, therefore, have a bandwidth of 9kHz.

HIGH AND LOW LEVEL MODULATION

When the modulating audio is applied to the carrier in a low power stage (that is, before significant amplification), this is said to be low-level AM.

On the other hand, if the carrier is amplified to a high power level before the modulating audio is applied, then the system of modulation is called high-level AM.

With low-level modulation, the double sideband (DSB) signal is produced at low power levels. The advantage here is that the audio power required is low; no high power audio frequency amplifier is required. If it is necessary to raise the power of the DSB signal (and it usually is), then all subsequent amplification must be done with linear amplifiers. In a high power AM system, the use of linear power amplifiers is usually avoided because of their lower efficiency. Low-level modulation is usually restricted to transmission systems that operate at low power levels such as small hand-held transceivers and telemetry devices.

Note: once a signal has been modulated i.e. it contains intelligence, all amplification must be linear otherwise distortion (further modulation or inter-modulation) will occur.

It is interesting to note that SSB is, in fact, a low-level AM modulation system, since it is far more efficient (overall) to remove the carrier when it is in the milliwatt region, than to amplify the modulated signal and then have to remove a high power carrier which by then could be a hundred watts or more.

When very high transmitter output power is required, it is usual to employ high-level modulation. In these systems (AM Broadcasters) the carrier is developed by an oscillator and amplified to the final transmit power, then the modulating audio is applied. Since the carrier has no intelligence before modulation, high-efficiency nonlinear stages (Class C 60-80% efficiency) can be used for amplification. In a broadcast transmitter, modulating audio is frequently applied to the Power Amplifier's plate (anode) circuit (high-level plate modulation). If the final carrier power is 10kW, then the modulator must supply 5kW of audio power to the modulated wave for one hundred percent modulation.

The relationship between carrier power and sideband power in AM system is:

where:

Pt= the total power transmitted

Pc= carrier power

m = modulation index

Examination of the equation shows that since the carrier power (Pc) remains constant, then the sideband power is given by the equation as:

Power Sidebands = 0.5m2Pc.

The modulation index (m) is simply the percentage of modulation divided by one hundred. As the percentage of modulation goes from 0% to 100%, the modulation index goes from O to 1.

A WORKED EXAMPLE

A 100 watt double side band (AM) transmitter is first modulated to 50% and then to 100%. What is the total power transmitted in each case?

From the equation given, at 50% modulation:

Pt= 100 + (0.5 x (0.5)2 x 100) = 112.5 watts.

One hundred watts is the carrier power and only 12.5 watts is the total side band power. That is, 6.5 watts in each side band. At 100% modulation:

Pt= 100 + (0.5 x (1)2 x 100) = 150 watts i.e. 25 watts in each sideband.

The only reason I've shown these calculations is to highlight the inefficiency of a double sideband AM system. At best (m=l) the power transmitted in the sidebands is only one-third of the total power being transmitted (e.g. in the example above for 100% modulation with m=1, 50 watts total sideband is one-third of the total power of 150 watts). The carrier does not convey any intelligence to the receiver. The carrier can be removed and all the information in the sidebands will remain.

You do not need to know how these waveforms on an oscilloscope are produced. However, you may be asked in the exam to identify one of them. As you can see from the way the waveform of an amplitude modulated signal is displayed on an oscilloscope, it does appear at a glance that the power in the carrier varies.

An oscilloscope displays resultant voltage and not power. Carrier power remains constant in an AM system.

AMPLITUDE MODULATION ON AN OSCILLOSCOPE

TRAPEZOID PATTERNS 

The trapezoid patterns (right hand side of figure 29-1) are another method of showing the percentage of modulation on the oscilloscope. Again, you do not need to know how this is done with the oscilloscope. However, such patterns have been shown in examinations and you may be presented with one pattern in the exam and asked a multiple choice question about what the display means.

I could explain to you how this is done. However, I think you have enough to remember without adding superfluous non-exam essential information. The trapezoid patterns have one advantage over the previous patterns - they show if the transmitter is linear. Look at the last two trapezoid patterns and you will see that their sides are bowed inward (concave) and outward (convex); this indicates the transmitter is operating in a non-linear way. You may be wondering what all the fuss about linearity is. Non-linearity causes interference, so it is highly undesirable. Whenever signals are fed to a non-linear device in an amplitude modulated system, some of the signals mix due to the nonlinearity and can create unwanted frequencies that can produce interference to other services.

In an amplitude modulated system no intelligence is transmitted by the carrier and the wanted intelligence is transmitted in both the upper and the lower sidebands. It is no wonder then that amplitude modulation is not a popular method of voice communication, though it is still used by AM commercial broadcasters (though many of these are converting to frequency modulation and digital radio).

On some transceivers, there is often a switch to change between AM (double sideband), upper sideband and lower sideband. Many radio operators have the impression that these are three different channels, when in fact, it is only one channel, with three distinct methods of transmission - all of them being amplitude modulation.

SINGLE SIDEBAND SUPPRESSED CARRIER (SSB)

SSB is a form of amplitude modulation (AM) where the carrier is suppressed (typically 50 to 70 dB) and one of the sidebands is removed.

For an interesting experiment on air particularly with amateur stations: Ask the other nearby station to key his or her transmitter say on upper side band and ask them not to say anything (don't modulate). Then you tune down about 1.5kHz and you will hear the suppressed but not eliminated carrier. You will hear a tone - this is the carrier.

Since all of the intelligence in a double sideband signal is present in each of the sidebands and none of the intelligence is in the carrier, it is possible to remove one sideband and the carrier before transmission.

The advantages of this are:

Conservation of spectrum space (an SSB signal occupies only half the band of a DSB signal);

The useful power output of the transmitter is greater since the carrier is not amplified. The SSB receiver is quieter due to the narrower bandwidth (receiver noise is a function of bandwidth - this will be discussed later).

The major disadvantage of SSB is that the carrier must be reinserted in the receiver, to down-convert the sideband back to the original modulating audio. Another important fact that many textbooks on SSB fail to emphasise is that the carrier must be reinserted with the same frequency and phase it would have if it were still present. This is why clarifier control on a CB radio is so fiddly if the carrier is not inserted exactly correct you get the Donald Duck type voice. The amateur operator will use the VFO or RIT (receiver incremental tune) to do the same thing.

A single sideband signal on entering a receiver will go through many frequency conversions before being converted to the original audio. If the carrier was left with the sideband, it (the carrier), would experience the same conversions, so the carrier must be reinserted at a frequency and a phase relative to the sidebands current position in the spectrum for demodulation of the original audio (demodulation is the opposite of modulation).

Because of the necessity for the carrier to be reinserted, the SSB receiver is more complex than the DSB (AM) receiver and requires continuous attention from the operator to keep the reinserted carrier exactly on the correct frequency and phase. If the receiver wasn't so finicky, the public broadcasting service would have adopted the SSB system long ago.

TWO-TONE TEST SIGNAL

If you have an oscilloscope, then two-tone tests are easy to do and this will be explained in the chapter "Tests and Measurement". You do need to know what a two tone test is for examination purposes.

A two-tone test signal provides a standard whereby measurements made on an SSB transmitter can be duplicated. If an SSB transmitter is voice modulated and the output fed to the vertical plates of an oscilloscope, the pattern produced is so complex and dependent on the voice characteristics of the individual operator that it defies interpretation. A two-tone test signal consists of two sinusoidal modulating audio frequencies of equal amplitude which are not harmonically related (one is not a multiple of the other). The two-tone test signal produces the identifiable and repeatable patterns that I've shown in this chapter.

The reason the two-tones of the two-tone test signal must not be harmonically related is that the linearity of any system can be determined by injecting two-tones in and looking for distortion products of these frequencies at the output.

Suppose tones of 1500Hz and 2300Hz were fed to an SSB transmitter in the upper sideband mode. The upper sideband output should then consist of two upper side frequencies: carrier + 1500Hz and carrier + 2300Hz. If any other upper side frequencies are present, this would indicate nonlinearity in what should be a linear system. If the tones were harmonically related, it would not be possible to distinguish easily between harmonics of the two-tones on a spectrum analyser

SINGLE TONE TEST

If an SSB transmitter was modulated with a single audio tone, what would you expect to appear on the oscilloscope?

Answer: An unmodulated carrier wave - see the earlier figure 29-1.

If an SSB transmitter was modulated with a single audio tone it would be very hard to tell the difference between it and a CW (Morse code) transmitter.

If a single audio tone is fed to the microphone of an SSB transmitter, then the sideband output would consist of a single side frequency - the transmission would be indistinguishable from that of a telegraphy transmitter with the key down. In fact, if the audio tone could be keyed on and off, telegraphy signals could be sent. With the addition of a second tone and alternation between the two-tones, code transmissions of teletype (RTTY) or facsimile (FAX) type are possible.

This method of modulating further SSB signals is called "audio frequency shift keying" or AFSK. This technique is extended further with slow scan television where a number of discrete audio tones are used sequentially to represent different shades of grey (these particular modes will be covered more fully later).

DOES MIXING SWAP THE SIDEBANDS?

In figure 29-3 we have a DSB signal with a carrier frequency of 10MHz. The frequencies are shown on the diagram in kHz. So the carrier is 10000kHz. The upper and lower sidebands are 3kHz wide.

The lower frequency of the lower sideband (F1) is then 9997kHz. The upper frequency of the lower sideband is the carrier frequency (Fc) 10000kHz. The lower frequency of the upper sideband is the carrier frequency (Fc) 10000kHz The upper frequency of the upper sideband is 10003kHz.

Now we are going to move the entire DSB signal on the left (Sig1) to a new carrier frequency of 27000kHz on the right (Sig2). One way to do this is to mix Sig1 in a mixer with an oscillator on 17000kHz.

There will be many mixing products at the output of the mixer, but the one we want is the sum of Sig1 and the oscillator. We get rid of all the other unwanted frequencies by using a bandpass filter, not shown here.

As you see the DSB signal which ranges from 9997kHz to 10003kHz adds to the oscillator frequency and is converted to the new range 26997kHz to 27003kHz.

This process, where we are summing the signal with the oscillator, does not change the relative positions of the frequency components in Signal 1.

See that F1 is still the lower frequency of the lower sideband and F2 remains the upper frequency of the upper sideband.

When a single sideband signal is summed with an oscillator to move it in frequency, the sideband that is the upper or lower sideband remains an upper or lower sideband.

Figure 29-4 shows the same process but this time, the oscillator frequency of 37000kHz is used. Our wanted signal is now the difference between the oscillator and Signal 1. That is, we are now subtracting each of the frequencies in Signal 1 from the oscillator.

Notice now that F1 the lower frequency of the lower sideband comes out at the highest frequency of the upper sideband. The highest frequency (F2) of the upper sideband is converted to the lowest frequency of the lower sideband.

When we use an oscillator on the high side of the signal and convert it using the difference between the signal and the oscillator the sidebands are swapped over. Not that it matters in the least as each sideband still represents all the frequencies in the modulating audio and can at any time be mixed with the carrier oscillator (BFO) in the receiver and converted to the original audio range so that they can be heard.

If you are asked a question about sideband conversion in the exam draw a sketch like figure 29-4 and you will see straight away if the sidebands are reversed through mixing - or not.

In commercial and amateur radio, it is customary to specify the transmitter frequency

for an SSB signal as that of the suppressed carrier. An amateur station transmitting on 28.5MHz USB means that the suppressed carrier is on 28.5MHz, on upper sideband. On upper sideband centre of the emission is 1.5kHz higher than the carrier and on lower sideband it is 1.5kHz lower.

CONVERTING AN SSB SIGNAL BACK TO THE ORIGINAL MODULATING AUDIO 

After all, the whole idea of radio transmission is to take an audio frequency from the microphone, convert it to a radio frequency, transmit or radiate it, receive at a distant location and recover the original audio.

With a single sideband signal, the missing carrier is reinserted into the sideband at the receiver in the exact position it would be had it not been removed. The carrier reinsertion is done in the product detector. The difference frequency between the carrier and each individual side frequency component is the demodulated audio.

To put this in other words and demonstrate the whole aspect of radio communications regardless of the mode used, the problem is that audio frequencies cannot be radiated from an antenna. So, regardless of the mode of transmission, the audio frequency from the microphone must be converted to a radio frequency so that it can be transmitted and received at some distant location. The purpose of the receiver then is to convert that radio frequency back down to the original audio frequency that entered the microphone at the transmitter.

SCHEMATIC DIAGRAM OF A MIXER 

The combination of a mixer and a local oscillator is often called a frequency converter. A mixer takes two input signals. Usually, a signal such as an AM, SSB or FM plus another signal from an oscillator is fed to the mixer. The mixer is just a non-linear device.

The non-linearity will cause the mixing to take place. If you feed two signals into a linear device, you will get only those two signals out.

We can even just use a diode as a non-linear device. However, better mixers consist of active devices biased to operate on the non-linear portion of their operating curve

The schematic in figure 29-5 shows a JFET mixer. One signal is fed to the gate of the JFET while the other is injected into the source leg. Mixing will occur because the JFET will be operating as a non-linear device. The bias used is 'gate-leak' formed by the 100pF capacitor and 1MΩ resistor.

At the output of the mixer is an IF transformer which acts as a bandpass filter passing the mixing products we want and rejecting the others.

The 220 ohm resistor and the 0.01µF capacitor act as a lowpass filter to prevent RF from entering the power supply.

Another popular method of mixing is to use a dual gate MOSFET. This is shown in the schematic of figure 29-6.

A dual gate MOSFET is ideal for use as a mixer as we have two gates. One for the signal to be moved in frequency and the other for the oscillator. The MOSFET would be biased non-linear to make mixing possible. A crystal bandpass filter is used in this circuit to pass the wanted mixing products and block unwanted products.

Mixers generally have a signal loss. A perfect mixer would have a conversion efficiency of 1 - which means no loss. It is desirable that a mixer's conversion efficiency be as close to 1 as possible.

30 - AM Transmitters & Receivers - I

Some revision: Definition of amplitude modulation.

Amplitude modulation is when the modulating audio is combined with a radio frequency carrier in such a way that the total wave power is made to vary in accordance with the modulating audio.

The normal type of AM is double sideband or, to be more specific, double sideband full carrier.

Recall that the carrier does not convey any intelligence to the receiver. The information is in the sidebands. Either sideband contains all of the information.

The advantage of double sideband full carrier is simplicity in reception. The disadvantages are that it is not very efficient power wise and the bandwidth is greater than is necessary for other modes, particularly voice communications.

The carrier is used in the transmitter to heterodyne (mix) with the audio to convert the audio to radio frequencies (the sidebands) so that they can be radiated from an antenna.

The carrier is transmitted along with the sidebands. The advantage of this is that the carrier is available to the receiver to heterodyne once again with the sidebands, this time, to convert the sidebands back to the original audio frequencies, which can then be heard.

If the carrier was not transmitted (SSB), then the receiver would have to generate its own carrier.

Mixing or heterodyning in a transmitter is called modulating, whereas in a receiver it is called demodulating. The stage in a receiver which does the demodulating is referred to as the demodulator though it is sometimes referred to by an older name, the detector.

The most basic AM (DSB full carrier) receiver is the crystal set. Let's have a look at how a crystal set operates. Figure 30-1 is the schematic diagram of a crystal set, part of which we discussed in tuned circuits.

The AM (double sideband full carrier) electromagnetic wave and all the others in the air pass by the antenna and induce voltages into it. The parallel tuned circuit of the crystal set is resonant on one of these frequencies and signals on that frequency only will create a voltage across it. The parallel tuned circuit is selecting the desired radio channel and rejecting others.

The AM signal then causes a current to flow in the circuit, which includes a diode.

Non-Linear means:

If we were to graph the voltage across a resistor versus the current through that resistor then our graph would be a straight or linear line. Voltage across and current through a resistor obeys Ohm's Law. Current is directly proportional to voltage. Any device that does not respond linearly to a changing voltage and corresponding current is non-linear. If a sound system is being overdriven making it non-linear we hear distortion. This distortion is a result of the non-linear amplifier in the sound system creating new frequencies that we do not want so we call them distortion. In radio we intentionally use non-linear devices to create new frequencies for us. We simply select the distortion products we want and discard the rest.

Now you can't get anything more non-linear than a diode. A diode is very non-linear as it conducts current in one direction only. Being non-linear, the AM signal will mix in the diode. The radio frequency carrier will mix with the sidebands, the result of which will be the original modulating audio. There will be all manner of other radio frequencies produced by the mixing in the diode as well - we don't care about them, we only care about the demodulated audio. So the output of the diode will contain the wanted demodulated audio and many other radio frequencies. The capacitor across the headphones has a low reactance to radio frequencies, so the radio frequencies do not go to the headphones, it would really matter if they did. The radio frequencies are bypassed to ground by the low reactance of the capacitor - so we are done with them. The low frequency demodulated audio passes through the headphones. The headphones, which will operate on the piezoelectric or the moving coil principles, reproduce the sound to the listener's ear.

That was not so hard was it? Perhaps you may need to read through the paragraph several times till you are happy with the way the simple receiver operates.

If we wanted to, we could add an audio amplifier and loudspeaker to do away with the headphones and sit back and listen in comfort to the audio.

If there were lots of strong radio stations around and in close proximity frequency wise, more than one tuned circuit could be used to provide the receiver with greater selectivity. These earlier versions of AM receivers (with audio amplification) were called Tuned Radio Frequency (TRF) receivers because all tuned circuits were tuned to the incoming radio frequency.

Selectivity is the ability of any radio receiver to accept one particular radio signal and reject all others.

Sensitivity is the ability of any radio receiver to detect weak signals and is measured in microvolts.

Just to get it firmly in mind, a linear device such as an amplifier is one which faithfully reproduces every signal at its input to the output without distortion. Signals do not mix together in a linear device.

A non-linear device, which can be as simple as a diode, or an amplifier operating in Class C, creates distortion of the incoming signals. What goes in is not what comes out. Yes, the nonlinearity causes all the individual frequencies entering the device to heterodyne or mix. In doing so, new frequencies which were not present at the input are produced in the output. The number of mixing products in a non-linear device are enormous, though if we know what we are after we can filter out the garbage and use the mixing products we want (the demodulated audio).

LOW LEVEL (AM) AMPLITUDE MODULATED TRANSMITTER

Figure 30-2 shows the block diagram of a low-level amplitude modulated transmitter. The carrier wave is produced by the oscillator. The buffer stage after the oscillator is just an amplifier which raises the power level coming from the oscillator to a usable level, without taking too much power (if any) from the oscillator. Trying to draw too much power from an oscillator could stop it from oscillating, or pull it off frequency, hence the buffer amplifier.

The signal from the microphone is amplified to a usable level and fed along with the carrier to the pre-driver. The pre-driver is just another amplifier - however the pre-driver is nonlinear, so it acts as a modulator. The output of the modulator will contain the double sideband full carrier signal, which is usually just referred to as AM.

After the pre-driver, which is acting as a modulator, we have created the signal that we want to transmit. All we need to do then is raise the power level to the desired level before feeding it to the antenna. All amplifier stages after modulation must be linear.

Whilst the low-level modulation was done in the pre-driver here; it can be done in any low-level transmitter amplifier, such as an IF amplifier.

The advantage of low-level AM modulation then is that not much audio power is required. The disadvantage is that all radio frequency amplifiers after the modulator (Driver in this case) must be linear. This is a disadvantage because linear amplifiers run at lower efficiency Class A or Class B push-pull.

HIGH LEVEL (AM) AMPLITUDE MODULATED TRANSMITTER

Figure 30-3 shows the block diagram of a high-level AM transmitter.

With high-level modulation, the carrier is created by the oscillator and amplified up to a high power level, in fact, the power level we want to transmit. The audio to be modulated is done in a high power stage. In this case, the power amplifier or otherwise called the final amplifier.

Because the carrier power is high, we need a lot of audio power to produce 100% modulation. This is a bit misleading, but the stages, microphone amplifier and modulator are just audio amplifiers to bring the low-level audio from the microphone up to a high level.

Modulation is not occurring in the stage labelled the modulator. Modulation is taking place in the Power Amplifier. For modulation to take place in the power amplifier it must, of course, be non-linear and is nearly always Class C.

The advantage of high-level modulation is that the carrier (the signal from the oscillator) can be amplified using high-efficiency Class C amplifiers. The disadvantage is that a large amount of audio amplification is required to modulate the high power carrier.

High-level AM modulation is typically used in high-power AM transmitters like broadcast stations and high power amateur transmitters which operate in AM mode only.

THE SUPERHETERODYNE RECEIVER

The superheterodyne has been around for a long time and is still the receiver system of choice in modern receivers. Though we are talking about AM in this chapter, the superheterodyne can and is used for other modes as well, but the principles are the same except the stage labelled detector will vary in its operation depending on the mode in use - we are going to stick with AM for now so the detector could just be a diode.

Earlier we mentioned that early receivers were called TRF (tuned radio frequency). Selectivity of a receiver is very important. We only want to hear the radio station to which we are tuned. In the TRF receiver, there would be several tuned circuits like the one on our crystal set. The problem with the TRF is that every time you changed to a new radio channel or signal, you had to re-tune all of these circuits to the new frequency. This was a very fiddly affair, to say the least.

The idea of the superheterodyne is to convert the signal (station) being received to a single standard frequency. This frequency is called the intermediate frequency. The

great advantage of the superheterodyne is that there is only one tuning control and the intermediate frequency amplifier, typically 455kHz, never has to be adjusted and can contain many sharply tuned, high Q circuits, or even special crystal filters, tuned to 455kHz. This means the receiver has a very high selectivity. The IF amplifier also has very high gain giving the receiver very good sensitivity.

I think they must have thought up the name of this receiver from heterodyne for "mix" and "super" because it was so darn good compared to the TRF.

The problem is that to take advantage of the highly selective intermediate frequency amplifier, all signals to be listened to have to be converted to the intermediate frequency.

In the block diagram shown in figure 30-4, the first stage is an RF amplifier. It amplifies an entire band of frequencies coming down the antenna (such as the entire broadcast band, or an entire amateur band).

All of the radio frequency signals with all their information are fed to a mixer, along with a signal from a local oscillator. The mixer is a nonlinear device, so frequency conversion takes place.

In the diagram, I have shown a 1200kHz signal arriving at the antenna. Of course, there will be many other frequencies at the antenna as well. The 1200kHz AM signal is amplified by the RF amplifier and then fed to the mixer along with a signal from the local oscillator. The local oscillator is the tuning knob on the radio. I have shown the local oscillator operating on 1655kHz.

Now, in the mixer, all sorts of radio signals will be present. However, only the desired 1200kHz signal will mix with a 1655kHz local oscillator to produce a 455kHz intermediate frequency.

So what we have effectively done with the mixer and the local oscillator is convert the desired signal on 1200kHz to 455kHz, by mixing it with a locally generated signal on 1655kHz.

This conversion of 1200kHz to 455kHz is just that, a frequency conversion. The 455kHz signal still has its carrier and sidebands intact and all with the same relationship to each other and contain all the information they ever had - we have just moved them from 1200kHz to 455kHz.

The filter following the mixer is a bandpass filter tuned to 455kHz. (filters of this type are to be discussed) The filter will only pass signals on 455kHz +/- the bandwidth of the signal we want to receive (a few kilohertz).

From here on the receiver never requires any adjustment by the user. The desired station on 455kHz passes through the bandpass filter and gets amplified by the 455kHz IF (intermediate frequency) amplifier. The IF amplifier is sharply tuned to amplify signals (our desired signal) on 455kHz +/- the small bandwidth the signal occupies.

The overall advantage of the superheterodyne receiver is immensely improved selectivity, sensitivity and simplification of operation over the TRF.

The intermediate frequency amplifier is very aptly named, as the desired signal is received and converted to a standard middle (intermediate) frequency before being demodulated.

SUPERHETERODYNE RECEIVER - IMAGE INTERFERENCE

There are always two signal frequencies which will combine with a given local oscillator frequency to produce the same difference frequency. This means there are two signals that can enter a superheterodyne receiver and be converted to the IF.

The figure 30-5 block diagram shows a superheterodyne receiver tuned to the desired frequency of 1200kHz. This 1200kHz desired signal is converted to the IF by mixing with the local oscillator of 1655kHz as shown.

Now an unwanted signal on 2110kHz can also mix with the local oscillator and be converted to the same IF. If a signal was present on 2110kHz, then this receiver would most probably pick it up. The unwanted signal is called the image frequency and the type of interference is known as image interference.

It is normal for most superheterodyne receivers to have the local oscillator on a frequency above the signal frequency as shown. The image frequency for any superheterodyne is twice the IF away from the wanted signal.

CURING IMAGE INTERFERENCE

Improving the selectivity of the RF amplifier will help with image interference. Also, use a high frequency first IF. Instead of a first IF of 455kHz we could use a first IF of say 10.7MHz.

Look at equation 30-1. Notice the image is twice the IF (2xlF) away from the wanted signal.

If the first IF is 455kHz, then the image is 910kHz away. An image this close it is hard for the first RF amplifier to reject. If an IF of 10.7MHz was used this would place the image 21.4MHz away from the wanted signal. The RF amplifier is capable of rejecting a signal so far away.

If we use a high frequency first IF we will eliminate the image problem but unfortunately we get rid of one problem and create another. An IF amplifier on 10.7MHz does not have the high selectivity of a 455kHz IF.

So a high first IF will give us great image rejection but poor selectivity. The solution is to have two intermediate frequency amplifiers, the first one a high frequency and the second one on low frequency for selectivity.

I have been using standard IF frequencies of 10.7MHz and 455kHZ - just remember this is just an example there are many other high and low frequency IFs that can be used.

The problem is that we rely on the IF for selectivity and gain and at an IF of 10.7MHz, it's a lot harder to obtain the high selectivity and gain. Therefore, an ideal receiver will have two IFs - a high first IF for good image rejection and a further low IF for improved gain and selectivity. A superheterodyne receiver with two IFs is called a 'double conversion.' If we had three IFs it would be a 'triple conversion.'

Conversion Efficiency (MIXER)

Conversion efficiency is simply a fancy name for how efficient a frequency converter is, or more precisely, the efficiency of the mixer in the frequency converter. A frequency changer or converter is just a mixer and its associated oscillator. Mixers do not amplify. We lose amplitude when we do a frequency conversion. Efficiency percentage is a function of: (power out) / (power in) x 100. A good mixer would have a conversion efficiency of close to 100% or '1'.

A DOUBLE CONVERSION SUPERHETERODYNE

Figure 30-6 shows our truly super, double conversion superheterodyne, receiver. I have called the detector a demodulator. These are one and the same. The intermediate frequencies could be different from that shown. There could be another conversion stage and a third IF. Little modification would have to be done to this block diagram for any receiver in any mode.

If this was an amateur radio DSB receiver, then the bandwidth would be 6kHz. In this case, the bandpass filters would have to have a bandwidth of 6kHz. That is the IF frequency +/-3kHz. One of the bandpass filters would be a crystal filter. If we changed to a mode that uses a different bandwidth, then the appropriate bandwidth filter would have to be switched in. Many radio transceivers do not come with all the crystal filters pre-installed; they are optional extras.

For example, CW (Morse code) needs a very sharp crystal filter around 300Hz wide. FM needs a crystal filter around 16kHz wide. If you have a multimode radio and you do not have these filters fitted, you are not going to get high-quality reception on the modes with the missing filters.

Notice that the second oscillator is crystal controlled. The oscillator is always converting (along with its mixer) 10.7MHz to 455kHz so it can be a fixed frequency and never have to be adjusted.

31 - AM Transmitters & Receivers - II

SINGLE SIDEBAND (SSB) 

Amplitude modulation occurs when the modulating audio is combined with a radio frequency carrier in such a way that the total wave power is made to vary in accordance with the modulating audio.

I would really like you to be very sure in your understanding of ordinary AM before we move to single sideband (which is another type of AM).

The basic principle of radio transmission is to convert the voice frequencies coming from the microphone to radio frequencies so that they can be radiated as an electromagnetic wave. At the receiver, the electromagnetic wave can be intercepted and the original voice frequencies recovered.

The audio frequencies from human voice range from about 100Hz to 3000Hz. Of course, the human voice can make sounds above this range, but for voice radio communications we do not need to use those higher voice frequencies. All of the intelligence (information) we need is contained in the voice frequencies below 3000Hz.

Because this is such an important topic, we are going to go over the process of amplitude modulation again with a slightly different approach. If we were to look at what was going on in an AM transmitter using an actual voice, there would be too many frequencies. Therefore, we are going to pretend that a sound is being made by a human voice, which only contains two frequencies. Our pretend human voice is making two audio sounds, one on 1000Hz and the other on 2000Hz.

The diagram in figure 31-1 shows the sound containing these two frequencies going into a microphone. The audio sounds are amplified by the microphone amplifier and fed to the modulator (a non-linear device). Also going into the modulator is a radio frequency signal of 1000kHz (1MHz) from an oscillator, called the carrier oscillator.

The modulator is going to mix the audio and radio frequency signals together to produce new signals. This is a balanced modulator, so it suppresses the carrier by 40- 70dB; other than that consider it a non-linear device. At the output of the modulator, there will appear the original carrier and the sum and difference of all the voice frequencies (which we have simplified to just two). The output of the modulator contains only radio frequencies and is called double sideband suppressed carrier, as shown. If it were not a balanced modulator, it would be a double sideband full carrier (DSB).

Look long and carefully at figure 31-1. The voice frequencies have been converted to two frequencies above the carrier and two below the carrier.

The balanced modulator is just a nonlinear device like any other modulator the difference being that it suppresses the original carrier - in this example on 1000kHz or 1MHz.

Look at what goes into the microphone at the far left. Two audio tones. What is the resultant output signal? The set of two tones (1000kHz and 2000kHz) is frequency converted to two sets of single RF frequencies. One set on 998kHz and 999kHz. Another set on 1001kHz and 1002kHz.

The carrier is still there as well, but it is suppressed since this is a balanced modulator. How one such modulator does this will be covered shortly.

Can you see that really all we have done is convert two audio frequencies into two sets of radio frequencies? If we were to down convert those two sets of radio frequencies using the same carrier oscillator frequency, we would end up with the audio that went into the microphone.

SIDEBANDS

The frequencies above the carrier are the upper side frequencies. Those below the carrier are the lower side frequencies. Collectively, all of the upper side frequencies are called the upper sideband (of frequencies). Collectively, all of the frequencies below the carrier are known as the lower sideband.

There is no information in the carrier (1000kHz or 1MHz) modulation is in the upper sideband and the lower sideband. We really do not need both sidebands because all of the information is in each of them.

If we choose to amplify and transmit the lot, fine, we have what most people just refer to as AM. The highest voice frequency being 3000Hz means that the total bandwidth of the signal is 6kHz - twice the highest modulating audio signal.

We do not have to transmit this entire signal. We could just transmit either sideband and then convert those sideband frequencies back to the original audio in the receiver. This has obvious advantages, the main one being the bandwidth of one sideband would never be greater that 3kHz. Spectrum space is not an infinite resource and this would mean we could get twice as many channels into the same spectrum space.

There is another advantage of using just one sideband - since the bandwidth is only 3kHz - or in most transmitters 2.8kHz the receiver noise is less. The narrower the bandwidth of any receiver the lower the noise. I am sure you have heard the noise level decrease when you change from DSB to SSB. Imagine the low noise level if you used CW with a 300Hz filter.

SINGLE SIDEBAND

To transmit and receive single sideband has many advantages, but is technically more difficult. The principle of SSB transmission is simply to remove one of the sidebands (either one) completely and also get rid of the carrier. In practice, it is easy to get rid of one of the sidebands; a sharp bandpass filter will do this for us. We can reduce the carrier by using a balanced modulator. The correct full name for SSB is Single Sideband Suppressed Carrier.

Now, if we were going to get rid of a sideband and suppress the carrier, it would make a lot of sense to do this down in the milliwatt range. Getting rid of a carrier of say 100 watts (and a sideband) would be silly when it can be done more efficiently at low power levels.

The advantage of SSB is not just more efficient use of spectrum space and less receiver noise. The radio spectrum contains noise from many sources. If you turn on any receiver and do not tune to a signal, you will hear noise. This noise is from hundreds of sources, both man made (QRM) and natural (QRN). Some noise is also generated inside the receiver by active devices and even resistors. The narrower the bandwidth of a receiver the lower its noise. Think of the bandwidth of a receiver like an open window. Think of the noise as rain. The more you close (narrow) the window, the less rain (noise) gets in. So yes, SSB is technically harder but well worth the benefits in power efficiency at the transmitter and noise reduction in the receiver.

SSB TRANSMISSION THE BALANCED RING MODULATOR 

A Balanced Ring Modulator produces at its output a double sideband signal with the carrier suppressed by 40-70dB.

There are several types of balanced modulators. The balanced ring modulator is the most common. If there is a circuit in your assessment to identify it will be a balanced ring modulator.

Figure 31-2 shows the schematic diagram of a balanced ring modulator.

You should learn to identify the circuit. I am going to provide a description of its operation. However, this is for interest sake only. Though you will need to know the operation as a block - that is inputs and outputs and what it does.

OPERATION OF THE BALANCED RING MODULATOR

With carrier input alone applied, RF currents will flow during one half-cycle through diodes D1 and D4 as shown. During the next half-cycle of RF, current will flow through D2 and D3. Notice that no matter which pair of diodes conduct, the current flows equally and in opposite directions through the upper and lower parts of the primary winding of L5. Because of these equal and opposite primary currents through L5, the voltage induced into the secondary L6 by the carrier will be zero.

This means that, provided the carrier controls the diode switching (conducting), no carrier will appear in the output.

With audio input only applied, current will flow through D3 and D4 or D1 and D2, depending on the polarity of the audio voltage, but no current will flow through L5 - so, for audio alone, the output voltage at L6 is again zero.

Suppose that both audio frequencies AF and carrier are applied with the instantaneous values as shown in the diagram. The carrier input level is 6 to 8 times higher than the AF and, as such, determines which diodes will conduct. The arrows show the current produced by the carrier. With the polarities as shown, the audio voltage is assisting current flow through the top half of L5 and opposing current flow through the bottom half. The current through L5 is now upset (unbalanced) and an output at the sideband frequencies will appear in L6.

In practice, some type of balancing of the circuit is required. This is usually a simple resistive voltage divider network, the resistance of which is adjusted to balance the modulator with carrier only. In an SSB transmitter, this control is inside the transmitter on the circuit board and labelled carrier balance on the schematic diagram.

A COMPLETE BLOCK DIAGRAM OF AN SSB TRANSMITTER

It's time we took a walk through the full block diagram of an SSB transmitter and discuss the operation of each stage.

The block diagram of figure 31-3 is that of an SSB Transmitter (TX) which will operate between 28 to 28.5MHz. The carrier oscillator produces the radio frequency voltage necessary to heterodyne with the modulating audio voltage in order to convert the audio signals to radio frequencies.

The carrier oscillator must be able to operate at two frequencies to enable switching between upper and lower sidebands if this is required. The carrier oscillator frequency will determine which sideband will pass through the crystal filter (to be discussed). The crystal filter is a high selectivity bandpass filter. The carrier oscillator frequency will place one sideband inside the crystal filter's passband. It is the crystal filter then that passes one sideband and rejects the other.

A bandpass filter passes a band of frequencies with minimum attenuation and rejects (attenuates) all others.

Following the carrier oscillator and all other oscillators in the block diagram, there would be buffer amplifiers (not shown) to prevent the carrier oscillator from being too heavily loaded - such loading could pull the oscillator off frequency.

The microphone amplifier increases the signal power from the microphone to the level required to obtain a satisfactory modulation percentage with the signal from the carrier oscillator.

Adjusting the power output of the microphone amplifier controls the percentage of modulation and the transmitted power. This is a control on the front of the transmitter usually called mic-gain.

The RF and modulating AF signal voltages are fed to the balanced modulator. The fundamental requirement of the balanced modulator is to provide non-linearity to enable the process of modulation to take place. Balanced modulators have a second important characteristic that enables the original carrier frequency to be suppressed. The output of the balanced modulator then will consist of two sidebands and a suppressed carrier. The carrier suppression should be typically at least 40dB down from the carrier's full amplitude.

The bandwidth of the crystal filter (bandpass filter) will only permit the passage of one sideband. Which sideband will pass through the filter is determined by which sideband is positioned on the centre frequency of the crystal filter. A typical crystal filter for this use will have a bandpass of about 2.8kHz, which allows most of the sideband to pass through.

The purpose of both IF amplifiers is to simply amplify the required sideband as much as possible while maintaining the high selectivity in a narrow band system (SSB is narrow band).

In any communications system, the greatest amplification is provided by the IF amplifiers. Amplification gains of 40-60 dB are typical, whereas power amplifiers usually have a gain of around 10dB. The IF amplifier can produce such high amplification gains because it is a fixed and sharply tuned amplifier.

A combination of a mixer and an oscillator provide the function of a frequency converter. Both mixers and their oscillators serve to position the required sideband on the output frequency. Notice how the first mixer has an oscillator which is crystal controlled. This is possible since the conversion from the first IF frequency to the second IF frequency is always the same, requiring no adjustment of the oscillator. The crystal oscillator also provides high frequency stability.

The variable frequency oscillator (VFO) connected to the second mixer enables adjustments to be made to the final transmit frequency. The VFO frequency should be low to obtain stability and is typically no more than 8MHz. At higher frequencies, the LC components of the VFO would become so small as to make the frequency of oscillation very susceptible to external effects such as temperature variations.

In modern transmitters the VFO can be made to operate at higher frequencies while still maintaining stability - these designs employ the phase locked loop (PLL) system. With the PLL type VFO, the output of the transmitter is adjusted in discrete increments, typically as low as 10Hz per step.

The chain consisting of the pre-driver, driver and final amplifier uses only linear amplification. Their sole purpose is to raise the power level of the selected sideband with minimum distortion. The best practical linear RF amplifier is Class AB.

As the carrier and modulating audio were combined at an early low power stage, the SSB transmitter is by definition a low-level modulation system - so all amplification after the balanced modulator must be done with linear amplifiers. A feedback path between the final amplifier and the pre-driver is drawn in as a line and marked ALC. ALC stands for Automatic Level Control. Part of the RF signal arriving at the final amplifier is rectified and turned into a DC voltage, which is used to control the gain of an earlier stage, which could be a pre-driver or an IF amplifier.

The purpose of ALC is to prevent the operator from over-driving the transmitter. The higher the transmitter output, the higher the ALC voltage - this ensures lower gain in the preceding stage that the ALC voltage is applied to. ALC is a type of negative DC feedback that prevents the transmitter from being over-modulated.

If the transmitter was to be over modulated the linear amplifiers would become nonlinear and further unwanted modulation and new frequencies would be created, causing out of channel interference. This out of channel interference is referred to as splatter.

MORE ON THE CARRIER OSCILLATOR OF AN SSB TX

As mentioned earlier, it is the carrier oscillator which determines on what range of frequencies each sideband ends up. If we want to transmit on the upper sideband, the  carrier oscillator must place the upper sideband on the band of frequencies that will pass through the crystal filter. Likewise, for lower sideband. So the carrier oscillator must be switchable between two frequencies and of course, crystal controlled for frequency stability.

The circuit of figure 31-4 is one of the best ways of switching the carrier oscillator and hence selecting the sideband to be used.

We have discussed oscillators earlier. Can you recognise what type of oscillator it is? The two capacitors C1 and C2 should give you a clue to the identification of this circuit. It's a Colpitts crystal oscillator.

Forward biasing the appropriate diode achieves sideband switching. A positive potential connected to the anode of D1 will cause D1 to be forward biased, connecting the sideband crystal (X1) to the rest of the circuit.

In this circuit, D1 and D2 are acting as electronic switches. When a diode is forward biased, the switch is closed. Without bias, the switch is open.

Nothing else has happened. Do not try and read anything complicated into this diagram. It is a frequency converter. We call it a carrier oscillator and balanced modulator only because of what we are doing with this frequency converter; that is, moving audio to radio frequencies in a DSB system. The two voice frequency tones remain the same distance apart in the radio spectrum as they were at audio. Their amplitude is the same. All we have done is move the two audio frequencies that is one set of voice frequencies (1000kHz & 2000kHz) to two sets of radio frequencies.

The bias applied to the diodes would upset the operation of the N-channel FET if it were not for the DC blocking capacitor C3.

You do not need to know this circuit for assessment purposes. However, you do need to be able to identify a Colpitts oscillator.

SSB RECEPTION 

To finish off the topic of AM transmitters and receivers, we need to look at two final things.

An SSB receiver is no more than a superheterodyne receiver. The difference is that the demodulator is called a product detector, along with another oscillator, called a beat frequency oscillator or BFO.

Imagine receiving a single sideband signal like the one we created at the beginning of this chapter. If the carrier was present as in a DSB full carrier signal, we would just have to feed the signal into a non-linear device. The carrier would mix with the sideband and one of the mixing products would be the demodulated audio.

When we just have a sideband in the receiver, we need to reproduce the carrier in the receiver. We need to create the carrier in the receiver, on the frequency, it would be on had it not been removed.

As you have seen, the sideband started as an audio frequency band of frequencies. It has been frequency converted i.e. moved through different IF stages, which involves changing frequencies. There may be many frequency conversions between transmission and reception. The important thing to realise is that all of the individual audio frequency components are still in the same place relative to each other - and if the carrier had been transmitted, it would be there for us to use. The carrier is at the bottom of the upper sideband and the top of the lower sideband.

In an SSB receiver, we don't have a carrier, so we need to make one. The oscillator that makes the carrier in an SSB receiver is called a BFO (Beat Frequency Oscillator) It's just an RF oscillator which reproduces the carrier. We feed the carrier and the sideband into a demodulator - and just to make life hard, they call the demodulator in an SSB receiver a product detector. The output of the product detector is the demodulated audio.

An SSB receiver would also contain a crystal filter (sharp bandpass filter) on one of its IF frequencies, to obtain high selectivity.

So, look at your superheterodyne diagram in figure 30-4 (page 353). Add a crystal filter in the IF stage. Call the detector a product detector and feed the carrier into the product detector from a BFO and you have an SSB receiver.

The product detector and BFO are really just another mixer and oscillator forming a frequency conversion of the sideband from RF back to audio. This audio is the original transmitted audio.

THE DUAL ROLE OF BFO AND CARRIER OSCILLATOR IN SSB TRANSCEIVERS

In SSB transceivers (transmitter and receiver) it makes sense not to duplicate circuitry. In many transceivers, the same oscillator is used for the BFO and carrier oscillator. So on transmit the oscillator is the carrier oscillator and on receive it functions as a BFO.

AUTOMATIC GAIN CONTROL - IN ALL RECEIVERS

Automatic Gain Control (AGC) applies to all receivers and not just for SSB. You are required to know what AGC is.

What ALC is to a transmitter, AGC is to a receiver.

Almost without exception all radio receivers whether AM, SSB or FM, are superheterodyne. Review the block diagram of the superheterodyne if you have forgotten it. The problem with receivers is that the signals they are receiving can vary enormously in strength. For example, one signal from one transmitting station could arrive at the receiver at a level of -120dBm (about 0.2 microvolts) and the operator may be in communication with another station whose signal arrives at-20dBm. There is 100 dB difference between these two signals. Without AGC the stronger signal would either be too loud or completely overload the receiver causing distorted output. To receive the weaker signal, the operator would probably have to adjust the receiver's gain control. AGC does all of this for you.

A small amount of received signal from an early receiver stage is rectified and converted to DC. This DC voltage is then used to determine the gain of an IF and/or RF stage in the receiver. Recall that most of the gain (amplification) in any receiver system occurs in the IF stages. Pretty simple eh! The AGC voltage determined by the strength of the received signal automatically adjusts the gain of the receiver.

That's about all you need to know about AGC for the exam. AGC can be a pain, though. For example, suppose an amateur station is in contact with two stations, one of which is very strong and the other which is very weak. After the strong one has finished transmitting the AGC has made the gain of the receiver low and if the weak station was to begin transmitting immediately, then he or she may not be heard for a while because the AGC has not acted fast enough to return the receiver to full gain.

For this reason, many transceivers (or receivers) have a switch for the AGC. This switch is usually marked Slow, Fast and Off.

In the 'Off' position the AGC is disabled. The 'fast' and 'slow' positions determine how fast the AGC returns the receiver to full gain. This gives the operator more control over the receiver. Slow is handy when talking to a single station on SSB, who pauses a lot during transmission. If the operator of an SSB transmitter pauses (to think perhaps), there is no sideband output. The receiver's AGC could interpret this brief pause as the end of the transmission, when it is not and raise the gain of your receiver. When the transmitting station transmits (speaks) again, your receiver may be overloaded. Therefore, the 'slow' AGC position is useful here. The 'fast' AGC position is great for controlling a signal which is fading up and down.

A COMPLETE SSB TRANSCEIVER.

Figure 31-6 brings together everything we have learned about SSB transmission and reception.

This block diagram is not a blueprint for all SSB transceivers since many configurations are possible. However, the principles are the same in all transceivers. Notice the stages which are common to both the transmitter and the receiver. The two frequency carrier oscillator is the beat frequency oscillator in the receiver. The sideband filter, is a crystal bandpass filter, with a bandpass of 3kHz. This filter is used on transmit to remove the unwanted sideband and again in the receiver to greatly improve selectivity.

The 14MHz crystal oscillator is used to do an upward frequency conversion in the transmitter to the 2nd IF amplifier and a downward frequency conversion in the 2nd IF of the receiver. Similarly, the PLL type VFO is used on transmit for an upward conversion to the transmit frequency and in the receiver as a downward conversion to the 1st IF.

The driver and power amplifiers would most likely be Class AB (linear). Instead of a changeover relay to a switch the antenna between the receiver and transmitter, electronic switching could be used.

The carrier oscillator can be switched to two frequencies for sideband selection. The chosen sideband will be positioned in frequency to pass through the sideband filter and the unwanted sideband will be stopped.

For reinforcement let us look at figure 31-7 the output of the balanced modulator on each sideband. Remember for either sideband to get through the sideband filter the centre of the sideband must be on 7MHz or 7000kHz. On USB the carrier is on the lowest extremity of the sideband. For LSB the carrier is on the highest extremity of the sideband. With the carrier oscillator on 6998.5kHz the USB passes through the sideband filter. When the carrier oscillator is switched to 7001.5kHz the LSB passes through the sideband filter. In each case the unwanted sideband is blocked by the crystal filter.

32 - Filters in Radio Communications

RADIO SIGNALS

In radio communications, we talk a lot about radio signals. A radio signal is a very broad expression. The radio signal from an analogue television transmitter is in the VHF, UHF or higher region of the spectrum and is about 7MHz wide. An SSB transmission from an amateur station on HF is about 3kHz wide. Therefore, when we talk about receiving, passing and rejecting 'signals' we need to keep in mind that the bandwidth of the signal can vary significantly. The bandwidth of a signal is how much spectrum space it occupies.

When radio communication was in its infancy, transmitters were very broad. Transmitters used a wide band of frequencies. Morse code was the only type of signal sent. Marconi, at first, had all sorts of problems selling his radio telegraphy because multiple transmitting and receiving stations would interfere with each other.

Selectivity is the ability of a receiver to receive only the wanted signal and reject all others.

With tuned circuits and crystal oscillators, we can now have a multitude of transmitters operating in a small space. Keeping them all from not being heard or interfering with each other is a mighty task, particularly in high-density metropolitan areas. I have worked on interference problems on Sydney Tower. At that time, there were hundreds of transmitters and receivers within a 600-metre radius of Sydney Tower. When transmitters do interfere with each other, we often have to resort to additional filters other than the ones already built into the transmitter or receiver.

RADIO FILTERS 

In electronics, radio and communications filters are used to select or pass desired signals and reject or block undesired signals. In other words, there may be frequencies or signals that we want to pass and others that we want to block. The only way of doing this is with a device that is frequency selective - it must behave differently towards different frequencies. Such a device is called a filter.

We have already encountered filtering. If you recall the chapter we did on power supplies, the object of the power supply is to convert alternating current to direct current. The first stage of the rectification process is to convert alternating current to pulsating direct current. We converted AC to pulsating DC using rectifier diodes. Immediately after the rectifier, we used a capacitive or inductive input filter.

The ripple frequency of a power supply is equal to, or twice that of the supply frequency. Typically, this is 50 or 100Hz. DC can be thought of as zero hertz. So the aim of the filter of a power supply is to oppose frequencies above zero hertz. A power supply filter is then a low pass filter. It passes DC (zero hertz) and blocks or makes it harder for higher frequencies to pass.

We previously defined the property of capacitance as that property of an electric circuit that opposes changes of voltage and inductance as that property of an electric circuit that opposes changes of current. In a power supply filter, whether it is capacitive or inductive input, we are using the properties of capacitance and inductance to convert pulsating DC to smooth DC.

TUNED CIRCUITS

Capacitance and inductance combined, we have learned, can form a tuned resonant circuit. The tuned circuits have a specific way of behaving at resonance and off-resonance.

Summarising:

Series resonant LC circuits have low impedance at their resonant frequency and higher impedance at all other frequencies.

Parallel resonant LC circuits have high impedance at their resonant frequency and lower impedance at all other frequencies.

A tuned circuit cannot be used to block or pass just one single frequency. We would need an impossibly high 'Q' to do this. Tuned circuits can be designed to pass or block signals or a range of frequencies.

Using the properties of parallel tuned circuits and series tuned circuits and the fact that capacitive and inductive reactance change with frequency, we can build circuits to pass certain frequencies and stop others. Inductors and capacitors are ideal components for building filters. However, there are other specialist ways to build filters and this will be discussed.

TYPES OF FILTERS

Irrespective of the mechanism by which the filter does its job, filters can be broken down into four basic types.

a) low-pass filter

b) high-pass filter

c) band-pass filter

d) band-stop filter

A Low-pass filter passes all low frequencies up to a certain frequency; from that frequency and above significant attenuation begins to occur.

A high-pass filter passes all high frequencies down to a certain frequency; from that frequency and below significant attenuation begins to occur.

Band-pass filters pass a band or range of frequencies only; outside this band of frequencies significant attenuation occurs.

Band-stop filters stop or attenuate a band or range of frequencies only; outside this band of frequencies all frequencies are passed with minimal attenuation. Band-stop filters are sometimes referred to as notch filters.

SIGNIFICANT ATTENUATION

It is important for radio engineers to agree on the point where a filter is considered to have significant attenuation. The frequency at which significant attenuation begins to occur is called the cutoff frequency of the filter. The cutoff frequency is the point on the filter's characteristic curve where the desired frequency has been attenuated by 3 decibels. Take for example a typical low-pass filter with a cutoff frequency of 36MHz. This filter should have a very small insertion loss of say 0.2 decibels for all frequencies up to and around 34MHz. Beyond 34MHz, the filter will attenuate the signal more until at about 36MHz; the attenuation has reached 3dB. This 3dB cutoff point is considered to be the higher limit of the operating range of the low-pass filter. Above the cutoff frequency, the low-pass filter will begin to start attenuating signals dramatically.

Figures 32-1&2 show the schematic diagram of the four basic types of filters. The circuits shown are the basic features only of each type. It is very common for filters to use a combination of the four basic circuits to obtain the desired filtering effect. However, for your radio assessments, you should remember these basic types and the best way to remember to learn how they operate.

The low-pass filter is just like our power supply filter. The reactance of the inductor is low for low frequencies and increases as frequency increases. As frequency increases the reactance of the capacitor becomes lower and lower, effectively shorting out higher frequencies.

IDENTIFICATION of FILTERS

Identification of a filter is determined not only by its electrical function, that is, highpass, low-pass, etc. but also by its physical shape when drawn in the schematic form. The components of a filter may form the letter 'L', T', or the shape of the Greek letter for Pi (n). Use of one of these letters is then made in the description of the filter. For example, low-pass filter 'L' type. For more complex designs letter designations are dropped. A further description of the filter may include the input reactance, such as low-pass, inductive input, L type.

The filters shown above will work as they are, however, more effective filters can be made by joining filter sections together. Each filter shown can be considered a filter section in a more complex filter design.

COMBINED FILTERS

The figure 32-3 circuit is a high quality combined high-pass-band stop filter that could be used on the back of a TV set to block the low HF transmission from a radio station and allow the higher VHF or UHF TV signals to pass. Although this is a more complex circuit, you should still be able to work out that it is a combined high-pass/bandstop filter. The series resonant circuits (L1,C1;L2,C2) provide for a bandstop on say 28MHz. If C1 and C2 were to be removed, we would just have a high pass filter.

INSERTION LOSS

Ideally, on the band or range of frequencies that a filter is supposed to pass unimpeded, the loss should be zero dB. In practice, LC circuits have some insertion loss. An insertion loss of less than 0.5dB is good, though some more complex filters may have insertion losses as high as 2dB. Remember, insertion loss is undesirable attenuation to the wanted signal.

The best way to identify the function of a filter is to remember the behaviour of XL and XC and, impedance of series and parallel circuits. This is the method I much prefer you to use. Having said that, if you have trouble identifying the electrical function of a filter you may use the following straight memory method:

Try to remember this:

a) Low-pass filters - inductance in series and/or capacitance in shunt.

b) High-pass filters - capacitance in series and/or inductance in shunt.

c) Band-pass filters - series tuned circuits in series and/or parallel tuned circuits in shunt.

d) Band-stop filters - parallel tuned circuits in series and/or series tuned circuits in shunt.

CONSTANT K 

If the values of inductance and capacitance are chosen correctly, any change of reactance of either one (due to a changing frequency) will be exactly offset by an equal and opposite change in the other. Therefore, the product of the reactances will always be constant. This product is known as the 'constant K.' This type of filter is called a Constant K.

CRYSTAL FILTER 

We learned in an earlier chapter that a quartz crystal has two resonant frequencies. A series resonant frequency and a parallel resonant frequency. A quartz crystal operating on its parallel resonant frequency behaves just like a parallel LC circuit; it has high impedance at this frequency and this frequency only. A quartz crystal operating on its series resonant frequency behaves just like a series LC circuit; it has low impedance at this frequency and this frequency only.

The practical advantage of quartz crystal is that it has an extremely high Q and therefore makes an excellent high selectivity filter. They are far more expensive than LC circuits and cannot handle the same amount of power.

One of the most obvious applications of a crystal filter that we have discussed earlier is the crystal filter in an SSB receiver. This filter is a band-pass filter about 2.8kHz wide and very sharp (selective). It is asking a lot of a band-pass filter to remove a single sideband and reject the other - the best way to do this is with a quartz crystal filter. An arrangement of quartz crystals connected to form a filter is called a crystal lattice filter network.

The crystal lattice filter shown in figure 32-5 is a band-pass filter, suitable for use as a sideband filter in an SSB transmitter-receiver or transmitter. X1 and X2 are series resonant at the centre of the required sideband, while X3 and X4 are parallel resonant at the same frequency.

For a discussion of the two resonant frequencies of a quartz crystal, please refer to 'Chapter 27 - Oscillators' on this topic. In the diagram of the crystal filter (figure 32-5), X1 and X2 being series resonant, behave as a series LC circuit. They have low impedance to the desired signals and exhibit increasing opposition to signals removed from their series resonant frequency. Also, X3 and X4 being parallel resonant, behave like parallel tuned circuits in shunt with the signal path. A high impedance in shunt with the signal path will not affect signal frequencies, but will provide a low impedance path for signals away from the pass band centre frequency, effectively short-circuiting them.

Some ceramics also exhibit the piezoelectric effect (PE). A good example is the ceramic microphone which is a PE microphone just like the crystal microphone. (both are high impedance microphones). Ceramic filters are also used in receivers along with crystal filters.

FILTER CURVES

A filter curve or selectivity curve is just a way of graphically describing how a filter works. These curves can actually be produced when testing a filter, using a spectrum analyser and a tracking generator. You will need to be able to identify each of the four basic filter curves.

The selectivity curve of a low-pass filter is shown in figure 32-6(a). This filter will pass all frequencies with minimum attenuation (the insertion loss of 0.5 dB) up to the cutoff frequency (fc), which for a typical HF transmitter would be around 35MHz. Beyond the cutoff frequency, the filter begins to attenuate or block signals quickly. At about 50MHz a low-pass filter of this type could attenuate signals by as much as 70dB.

It is a trap to assume that a low-pass filter is only used at low frequencies such as the HF radio band. A low-pass filter could have a cutoff frequency of 112MHz for use with say an FM broadcast station. Such a filter would still pass all frequencies up to 112MHz.

The selectivity or characteristic curve of a high-pass filter is shown in figure 32-6(b). A typical high-pass filter may be used on the back of a TV set where the antenna leads connect to the set. The high-pass filter will pass the high TV signals (with the insertion loss of 0.5dB) and attenuate all frequencies below the cutoff (fc) to give the TV extra protection from say a nearby HF radio transmitter.

There are many other applications for a high-pass filter besides this one. The important thing is that you understand and can identify the curve. The output of the filter is high for frequencies above cutoff and low for frequencies below the cutoff (fc). I have not shown specific frequencies on the horizontal scale as the frequency range can be anything. In practice, the vertical axis would be marked in decibels and the horizontal axis in megahertz or kilohertz.

The band-pass curve in figure 32-6(c) shows that all frequencies between two cutoffs, fc1 and fc2, will be passed. Signals outside that band will be significantly attenuated.

The curve of a band-stop or notch filter in figure 32-6(d) looks a bit strange to begin with.

You may have a FM broadcast station nearby that is overloading one of your receivers. The FM broadcast band is from 88-108MHz. Therefore, a notch filter for FM broadcast would have an fc1 of 88MHz and an fc2 of 108MHz - or at least somewhere in that band.

Again, it is important you can recognise the curve. I suppose I should point out that your examiner could get cunning and change the axis. For example, "Output" could be shown increasing downward, instead of as I have shown it.

PLACEMENT OF A LOW-PASS FILTER

Probably one of the most useful and most commonly found filters in HF radio stations is the low-pass HF filter. The idea of placing a low-pass filter at the output of an HF transmitter is to make doubly sure that all emissions (and they do exist at all stations) above the HF band are attenuated even further, to reduce greatly the potential for interference.

There is an important rule with all filters, irrespective of their type and frequency range: filters are made with a specific input and output impedance which is usually the same. A filter could have an impedance of 50Ω or 300Ω to cite just two examples.

If you do not place a filter into a system that matches its impedance, then it will simply not work as it is intended. In a radio system, the degree of impedance match or mismatch is normally determined by measuring the VSWR, with a VSWR meter (to be discussed in full later). If you have 50Ω coaxial cable, it will only behave like 50Ω coaxial cable if the VSWR is 1:1. If you are going to insert a 50Ω low-pass filter into a 50Ω coaxial line, then there must not be significant VSWR on the line at the point of insertion. Otherwise, the filter may not work and can even be damaged by high voltages and cause interference.

In the diagram of an HF radio system in figure 32-7, the low-pass filter is placed last, but before the Antenna Tuning Unit. If there was no ATU, then the low-pass filter would be last, but the VSWR must be near to 1:1. In this arrangement, you should not swap the positions of the VSWR meter and the low-pass filter. A VSWR meter can actually produce harmonics (interference because of the diodes used) and these can only be stopped by a low-pass filter placed after it. So, a low-pass filter should be connected to a line that matches its impedance and it should be the last device in a transmission line with the exception of an ATU and antenna.

A MAINS FILTER

A 240 volt household power line filter is more commonly called a mains filter. The purpose of a mains filter is usually to prevent radio frequency energy from going into the mains network and causing interference to other devices in your own or to nearby households. Alternatively, a mains filter can be used to protect a device from radio frequency interference coming in via the mains.

If you can imagine your house being invisible with only the electrical wiring remaining in place, then you can start to imagine the large antenna system courtesy of your household wiring.

The diagram of the mains filter is a configuration called double Pi type. A mains filter is a low-pass filter, passing the mains frequency and blocking the higher radio frequencies. Notice the iron core inductors - these are a good indicator of large inductance and low-frequency operation. Ceramic capacitors are normally used to obtain the necessary high voltage rating, which is typically 2kV. The high voltage rating is necessary to prevent damage from possible high voltage line transients (voltage spikes). This type of filter could be placed in the mains lead of a TV receiver, to prevent RF energy entering the receiver after being picked up by the household wiring. The filter may also be useful in preventing power tools from interfering with radio and television reception, provided the interference is conducted from the power tool to the affected device via the mains lead. A mains filter will not be of assistance where the interference is being radiated and not conducted by household wiring.

CAVITY FILTERS

Cavity filters are used a lot in radiocommunications. Radio repeater stations nearly always use cavity filters. Cavity filters can be made to act as band-pass or band-stop (notch) filters.

The advantage of cavity filters is that they are very high Q, but not as high as a crystal filter. However, they have the advantage of being able to handle high power levels. You will find cavity filters, or combinations of them, at the output of receivers and transmitters, used as repeater stations or in high RF environments.

A repeater station is a receiver and transmitter connected to a single or two antennas with the purpose of extending the range of mobile, base or handheld transceivers. Whatever is received by the receiver is retransmitted on the transmitter, relaying the radio operator's message. The repeater is usually placed in a prime location to give extended coverage and may run at high power. The problem is keeping the repeater's transmitter from interfering with its own receiver. The transmit and receive frequencies may only be 600kHz apart. A combination of band-pass and notch filters made from cavities can easily achieve the amount of receiver-transmitter isolation (in decibels). By the way, the receiver and transmitter of a repeater often share the one antenna, though they do not have to.

Cavity filters are rarely used below 30MHz as below this frequency they are physically too large. The arrangement of 4 cavity filters shown in figure 32-9 is called a duplexer. A duplexer is just a system of cavities comprising of notch and band-pass filters, to enable a transmitter and receiver on close frequencies to share a single antenna.

The cavities shown in figure 32-9 are about 300mm in diameter and about 700mm long and operate in the VHF band. The most common shape of a cavity filter is that of a cylinder as shown, however any shape can be used such as squares or rectangles.

Imagine for a moment a parallel tuned circuit with a conventional L and C. Figure 32- 10. Now remove the L and replace with a single wire. That single wire has some inductance - though not much and you would expect the resonant frequency to be very high. What if you paralleled more straight wire inductors across the capacitor? Well, inductances in parallel cause the inductance to decrease so the resonant frequency increases. Now get carried away and place many straight wire L's in parallel with the capacitor that you form a solid cylinder around the capacitor. You now have a cavity resonator. All you need is coupling loops and a method to adjust the internal C to tune the cavity.

REPEATER DUPLEXER

A repeater duplexer is shown in figure 32-11. The purpose of the duplexer is to prevent the repeater's transmit signal from overloading, desensitising or blocking the repeater's receiver. This is called transmitter-receiver isolation and is measured in decibels. The transmitter has two cavities to allow the transmitter frequency signal to pass through with minimum attenuation and cause all other signals to be attenuated. Similarly, the receiver has two cavities that pass the received signal and block everything else.

This duplexer is a fairly simple one. How much filtering is required depends on the RF environment where the repeater is located. If it is a multi-transmitter site, then more cavity filters may be required and a device called an isolator may need to be installed to stop other transmitters getting into the repeater's transmitter and causing transmitter intermodulation. Likewise, on a multi-transmitter site there are other transmitters that may get through the duplex and cause receiver intermodulation interference.

There are many ways to tune a duplexer using simple equipment. The best way to tune cavities in a duplexer is to use a spectrum analyser with a tracking generator. This produces an easy to understand graphical display of the bandpass and bandstop characteristics of the duplexer.

The duplexer will introduce an insertion loss of about 0.5dB. Increasing the insertion loss is sometimes done deliberately to achieve sharper bandstop and bandpass characteristics. It is a bit of a trade-off between insertion loss and duplexer characteristics can be chosen considering the RF environment where the repeater is located.

Another method that helps create better isolation between the transmitter and receiver is to use two antennas rather than one. If this method is used an extra 20dB or more isolation can be achieved with cautious mounting of the two antennas with vertical separation.

CIRCULATORS (Ferrite)

An RF isolator is a two-port ferromagnetic passive device which is used to protect other RF components from excessive signal reflection. If one port of a circulator is terminated in a resistive load the circulator becomes an isolator.

To understand how these components control the signal flow, think of a cup of water into which you place a spoon and stir in a clockwise motion. If you sprinkle some pepper into the cup and continue to stir, you will notice that the pepper easily follows the circular motion of the water. You can also see that it would be impossible for the pepper to move in a counterclockwise direction because the water motion is just too strong. The interaction of the magnetic field to the ferrite material inside isolators and circulators creates magnetic fields similar to the water flow in the cup. The rotary field is very strong and will cause any RF signals in the frequency band of interest at one port to follow the magnetic flow to the adjacent port and not in the opposite direction.

Figure 32-13 shows the schematics for a circulator and an isolator. Notice how an isolator is a circulator with the third port terminated. The arrows represent the direction of the magnetic fields and the signal when applied to any port of these devices. Example: If a signal is placed at port A, and port B is well matched, the signal will enter port A and exit at port B with very little loss (typically 0.4dB). If there is a mismatch at port B, the reflected signal from port B will be directed to port C. If port C is terminated in a nominal resistive load of 500 then the reflected power will be dissipated as heat.

Any signal entering B will exit C and be dissipated as heat. There is then a significant loss or isolation between B and C.

An important consideration when specifying an isolator or circulator is to ensure the device has adequate isolation for your given application. Isolation is a unit of measure (in dB) that states the separation of signal levels on adjacent ports of a device. The greater the isolation value, the less interference from a signal on one port is present at the other. The amount of isolation is directly affected by the VSWR presented at port 3 of the isolator. If the match on port 3 is poor, you can expect isolation below 10 dB, but if the match is improved to 1.10:1 by using a good termination device in the circuit, then the isolation would improve to over 20 dB.

One common application of circulators is as a simple duplexer-a device that allows bi-directional communications using a single path. Figure 32-14 shows a transmitter and a receiver sharing one antenna while isolated from each other.

When the transmitter sends a signal to the circulator it goes in port A and out of port B to the antenna with little loss, typically 0.4dB. The signal is transmitted and the receiver is isolated form the transmitted signal by about 20dB(100 times). When the antenna receives a signal, it enters port B and exits port C with little loss.

An important consideration when specifying an isolator or circulator is to ensure the device has adequate isolation for your given application. Isolation is a unit of measure (in dB) that states the separation of signal levels on adjacent ports of a device. The greater the isolation value, the less interference from a signal on one port is present at the other. The amount of isolation is directly affected by the VSWR presented at port B of the isolator. If the match on port B is poor, you can expect isolation below 10dB, but if the match is improved to 1.10:1 by using a good termination device in the circuit, then the isolation would improve to over 20dB.

It may be strange for you to think about transmitters receiving signals from other transmitters. Why not? Transmitters have antennas - those antennas receive signals from other transmitters and funnel their energy into the output stage of the transmitter. The transmitter you will recall, often has a non-linear output stage. The external signals from other transmitters will enter our transmitter and mix with our transmitter signal in the power amplifier and re-radiation will occur. The result it a great mess of unwanted signals very likely to cause interference. This interference is

called transmitter-intermodulation.

In figure 32-15 our transmitter is connected to port A. A 50Ω load is connected to port C. Our antenna is connected to port B. Our transmitted signal enters port A and exits port B to the antenna.

Any signals coming down our antenna (from other transmitters) will enter port B and exit port C and be dissipated in the 50Ω load. What we have achieved is isolation between our transmitter and all other transmitters on the same or nearby radio site.

A single isolator reduces the levels of other nearby transmitters in our transmitter's power amplifier by about 20dB. If we did not do this external signals could enter our transmitter's power amplifier and mix with our transmit signal to produce new frequencies that are re-radiated causing interference to other receivers. This is called transmitter intermodulation.

If more isolation is needed then two single isolators can be placed in series or a dual isolator, which is two signal isolators in the one package, can be used. Figure 32-15 is a picture of a dual isolator. With such an isolator you can expect at least 40dB of isolation and up to 50dB. With the additional use of cavity filters and careful antenna placement an isolation of more then 100dB can be achieved.

STRIPLINE FILTERS

At UHF and above, normal filter components like capacitors and inductors would become too small physically to be stable. From UHF and beyond a common filter used inside communications equipment is the stripline. I am not going to go into the operation of these filters here as their principle of operation requires some knowledge of transmission line theory, as this is how these filters operate. Suffice to know for now that ordinary capacitors and inductors cause problems in filter construction for UHF and above and an alternative is the stripline filter, with its operation to be covered in the chapter on transmission lines.

See chapter 38 (Transmission lines) for more information on how stripline filters work. Striplines are covered in transmission lines because they use transmission line principles for their operation.

Radio & TV broadcast filters

A high-pass filter suitable for a television receiver will cure the majority of interference problems between an HF (0-30MHz) radio station and a TV set which is being overloaded. Good filters of this type can be expensive - read later how a very cheap transmission line notch will often quickly, simply and cheaply do the same job.

In the chapter on transmission lines we will learn how to use a simple length of ribbon or coaxial cable to make a quarterwave transmission line notch (band-stop). Such a notch can be used to reduce the level of a nearby transmitter at a receiver by easily 100 times (20dB). The vast majority of overload problems from radio frequencies to domestic RF receivers can be cured using such a notch filter.

33 - Interference

In this chapter we will discuss the many types of interference to domestic appliances from radio and also interference to radio communications service including amateur radio repeaters.

As a radio experimenter, you are expected to be able to identify interference, particularly to television, radio and domestic electronics. You need to be able to determine if you are the cause of the interference and the steps you can take to fix your station.

Even though you are licensed it is common for you to get the blame for almost everything. If you were not there with your radio station, there would be no problems right! I have also heard: "We didn't have the problem until you moved in".  Your neighbour, being non-technical, will not appreciate being told by you that the problem is theirs even if it really is. The very best thing that you can do for yourself is to ensure that you have no interference whatsoever in your own home. You need to be very cautious in assisting a neighbour with their interference problem. If you do not know what to do or if you just do not want to risk touching expensive equipment in your neighbour's home, advise them to contact the radio licensing authority; just make sure your own house is in order first.

TELEVISION INTERFERENCE (analogue)

Digital TV has become the most common domestic TV service. Analogue TV developed over many decades and the electromagnetic immunity (EMI) standards were never really agreed to by all nations. Analogue TV is more prone to interference due to poor implementation of EMI standards. Many analogue TVs did have very good EMI but others were so poor they nearly always had problems in the presence of nearby radio transmitters.

Analogue TV does have one big advantage when investigating interference and that is that the different types of interference had signature effects to the television picture. The analogue picture helps you diagnose the problem. This is so useful that I have used a portable miniature analogue TV to find digital television interference.

Several types of the most common analogue TV interference are shown in figure 33-1.

Figure 33-1(a) is a normal analogue television picture without interference. Figure 33-1(b) is a normal picture with no interference and weak signal strength (snow).

Figure 33-1(c) is interference from an AM radio transmitter. This interference pattern is referred to as a "herringbone weave" because there are alternate bands with diagonal lines in them sloping the opposite way. If you use your imagination a little it is a bit like a herringbone of a fish. This interference could be from any modulated AM transmitter and there would likely be some interference to the sound but this may not be intelligible.

Figure 33-1(d) Is interference from a modulated FM transmitter. The interference lines may "wiggle" with modulation. Sound may be affected and if it is it might very likely be unintelligible. The width of the interference lines become finer as the frequency of the source FM transmitters increase. With practice an interference investigator can make an estimate of the transmitter's frequency.

Figure 33-1(e) is electrical interference. This could be from almost any electrical device and usually close by. Perhaps in the home of the viewer. If the horizontal bands of interference are in two distinct bands the most likely source is powerline interference. The two bands of lines are caused by flash over of the insulators twice for each cycle of AC. If the interference comes and goes with some sort of routine, then suspect devices that are controlled by a thermostat. Most types of electrical interference (except powerlines) are easy to locate by turning the power circuits off and using a process of elimination.

Figure 33-1(f) is co-channel interference from another transmitter that could be far away. It is a bit like ghosting but the displaced image is not the same as the main image.

Figure 33-1(g) is called ghosting. The main image appears twice and shifted in distance. This is nearly always caused by multipath signals. That is the same signal arriving at the TV receiver via more than one path. This can be reflection from buildings, aircraft or even mountain ranges. Aircraft in the vicinity can cause temporary ghosting. The best approach for this is to improve the directivity of the TV antenna and experiment with its direction. Ghosting can be because of standing waves of a faulty TV antenna system. Figure 33-1(h) is called "sound bars". This is usually interference from an RF transmitter that is very close and being overmodualted.

These types of interference are becoming far less with the move to DTV. They will still occur but you will not have the picture on an analogue screen to use as a diagnostic tool.

BE DIPLOMATIC, CAUTIOUS AND CONSIDERATE 

There was a time when I would have recommended that a radio experimenter intervene and do all they could to help a neighbour with the interference. Install filters and the like. These days home entertainment equipment is far more complicated and expensive. I would be reluctant to touch it. What if you do install a filter and the appliance develops an unrelated fault a few days or weeks later? Well, it was fine before you touched it!

You must have a common sense approach to establishing a radio station toward potential interference. Suppose you have an amateur station and the output power is in of the order of +50dBm to +56dBm of output power (100-400 watts). You place your transmitting antenna on the same property boundary as your neighbour's TV antenna. Worse still you point your directional antenna at your neighbour's TV antenna. The distance between the antennas is just a few metres.

Would you really expect there to be no interference problems? Then, even if your neighbour's TV antenna is correctly installed and has filters connected, there is still going to be an overload problem and morally it is your problem, though technically the problem lies with the TV receiver being unable to reject such a strong nearby off channel transmission.

In circumstances like this or similar, and cooperation is not forthcoming, particularly from the amateur station, then the radio inspector can change the license conditions of the amateur on the spot so that the station cannot be used above a certain power level. If your antenna is rotatable and interference only occurs when the antenna is pointed at the TV antenna, then the inspector could give you instructions not to transmit in this direction. In extreme cases, the inspector could direct you to transmit during particular hours of the day.

Usually, sensible placement of antennas, consideration for neighbours and good communications skills eliminate all problems even if the help of an inspector is required. Keep in mind also that if your neighbour does call an inspector to investigate the problem and the problem is found to be the neighbour's TV antenna, feedline, or TV itself, then they will be paying for the inspector's advice. How the regulator will respond to you and interference depends on the regulations of your country.

OTHER TYPES OF INTERFERENCE

HARMONIC INTERFERENCE

Every radio transmitter emits some energy on multiples of its operating frequency. These unwanted frequencies on multiples of the operating frequency are called Harmonics. It is not a matter of if and when harmonics occur; it's a matter of what level the harmonics are. It is no accident that most of the radio experimenter's bands are harmonically related to each other. This is so that harmonics generated by experimenters will most probably fall on other experimenter bands. An interesting experiment is to search deliberately for harmonics with a receiver, whether they are yours or that of another station or even a commercial broadcaster.

Harmonic interference is a transmitter problem and should be cured at the transmitter with filtering - usually a low-pass filter.

An example of harmonic interference:

An amateur transmitter is operating on 28MHz and only causes interference to a TV receiver when it is tuned to Channel 9 (196.25MHz Vision). What is the most likely cause of this interference? What cure would you suggest?

Since the interference is to Channel VHF 9 only, the most likely cause is in-band interference. That is, energy is being radiated from the amateur transmitter within the band of frequencies used by Channel 9. Channel 9's vision carrier is 196.25MHz, the seventh harmonic of an amateur transmitter operating in the 28MHz band of frequencies will fall within the channel allocation for Channel 9. Since harmonic radiation is the problem, the only solution is to install a low-pass filter at the transmitter.

The clue given in the question was that interference was to one Channel only. If fundamental overload, intermediate frequency (IF), or audio rectification was the cause, then interference would generally occur to all channels (including unoccupied channels).

FUNDAMENTAL OVERLOAD

Fundamental overload is not a transmitter problem. When a transmitter is producing fundamental overload, that is, receiver overload to a receiver not tuned to the transmitter's frequency, then it is a receiver problem. However, when speaking about the problem from the transmitting station's point of view, we call it fundamental overload. Provided you are operating within the prescribed power levels you are not at fault, though do read the advice given on this matter earlier in this chapter. The majority of interference, particularly to TV, is from fundamental overload. Fortunately fitting a high pass filter to the TV receiver usually cures this problem.

A high pass filter installed on the back of a TV receiver blocks (attenuates) the HF radio transmissions and allows the VHF/UHF TV signals to pass virtually unattenuated.

You can identify the interference as fundamental overload because the interference is to many or even all channels. The TV receiver is not able to reject the nearby strong HF signals. This technically is an issue with the selectivity of the TV receiver. However, morally the interference is not always clearly the fault of the TV. If the two antennas a very close and/or high power is being used at the transmitter then both parties may need to cooperate to resolve this interference. Fitting a highpass filter may well fix the problem. If it does not then collaboration between the complainant and the HF station operator is essential to resolving the problem.

SPECIFIC FREQUENCY OVERLOAD 

If there is just one frequency affecting a domestic appliance such as a television then the easiest method is to use a bandstop filter on that frequency. Suppose in figure 33-2 it was not overload from HF frequencies. Instead the interference occurs when using VHF or UHF. A bandstop filter will often fix the interference. Take as an example problems with a TV rejection 146MHz. Place a "T" piece into the feedline at the back of the television and to the spare connection on the "T" piece connect an open circuit quarter wave stub. This will give you 20dB rejection on the stub frequency. With parallel feeder you do not need a "T" piece. Start with the stub slightly longer and prune it while observing the interference.

See the chapter on transmission lines for details on how to calculate the length of a quarter wave notching stub.

IF INTERFERENCE

When a transmitter causes interference to an IF stage of a radio or TV receiver the interference will occur without change no matter what channel or frequency the affected receiver is tuned to. This Interference is to an IF stage. One typical IF frequency is 10.7MHz though there are many others. Generally, again this is a receiver problem and is normally due to lack of receiver shielding. Don't laugh! To prove IF overload, I have had to wrap receivers and TV sets in aluminium foil to prove to the owner or their TV technician that the IF is insufficiently shielded.

AUDIO RECTIFICATION

Many household appliances contain audio amplifiers. TVs, radios, sound systems and intercoms to name just a few. Bedside clock radios send a tremor down my spine! Now, audio amplifiers are not supposed to pick up radio signals are they? Well, if enough RF energy does get into any audio amplifier, the AF amplifier will become overloaded, become non-linear and start acting like a demodulator for radio frequency signals.

The problem is with the audio equipment for sure. Sound systems often use cheap figure eight cable for the speaker wires and there are usually bundles of it shoved behind the system. Fortunately, the fix is usually very easy for sound systems. Winding the excess speaker cable around a ferrite rod, say 10mm diameter and 250mm long, will usually get rid of the problem. You are just adding inductive reactance to the audio line, which hardly affects the audio performance at all, but offers a high reactance to high RF currents.

At the back of the amplifier, or where the speaker leads go into the sound equipment, wind the excess speaker leads around two ferrite rods as shown in figure 33-3. The good part about using rod rather than toroid ferrite is that it provides more inductance and you do not have to remove audio plugs or cut any wires.

An RF choke as shown in figure 33-3 is one of the best friends of the RF interference investigator. Such as choke can be placed on:

Internet routers.

Telephone copper pair lines.

Computer speaker leads or any other computer leads that are getting RF interference. Microphone leads.

Printer cables.

Power supply lines, both mains and low voltage DC. Coaxial cables leaving the station.

INTERNAL CHOKING AND BYPASS 

In severe cases of audio overload and rectification the device may need internal choking and RF bypassing fitted. This will require a technician or other competent person. In some cases, for example with cheap clock-radios, it is less expensive to purchase a new clock-radio that is not prone to RF interference.

MAINS INTERFERENCE 

RF interference can enter the affected equipment via the mains from a non RF source. Or the mains itself can be the source of interference. If mains interference is suspected, or you just want to eliminate it, the best thing to do is turn the mains OFF. If the equipment being interfered with is mains operated then you will need to operate it from another power source. This mean using a battery or a battery and an inverter.

TELEPHONE INTERFERENCE

Telephones are not supposed to pick up radio signals, but sometimes they do. Usually, a simple 0.5µF or higher capacitor across the line will fix the problem - the line is usually a blue/white and/or red/black cable - better still, call the Telephone company and complain to them. You can also try wrapping the telephone lead around a ferrite rod to form an RF choke.

INDUSTRIAL HEATING

Industrial machines, of which there are many, can cause severe interference. Such interference is non-selective and can happen to anyone. Report it to the radio licensing authority in your country or track it down and advise the owner of the machine about the problem.

This can be extremely costly interference to fix and the only way is to advise your licensing or regulatory authority who investigate large numbers of interference problems for the public, in most cases for no charge. If this type of interference occurs it will affect a large number of households and commercial radio services.

ALTERNATOR WHINE

A mobile radio station experiences a variable pitch whining noise in the receiver. What is the likely source?

Of course, I can hear you say, the alternator (AC generator) in the car. The diodes in the rectifier diodes in the alternator can cause this interference. The diodes are needed to convert the AC to DC to charge the car battery. The sharp switching of these rectifier diodes cause RF interference. The varying pitch is due to the changing RPM of the car engine.

This interference is usually eliminated by installing a 1µF or larger coaxial capacitor at the alternator output terminal.

Alternator whine can also be transmitted and not heard. If other radio stations report to you a variable pitch whining noise on your signal, do something about it, it is most irritating to listen to.

While it is a simple job to fit an RF bypass capacitor to an alternator it is inexpensive and quick to have an auto-electrician do it for you.

IGNITION NOISE

If in a mobile installation you hear a popping sound that varies in popping rate with the engine RPM then you are getting ignition interference. The first thing to check is that no leads are loose and arcing in any location. If loose leads are not the cause then you can fit spark plug audio frequency interference (RFI) suppression leads. These are made of a composite compressed carbon as the conductor to add resistance to the leads which suppresses the RF. Still better leads are stainless steel wire wound as a coil in the lead with a resistance of about 1300 ohms/meter. These leads add resistance and inductance to the leads.

PERIODIC RFI

If the interference occurs at certain times of the day in a regular manner then you are most likely looking for a source of RFI that is on a timer. Suppose the interference is at night and never through the day, then it could be an electric blanket switching ON and OFF. Or a pool chlorinator which is usually set to run late at night or early morning. Refrigerator butter conditioners also have a thermostat that can operate at random times to keep the butter soft and spreadable. There are many other potential RFI sources that are timed. You either have to eliminate them one at a time or turn the mains OFF and eliminate an entire residence.

POWERLINE INTERFERENCE (PLI)

Powerline interference is radiated from power lines that for some reason have arcing of the hardware. This could be lines arcing across broken or even just dirty insulators. It could be from loose cross arms or other pole hardware. The interference is stronger at lower frequencies. It often would affect the low VHF analogue TV channels and be seen as two distinct sparky bands on the screen. The two bands are caused by the flashover on the pole with the voltage reaching peak value twice per cycle.

This type of interference has to be fixed by the electrical authority who owns the pole route. However if you can locate the pole(s) this may get you a quicker response from that authority.

Since this interference drops off with frequency you can walk the pole route while listening on a portable AM receiver and take notice of the level of the noise. When you receive the noise strongly move up in frequency and continue to walk to the strongest spot again, until you are right under the source, assuming there is only one source, you should hear the interference into high VHF (300MHz).

If you think you are very close to the pole then, if it is a wooden pole, you can "tap" the base of the pole with a rubber mallet. The small movement at the base of the pole will translate to a much greater movement at the top and you should be able to detect changes in the level of interference on your receiver.

You need to be very careful when tapping a pole with a rubber mallet as if there is loose hardware it can come down on top of you, I speak from hard experience. Actually I did tap a pole once and the entire pole came down as the base was rotten and the pole was just being held up by the wires. The upside is the interference was fixed.

Electrical arcing causes ultrasonic sound to be emitted. Another way to find the source of powerline interference is to use a directional ultrasonic detector.

If power line interference is due to dusty insulators it is not surprising then that the interference disappears after rain only to return some time later.

WIDE AREA PLI

A piece of wire, perhaps an old coat hanger can get caught on a single powerline leg. Don't ask me how they get there, they just do. Coat hanger size is pretty close to the VHF 2 Metre amateur band. So, here you have this short length of wire snagged on a higher voltage power line of 11kV and up. Over time where the wire contacts the powerline there will be corrosion through the touching of dissimilar metals. As the wire moves ever so slightly in the breeze the resistance changes at the point of contact and an arc occurs which shock excites the wire into RF oscillation on its resonant frequency. The wire will radiate and the radiation can cause interference over a fairly large area. I have seen this cause television interference (TVI) to one channel over an entire suburb.

INTERFERENCE TO DIGITAL SERVICES

Diagnosing the cause of interference for digital TV, radio and other things like modems is more difficult as the nature of the interference on the device does not tell you very much about the nature of the interference.

Suppose you or your neighbour have interference to digital TV reception. Where do you start? The on-screen interference is pixelation or picture drop out.

The best place to start is to first determine that the interference does not coincide with your transmissions. Let's say you have done this, what now?

The next obvious thing is the DTV's antenna system and if there is sufficient signal voltage arriving at the DTV. All DTVs have a user option to check the level of the TV signal to the receiver.

Access the menu system and check the signal strength. It won't give you an absolute reading in decibels relative to a micro volt (dBμV) usually, but it will tell you if it is good, fair or bad. If it is not good, then go no further, make it good. Look at what could be wrong with the feedline, antenna, connectors or any amplifiers inline.

DTV WEAK SIGNAL

Make sure the antenna is of the right type and pointed in the correct direction. Many people install an antenna going by their neighbour's installation. This is usually okay but sometimes it is the blind leading the blind and they all end up pointing the wrong way. Better is to move the antenna while looking at the signal meter on the DTV.

Check the coax cable, the connectors and inline amplifiers. Masthead amplifiers need a DC supply from a small plug pack inside the house. Check the DC output - if you can to make sure that DC is getting to the masthead amplifier. Make sure all the DTV connectors are properly 'home' in their sockets. The plugs and sockets oxidise over time so clean them up with a bit of emery or light sandpaper.

Internal amplifiers need a DC supply as well. Check the signal strength with the amplifier in and out of the circuit. There should be a large difference if the amplifier is not working. A faulty amplifier will act as an attenuator, that is, the signal will be better without it.

One of the problems with masthead amplifiers is they can oscillate. If they do you will have pixilation or no picture and it is very likely, your neighbours will have it from your oscillating masthead amplifier. To determine if a masthead or another amplifier is oscillating switch off the DC power while watching the interference on another system.

So you have checked everything about the DTV system, antenna, feedline, connectors, amplifiers and signal strength are all good. So we can rule out a problem with the receiver.

If the interference is external to your radio station. You may have to canvass neighbours and ask if they are getting it as well and work from there.

If the interference is to your radio station then if possible, run the affected receiver from battery power and switch off your mains. You then eliminate your entire property in one hit. If the interference is external, you may have to use a portable receiver and even a directional antenna to locate it. One thing to remember about external sources if they are broad bandwidth (which most are) is that the higher you go in frequency and can still receive it then the closer you are to the source.

Ask for help from experienced radio users. If the external interference is to your and your neighbour's domestic TV and radio devices, then your regulatory authority would generally investigate the problem particularly if it is affecting a large number of people.

INTERMODULATION INTERFERENCE 

We are done with domestic interference, not that there is no more to know, but we have covered the primary causes of the most common types of interference. It is time to look at interference to radiocommunications systems. Intermodulation interference affects amateur repeaters and VHF and UHF land mobile systems.

WHAT IS INTERMODULATION? (IM)

Intermodulation occurs when two or more signals pass through a nonlinear device. The output of the nonlinear device will contain new frequencies. These new frequencies are called intermodulation products.

Figure 33-7 shows what happens when two or more RF signals enter a nonlinear device. The output of the nonlinear device will contain hundreds of intermodulation products on different frequencies. The products most likely to cause interference are shown in figure 33-7.

These products are the most troublesome because their frequencies will be close to the frequencies that generated them. For practical purposes most of the intermodulation products can be ignored. The intermodulation products that cause the greater likelihood of interference are the odd order products 3, 5 and 7.

The nonlinear device, may be an early receiver stage, the power amplifier in a transmitter, or even something as vague as a rusted piece of tower hardware. The odd order products will fall close to either the receiver or transmitter's operating frequency. In the case of a receiver, products that fall within the receiver's passband will be heard as interference. Products are created in the transmitter's output stage and will be transmitted along with the desired signal and may cause interference to receivers co-sited or as far as 10km away.

The mixing combinations most likely to cause interference are:

A-B=C 2nd order, two frequency

A+B=C 2nd order, two frequency

2A-B=C 3rd order, three frequency (very common)

A+B-C=D 3rd order, three frequency(also common but not as much as 2A-B)

Other mixing products can produce interference but such interference is very rare. A+B and A-B usually only occur when a high power broadcast transmitter or paging service is part if the mix.

The essential ingredient for intermodulation to take place is the presence of a nonlinear device. Receiver mixer stages are nonlinear by design. Linear RF amplifier stages can be overloaded (by strong signals) and become nonlinear. FM transmitters have the power amplifier stages biased Class C for efficiency (Class C is nonlinear). Filters and isolators and other transmission line components inherently have some degree of nonlinearity.

TYPES OF INTERMODULATION INTERFERENCE

Receiver intermodulation

Receiver intermodulation occurs when two or more radio signals enter a receiver, mix, and produce an interfering new signal on, or close to, the receiver's frequency. Receiver intermodulation is most likely to occur in:

1. The first mixer stage.

2. Radio frequency amplifiers preceding the mixer.

3. The distribution amplifier in the multicoupler system.

Receiver intermodulation is most likely to occur with single frequency simplex systems because the transmitter and the receiver are on the same frequency. At high density radio sites where the frequency separation between users may be less than 2MHz. It is not uncommon for receiver intermodulation to occur on two frequency UHF duplex systems.

For example two transmitters are co-sited and operate on 165 and 166MHz. Interference can be heard in a receiver tuned to 167MHz. The receiver may be a few kilometres away from the two source transmitters. On entering the receiver, 165 and 166MHz could mix in the combination 2 x 166 - 165 = 167MHz. This is a two frequency, third order intermodulation product.

Of course this interference will be intermittent as both 165 and 166MHz must be on air simultaneously for the product to be created on 167MHz. To frustrate matters further, the resultant demodulated audio from the product on 167MHz will be garbled, making identification of the signals by traffic content or callsign difficult.

All is not lost because for practical purposes it is not necessary to identify the source transmitters. If the cause is receiver intermodulation, then it can only be cured at the receiver. This normally means fitting a cavity filter to the affected receiver to improve its rejection of the off-channel signals on 165 and 166MHz.

A notch (bandstop) filter may be fitted to the receiver to reduce the level of one of the source transmitters at the affected receiver. If the source transmitters are widely spaced in frequency then a simple high Q transmission line notch is the most economical way to resolve the problem. A transmission line notch should be one half wavelength at the frequency to be rejected and terminated in a short circuit. See the chapter on transmission lines for details of this notch. If possible it is best to install the notch in a receiver path only as it can upset the system match. Around 25-30dB can be obtained with a single transmission line notch.

Transmitter intermodulation 

Transmitter intermodulation occurs when two or more signals enter a transmitter's output stage and mix. Intermodulation products will then be transmitted along with the desired signal.

Using our two co-sited transmitters on 165 and 166MHz again (see figure 33-9), mixing could occur in either or both transmitter output stages to produce a third order product on 167MHz. The 167MHz signal is now being transmitted to the receiver on channel. In this case nothing can be done at the receiver. Bandpass cavity filters fitted to either or both will usually eliminate the problem.

In severe cases where transmitter isolation is very poor(e.g. transmitters mounted on the same horizontal plane) isolators may need to be fitted or the antennas relocated to obtain better isolation.

Transmitter intermodulation between transmitters at the same site is a direct function of intrasite antenna isolation. This isolation can be improved by the use of cavity filters and isolators. These devices are expensive. It is better to try to achieve maximum isolation by thoughtful antenna placement. We can achieve maximum natural and free isolation this way, and reduce the expenditure on ancillary artificial isolating devices.

The best antenna isolation threshold that can be achieved between two antennas mounted on the same tower and in the vertical plane is 80dB. Higher decoupling cannot be achieved because the metallic structure of the tower creates an irreducible amount of cross coupling. Antennas mounted in the same horizontal plane and only a few feet apart will have as little as 15-20dB isolation.

With horizontal separation, and outside the near field distance, the best isolation is equal to the free space path loss calculated from:

If 80dB isolation is the best and 15dB the worst, a good practical figure to strive for with antennas on the same tower is 65dB.

Figure 33-10 shows the amount of isolation that can be obtained using vertically spaced vertical dipoles. These values are based on a large number of real world measurements.

The overall objective in multicoupling is to maximise transmitter to transmitter isolation. A total isolation of 90dB can be achieved by a combination of antenna placement, filters and isolators. With this degree of isolation the radiated intermodulation products would be in the region of -100dBC to -110dBc (dB below the carrier) or -53dBm to -64dBm for a 50W(+47dBm) transmitter.

External intermodulation

External intermodulation occurs outside both transmitters and receivers. Metal junctions, particularly if rusted can form rectifying nonlinear elements. Signals induced into such elements are mixed and re-radiated on product frequencies. The nonlinear element could be formed by a faulty antenna, corroded guy wires, or a rusted tower to name just a few. There are some that believe external intermodulation is just something in textbooks and it does not happen in the real world. It does happen. When it does it can usually be easy to find but very difficult to fix. I recall one situation when a large rusted tower was the cause in a very remote area and the cost to fix it ran into hundreds of thousands of dollars. This would have been avoided had the tower received some routine maintenance.

On another occasion severe interference was being caused in the Sydney CBD. After many days the culprit was found to be a small length of chain. This chain was used to secure a camera to the top of a building. The camera had been removed but the chain was left dangling in the wind. It rusted and became a wonderful mixer and re-radiator that disrupted communications for some weeks.

RESOLVING INTERMODULATION INTERFERENCE

Of the types of intermodulation the one most likely to occur is receiver intermodulation. It is also the easiest to fix even if the mixing partners are not found. Placing a bandpass cavity on any receiver suspected of having receiver intermodulation interference will fix it. If the interference is transmitted to the receiver then the filter will have no effect.

If no filter is available, try placing a small amount of resistive attenuation (3-6dB) in the receiver line. Inserting 3dB of attenuation will reduce the desired signal by 3dB. However, the receiver intermodulation will be attenuated by the attenuation added times the order of the intermodulation product.

Hence, 3dB of attenuation will cause a third order intermod to be attenuated by 9dB. If adding a resistive pad or filter does not reduce or eliminate the interference then receiver intermodulation is not the cause.

Transmitter intermodulation is the most difficult to find and cure. You will usually need a list of all services within the region where the interference is suspected of coming from. Computer algorithms are used to determine if mixing products are possible and indicate their likelihood of being the source. Operators of the affected service can keep a log book of the interference and record anything that might be a clue to identifying the transmitters responsible. Even small details like the nature of the voice of an operator can help. When suspect transmitters are located it comes down to doing measurements using cavity filters and a spectrum analyser to determine in which transmitter the mixing is taking place. Transmitter intermodulation is a costly time consuming task.

This is why repeaters are an assigned service. Before a repeater licence is granted the area where the repeater is to be installed is analysed to determine if the repeater frequencies will fit with the other services and not cause intermodulation.

Adding subtone (CTCSS) to the repeater's receiver is also important to help reduce interference. It will not get rid of a transmitted intermod but it will keep the repeater from being triggered as much.

34 - Frequency Modulation

WHAT IS FREQUENCY MODULATION?

Before defining Frequency Modulation, let's just go over again what we mean by modulation as applied to radio communications. Modulation is the process of converting low-frequency signals into high-frequency signals so that they can be radiated and recovered at a remote location. Usually, the intelligence we are trying to transmit is voice, but of course, can be other things such as encoded video or data. With amplitude modulation, we combine the modulating audio with the radio frequency carrier in such a way that the total wave power of the transmitted wave is made to vary. Remember, the total wave power varies. The RF carrier power in an AM system remains constant.

Now besides using the modulating audio to change the total power of the wave being transmitted, we can make the modulating audio change the frequency of the RF carrier.

FM is a system by which the modulating audio is made to change the instantaneous frequency of the carrier.

Popular belief is that in an AM signal the carrier power varies and in an FM signal the carrier power remains constant. This is incorrect. In an AM system the total wave power varies with modulation and the carrier power remains constant and in an FM system the total power transmitted remains constant and the power in the carrier varies.

The simplest FM transmitter is where the modulating audio is fed directly to an oscillator and the voltage level of the modulating audio causes the frequency of the oscillator to vary.

A SIMPLE FM TRANSMITTER

Modulating audio could be fed to a capacitor microphone that forms part of an LC circuit that in turn controls the operating frequency of an oscillator. Hence, the voltage of the modulating audio controls the frequency of the oscillator.

This signal could then be amplified and transmitted to the receiver. At the receiver, we would need a method of converting RF frequency changes back into audio.

BACK TO THE VOLTAGE CONTROLLED OSCILLATOR (VCO)

In an earlier chapter, we discussed how voltage could be used to control the frequency of an oscillator. We did this by using a varactor diode. The reverse bias on the diode changed its capacitance and in turn that capacitance change was used to make small changes in the operating frequency of a quartz crystal. To jog your memory, have a look at the circuit of the VCO again, shown in figure 34-2.

The potentiometer (a variable resistor with a centre tap) can be adjusted to bring about small changes in the frequency of the quartz crystal. Everything to the left of the radio frequency choke (RFC) in the circuit provides a regulated DC voltage using a zener diode.

Now, what if we did away with the zener diode and applied (modulating) audio to the varactor diode. We would have a method of producing FM.

It is that easy to produce frequency modulation. Simply feed the modulating audio to a varactor diode and the diode will bring about frequency deviations of the quartz crystal proportional to the modulating audio amplitude.

I have not drawn the complete circuit of the oscillator, as it could be any type. As you can see, the modulating audio is used to change the reverse bias on the varactor diode, hence changing its capacitance and in turn the frequency of the oscillator.

The RFC (radio frequency choke) prevents the RF from getting into the AF circuit.

To make sure you have got exactly what we are on about here, let's go over it. Without any modulating audio, the reactance modulator (which is just a fancy voltage controlled oscillator) will produce RF energy on a single frequency only. This is shown below as the 'carrier' figure 34.4 - the frequency is irrelevant, but it would be high, at least in the order of a few megahertz. This is called the centre frequency.

We have the audio frequency coming from the microphone, which in the case of radio voice communication would be somewhere between 100Hz and 3kHz maximum.

This modulating audio is applied to the varactor diode in the reactance modulator causing the frequency of the quartz crystal to change up and down from the centre frequency. So we end up with a frequency modulated wave as depicted at the bottom of figure 34-4. The total wave power does not change, the frequency does.

These graphs could be shown on a device called an oscilloscope. The oscilloscope clearly shows the amplitude (power) of the FM wave does not change, but it is evident that the average power of the centre frequency does change as it is not there all the time.

Frequency modulation is a method of modulating a carrier wave whereby the amplitude of the modulating audio causes the frequency of the carrier to change.

Major E.H. Armstrong developed the first working FM system in 1936 and in July 1939 began the first regular FM broadcasts from Alpine, New Jersey.

The capacitance of the diode in the reactance modulator has a direct effect on the oscillator's frequency. The following important conclusions can be made concerning the output frequency:

1. The frequency of the sound waves arriving at the diaphragm of the microphone determines the rate of frequency change.

2. The amplitude of sound waves arriving at the diaphragm determines the  amount of frequency change.

The previous diagrams illustrate the fundamental differences between an FM and AM wave. If the sound wave striking the diaphragm was to be doubled in frequency from 1kHz to 2kHz with the amplitude kept constant, then the rate at which the FM wave swings above and below the carrier would change from 1kHz to 2kHz. However, since the intelligence (amplitude and frequency) of the sound wave has not changed, the amount the frequency swings above and below the carrier frequency will remain the same.

On the other hand, if the frequency of the modulating audio was constant but the amplitude was doubled, then the rate of frequency swing above and below the carrier would remain at 1kHz and the amount of frequency deviation (movement from the centre frequency) would double.

DEVIATION OF AN FM WAVE 

Without modulation, an FM transmitter produces a single carrier frequency (fc). When modulation is applied, the output frequency will swing above and below the unmodulated carrier frequency (fc). The amount of decrease or increase around fc is called the frequency deviation.

MODULATION INDEX OF AN FM WAVE

The modulation index is the ratio of the amount of frequency deviation to the audio modulating frequency. Suppose an FM broadcast transmitter has a deviation of 75kHz when a modulating audio frequency of 15kHz is applied to the microphone input, then:

modulation index(µ) =deviation/ modulating frequency

modulation index(µ) = 75/15=5.

The modulation index has no unit. In this text, the modulation index will be denoted by the Greek letter (µ). Sometimes the modulation index is denoted by the letters (mf).

There is a special case concerning modulation index and this is when the frequency of the modulating audio is at its highest. In such a case the modulation index is called the deviation ratio. For narrow band voice FM transmissions, the deviation is restricted by regulation to 5kHz. However, this may differ in some countries. Also some regulatory authorities are loosening up the rules on occupied bandwidth. Since the highest modulating audio used for voice communications is 3kHz, the deviation ratio for an amateur FM transmitter is then:

Deviation/ highest modulating frequency= 5/3 =1.66.

The modulation index is known as the deviation ratio when the highest modulating audio frequency is used. Radio experimenters do not generally use 'deviation ratio' they would simple refer the 1.66 as the modulation index.

SIDE FREQUENCIES OF AN FM WAVE AND MODULATION INDEX

When a carrier (fc) is frequency modulated by a signal (fs), then theoretically an infinite number of side frequencies will be produced on each side of the carrier.

The distance between each of the side frequencies is equal to the frequency of the modulating signal (fs).

The amplitude of each side frequency does not follow any simple pattern and is dependent upon the modulation index (µ) or deviation ratio.

At a certain distance from the carrier (fc) the power in the side frequencies will decrease to a level where they can be considered insignificant. A side frequency is considered insignificant if its voltage amplitude is less than 10% of the unmodulated carrier amplitude. The number of significant side frequencies is directly proportional to the modulation index and can be found from: significant side frequencies = 2 (µ+1), where µ = modulation index. To determine the relative amplitude of each of the side frequencies, it is necessary to consult a table of Bessel functions of the first kind.

Example 1. A commercial FM broadcast transmitter has a deviation ratio of 5 and the frequency of the modulating audio is 15kHz. Determine (a) the amount of frequency deviation and (b) the occupied bandwidth (BW) of the transmission.

Answer: the deviation is 75kHz and the occupied bandwidth is 180kHz.

Explanation: 

We learned that modulation index = deviation / frequency of the modulating audio. This is more often written as µ = Δf/fs.

This equation can be transposed to give: Δf (deviation)=µ x fs and for our problem this gives Δf (deviation) = 5 x 15kHz = 75kHz.

The significant number of side frequencies present in the transmitted wave is given by:

significant side frequencies= 2(µ+1) = 2(5+1) =12.

Since each of these 12 significant side frequencies are spaced apart by an amount equal to the frequency of the modulating audio (15kHz), then the bandwidth is:

BW=12x15kHz=180kHz.

A slightly easier method for determining the bandwidth of an FM wave can be derived. In the last example we found the bandwidth from:

BW=2(µ+1) x fs

By multiplying each term within the brackets by fs we get:

BW = 2(µ x fs + 1 x fs).

Since µ x fs equals the deviation, the equation can be simplified to:

BW=2(Δf + fs)

The bandwidth (how much spectrum space it occupies) is equal to 2(Δf + fs). Where Δf is the deviation and fs is the frequency of the modulating audio.

Example

Assume a transmitter has a peak deviation of 3kHz (which is typical for narrow band voice) and that the frequency of the applied modulating audio is 3kHz). With the aid of Bessel functions, construct the spectrum of this wave as would be seen on a spectrum analyser.

The modulation index 'µ' of this wave is 1. There are 2(µ+1) or 4 significant side frequencies (two each side of the carrier) each spaced apart by (fs), or 3kHz. By consulting a table of Bessel functions, we see that the voltage amplitude of the carrier for a modulation index of 1 is 0.77 and the first two pairs of side frequencies have amplitudes of 0.44 and 0.11. The third pair of side frequencies has a relative amplitude of 0.02 and since this is less than 10% of the unmodulated carrier value of 1, the third pair of side frequencies can be considered insignificant.

We can now construct the graph from the above information as shown in figure 34-6.

Show using a table of Bessel functions that the total power of an FM wave remains constant.

A table of Bessel functions gives the relative voltage amplitude for the carrier and each pair of side frequencies. Since the power is directly proportional to the square of the voltage, the relative power amplitude of the carrier and its side frequencies can be found by squaring each value listed in the table. In addition, since the total power in an FM wave remains constant, the sum of the squares of the values in the Bessel table should equal 1 for any particular modulation index.

The figures given on tables of Bessel functions are for practical purposes rounded, usually to two decimal places. So the sum of the squares will be almost, but not quite, 1. If we used Bessel functions taken to say six significant places, we would find the result is extremely close to 1.

Here we have demonstrated that the total power in an FM wave remains constant. If we did the same for any other modulation index, we would find the same result. The reason it may seem I have carried on about this a bit is because there is a popular false belief that the power of the carrier of an AM wave varies with modulation and the power of an FM carrier remains constant - when precisely the opposite is the case.

SUMMARY SO FAR

AM - a system of modulation whereby the modulating audio is combined with the carrier in such a way as to create new frequencies (sidebands) and where the total wave power transmitted varies with modulation.

FM - a system of modulation whereby the modulating audio causes the frequency of the carrier to vary in proportion to the amplitude of the modulating audio. The total power transmitted does not vary. The power in the carrier does vary and can fall to zero (for example, look at mf=2.405 in Table 34-5).

THE ADVANTAGES OF FM WHEN COMPARED TO AM 

An FM system provides a better signal-to-noise ratio than an AM system. Put simply; this means it has less noise.

During its transmission (propagation), a frequency modulated wave will be subject to noise and interference voltages. The effect of these unwanted voltages is to vary the amplitude and phase of the FM wave. The noise amplitude variations have no effect on the performance of the system. Intelligence, information or modulation if you like, are not carried in the amplitude of an FM wave. Amplitude variations are removed in the FM receiver stage called the limiter. The phase deviation caused by noise means the carrier is effectively frequency modulated and some noise will appear at the output of the receiver.

The improvement in the signal-to-noise ratio that FM has over AM is primarily dependent upon the system deviation ratio (D). This is why FM broadcast stations sound so good. The degree of improvement can be determined by the equation:

Signal-to-noise ratio improvement= 20Log(D√3)dB

The deviation ratio used in mobile FM voice communications (narrow band FM) is 5/3 or 1.66. The signal-to-noise ratio advantage over AM, by using the previous equation, is found to be 9.21 dB. Nothing to get excited about, but it is none-the-less a worthwhile improvement. Significant advantages in signal to noise ratio are only realised by commercial broadcasters. FM broadcast stations have a system deviation ratio of 5, giving a signal-to-noise ratio advantage of 18.75 decibels compared to AM.

THE DISADVANTAGES OF FM WHEN COMPARED TO AM

FM has a greater bandwidth requirement than AM. Narrow band FM occupies 2(5+3) =16kHz of spectrum space compared to AM's 6kHz (or in the case of single sideband 3kHz).

FM systems generally have a much wider bandwidth than AM systems. This makes FM (or any wider bandwidth signal) more prone to selective fading. Selective fading applies primarily to, but is not limited to, HF propagation - see the chapter on propagation for more information.

CAPTURE EFFECT 

Another disadvantage of FM is that of capture effect. Capture effect is the ability of an FM receiver to lock onto and capture one transmitting station only. This can be a good thing, but it can lead to weaker signals not being heard at all. Typically, if a signal is about 3dB weaker than the desired signal, then it will not produce an output from the receiver. The receiver's limiter stage has "captured" the stronger signal. This explains the reluctance of airport authorities to switch to FM. Using an AM system allows an aircraft to break into a working channel should an emergency situation develop.

PRE-EMPHASIS AND DE-EMPHASIS

Pre-emphasis is used at the transmitter to boost the modulating audio frequencies above 1kHz. De-emphasis is employed in the receiver to restore the modulated audio back to its original power distribution.

Pre-emphasis and de-emphasis have the effect of improving the signal-to-noise ratio at the receiver for higher audio frequencies.

Pre-emphasis - boosting of audio frequencies above 1kHz in the FM transmitter.

De-emphasis - attenuation of frequencies above 1kHz in the FM receiver

Frequencies contained in human speech mostly occupy the region from 100 to 10,000Hz, but most of the power is contained in the region of 500Hz for men and 800Hz for women. The problem is that in an FM system the noise output of the receiver increases linearly with frequency, which means that the signal-to-noise ratio is poorer at the higher audio frequencies.

Also, noise can make radio reception less readable and unpleasant. This noise is greatest in frequencies above 3kHz. The high-frequency noise causes interference to the already weak high-frequency voice. To reduce the effect of this noise and ensure an even power spread of audio frequencies, pre-emphasis is used in the speech amplifier of the transmitter.

A pre-emphasis network in the transmitter accentuates (boosts) the audio frequencies above 1kHz, so providing a higher average deviation across the voice spectrum, thus improving the signal-to-noise ratio at the receiver. Without corresponding de-emphasis at the receiver, the signal would sound unnatural.

Pre-emphasis and de-emphasis are obtained by using simple audio filters. Normally we use LC filters for high and low pass filtering, however for simple low power audio, where we are not concerned about some resistive loss, simple RC filters can be used. You may be required to identify one of the circuits in an Advanced Radio assessment. The pre-emphasis circuit produces higher output at higher frequencies because the capacitive reactance of 'C' is decreased as frequency increases. As the resistor and the capacitor form a voltage divider and the reactance of the capacitor has decreased, more voltage must appear at the output across the resistor.

A similar reasoning, but reverse in effect, can be applied to the de-emphasis circuit.

The standard time constant (T=CR) for these circuits in narrow band transceivers is 75 microseconds (µS).

Summary

Pre-emphasis is used in the transmitter to boost (emphasise) the higher audio frequencies in speech (above 1000Hz).

Pre-emphasis increases the average deviation of a transmitter resulting in better signal-to-noise ratio. In addition, the effects of higher frequency noise is less noticeable.

De-emphasis in the receiver attenuates the high audio frequencies in the receiver to restore the original audio.

THE BLOCK DIAGRAM OF AN FM RECEIVER 

Figure 34-9 below shows the partial block diagram of an FM receiver. All the stages preceding the last IF amplifier would be the same as that of any superheterodyne receiver. The bandwidth of the IF amplifier would be approximately 16kHz in an amateur FM receiver. Compared to an AM receiver, the IF amplifiers would have sufficient gain to allow for full limiting action to occur at the limiter. We will discuss the limiter stage shortly. By the time the FM signal reaches the limiter, it has been amplified sufficiently for the limiter to be able to remove any amplitude modulation. Any amplitude modulation would be noise in an FM system. The stage following the limiter is called the discriminator. The purpose of a discriminator is that of an FM demodulator. An FM demodulator's job is to convert frequency variations in the signal back to the original modulating audio (the audio that went into the microphone at the transmitter). The discriminator can work on one of several principles. You will not have to know how these work, but you may have to know what they are called. The basic types of discriminators are the Foster-Seeley, Ratio Detector and the PLL type. The PLL type being the most commonly used FM demodulator today.

All these discriminators perform the same function in that they convert frequency variations into audio amplitude variations. The greater the frequency deviation, the higher (louder) the audio output voltage. The discriminator's job is to convert frequency variations back to amplitude variations - which is the demodulated audio.

The de-emphasis circuit (usually part of the audio amplifier) restores the audio to its original power distribution by attenuating frequencies above 1kHz. All FM receivers contain a mute or squelch circuit to cut off the input signal to the audio amplifier in the absence of an FM input signal.

OPERATION OF THE LIMITER STAGE 

Figure 34-9 shows what happens to the input signal after being fed to a limiter. Positive and negative amplitude peaks drive the FET (though other active devices could be used) into cutoff or saturation, therefore slicing off the amplitude variations which represent noise. The limiter is actually an over-driven RF amplifier. If the signal entering the limiter was not of sufficient amplitude to drive the FET between cutoff and saturation, then limiting action would not occur. This happens on weak signals and considerable noise is heard at the receiver output. In an attempt to ensure full limiter action, most FM receivers have more IF amplification than AM types.

The limiter action shown in figure 34-10 could be achieved by using a sharp cutoff FET. You can see that the input to the gate has amplitude variations (noise). The output from the drain has all of the amplitude variations removed. The intelligence in the frequency is unchanged by the limiter action.

THE FOSTER-SEELEY DISCRIMINATOR

The Foster-Seeley circuit (figure 34-11) and its operation are explained in detail. You do not need to explain the operation for assessment. You may need to know the schematic's name and to be able to identify it.

Operation:

Remember first - the purpose of any FM demodulator is to convert frequency changes back to amplitude changes. The changes in amplitude are our recovered audio.

In order to understand the operation of the circuit, it is important to realise that the capacitances C1, C3 and C6 have very low reactances at the operating frequency. The left side of L3 is connected to the top of L1 via C3 and because of the low reactance of C3, there is no appreciable voltage across C3. Therefore, the left end of L3 and the top of L1 are at the same potential. Similarly, the right end of L3 is connected to C6 and C1 to the bottom end of L1 and is the same potential as the bottom of L1.

L3 is electrically in parallel with L1. The FM signal from the last IF stage produces a voltage Ep across L1 and since L1 is in parallel with L3, then the voltage Ep will also appear across L3. There will be a voltage induced into L2 from L1. Because of the centre tap, half of the induced voltage will appear as Ea on the top half of L2 and as Eb on the bottom half. The total voltage applied to D1 is then Ep + Ea and the voltage applied to D2 is Ep + Eb.

At the centre frequency (no deviation) Ep + Ea = Ep + Eb. Also, the currents I2 and I3 through R2 and R3 will be equal and opposite. Likewise, the voltages appearing across R2 and R3 will be equal and there will be no net output voltage. The output voltage is the net or resultant voltage across R2 and R3. This is as it should be with no deviation. At the centre frequency, the tuned circuit consisting of L2 and C4 is resonant and as such the current and voltage are in phase.

At any frequency other than the centre frequency (when modulation is present) there is a change of phase between Ea, Eb and Ep. This means that Ep + Ea will not equal Ep + Eb. How much difference exists will depend on the deviation from the carrier frequency. Whether Ep + Ea is greater or less than Ep + Eb will depend on which way the frequency swings. The overall result is that for any frequency other than the centre frequency, currents I2 and I3 will not be equal. The voltages R2 and R3 will not be equal and opposite and a net voltage will appear at the output with an amplitude directly proportional to the deviation. By converting the deviation into amplitude variations, we have recovered the original modulating audio.

A de-emphasis circuit is formed by R4 and C7. R4 and C7 form a simple low-pass filter.

THE RATIO DETECTOR - another FM discriminator 

In a ratio detector, one of the diodes is reversed so that current can flow in the overall circuit. The circuit operation is similar to the Foster-Seeley discriminator, but the output voltage is now taken from the points (A) and (B) as shown in the schematic diagram. Because C9 is connected in parallel with R2 and R3 and also C5 and C6, the voltages C5+ C6 and R2 + R3 are held at a constant value by the charge on C9.

At the centre frequency, there will be no potential difference between points (A) and (B). When deviation is present, one of the diodes will conduct harder and the voltage across its associated capacitor will increase; the voltage on the other capacitor will decrease (the total voltage C5 + C6 remaining constant); the circuit is unbalanced and a potential difference must now exist between points (A) and (B). This net voltage is the demodulated audio output. Because amplitude variations do not unbalance the circuit, a ratio detector does not theoretically require a limiter stage. In practice, however, most manufacturers provide a limiter stage, as large amplitude variations will produce some noise output.

PHASED LOCKED LOOP (PLL) FM DISCRIMINATOR 

The PLL discriminator is one of the common methods of FM demodulation today. It is not necessary to have a broad knowledge of PLL systems for Advanced exam purposes. The block diagram of a PLL FM detector is shown in figure 34-13.

The FM signal from the limiter is fed to the phase detector. At the centre frequency, only the carrier will be present and the PLL circuit will lock onto the carrier and is held there by the correction voltage produced by the phase detector (VCV). If the IF was 10.7MHz, then the VCO would now be oscillating at 10.7MHz. When deviation is present, the carrier swings above and below the centre frequency. The PLL circuit will attempt to stay in lock by producing a correction voltage (VCV) which makes the VCO track the carrier frequency swing. As the correction voltage is proportional to the amount of deviation from the centre frequency, the correction voltage is the demodulated audio.

FM TRANSMITTERS 

Let's look at the block diagram of the FM transmitters shown in figures 34-14(a) and 34-14(b). The transmitter in figure 34-14(a) is the most common type used in amateur and general radiocommunications. The audio voltage from the microphone is increased in level by the microphone amplifier. The amplified audio is then applied to the reactance modulator which, in most cases, consists of little more than a reverse biased varactor diode. The audio voltage will cause the effective capacitance of the diode to vary. The varactor diode is connected across the crystal in the 10.695MHz oscillator thus, the applied modulating audio makes the crystal oscillator vary above and below its centre frequency. The microphone amplifier will have an internal gain control that can be adjusted to obtain the required amount of deviation from the crystal. The output of the crystal oscillator has the required deviation for transmission.

The signal is then fed to the mixer stage along with a very high frequency carrier from the heterodyne oscillator (VFO). For stability, the heterodyne oscillator (VFO) would consist of a PLL circuit.

At the output of the mixer will be the required transmit signal which is passed through a band-pass filter in order to remove other unwanted mixing products. The FM signal is then amplified by the power amplifiers that typically consist of 3-4 active stages. RF amplification can be Class C for maximum efficiency.

The block diagram of two types of FM transmitter

A COMPLETE FM TRANSCEIVER

Now is a good time to consolidate transmitters and receivers by looking at the complete block diagram of a typical (and real) 2-metre amateur band transceiver.

The block diagram (figure 34-15) is that of an amateur transceiver capable of operation on the 2-metre amateur band. I have not shown buffer stages as they should be assumed.

Although there are two antennas shown in the diagram, there is only one and a small changeover relay is used to switch the antenna between the transmitter and the receiver. This transceiver is PLL controlled and the PLL's programmable divider is controlled by a microprocessor. The microprocessor also controls the LCD display and keypad. The operator only has to key in the transmit and receive frequencies on the keypad and the microprocessor will set the programmable divider to the correct value (300-1100). The microprocessor will also take care of displaying the appropriate transmit and receive frequencies. It is common to work through repeaters on the 2- metre band and the 'standard' transmitter/receiver offset is 600kHz. The offset can be set via the keypad and the microprocessor looks after the rest. Notice first that the receiver section is drawn in 'blue,' the transmitter in 'green' and the PLL section is 'orange.' If you are reading this in greyscale the receiver is at the top, transmitter in the middle and PLL at the bottom.

Assume the transceiver is set to transmit and receive at 147.995MHz. This frequency would have been entered on the keypad by the operator and the microprocessor will display the TX and RX frequency on the LCD display as 147.995MHz. To operate on this (147.995) frequency, the microprocessor sets the programmable divider to divide-by-1100.

The reference oscillator is part of the PLL and provided by OSC3 on 5.76MHz. This frequency is divided by the fixed divider (divide-by-1152) down to the reference frequency of 5kHz.

The 5kHz reference frequency signal is fed to the Phase Detector. This means two things:

1. The PLL will be in lock on 5kHz and

2. The channel spacing for this radio (the increments between the individual channels) is 5kHz.

When I say the PLL is in lock on 5kHz it means that for "lock" to occur the signal coming from the programmable divider is 5kHz. If the signal coming from the programmable divider is not 5kHz, then the PLL will not be in lock and the VCO frequency will change until the PLL comes into lock. The VCV is the DC control voltage from the phase detector to the VCO. The VCV voltage will make the VCO move in frequency very quickly to 131.095MHz. When the VCO hits 131.095MHz, the PLL comes into lock and the VCO is held on frequency.

When the VCO is on 131.095MHz, the PLL will come into lock. The 131.095MHz signal is fed from the VCO to MIXER4 along with a signal of 125.595MHz from OSC2. This produces a frequency difference F1-F2 of 5.5MHz which, when divided by 1100, equals the reference frequency of 5kHz, which is fed to the right-hand side of the phase detector.

The display says the transmitter and receiver are on 147.995MHz and the PLL is producing a very stable signal on 131.095MHz, for use by both the transmitter and the receiver.

TRANSMISSION

The microphone most likely works on the dynamic or capacitor microphone principle. The audio signal from the microphone is amplified and pre-emphasis is applied. The audio signal is then fed to the Reactance Modulator, which operates on 16.9MHz. Since there is no frequency multiplication in this system, an FM signal with full deviation must leave the reactance modulator (F2). The FM signal F2 is frequency converted to 147.995MHz by summing it with the VCO signal Fl in MIXER3. The output of MIXER3 also has other unwanted mixing products and these are eliminated by BANDPASS2. The FM signal is then amplified using efficient Class C amplifiers and radiated from the antenna.

RECEPTION

The operator releases the PTT (push-to-talk) button and the antenna is switched quickly to the receiver circuit. The received FM signal is fed from the antenna to a wideband RF amplifier and then into MIXER1 where it is mixed with the signal from the VCO on 131.095MHz. The product F1-F2 of MIXER1 is 16.9MHz. BANDPASS1 at the output of MIXER1 eliminates unwanted mixing products from MIXER1. The wanted FM signal (now on 16.9MHz) is fed to MIXER2 and frequency converted to the IF frequency of 455kHz.

The 455kHz FM signal is then highly amplified by the IF amplifier before being fed to the LIMITER to remove any amplitude modulation (which would be noise). Upon leaving the LIMITER, the FM signal is demodulated by the discriminator. The recovered audio from the discriminator undergoes de-emphasis and further audio amplification before being fed to the speaker.

That's it! The full system operation of the transceiver. You should now have a good idea how an FM transceiver works and what all the stages do.

What would happen If the programmable divider was moved from divide by 1100 to divide by 300? What would the frequency of the VCO now be? Setting the divider to 300 will mean that output from mixer4 would have to be equal to 5kHz x 300 = 1.5MHz for the PLL system to be in lock. Therefore the output frequency of the VCO is equal to the oscillator frequency plus the output frequency from the mixer.

VCO frequency = 125.595MHz + 1.5MHz

                          = 127.095MHz

What is the new transmit and receive frequency?

The new transmit frequency is equal to the sum of the VCO output frequency and the 16.9MHz signal from the reactance modulator.

Transmit frequency = 127.095MHz + 16.9MHz

                                = 143.995MHz

The receiver frequency must produce a 16.9MHz difference signal when mixed with the VCO output frequency.

Receiver frequency - VCO frequency= 16.9MHz

Receiver frequency = 16.9MHz + VCO frequency = 16.9MHz + 127.095MHz

                                                                               = 143.995MHz

35 - Digital Modulation

Digital radio modulation means encoding the information we wish to send via radio on to an analogue carrier wave. The modulated carrier wave is not digital however it contains digital information that, when demodulated, can be processed digitally.

When information, be it voice or ASCII characters, is in a digital format it is easier to determine the message from the noise. For example, Morse Code (CW) is a form of amplitude shift keying. The amplitude of the carrier wave is keyed ON and OFF to represent the data being sent in the form of dits and dahs with appropriate spaces. With CW we know what to expect at the receiver.

The human operator can recognise what is noise and what is information. A distorted dah is still a dah. A computer receiving CW can also differentiate noise from signal even better than most human operators.

HOW CAN WE MODULATE A CARRIER WAVE?

A carrier wave is just a radio frequency sinewave.

What are the methods we can use to place information on this sinewave? Suppose we wanted this analogue sinewave to represent two-states. This could be a 1 and a 0. How we define and use the two-states is up to us. Let's call the two-sates a (one) 1 and a (zero) 0 and further let's call each of these states a symbol.

If we can find a way to do this then we only need to expand the system to be able to handle more symbols.

Figure 35-2 shows how we could change the amplitude of the carrier to represent the symbols 1 and 0. This is much like (Morse Code) or CW. The short duration high amplitude could be a '1'. A longer high amplitude duration could be a series of 1s. No amplitude may be determined to mean a 0 or a series of 0s. Here we change between full amplitude and no amplitude. Instead of the amplitude falling to zero we could have two defined amplitudes for 1 and 0.

If we wanted to encode more than two symbols, we could have three or four or even more defined amplitude levels.

Instead of determining our symbols using amplitude we could use phase. The carrier wave in figure 35-3 has it's phase shifted by 180 degrees in four positions. Can you see where the phase is shifted?

No phase shift could be a '1' and the 180 degrees phase shift a '0'. Notice the frequency of the carrier wave does not change.

With two-states, no phase shift and 180 degree phase shift we can encode two symbols. If we wanted to encode more symbols there is no reason we could not have more than two phases. For example, if we had these phase shifts; 0, 90, 180, and 270 degrees we could encode 4 symbols.

There is just one other characteristic of a carrier wave that we can change in order to encode information and that is the frequency as in figure 35-4.

Here we have two frequencies presenting our two symbols 1 and 0. Again if we wanted more than two symbols, we just have to define our protocol with more frequency shifts.

There is nothing else we can do with a sinewave carrier to encode information. We can change the amplitude, phase and the frequency. These three methods are the foundations of all digital communications. Our modulated carrier is not digital. The modulated carrier has been encoded with a digital message.

What if we need to send a large number of symbols? Perhaps 16 or even 128. What could we do? We could use a combination of all three methods we have just discussed.

PHASOR DIAGRAMS 

It is awkward to draw carrier wave changes using waveform diagrams. An easier method is to use a phasor diagram. Figure 35-4 is binary phase shift keying (BPSK). It is binary because we only have two phase shift states between 0 and 180 degrees. Figure 35-5 shows how we would depict such a signal on a phasor diagram.

There are two amplitude vectors one pointing from the centre of the diagram to the right and the other to the left. The length of these vectors represent the amplitude and the angle between the vector and zero degrees is the phase. With BPSK the amplitude carries no information. The length of the amplitude vectors does not change. The phasor diagram does show a phase shift between 0 and 180 degrees. These phase shifts do not occur at the same time. The carrier wave is either sitting at phase shift 0 then switching to phase shift 180 degrees depending on the data being sent. If you were looking at this phasor diagram in real time you would see a signal with the same amplitude rapidly changing its phase.

Figure 35-6 shows a carrier wave modulated between two amplitudes while the phase is kept constant. With CW the amplitude goes between zero and maximum. Here we have two discrete amplitude levels.

Now suppose we wanted to send more than just two symbols representing a 1 and 0. For example how could we use a carrier wave and encode on it four two-bit symbols 00, 01, 10 and 11?

How about we modulate a carrier wave keeping its amplitude constant and shifting it between four different phase angles. Such a system is called Quadrature Phase Shift Keying (QPSK) or Quadrature Amplitude Modulation (4-QAM). We are not discussing how such a signal is manufactured, not just yet, but how we can encode a carrier with 4 two-bit symbols.

Figure 35-7 shows our QPSK system. We have four symbols each of two bits as per the table. We are not changing the amplitude to get these four symbols. It should be beginning to become obvious how we could get more symbols. We could add more phase changes and we could have one set of phase changes at one amplitude and then do it all over again at another amplitude.

QPSK MODULATOR

Below is the conceptual diagram of how QPSK modulation is produced. The data input is fed to a serial to parallel converter. This sends one bit to each DAC. Recall QPSK is a 4 symbol, of two bits each, system. One bit is fed to a mixer1 along with the carrier oscillator. The output of mixer1 is the "In-Phase" or I-signal. The second bit is fed to a mixer2 along with the carrier phase shifted by 90°. The output of mixer2 is the out of phase or Q-signal. The I and Q signals are combined and this combination produces the QPSK waveform which can then be transmitted. QPSK modulators can be purchased as off the shelf units. For demodulation, the process in figure 35-8 is just reversed.

16QAM

The system of quadrature amplitude modulation can be increased to contain a larger number of symbols. 16 QAM has 16 symbols. This can be represented on what is called a constellation diagram. This diagram is just the phasor diagram labelled a little differently.

Take a look at figure 35-9. Here we see the constellation diagram of a 16 QAM. Each symbol in the signal is represented by a unique amplitude and phase. Any two symbols may have the same phase angle but they will have different amplitudes. Symbols can share the same amplitude but they will have a different phase angle.

If we really wanted to, we could use basic trigonometry and easily work out the exact phase angle and amplitude of each symbol. Do we really care about that? It is enough to understand that we can have 16 symbols that have their own unique amplitude and phase angles.

Notice on the graph that the horizontal axis is labelled -Q to Q and the vertical axis is -I to I. This reminds us that we just have two signals that produce this complex waveform. "I" is the in-phase signal and "Q" the quadrature of 90 degrees out of phase signal. Two IQ signals can produce a 16 QAM analogue signal encoded with digital information. We say this waveform is complex only because it is difficult to visualise. All we are doing is using the I and Q signals to create a new signal with many different amplitude and phase shifts to designate a "state" that we call a symbol. All the symbols do not exist at the one time.

The bit size of any QAM signal is the square root of the number of symbols. 16 QAM has 16 symbols so the bit size is 4 from binary 0000 to 1111.

NOISE

When a QAM signal is affected by noise the amplitude and phase of a symbol becomes blurred as in figure 35-10. All symbols may be fuzzy or blurred. Here we have just added noise to the top right-hand side symbol. Any noise only becomes a problem for a QAM signal when the blurring moves into the phase and amplitude space of another symbol. This is the power of digitally encoded signals. Like Morse Code we know what to expect in our signal. Any deviations in symbols amplitude or phase due to noise can, up to a point, be removed. If the noise is too great we lose the signal entirely. With digital communications it tends to be all or nothing.

It would be unlikely that only one symbol had noise as illustrated in figure 35-10. Most likely all of the symbols would have some noise. That noise blurs the position of the symbols by altering their phase and/or amplitude.

An electronic constellation display of 4096 QAM.

FORWARD ERROR CHECKING (FEC) 

We can encode a digital signal with information that we can check to see if the signal arrived correctly. There are many such systems for detecting errors but to understand the basic idea let's explore a simple error detection method illustrated in figure 35-12.

The digital binary message to be sent is the 4x4 block at the top left. The binary numbers on the right-hand side and bottom are the error detection codes. A '1' indicates that a row or a column has an ODD number of 1s. A '0' indicates that a row or a column has an EVEN number of 1s.

When this message is received with the error detection codes a simple algorithm can run and determine if an error has been received and in most cases correct it. To help ensure that the error detection codes are correct the signal could be sent more than once. This would slow down the data rate but enhance the prospect of less errors.

AUTOMATIC REPEAT REQUEST (ARQ)

A more supplicated error checking and correction method is to enable the sender and receiver to handshake or communicate with each other. The sender would generally bundle the data to be sent into packets with the error checking code. When the receiver gets the packet or series of packets an algorithm is run at the receiver to determine if a packet has an error. If an error has been received, then the receiver will communicate with the sender and request what packet or series of packets needs to be resent. This continues until all the packets have been received correctly. ARQ permits virtually error free communication of data. However if the communications circuit is of poor quality then the transmission speed can be slowed a great deal.

THE FUTURE OF QAM & IQ

Some examples where QAM is used are WIFI (802.11ac) 256 QAM, Modem communications, cellular telephones and Digital TV. Frequency division multiplex (FDM) is the separation of communication channels by frequency. This is how radio communications work. We have many communication channels on different frequencies so that they do not interfere with each other. QAM and FDM can be combined to have many QAM channels separated by frequency. This is what is done with Internet MODEM communications.

Do you recall when 1200 baud was fast! Then came 2400 then 4800 baud and we wondered where it was going to stop. Certainly, when we reached 48kb/s that had to be the end of it right? It was the development of QAM and FDM that permitted faster and faster communications along plain copper wires. Today we are up into the many tens of megabytes per second. Of course, if we are not in copper wire then gigabytes per second are possible still using QAM modulation techniques.

Experiments are being done with digital television using 4096 QAM! QAM has the advantage that many transmission types can be combined into one channel. For example, television picture and sound, as well as electronic program guides and even a radio station can exist in the one coded channel.

I and Q signals can create any modulation type. DSB, SSB, FM and PM and just about anything else.

IQ modulator/demodulators are ideal for use in software defined radio. The IQ portion of the SDR is often implemented in a device called an FPGA - a field programmable gate array. An (FPGA) is an integrated circuit (IC) that can be programmed in the field after manufacture. FPGAs are similar in principle to, but have vastly wider potential application than, programmable read-only memory (PROM) chips. FPGAs are used by engineers in the design of specialised ICs that can later be produced hard-wired in large quantities for distribution to computer manufacturers and end users. Ultimately, FPGAs might allow computer and radio communication users to tailor microprocessors to meet their own individual needs.

SOFTWARE DEFINED TRANSMITTERS AND RECEIVERS 

Quadrature modulation and demodulation is not only used for digital communication systems. QAM modulators and demodulators can be used in analogue systems to produce AM and SSB (DSB) and other modes. The IQ signals can be manipulated in software and firmware to control filtering, bandwidth and apply digital signal processing. The ICOM 7300 is one of the first software defined transceivers available commercially. It uses quadrature modulators in the transmitter and the receiver. FPGAs (field programmable gate arrays) are programmed to do the modulation and demodulation of AM, SSB and FM. The ICOM 7300 (figure 35-13) is a direct sampling receiver. This is where the incoming RF signal is directly converted to digital data.

36 - Transmitter Faults

As a radio experimenter you have a responsibility to ensure that your transmissions do not interfere with other radio users, domestic electronics, radio and non-radio devices. You may have no interest in building your own transmitting equipment, but your qualification along with a licence enables you to do this if you so choose. Even if you do not build your own equipment, you will most likely make internal adjustments, repairs or modifications. This chapter will cover some material already covered and some new material, all relating to what can go wrong with a transmitter and cause interference.

CHIRPING

Chirping only applies to CW (Morse) transmitters. Keying chirps are quick changes in the frequency of a transmitter and occur each time the telegraphy key is closed or opened. Keying chirps are usually caused by an oscillator stage in the transmitter being pulled off frequency each time the transmitter is keyed. Chirping was more of a problem when many radio experimenters used to build their own equipment and when CW was more popular. CW is still very popular today in spite of it no longer being a licence requirement.

In CW mode, if the stage being keyed is too close to the oscillator, then the oscillator may shift slightly off frequency each time the key is closed. These quick changes in frequency sound very much like a canary chirping, hence the term chirping. Chirping can also occur if the voltage regulation to the oscillator stage is inadequate. A well regulated power supply and good buffer amplification will prevent chirping.

KEY CLICKS

Key clicks only apply to a CW transmitter.

Key clicks occur when the CW transmitter is being turned ON and OFF by the Telegraphy Key (Morse Key if you like) too quickly. When the telegraphy key is closed, the transmitter begins to transmit, when the key is opened it stops. The clicks occur when the telegraphy key is opened and closed. If the transmitter is powering up and down too sharply, then the leading and trailing edges of the Morse signal will have a very short rise and decay times much like the leading and trailing edges of a square wave.

This results in sidebands being produced on each side of the carrier frequency. The diagram in figure 36-1 shows part of a telegraphy character on an oscilloscope. The key clicks are identified by an almost vertical attack and/or decay time of each element in the character.

Take any sinewave and add to it all of its harmonics and you produce a square wave. The more harmonics that are added, the more perfect the resulting square wave. If a fundamental sinewave plus its harmonics can produce a square wave, then a perfect square wave must be made up of its fundamental plus all of its harmonics. If a series of square wave dots is transmitted (dots with key clicks), then the signal must be made up of the dot frequency plus the many harmonics of the dot frequency. If the dot frequency is 10Hz (10 dots per second) and the wave shape of the dots is square (it has key clicks like in the oscilloscope diagram of figure 36-1), then there may be 50 or more strong harmonics present that will produce sidebands on both sides of the carrier, extending the bandwidth the telegraphy signal by 1kHz (2 x 10 x 50). The resultant received signal sounds broad and a clicking sound can be heard.

Installing a "key-click filter" in the keyed stage will prevent transmitter key clicks. The filter normally consists of a simple RC time constant that prevents the bias of the keyed stage from turning ON and OFF too quickly. The waveform at the beginning and end of some Morse elements is shown on the right hand side in figure 36-1. Take note of the slower decay and attack time.

It is a fallacy that key clicks are caused by dirty telegraphy key contacts. Dirty contacts may cause the key to stick closed or become sloppy. This is called squawking. Some examiners are aware of this fallacy and may use distractors (wrong answers) that target this to really test you. Also, clicks have nothing to do with the speed of the Morse key. When the Morse key is closed the transmitter should take a few milliseconds to come to full power. When the key is opened the transmitter power needs to drop to zero power over a few milliseconds. If this does not happen key clicks will occur. Your bandwidth is increased and it sounds awful.

SELF-OSCILLATION

Self-oscillation is caused by unwanted positive feedback (regeneration) in an amplifier. If the positive feedback is sufficient, the amplifier will break into oscillation on the operating frequency. The amplifier is no longer operating effectively as an amplifier. Self-oscillation in an RF stage of a transmitter could cause that transmitter to come 'on air' by itself. To prevent self-oscillation, an equal amount of negative feedback (degeneration) is applied to the amplifier, cancelling out the unwanted positive feedback. This process is called neutralisation.

All active devices have some unwanted capacitance between the input and output terminals. In a bipolar transistor it is the capacitance between the collector and the base; in the FET it is the capacitance between the drain and the gate; in the electron tube, it is the plate to control-grid capacitance. At low frequencies, this capacitance is not a problem as the capacitive reactance is high. At higher frequencies this reactance decreases and more signal is coupled from the output to the input. This feedback is regenerative and if it becomes too high, it will cause the amplifier to oscillate.

The partial schematic diagram of a power amplifier in figure 36-2 illustrates one method of applying an equal and opposite amount of negative feedback to prevent self-oscillation.

The capacitance shown dotted as 'Cbc' is the internal capacitance of the BJT - it is not external as shown.

Negative feedback is applied by the variable capacitor Cn (a trimmer capacitor). Notice that the collector supply is connected to the centre tapping of the inductor in the collector tank circuit. Since the supply is bypassed to ground, the centre tap is at RF ground potential. When the top of the tank is positive, the bottom must be negative and vice versa. Hence, negative feedback is available at the bottom of the tank circuit.

Figure 36-3 shows another method of obtaining neutralisation. In this circuit, the negative feedback is taken from the secondary winding of the RF transformer. Since transformer action induces a 180 degree phase change between primary and secondary, the secondary voltage provides the necessary negative feedback.

PARASITIC OSCILLATIONS

A parasitic oscillation is an unwanted oscillation on any frequency other than the operating frequency. A parasitic oscillation is caused by stray resonant circuits in an amplifier causing the amplifier to act as a tuned-input tuned-output oscillator.

The tuned-input tuned-output oscillator has not been mentioned before and it is not in the syllabus. Basically, a tuned-input tuned-output oscillator is an RF amplifier with a tuned resonant circuit at its input and at its output. Both these tuned circuits are resonant on the same frequency. Add some positive feedback and we have a pretty good oscillator.

Parasitic (unwanted) resonant circuits could be created by bypass capacitors and radio frequency chokes. If the stray reactances are high, then low-frequency parasitics can be created. On the other hand, if the stray parasitic resonant circuits are created by wiring loom capacitance and inductance, the parasitic oscillation will be near to or even above the operating frequency and in this case, they are called high-frequency parasitics.

Parasitic oscillations generally produce a large number of harmonics. If a transmitter operating on 28MHz has a low-frequency parasitic on 500kHz, spurious signals may be heard from the transmitter across the spectrum every 500kHz up to and beyond the operating frequency. You will only know you have a parasitic if other operators tell you or you look at the spectral purity of your transmitter on a spectrum analyser. The fundamental frequency of the parasitic can be determined by using a remote receiver.

When you know the fundamental frequency of a parasitic, a dip oscillator may be used to find the physical location of the parasitic.(to be discussed further). With the dip oscillator tuned to the parasitic frequency, it can be moved around the circuit (inside the transmitter which is turned OFF). Tuned to the parasitic frequency a dip will indicate the physical location of the parasitic circuit.

PARASITIC STOPPER

In electron tube amplifiers that only carry a low current, the easiest method of eliminating parasitic oscillations is to install a low-value resistor (10-100 ohms) in the grid and plate circuits as close to the electron tube as possible. In high current circuits, 10-20 turns of wire can be wound over a resistor and soldered to each end. This, in effect, creates a low-Q RF choke. Such a device is called a parasitic stopper.

For assessment, you may need to know:

(a) what are parasitic oscillations,

(b) the difference between high and low-frequency parasitics,

(c) what is a parasitic stopper,

(d) how to physically locate the parasitic circuit causing the problem and fix it.

In transistor amplifier stages, small ferrite beads can be threaded over the leads of the active device to form a parasitic stopper.

How parasitic stoppers work 

All types of parasitic suppressors work by increasing the resistance in the parasitic circuit to a value equal to or higher than the critical resistance. When any resonant circuit (in this case a parasitic) has a resistance equal to equation 36-1, the circuit is said to be critically damped and it will not oscillate. By critically damping the parasitic circuit, oscillation is prevented. Critically damped means the Q is so low that oscillation cannot be sustained.

OVER DRIVING A LINEAR RF AMPLIFIER

Over driving a linear RF amplifier stage will cause 'splatter' and therefore a widening of the occupied bandwidth and possible interference. Remember that you may over drive linear amplifiers in an SSB transmitter simply by turning the microphone gain up too high.

When a complex waveform such as an SSB signal is fed to a linear RF amplifier, it is increased in amplitude by the gain of the amplifier. All linear amplifiers have some non-linearity that results in some distortion. Non-linearity causes the individual frequency components within the signal to mix with each other and produce new signals. New signals (frequencies) are distortion. Normally the amount of non-linearity is so low as to be insignificant. When a linear amplifier is over-driven it ceases to behave in a linear fashion and severe distortion may result. Excessive harmonics and spurious side frequencies are created, which almost certainly produce interference to other services such as television reception and other nearby operators will report 'splatter.'

FLAT TOPPING

Flat topping results from over driving an amplifier stage. The input signal becomes so high that the amplifier is driven into saturation and/or beyond cutoff. The resultant waveform on an oscilloscope appears as though the top and bottom peaks have been flattened. The term 'Flat Topping' is applied to SSB signals only.

Pi-Coupling at the transmitter output

The schematic diagram of a pi-coupler is shown in figure 36-6 and redrawn to emphasise that a pi-coupling network is just an extension of the output 'tank' circuit.

The Pi-coupler does a few important things, namely:

a) Matches the impedance of the power amplifier of the transmitter to the transmission line (feedline).

b) Acts as a low pass filter for suppression of harmonics.

c) It can if necessary, supply the flywheel effect (FM or CW).

It is evident from the configuration that the circuit will function as a low-pass filter. If this is not clear to you, then I suggest you revise the chapter on filters.

To see how the pi-coupler is used to obtain impedance matching, it is best to visualise the redrawn lower part of figure 36-6. The pi-coupler is simply a parallel tuned circuit with a tapped capacitance across the inductor. The impedance of the parallel tuned circuit at resonance is very high. However, the impedance seen across A-B and B-C will depend on the ratio of the two variable capacitors.

When the transmitter is tuned properly, that is, the pi-coupler is tuned to match the transmitter impedance to the transmission line, the output impedance of the transmitter will be equal to the impedance seen between A and B and the impedance between B and C will equal that of the transmission line.

When the output of the amplifier is matched to the input impedance of the transmission line, maximum power transfer will be obtained. In practice, the operator alternately adjusts the three controls on the coupler for maximum power or minimum output current. I have labelled the controls in figure 36-6 as, Transmitter, Band and Antenna. They can be called other names for example, Tune, Inductance and Load. It really does not matter. A good trick is to adjust all three controls for greatest receiver noise. Then check if the frequency is clear, identify in a mode that can be understood by listeners, announce a test or tuning, then switch to a full carrier mode set to low power and adjust the controls alternately for maximum power while transmitting.

It is possible to adjust the pi-coupler by monitoring the circuit current drawn in the output of the final amplifier. At resonance, the circuit impedance will be high and anode (or equivalent) current drawn will 'dip' to a minimum. The operator will see the 'dip' by monitoring the anode current or collector current.

Either method (dip or maximum RF output) can be used alone, or in conjunction, to tune any transmitter output stage. All transmitters with tuneable pi-coupling in the output, or some variation of it, work this way.

CARRIER SUPPRESSION

Operating on SSB means transmitting one sideband, either upper or lower, by getting rid of the unwanted sideband using a band-pass filter and suppressing the carrier. Carrier suppression in an experimenter's SSB transmitter should be 40dB or better. The stage looking after carrier suppression is the balanced modulator.

The carrier balance is one of the 'inside controls' you will most likely adjust at some time. If you are 'on air' talking to another station on say USB, transmit but do not send any audio to the SSB transmitter (just be quiet). The only thing being transmitted now will be your suppressed carrier. Have the nearby station you were just talking to tune down about 1-2kHz and they will hear and report back to you that they can see your suppressed carrier on their S-meter. They will report a tone as well; it is their receiver that produces this tone when it picks up your suppressed carrier.

A better way is to use another receiver at your station and have your transmitter going into a dummy load. You can then do the same thing and adjust the 'carrier balance' control in the balanced modulator for maximum carrier suppression. Modern transmitters have no trouble achieving 40dB or more of carrier suppression.

I have heard SSB stations on the air with such badly adjusted carrier balance that they were transmitting single sideband full carrier, or at least close to it.

37 - Antennas

The purpose of an antenna is to transmit and receive electromagnetic radiation. When the antenna is not connected directly to the transceiver, we need a transmission line (feedline) to transfer the received or transmitted signal to and from the antenna.

I will mostly be talking about transmission. Whatever is said about transmission applies equally to reception. This is known as reciprocity. An antenna's characteristics are the same on transmission and reception.

In a perfect transmitting system, the transmission line would transfer all of the power from the transmitter to the antenna without any losses. The antenna should then radiate all of the power it receives as electromagnetic radiation.

We have discussed the mechanism by which an electromagnetic wave is radiated by an antenna. If you have forgotten this, refer back to the chapter on electromagnetic radiation.

THE HALF WAVE DIPOLE

If you take a basic balanced transmission line such as 300Ω TV ribbon, split it and pull it apart, you will form a dipole antenna (refer to figure 37-1). Each side of the half wave dipole will be ¼ wavelength. We learned earlier that the free space wavelength of an electromagnetic wave is found from:

This equation is derived from:

Where c = 300,000,000 metres/second.

The constant 'c', is the velocity of any electromagnetic wave in free space.

A halfwave dipole is physically approximately 5% shorter than its free space wavelength because the velocity of propagation of the wave along each leg of the dipole is slower than 'c'.

The capacitive end effect, and the dielectric constant of the antenna conductor, whilst very low, are enough to slow a wave down.

Example: If we wanted to make a halfwave dipole for 28MHz then:

Dipole length in metres= 300/28 x 0.95 x 0.5 = 5.09 metres.

We calculated the free space wavelength with 300/28, took 5% off it by multiplying by 0.95, then found a half wavelength by multiplying by 0.5. I strongly recommend you do not simply memorise the equations for antennas as some textbooks provide, but rather understand the calculations.

CURRENT AND VOLTAGE DISTRIBUTION ON A HALFWAVE ANTENNA

When a wave leaves the transmission line and enters a halfwave antenna, electromagnetic radiation is radiated. Any antenna which is a ¼ wavelength or any multiple thereof that antenna is resonant; you will see why shortly.

Currents and voltages will occur along the length of a dipole antenna. We do not care about the individual values of voltage and current. What we are most interested in is the ratio of the voltage to current at different points on the antenna.

Why? Do you remember earlier we talked about 'impedance' not actually being a physical thing? Any E/I ratio is, in fact, impedance. If we were actually to measure the current flowing in a dipole antenna, we would have to move an RF ammeter along the dipole and record the current at the centre, move out a bit and record the current again and so on many times until we got to the end of the antenna.

If we did this, we would be able to plot the current and voltage distribution of a dipole antenna. Figure 37-3 shows what we would get:

This is an important diagram. It is a halfwave dipole, but has many other uses as well, so we must learn what this diagram means.

The voltage distribution is labelled 'E' and the current 'I'. What sort of voltage current ratio do we have at the centre of the dipole? Well, current is high and voltage is low. If I told you that I had a high current for a low voltage anywhere, what could you tell me about the impedance? The impedance must be low, as that's what a low impedance is, namely lots of current with little voltage. So the impedance at the centre of a halfwave dipole is low. The impedance is lowest at the centre than anywhere else on the dipole.

Look at the ends of the dipole. Voltage (E) is high and current (I) is low. This must mean that the ends of a dipole have a high impedance, as that's what a high impedance is, a lot of 'E' for only a little bit of 'I.'

Why can we say that the halfwave dipole antenna is resonant? Simply because it is the correct physical length to accommodate the complete halfwave of current and voltage distribution.

Let's look at this idea of resonance from a different perspective. On the dipole antenna in figure 37-3, the length of the antenna is long enough to fit in a full halfwave of current and voltage distribution. A full halfwave is simply two-quarter waves.

At the centre of the antenna the current and voltage represents a low and resistive impedance. The impedance at the centre is approximately 72 ohms. At the ends of the antenna, the current and voltage are representative of high and resistive impedance. The impedance at the end is 2000-3000 ohms. In theory, the centre is zero ohms and the ends infinite ohms.

You also know now what the current and voltage distribution on a ¼ λ antenna is, it's just half of the distribution shown on the antenna in figure 37-3. That is, from the centre to one end.

We can say that a quarter wave antenna is resonant simply because it is the correct physical length to accommodate a complete quarter wave of current and voltage distribution. At either end of a quarter wave, the impedance is resistive only. Being resistive implies resonance. With antennas, like tuned circuits, being resistive is synonymous with being resonant. Any antenna which is ¼ λ or a multiple of ¼ λ is a resonant antenna.

Why are we concerned so much about impedance? Well, we have learned that for a load to dissipate (or radiate in the case of an antenna) all of the power it must be resistive and the resistance must match the source resistance; remember Jacobi's Theorem. In the case of an antenna system, the source is usually, though not always, the end of the transmission line. For a halfwave dipole, we know (irrespective of what frequency it operates on) that the feedpoint impedance at its centre is about 72Ω and resistive, provided the antenna is resonant (the right length). So ideally we should feed a dipole with 72Ω transmission line and if we don't we need to do an impedance transformation, say from 50 to 72Ω using a transformer (balun). In practice using 50Ω line to a centre fed dipole is close enough. However, a 1:1 balun must be used on any coaxial fed dipole, or you will not have a dipole and the feedline will radiate.

In practice, the actual feedpoint impedance, radiation pattern and many other properties of a dipole or any other antenna are affected by the environment. Some factors to consider are the height above ground, the proximity to metal roofs and other conductive objects including antennas. Figure 37-4 shows the variation in dipole impedance versus height above earth for horizontal and vertical dipoles.

* The broken line portion of the curve for a horizontal dipole shows the impedance over real earth whereas the solid line is for a perfectly conducting ground. Source; Reference Data for Radio Engineers 5th Edition.

PHYSICAL AND ELECTRICAL LENGTH 

Because the velocity of propagation of a wave along an antenna is slower than through free space, the electrical and physical antenna lengths are not the same.

The physical length of an antenna is the material length in metres you would get with a measuring tape.

The electrical length is not a physical measurement. It is the electrical wavelength and this cannot be physically measured. The electrical wavelength must be calculated. The electrical wavelength is typically 5% longer than the physical length of the antenna that has open elements such as a dipole. Loop antennas, do not have the same end effects as open ended antennas.

ISOTROPIC ANTENNA

An isotropic antenna is a theoretical antenna. An isotropic antenna is one which radiates equally in all directions. If you imagine an isotropic antenna at the centre of a large balloon and the isotropic antenna is radiating visible light, then the surface of the balloon would be equally illuminated.

The isotropic antenna is used as a mathematical model in order to evaluate the directional properties of practical antennas. Almost all antennas have a gain greater than an isotropic. If an antenna with gain was placed at the centre of a large imaginary balloon and the radiation was visible light, the illumination of the balloon would not be even. There would be brighter regions because the antenna has gain in the direction of those regions.

A dipole has a gain of 2.14dB above an isotropic. Hence, a dipole antenna is said to have a gain of 2.14dBi, i.e. dB relative to an isotropic. Electrically a very short rubber helical antenna, often referred to as a 'rubber duck', has a loss of several dB when compared to an isotropic. Such a lossy antenna would be described as having a gain of -ndBi. A negative gain means less gain than an isotropic antenna.

Some antenna manufacturers will use the isotropic antenna as their reference point when quoting antenna gains; others will use the dipole as the reference. The purchaser should be aware which reference is used when gain figures are quoted, as there is a 2.14dB difference between the two reference levels. A gain of 3dBd - means 3dB gain above a dipole. The same antenna would be 3dBd + 2.14 - 5.14dBi The last gain figure looks better. This is often done to promote the sale of the antenna.

ANTENNA GAIN 

Most radio communications are point to point or at least confined to an area. An antenna which directs most of its energy toward the receiving station can be said to have a power advantage over an omnidirectional antenna. The power gain of a transmitting antenna is the ratio of the power radiated in its maximum direction of radiation compared to that radiated by a standard antenna, usually a dipole or the theoretical isotropic.

Suppose radio stations (A) and (B) are in contact with station (C). Station (A) is using a dipole antenna and (B) a Yagi with a gain of 6dB above a dipole.

How much would station (A) need to increase their transmitter power to the same power advantage of station (B)?

Station (A) would need to increase their transmitter power by 6dB or, in other words, quadruple it!

A transmitter power increase by a factor of four or an antenna gain of 6dB should increase the received signal by one 'S' point. That is, provided the S-meter is correctly calibrated.

There are many traps when attempting to evaluate antenna performance on air, as in the latter example. Sometimes a dipole antenna will out-perform an antenna with higher gain because it has a more favourable angle of radiation for the propagation conditions in existence at the time of the comparison. Improved communications when using a directional antenna may at times be due to enhanced received signals and reduction in noise at the receiver, rather than transmit power gain.

The great advantage of antenna gain over increasing transmitter power is that you get the gain advantage twice. A gain antenna gives you gain on both transmit and receive.

RADIATION RESISTANCE

Radiation resistance is an imaginary resistance which, when put in place of an antenna, dissipates as much power as the antenna radiates.

The higher the radiation resistance, the more efficient the antenna is as a radiator. With some antennas (e.g. a dipole or a quarter wave antenna) the feedpoint impedance and the radiation resistance are the same. If the feedpoint impedance of an antenna was to be changed by some impedance conversion device, this would not alter the radiation resistance.

LOSS RESISTANCE

Loss resistance is an imaginary resistance that represents all the power losses of the antenna. For example, some power is lost due to the electrical resistance of the antenna, ground losses and nearby conductors.

FEEDPOINT IMPEDANCE

Feedpoint impedance is that impedance seen by the feedline where it connects to the antenna. Feedpoint impedance is determined by the E over I ratio at the point of connection.

MORE ON RESONANCE AND RESISTANCE 

Any tuned circuit is resonant when both the inductive and capacitive reactances are equal.

At resonance the reactances completely cancel, leaving only the resistive part of the impedance. The shortest length of wire that can be resonant without any artificial loading is a quarter wavelength. A quarter wavelength of wire will have zero net reactance and a resistive feedpoint impedance of about 360 (half of the dipole).

If an antenna is less than a quarter wave, it will appear capacitive and will require the addition of some inductance, known as a loading coil. The added inductance cancels out the capacitive reactance and resonates the antenna. An antenna which is longer than a quarter wave but less then a half wave will have a net inductive reactance and will require the addition of some capacitive loading to resonate it.

An antenna which is longer than a quarter wave but less than a half wave will have a net inductive reactance

and will require the addition of some capacitive loading to resonate it.

Antennas that are too short are capacitive and need inductance to be added.

Antennas that are too long are inductive and need capacitance to be added.

Example 1.

Say you are going to use an end-fed antenna (just a piece of wire from the antenna tuner) on 80 Metres and the length of wire you have is 25 metres. Is this antenna too short or too long and if it is not the correct length will you need to add capacitance or inductance to it?

There is no need to run to the calculator. This antenna is to be used on the 80-metre band; that's a broadsword but close enough to tell us a quarter wave is roughly 20 metres. We have 25 metres of wire and we only need 20 metres. If you use all the wire, then the antenna will be too long. All long antennas are inductive; therefore, they need capacitance added to cancel out that inductance. This antenna will also require impedance matching. This is all done by the ATU. The ATU is doing the impedance match and also adding capacitance to bring the antenna to resonance.

Example 2.

An end fed wire antenna is 2.2λ long. Is it too long or too short and what do you have to do to bring it to resonance? We will assume that you do not want to cut the wire. Okay first is it too long or is it short? What is the nearest multiple of a ¼ λ? Well, it is definitely 2.25λ, so the antenna is a bit short. Short antennas are capacitive; therefore, they need inductance to be added and also an impedance match. The ATU will do this for us by adding inductance and impedance match to make the antenna electrically 2.25λ.

THE QUARTER WAVE ANTENNA

A quarter wave antenna (figure 37-5) is normally used with radials or installed on a flat conducting ground plane, such as the roof of a car or house/shed, or just a good conducting ground.

A ground plane is simply a reflector. Some of the radiation from the antenna will be reflected by the ground plane and this reflected wave will interact with the incident wave from the antenna in such a way as to modify the radiation pattern of the antenna. In the case of a quarter wave antenna, the 'ground' should be as uniform as possible around the antenna so as to provide an omnidirectional pattern. This antenna has a low angle of radiation which makes it a good DX antenna.

Where it is not possible to mount the antenna on a conducting surface such as the earth or a car body, the ground plane effect can be simulated by attaching at least three; quarter wavelength radials to the feedpoint on the earth side of the feeder. Radials have another advantage, in that by lowering them to an angle of about 45 degrees to the horizontal, the feedpoint impedance can be raised from 36Ω to 50Ω to provide a closer match to a 50Ω coaxial cable.

I have seen it asked in exams why the radials of a ground plane antenna are drooped downwards at 45 degrees. One of the amusing answers, which I have often seen ticked as correct is, "to prevent birds from standing on them"! - Wrong.

ANTENNA LOADING 

Loading, as discussed earlier, is adding inductance or capacitance to an antenna in order to make it resonant. An antenna is a resonant system. The resonant frequency is determined by the antenna's inductance and capacitance. When we get the correct amount of L and C the antenna will be resonant on the frequency we want.

Top loading is a name given to various methods of adding capacitance or inductance to the top of the physically short antenna. Top loading not only adds the desired reactance to resonate the antenna but shifts the current distribution pattern higher up the antenna, increasing the radiation resistance and hence the radiation efficiency. What I am saying is that top loading is preferable to bottom or even centre loading. However, for mechanical reasons, particularly with mobile antennas, bottom loading is often used. The higher the loading coil, the better. An alternative is to distribute the inductance along the length of the antenna, perhaps even winding turns closer as you approach the top. This can be done on a fibreglass rod and the whole antenna coated with paint or sealant, or heat shrink tubing can be used. This is the method used for so called helical mobile antennas.

On the low HF bands, the length of a grounded quarter wave can become impractical. An antenna that is physically short will not be resonant and its input impedance has a high capacitive reactance. Consequently, antenna current decreases and radiation decreases.

The radiation resistance decreases from 36Ω for a quarter wave antenna towards zero as the length is reduced. Because of the short length, the current maximum will not occur on the antenna, but on the transmission line. The loss of the high current peak on the antenna drastically reduces the radiated power. Adding a loading coil at the base of a short vertical would resonate the antenna and increase the radiation resistance by about five ohms. However, the current loop would still be low on the antenna and high 12R losses in the coil would reduce the radiation efficiency.

These difficulties are overcome by using top loading. A cylinder, sphere or disc placed at the top of the antenna acts to increase the shunt capacitance to ground which, in effect, is the same as adding inductance in series with the antenna, thereby bringing the antenna to resonance. The current distribution on the antenna is "pulled up" higher on the antenna resulting in higher radiation resistance and efficiency. There is no real significance in the shape of the metallic top loading device. The shapes mentioned earlier are normally used for the ease of capacitance calculation and appearance sake. A piece of wire can be used for top loading making the antenna appear as an inverted "L" or a ''T".

Figure 37-7 - A capacitive hat creates shunt capacitance between the top of the antenna and ground. This shunt capacitance is in series with the antenna's capacitance. When you connect capacitors in series the capacitance is reduced.

The price paid for loading any antenna.

All antenna loading comes at a cost. The biggest cost is that the more an antenna is loaded the narrower its operating bandwidth. For example, a full size quarter wave antenna on low HF may operate across an entire amateur band (200-300kHz) whereas a linear loaded two-metre-long whip antenna may only operate across 20- 30kHz before adjustment has to be made.

Loaded antennas have:

1. less operational bandwidth.

2. lower feedpoint impedance sometimes making matching more difficult.

3. greater losses - the loss resistance is greater.

FIVE-EIGHTH WAVELENGTH 

One popular antenna is the ⅝λ vertical (figure 37-8). Now a ⅝λ antenna cannot be resonant since it is not a multiple of a quarter wave. The whip part of the antenna is in fact ⅝λ and has a net capacitive reactance.

All ⅝λ antennas have an inductance (loading coil) fitted somewhere along the length of the antenna to cancel out the capacitive reactance and resonate the antenna. The ⅝λ antenna is tuned by the loading coil to resonate as a ¾ λ antenna.

Therefore; a ⅝λ antenna is electrically a ¾λ 

The ⅝λ antenna has a little more gain than a ¼λ How can an omnidirectional antenna have gain? The ⅝λ radiation pattern is more compressed in the horizontal place. Think of the radiation pattern looking like two dinner plates held together face to face. You have a flattened disk. This is approximately the radiation pattern of the ⅝λ antenna

SLOPERS AND INVERTED Vs

Figure 37-9 shows a halfwave sloper. When you do not have the room or the anchor points for a horizontal dipole the sloped dipole allows the use of a smaller space with not too much compromise. Any dipole fed with coaxial cable must have a balun to prevent RF energy travelling back down the coaxial cable. The support can be a tree, side of a house or shed or a purposely installed pole.

The conventional sloper (figure 37-10) is a just a quaterwave antenna. This sloper will fit into an even smaller space. Being a ¼λ this antenna needs a counterpoise as shown. The counterpoise can be any type of wire preferably ¼λ long. If the attachment point is to a metal roofed building then the building can be used as a counterpoise.

The inverted 'V' antenna is just a dipole mounted in the centre and the two sides drooped down. This is a very popular antenna for restricted space and being a dipole it does not require a counterpoise. The inverted 'V' can be used for multiple bands by adding further dipoles and converting it to a fan-dipole.

DISCONE

The discone is an antenna whose impedance can be directly matched to 50 ohm coaxial transmission line over a very wide frequency range.

The outer conductor (shield) of the transmission line is connected to the cone at the gap and the inner conductor to the centre of the disc. The dimensions shown in figure 37-13 give the best impedance match over a wide range of frequencies. Since the bandwidth is inversely proportional to Cmin that dimension is usually made slightly larger than the diameter of the coaxial transmission line. The dimensions S and D are determined from S=0.3Cmin and D=0.7Cmax. L and θ determine how the standing wave ratio varies with frequency at the low end of the frequency range.

A discone with θ=60° and Cmin/L=1/22 has a standing wave ratio of less than 1.5:1 over at least a 7 to 1 frequency range and a standing wave ratio of less then 2:1 over at least a 9 to 1 frequency range.

A discone's "disc" and "cone" can made from multiple elements as shown or from a metal mesh. In some applications this is done to keep the weight and wind resistance down.

Figure 37-12 - Photograph of a discone antenna.

YAGI ANTENNA

The parasitic beam, or Yagi array (named after Dr. Hidetsugu Yagi of Tokyo University), was invented in 1926 and was first used in the amateur service about 1935.

A Yagi antenna must have one driven element, a dipole and at least one other parasitic element (refer to figure 37-14). In our earlier discussion of a dipole, I mentioned that the radiation pattern, input impedance and many other characteristics, are determined by the height above ground and nearby antennas, among other things.

Well, a Yagi is just a dipole with other parasitic dipoles nearby (on the same boom). The parasitic dipoles receive radiation from the dipole and then re-radiate. So, we have energy being radiated from the main driven element and then after a time delay, the energy is picked up and re-radiated by the parasitic elements. By controlling the spacing and length of the parasitic elements, the antenna array can be made to have a main lobe in one direction, providing substantial gain.

This antenna has three elements: driven element, reflector and director. The main lobe of radiation is in the direction of the driven element to the director. The physical length of the driven element is found by the same equation as that given for a dipole. The reflector is 5% longer than the driven element and the director 5% shorter. The spacing between the elements can vary from 0.15 to 0.2λ. Maximum forward gain is obtained at a spacing of 0.18λ wavelengths.

The director and reflector are called parasitic elements as they intercept energy radiated from the driven element and then re-radiate it. When the parasitic elements absorb power, they re-radiate it with a wave pattern like that of a dipole. However, because of the propagation delays introduced by the spacing of the elements, wave cancellation occurs toward the rear of the antenna and wave reinforcement in the forward direction. This wave reinforcement results in a gain of about 6-8.5dB over a dipole. The feedpoint impedance is about 18-25Ω. Some type of matching device is required to convert the feed point impedance to 50Ω if coaxial cable is used.

Additional parasitic elements can be added to a 3 element Yagi to increase the power gain further. Additional elements are always directors, placed in front of the driven element. Adding more reflectors provides no appreciable gain advantage at HF frequencies. Doubling the number of directors will increase the power gain by approximately 3dB. Adding parasitic elements to a Yagi array decreases the antenna bandwidth.

The front-to-back ratio of a three element Yagi varies from about 15dB to a maximum of 25dB. The front-to-back ratio is the ratio of the power radiated in the forward direction to that radiated to the rear of the antenna, expressed in decibels.

Each element of a Yagi antenna has a current and voltage distribution like that of a simple dipole. As the impedance at the centre of each element is the same no current will flow between points of equal impedance on an antenna, a metallic boom may be used.

If two identical Yagi antennas are stacked in phase and the gain of each individual Yagi is 6dB, the stacked array will have a total gain of 9dB, that is, 3dB more.

The additional second antenna would theoretically double the amount of power radiated in the forward direction. This is an effective power increase of 3dB, giving a total system gain of 9dB. In practice, the additional gain would be slightly less than the theoretical maximum. Stacking a third antenna would result in an improvement of an additional 33% or 1.24dB at best.

The impedance of a Yagi depends on the number of elements. The elements are just dipoles in parallel. Think of 72Ω resistors in parallel, if you had 7 elements you can expect the impedance to be close to 72/7=10.2Ω.

FOLDED DIPOLE 

A folded dipole antenna (refer to figure 37-15) can best be described as two dipoles connected in parallel at their ends. Folding a dipole has the effect of increasing the feedpoint impedance. With two parallel dipoles, the feedpoint impedance is increased by a factor of 22 = 4, giving a total impedance of 300Ω for a standard dipole. With three parallel dipoles, the feed point impedance becomes 23=8 times the original feedpoint impedance. The dipole forming the driven element of a Yagi antenna is often folded to increase the feed point impedance by a factor of 4.

Folding a dipole also increases its bandwidth; the more parallel dipoles you have with their ends shorted, the greater the bandwidth. This technique to obtain very wide bandwidth is used by commercial stations on HF.

SINGLE QUAD LOOP ANTENNA 

Most loop antennas are just one wavelength loops. As there is no end effect like this say for a dipole, the electrical length of a one wavelength loop is a little longer than 1λ. A good place to start is about 5% longer. There are many loop antennas that simply take their name from the shape. Delta; shaped like a triangle, quad; shaped like a square. On VHF and above (due to the ease of mounting small size loops) you could use a circle. The loops can form the elements of an array like a Yagi. So you could have a 3-element delta loop beam for an example. A cubical quad is just a two element beam made from two quad loops one for the driven element and the other for the reflector. If you are only using two element beams, then you would choose a reflector over a director for a small gain advantage.

A quad antenna is really a "pulled out" folded dipole. Just imagine pulling out a folded dipole to form a square or diamond. A folded dipole has a radiation resistance of 288λ (4x72). When half pulled out to form a quad loop, the antenna is half way between being a folded dipole and a shorted transmission line (see next chapter). A shorted half wavelength of transmission line would have an input impedance of zero ohms one-half wavelength back from the termination. It is not surprising that the feed point impedance of a single quad loop is the mean (average) of these two values: (288+0)/2 = 144Ω. When fed at the centre of one side, the impedance decreases slightly to 125Ω.

With this antenna, there is no "end" to the wire elements as the quad forms a continuous loop. The shortening effect which occurs with other antennas is not applicable since there is no "end effect". In fact, for a quad loop to be resonant, it has to be slightly longer than a quarter wave on each side.

Summarising the important characteristics of a quad loop:

Radiation resistance is 144Ω when fed at a corner.

Radiation resistance is 125Ω when fed at the centre of one side.

Power gain is 1.4dB above a dipole.

Bi-directional radiation pattern.

The physical length of each side is 0.257λ.

TRAPPED DIPOLES AND VERTICALS 

Traps used on HF antennas are parallel tuned circuits. Recall that at resonance; a parallel tuned circuit has very high impedance. The higher its "Q", the higher the impedance. In fact, if the "Q" was high enough, a parallel tuned circuit impedance could be likened to an open circuit switch.

Trapped antennas use the high impedance of a parallel tuned circuit to switch in and out different sections of the antenna. Have a look at the three band trapped dipole of figure 37-17.

The highest frequency band is 20 metres. The Trap1s will be parallel resonant on a 20 metre frequency and the transmitter will only "see" the smaller antenna in the centre. On 40 metre the Trap1s are no longer resonant. The 40 metre band is the middle section of the antenna shown. The Trap2s are parallel resonant on 40 metres, isolating the ends of the antenna. On the 80 metre band (the lowest frequency) the whole antenna is used. When the traps are not used at their resonant frequencies, they act like loading coils and effectively shorten the length of antenna wire needed.

Half of this antenna could be stood up vertically and you would have a trapped vertical. You can even make a trapped multiband Yagi using this same principle for the driven element, directors and the reflector.

The traps may be made from an actual high "Q" inductor and capacitor. However, there are easier methods on HF. On VHF and above the options for traps and other matching techniques become more difficult.

MULTIBAND DOUBLET

The simplest multiband dipole is just an ordinary dipole fed with good quality balanced transmission line. To permit operation on multiple bands an antenna tuner (ATU) must be used. This dipole will be resonant on any band where it is a halfwave long or a multiple of a halfwave. If a radio experimenter does not have sufficient room to put up a resonant dipole then, if a good ATU is available, the operator can put up a dipole of any length. This is usually the maximum length that the available space will permit.

Such an antenna is often referred to as a doublet rather than a dipole as a dipole infers a halfwave antenna. Figure 37-18 shows a doublet antenna fed with parallel line. It is best if each side of the doublet is the same length as you want it to be a balanced antenna. If you can't get exactly the same length do not be overly concerned. You can configure the doublet as an inverted 'V'. This antenna will operate well on any band that you can achieve an impedance match to your transmitter using the ATU.

Entry to your station can be a problem because you have to maintain the balance of the transmission line. You can make a short shielded balanced line using to two short lengths of coaxial line configured as a length of shielded balanced line. You must use balanced line to the antenna as this antenna may have high SWR. With reasonable quality balanced line, you do not care what the SWR is, as long as your tuner can provide a match to the transmitter. This antenna system will be efficient due primarily to the use of balanced line. High SWR on balanced line will not substantially increase the line loss as it would if coaxial cable were used.

Is this antenna resonant on all bands used despite its short length? Well it might seem odd but, yes it is resonant. The antenna system is brought to resonance by the ATU. That is the ATU provides the reactance necessary to make the entire antenna system (feedline and antenna) resonant. Since the feedline is balanced and does not radiate, the radiation is being done by a resonant antenna. Suppose on a particular band the antenna had a feedpoint impedance of 100-j20Ω. The 20Ω of capacitive reactance indicates that the antenna is not resonant right? No. When we match this antenna with an ATU in the station, the ATU will reflect the conjugate impedance to the antenna. That is, impedance reflections created by the ATU will reflect to the antenna the conjugate of 100-j20Ω which is 100j20Ω. This is why the antenna is reflected a reactance which makes it resonant. It does not matter what the 'R' is, it just matters that there is no reactance. Such a doublet will not behave exactly like a resonant dipole because it is the wrong length. However, it will behave as a resonant antenna.

If we tried to do the same thing with coaxial cable it would just not work as well. Why? This antenna system will have high standing waves on some bands, probably most of them. If coaxial cable was used the line losses would be much greater due to the electrical stress the standing wave produces on coaxial line. This means that the ATU will provide the correct conjugate impedance; but the coaxial line, due to its losses, will not reflect this conjugate to the antenna and the antenna will not be brought to resonance. It will still work, but not nearly as well and the losses will be much greater.

This doublet fed by parallel line is arguably the one of best multiband antenna you could use, if you have space restrictions.

THE FAN DIPOLE

The Fan dipole is just a number of resonant dipoles connected at the same feedpoint. This is shown in figure 37-19.

This antenna works very well on each band where there is a resonant dipole. The only downside to the fan dipole compared to a single dipole is that the dipoles not in use do have some affect on the active dipole. This means they are fiddly to tune. If you're willing to do this then once you have got it right, or nearly right, you will have a good and efficient multiband antenna. This antenna is called a 'fan' because of the multiple centre fed dipoles look a bit like a hand 'fan'. The dipoles can be parallel with each other and supported by spacers. The less bands you build it on the easier it will be to tune. The fan dipole is great antenna for restricted space. If you only have enough room for a 40 metre antenna then you can add dipoles for 20, 15 and 10 metres. If you wish you could feed the antenna with parallel line which would make it even more efficient. If you use coaxial cable, which is unbalanced, to feed any balanced antenna you must use a choke balun at the feedpoint. The fan dipole shown in figure 37-19 must have a 1:1 balun at the feedpoint. This balun could just be the coaxial feedline wound around a ferrite rod and held in place by PVC tape or potted in a short length of PVC pipe using encapsulating resin.

Just like a dipole can be turned on its side with one element removed and replaced with a one or more counterpoise wire then the fan dipole can also be turned on its side to make a multiband vertical antenna.

See figure 37-20. Each vertical has a common feedpoint at the bottom. The verticals are closely spaced around a fibreglass pole such as a large telescoping fishing pole. Additional "support disks" can be added up the pole to support the verticals. There is some interaction between the verticals, however such an antenna is not difficult to tune laying down and on support about 1 metre high. You will need radials for this antenna. A good compromise is to use two wavelengths of radial wire for your lowest band of operation. That is 8 quarter wavelengths (2 wavelengths in total) on your lowest band. You could even use 16 one eighth wavelength radials - it will work.

OFF-CENTRE FED (OCF) DIPOLE

Any dipole not fed at the centre is an off-centre-fed dipole. The OCF dipole normally refers to a dipole antenna that is fed at a point 1/3 from one end. Sometimes this dipole is referred to a 1/3 - 2/3 dipole. The reason for feeding the antenna at this point is that the impedance at that point is in the vicinity of 200Ω.

If the OCF is designed for the 80 metre band it will be a ½λ long on 80 metres. Use the standard half wavelength equation to work out this length, not forgetting to reduce the physical length by 5%. If this OCF is used on 40 metres it will be 1λ. However the feedpoint impedance will still be in the vicinity of 200Ω. This is the same with 20 metres and 10 metres. Figure 37-21 shows the dimensions of an OCF dipole.

The balun is a 1:4 (200Ω:50Ω). The balun should be placed right at the feedpoint. Since the impedance at the feedpoint is around 200Ω the balun will be around 50Ω on the coaxial cable side. The impedance of the feedpoint will not be 200Ω on all bands but the balun will give us close to 50Ω for connection to 50Ω coaxial line. The impedance may vary at the feedpoint for 100Ω-300Ω. On the transmitter side this will translate to around 25-100Ω for a reasonable SWR, at no more than a little over 2:1. So it works well with a bit of a compromise. We are breaking a rule here which I will talk about shortly.

Figure 37-22 shows the current distribution on four radio bands 80, 40, 20 and 10. Notice how the current at 60° is much the same for all of these bands. The current is almost maximum for each band. If the current is about the same then the impedance at that point is about the same. This makes it possible to operate on the four bands shown and get an impedance we can easily cope with. You may have to tweak the SWR a little with an ATU.

The OCF is not, strictly speaking, a balanced antenna. There is a degree of unbalance due to the different lengths of antenna on each side of the feedpoint. We have neglected this rule. We get away with it because the amount of unbalance is not great. Secondly, baluns have two main purposes. They allow us to connect two unequal impedances and they choke common mode currents. See Chapter 38 "Transmission Lines" for details of how transmission line baluns work and how to build one yourself.

For some, having space to put up an 80 metre halfwave dipole is difficult. You can build the OCF just the same as described on 40, 20 and 10 metres. You can droop the sides of the OCF within reason - just be careful not to unbalance it too much. If you are pruning the length of an OCF remove antenna wire proportionately from both sides to maintain the one third two thirds ratio. For all wire antenna adjustment, it is better to fold the wire back along the antenna rather than cut it off.

The OCF performance is close to that of a standard full size dipole on each band. The difference being that as the length of the antenna increases in wavelengths new lobes are produced towards the long dimension of the antenna. This is usually not a problem with the lower HF bands. All long wire antennas behave this way. The longer an antenna is in wavelengths, the more directional it becomes, in the line of the antenna conductor.

CO-LINEAR ANTENNA

In radiocommunications, a co-linear antenna array is an array of antennas mounted in such a manner that the corresponding elements of each antenna are parallel and co-linear, that is they are located along a common line or axis.

Co-linear arrays of dipoles are high gain omnidirectional antennas. A dipole has an omnidirectional radiation pattern when in free space and not influenced by any other conductors in that it radiates equal radio power in all azimuthal directions perpendicular to the antenna, with the signal strength dropping to zero on the antenna axis.

The purpose of stacking multiple dipoles in a vertical co-linear array is to increase the power radiated in horizontal directions and reduce the power radiated into the sky or down toward the earth, where it is wasted.

All dipoles of a co-linear need to be fed in phase, this is not a problem with the parallel-fed co-linear. The other two co-linears have quarter wave sections between them to create a phase delay.

Theoretically, when stacking idealised lossless dipole antennas in such a fashion, doubling their number will produce double the gain, with an increase of 3.01dB. In practice, the gain realised will be below this due to imperfect radiation spread and losses. The approximate gain of a co-linear is 10Log(n) where n is number of elements. So for a 4 element co-linear array of dipoles the gain is 10Log(4) = 6dB. Co-linear arrays do not have to be made of dipoles, they could be Yagis or many other types of antenna. There is little point in having more than 7 elements on a co-linear due to diminishing returns. The antenna gives a very good gain advantage with just two elements. Co-linears are very commonly used on repeaters for VHF/UHF, amateur radio and for land mobile radio. Figure 37-24 shows two photographs of co-linear antennas using four stacked dipoles.

They are also sometimes used for broadcasting. Multiple directional antennas mounted vertically separated are referred to as "stacked" and if alongside each other as "bayed".

THE CORNER REFLECTOR

The corner reflector and related antennas with a reflector sheet or screen behind a dipole can achieve an antenna gain approaching 10dB. Corner reflectors become very practical at UHF frequencies. The corner reflector is related to the parabolic reflector shown in figure 37-25(A). The parabolic reflector is analogous to the parabolic mirror found in optical systems. If a parabolic reflector is sufficiently large, so the that the distance from the focus to the reflector is many wavelengths then optical conditions are approached.

If the reflector is close to the same dimensions as the operating wavelength, or less, the analogy to optics is not complete, since the radiator is coupled to the reflecting sheet.

An alternative reflector consists of two flat conducting sheets which intersect at an angle so as to form a corner. This is called a corner reflector antenna, 37-25(B) and (C) show two views of a corner reflector. An advantage of such a sheet reflector, as long as the sheet is sufficiently large, the dimensions are not critical and there are no tuning adjustments. There is no focus point as there is with a parabolic reflector.

I have shown a vertical end fed antenna in figure 37-25. A centre fed dipole is more often used. The corner does not have to be exactly 90°. At 180° we would have a flat sheet reflector with some loss of gain. The distance from the corner to the radiator is not critical and can be varied over wide limits with little change in the directivity of the antenna. Especially suitable are values of 0.35λ and 0.5λ. The antenna can be rotated for vertical or horizontal radiation.

You may have seen a so called coke-can antenna to improve mobile telephone reception. These are just a coke-can unfolded to make either a parabolic or corner reflector held behind the phone's antenna. They do work; though you do not have to use a coke-can. Try it if you have poor mobile phone reception.

THE V-BEAM

The unterminated V-Beam is a long dipole parallel to the ground drawn into a "V" and at least one wavelength on each leg. The radiation pattern of the unterminated version is bidirectional much the same as if you had two Yagis back to back.

The exact gain depends on the angle between the antenna conductors and their length. At a length of 1λ and an angle of 90° the gain is approximately 5dBi. At 5λ and 40° this increases to 10dBi.

The V-beam can be converted to a unidirectional antenna by terminating the ends of the antenna through a 500-600Ω non-inductive resistor to ground. The terminating resistors prevent reflected waves on the antenna. The direction of radiation is then mainly from left to right as shown in figure 37-26.

BASIC RADIATION PATTERNS 

Figure 37-27 shows the radiation patterns for a horizontal dipole at different heights above ground. The dipole has a theoretical gain of 2.14dBi. The thing to notice is that the closer the dipole is to ground the higher the radiation pattern. At ⅛λ most of the radiation is straight up! Suppose you were on the 80M band using a half wave dipole 10 metres above the ground - then you can expect to have a cloud warmer! However how many of us can get our antennas up higher than 10-12 metres? So we just put up with the fact that much of our radiation is going upward and our skip distance is short.

The typical free space radiation pattern of a horizontal dipole is shown in figure 37-28. This is the radiation pattern as seen from above. A horizontal dipole running East-West will radiate best North-South. The horizontal dipole is bidirectional. If the dipole is made longer than one-half wavelength, radiation moves towards the ends of the antenna conductor. Such is the case if you have an OCF (off centre fed) dipole for 80 Metres and used it on 10 metres. A standard dipole running East-West will radiate the best in a North-South direction. Inverted Vs and G5RV etc. are just different versions of a dipole with different mounting shapes and strategies to overcome impedance matching and/or multiband operation. None will work as well as a dedicated dipole for that band, but the G5RV and the OCF offer greater band coverage with a single antenna with  a small performance trade-off.

GAMMA MATCH

The Gamma match (figure 37-29) is most often used for matching a Yagi. The impedance of a Yagi depends on its number of elements. The elements are just shorter or longer dipoles than the driven element and act as if they are all connected in parallel. The gamma match is really a stub match. The centre of the feedpoint impedance of a Yagi with several elements can be very low, 10-20Ω. As you move out from the centre of the driven element the impedance increases. At the end of the driven element the impedance is very high. It is logically then somewhere between the centre and the end of the driven element the impedance will be 50Ω. The gamma match extends the centre of the coaxial cable out along the driven element to where the impedance is 50Ω. This position is adjusted by the shorting bar. The gamma rod has a small amount of inductive reactance. A series capacitor exists between the gamma rod and the sliding capacitor rod to tune out any inductive reactance with an equal amount of capacitive reactance.

The shorting bar and capacitor rod are adjusted for minimum SWR or using an impedance meter; the correct impedance, usually 50Ω, and no reactance.

This type of matching arrangement can be used on many other antenna types. It is not difficult to adjust in conjunction with an SWR meter. When you are adjusting most matching devices you are not bringing the antenna to resonance, but adjusting for the best impedance match between your feedline and the load, your antenna. The gamma, and other stub type matching, is so effective you could get a match to one or two soft drink cans in series. I have also heard of people "loading up" tree trunks! A gamma and other stub type matching will allow you to match to almost anything. This match will have little effect on the efficiency or performance of your antenna.

J-POLE

The standard j-pole is just an end fed halfwave antenna as shown in figure 37-30. The end of a halfwave dipole is a high impedance. The low section of the j-pole is a quarter wave short circuit stub at the bottom and an open circuit at the top. The end of the halfwave antenna 'sees' a high impedance at the open end of the stub. Between the open and short circuited ends will be a 50Ω impedance where you can connect your cable for 1:1 SWR. Usually some mechanical sliding arrangement is used to move the feedpoint on the stub up and down. The j-pole is made from one piece of aluminium or copper pipe. The stub can be clamped to a metal pipe to raise the antenna height if needed.

It is a good idea to place a simple 1:1 choke balun (Guanella) on the feedline close to the antenna. Just wind the feedline around some ferrite rod and tape it in place. You can pot the balun in resin if you want but there is no need if the coaxial cable is designed to be in the weather. If you are going to put connectors on the balun, then you will need to box or pot it. Once again a stub balun will match almost anything. The transmitter does not know or care about what sits on top of the stub. Adjusting the stub is not tuning the antenna. The stub just provides the correct match for the feedline. A good SWR does not mean anything about the performance or efficiency of the antenna as a radiator.

HORIZONTAL LOOP

The full sized horizontal loop, also called the Loop Skywire, is a low cost easy to build antenna that can be made to operate on multiple bands. The best way to feed a horizontal loop is with open wire ladder line and use an antenna tuner in the shack to provide a low SWR. The total length of the loop in meters is approximately L=300/(F(MHz) x 0.95. This is close to the correct length but like most antennas final adjustment must be done in-situ. The height above ground will have a bearing on the tuning and also the radiation pattern. A good height to strive for is 12.0 metres or higher. Realistically many suburban radio operators cannot achieve this height. It just means there will be a higher radiation angle. High angle of radiation is not such an issue on the low HF bands like 80 and 40 metres.

The horizontal loop does not have to be a square. It can be any shape and have multiple sides and anchor points if needed. What you are after is the maximum enclosed area of the loop. A circle would be best but not very practical. These antennas work surprisingly well on low HF bands.

MORE ON LOOP ANTENNAS

Self resonant loop antennas are relatively large and the size governed by the wavelength of operation. They are mainly used at frequencies above 3.5MHz where their size is feasible. They can be viewed as a folded dipole pulled out into an open shape, just as a folded dipole is a full-sized loop, bent at two ends and squashed into a line. The loop's shape can be a circle, triangle, square, rectangle, or in fact any closed polygon. The only requirement for a full size self resonate loop is that its perimeter be one wavelength. Such a loop will be self resonant. This means it will have intrinsically, the right amount of inductance and capacitance to be resonant.

The maximum radiation for a 1 wavelength loop is at right angles (broadside) to the plane of the loop. On the low HF bands a full loop is physically quite large, and for this reason they are installed lying flat or parallel to the ground. The main lobe of radiation is then upwards. At higher HF frequencies the full wave loop is smaller, and it becomes practical to stand it up vertically which has the advantage of a lower angle of radiation and greater likelihood of refraction from the ionosphere.

The polarisation of a full size, vertical loop antenna is not obvious by looking at the loop itself, but depends on the feed point (where the transmission line is connected), and whether it is being operated as a 1, 2, or 3 wavelength loop. If a vertically oriented loop is fed at the bottom at its 1 wavelength frequency, it will be horizontally polarised; feeding it from the side will make it vertically polarised.

SMALL LOOPS 

Small loops are "small" in comparison to their operating wavelength, typically between 5% and 30% of a wavelength in circumference, with transmitting loops tending to be closer to 30%. As with all antennas, smaller antennas are less efficient radiators than larger antennas. However, small loops become practical at lower frequencies where wavelengths are very long. Small loops may not be as efficient as we would like but they certainly become practical.

A common distinguishing feature of small loops is that their direction of maximum transmission or reception is within the plane of the loop - the opposite of large loops, whose maximum is perpendicular to the plane. In the direction that large loops produce their strongest signals in both transmit and receive, small loops have a null in their pattern.

Carefully designed and built small loops have advantages for reception on frequencies below 10MHz. Although a small loop's losses can be high, the receiving signal-to-noise ratio may not suffer if the loop's diameter is at least 1 or 2 meters, regardless of frequency. The very high Q rejects off-frequency interference and overload but also dictates that the loop must be carefully tuned to the exact operating frequency. The ability to rotate may help reject either local noise or distant interference, by orienting the "deaf" side of the loop towards the unwanted interference.

MAGNETIC LOOPS 

Small transmitting loops are "small" in comparison to a full-wave loop, but considerably larger than the small receiving loop, and unlike receiving loops must be "scaled-up" for longer wavelengths. They are typically used on frequencies between 3-30MHz. They usually consist of a single turn of large diameter conductor and are typically round or octagonal to provide maximum enclosed area for a given perimeter.

The smaller of these loops are much less efficient than full-sized self-resonant loops. However if space is an issue, and it commonly is on lower HF then magnetic loops can provide effective communications. Small loop antennas are also inexpensive and easy to build.

Figure 37-32 shows a photograph of a magnetic loop antenna. At the top the coupling loop can be seen and at the bottom the high voltage variable capacitor.

A magnetic loop, with a circumference 10% of a wavelength or less, will have a relatively constant current distribution along the conductor, and the main lobe will be in the plane of the loop. Small loops (less the 10% of a wavelength) do not have sufficient intrinsic capacitance to be resonant. For this reason a series capacitance is added to the loop circumference.

The current distribution around a 0.1λ or less loop is more or less constant however the voltage distribution has a peak across the tuning capacitor. The amount of voltage depends on the power used but it can easily be a few thousand volts. You could use any reasonably air spaced capacitor if you are willing to reduce the power. Dry air has a breakdown voltage of about 800 volts per millimetre and the capacitor can have a few thousand volts across it at moderate power levels. Some magnetic loop builders use a vacuum capacitor. An alternative is to build your own mechanical capacitor with a wide air spacing. There have been many different schemes used for this and you are encouraged to do a little research on the methods employed.

Magnetic loops require re-tuning even if you move in frequency by as little as 10kHz. For this reason serious builders incorporate a remote tuning system for the capacitor. There are some ingenious methods devised and again you are encouraged to do your research as there are too many to mention. While the figure 37-33 shows a variable capacitor with a range of 15-500pF smaller ranges can be used.

A common method of making the loop is to use 10-20mm copper water pipe. This can be bent into a circle using a simple homemade bending jig or you can make the loop octagonal and use straight pieces of copper pipe and eight 45° angle pieces. Keep resistance low, it is important to keep all resistance as low as possible. All joints should be soldered. Avoid using potentially higher resistance compression type fittings.

Matching to the transmitter

In addition to other common impedance matching techniques such as a gamma match, transmitting loops are sometimes impedance matched by connecting the feedline to a smaller feed loop inside the area surrounded by the main loop. Typical feed loops are 1/8 to 1/5 the size of the antenna's main loop. The combination is in effect a transformer, with power in the near-field inductively coupled from the feed loop to the main loop, which itself is connected to the resonating capacitor and is responsible for radiating most of the power. There are other methods of coupling, but simple loop coupling is the most popular. The coupling loop can be just the shield of thick coaxial cable. Thick and stiff so that it holds its shape.

38 - Transmission lines

A transmission line connects between a transmitter and an antenna and its purpose is to deliver all the signal power to the antenna. A perfect transmission line does not radiate or receive any energy and does not have any losses. We want the transmission line to have minimum loss and not to radiate or receive signals.

CHARACTERISTIC IMPEDANCE 

When an electromagnetic wave travels through free space, the current and voltage distribution of the wave settles into a particular ratio. In free space, the current and voltage distribution of an electromagnetic wave settles into the ratio E/I equal to 120πΩ or 377Ω. So we say the characteristic impedance (Zo) of free space is 377Ω.

As we learned in the chapter on electromagnetic radiation, it is the properties of free space that determine the velocity of light and all other electromagnetic radiation. The permittivity and permeability of space determines not only the characteristic impedance of space but also the velocity at which radio waves can travel through space. In the case of space the velocity is "c" or approximately 300,000,000 metres per second.

As with space it is the permittivity and permeability of a transmission line that determine the characteristic impedance of the line and how fast the wave will travel through it. Permeability and permittivity are governed by the type of materials from which the line is constructed and also the physical dimensions of the line, how large the conductors are, the spacing between them and the type of dielectric material used.

When a wave travels along an antenna or in a transmission line of infinite length, the current and voltage distribution of the wave will settle to a particular ratio of E/I and this is called the characteristic impedance (Zo) of that line. Now the reason why I said a line of infinite length is to eliminate what is connected to the end of the line, that is, the load.

Take a length of transmission line without losses and of infinite length. Transmit a wave into this transmission line. If we were to measure the current or voltage at any two points on this transmission line, we would get the same E and I. The ratio E/I will be constant and equal to the characteristic impedance of the line in ohms.

The transmission line in figure 38-2 is of infinite length and it has no losses. A generator (transmitter) is connected and an electromagnetic wave begins to propagate down the line. Let us assume the power into the line is 100W. Also that the first ammeter measures 2 amperes. What would the first voltmeter read? We have 100W so the first voltmeter must read 50 volts since 2A x 50V = 100 watts. We arbitrarily said the power into the line was 100W and the first ammeter reads 2 amperes. If we actually measured this we would no doubt get different numbers but the principles are the same. The meters will indicate the power moving through the line and the product of I and E will be that power in watts.

The characteristic impedance is then Z=E/I = 50/2 = 25Ω 

We said the line was lossless, so there will be no attenuation. All of the ammeters will measure 2A and all of the voltmeters will measure 50V. If there was attenuation then the meters will read less as we move towards the end of the line. However the ratio of E/I (the characteristic impedance) will remain the same and equal to 25Ω so the "character" of the impedance of this line is 25Ω.

PROPAGATION TAKES TIME

The meters in figure 38-2 are not all going to read 2A and 50V suddenly. The progression of an electromagnetic wave, as fast as it is, still takes time to propagate down the transmission line. Typical transmission lines like coaxial cable carry the wave at about 66% of light velocity and parallel line about 95%.

Figure 38-3 shows the same transmission line as in figure 38-2. However now we are looking at the progression of the electromagnetic wave front down the line over time. Let us say the distance D shown in the diagram is 300,000,000 metres. Let us also assume the time taken for the wave to cover the distance D is 1 second. We know it is a bit slower than that but the precise velocity is not important at this time.

At A the wavefront has just entered the transmission line. The energy in the electric and magnetic fields have already settled into a ratio of 25 (25Ω) the characteristic impedance. This is not magic. It is the characteristics of the line that enable the settling of voltage and current into this ratio.

The first set of meters have not been reached by the travelling wave yet so they would be measuring zero. Figure 38-3(B) shows where the wave will be in a bit less then 2 seconds. The wave has passed two meter sets and both of these sets of meters will read the current and voltage distribution. That is the ammeters will both read 2A and the voltmeters 50V. These readings will be the RMS value since the wave is radio frequency alternating current (AC).

After just under three seconds in figure 38-3(B) the wavefront arrives at the third set of meters and then spring to life reading the same current and voltage as the first two meter sets. If the line has loss then each successive meter reading would be slightly lower, however the ratio of E/I would remain the same as this is the characteristic impedance of this line.

In figure 38-3(C) the wave front has not yet reached the last meter set. This means the generator (transmitter) does not know what is at the load. Think about this! The transmitter could be connected to an open or short circuit but the transmitter has no way of knowing this until the wave front arrives at the load. Will the transmitter know the load conditions when the wave front reaches the load? Well no, it won't. A message has to come from the load all the way back to the transmitter to tell the transmitter the load is a short or open circuit.

WHAT IS A TRANSMITTER'S LOAD?

When you connect an antenna directly to a transmitter, the load for the transmitter is the antenna. When we use a transmission line to connect a transmitter to an antenna located elsewhere, the load for the transmitter is no longer the antenna. It is the transmission line's input impedance which, under most circumstances, will be the same as the characteristic impedance (Zo).

We have discussed before the importance of matching a source (transmitter) impedance to a load (transmission line) impedance. Do you recall when we did the exercise on connecting different resistors to a battery? Only when the resistance connected to the battery was equal to the internal resistance of the battery did we get maximum power dissipated in the load resistor. Likewise, for maximum power to be transferred from the transmitter to the transmission line, the output impedance of the transmitter must match the input impedance of the transmission line. Keep in mind again that although we are talking about transmitters, the same applies to the reception of radio waves.

WHEN IS A 5O OHM TRANSMISSION LINE 5O OHMS? 

At first, this may seem like a very silly question. After all, if you purchase 50Ω transmission line you expect it to act like 50Ω line. Unfortunately, whether a 50Ω transmission line behaves like 50Ω transmission line depends on how we use it. Just because it has 50Ω written on its side is no guarantee that it will behave as 50Ω. That's up to us to ensure! A transmission line will only exhibit its characteristic impedance when it is terminated in a load equal to its characteristic impedance. A 50Ω cable is 50Ω when it is connected to a load consisting of 50Ω of pure resistance. If a transmission line is terminated in a load not equal to its characteristic impedance, then the impedance of that line will vary from one point to the next along its length due to the presence of standing waves. More about standing waves shortly.

FACTORS THAT DETERMINE CHARACTERISTIC IMPEDANCE

The characteristic impedance of any transmission line is a function of the size and spacing of the conductors and the type of insulating material (dielectric) between them. If the distributed inductance and capacitance per unit length of a line is known, then the characteristic impedance can be found from:

The inductance and capacitance is measured , or known, per unit length. It does not matter what the length is as long as you measure the L and C for the same length.

To find the distributed inductance and capacitance per unit length, you can either measure it or look it up from a cable data book. A data book will tell you what the distributed L and C of a cable is for example a one-metre length. It does not matter what the length is as long as it is the same length for both Land C. Using this L and C, you can calculate the Zo.

For example, looking up engineering tables for the inductance and capacitance per unit length for RG58 we find: -

Inductance=L=333x10-9 Henry/meter or 333nH/metre

Capacitance=C=1.333x10-10 Farad/meter or 133.3pF/metre

If we insert this L and C into Equation 38-1 we get: -

Do the division first then find the square root of that answer.

If we know the physical dimensions of the coaxial line, we can calculate the Zo using equation 38-2. You very likely will not have to do this in radio assessments however you will probably need to know what determines the characteristic impedance of any cable. The answer is its dimensions and the materials, particularly the dielectric, used to make the cable. Equation 38-2 shows how to calculate Zo from the construction of a coaxial cable, ε in these equations is the permittivity of the dielectric.

Similarly, the characteristic impedance (Zo) of a parallel line can be determined by primarily the dielectric used and its physical construction.

RANGES OF Zo 

In the design of transmission lines, there are certain constraints which restrict the range of practical impedances that can be achieved. For two wire parallel lines, the Zo is usually restricted to a range of 100Ω to 600Ω, while for coaxial lines the practical range of characteristic impedance is typically 30Ω to 100Ω.

Interestingly, it is no accident that in radiocommunications a Zo of 50Ω is most common for transmission. However, for receive-only systems 75Ω cable is the most common. The reason? It can be proven that 50Ω is the best compromise between power handling ability and losses, whereas 75Ω cable is optimised for having low losses with no regard to the power handling ability.

BALANCED AND UNBALANCED LINE

On a balanced line, such as a parallel wire line, the impedance between each leg of the line above the earth is the same. This line is said to be "balanced." On the other hand, a coaxial line has a larger outer concentric conductor with a smaller diameter solid conductor through the centre. Because of this construction, it is impossible for each leg of the line to have the same impedance above the earth. A coaxial line is said to be "unbalanced."

If you find this concept hard to understand, imagine placing an ohmmeter between each side of a parallel line and ground (as in dirt, earth). You will measure a very high resistance (impedance) in the megohm range. However, you will measure the same value between each leg and ground. This line is balanced. This is why we have twisted pair cable and why 3000 ribbon is often twisted - in order to maintain the balance. A coaxial line, on the other hand, has its centre conductor at megohms above ground while the sheath (outer conductor) is at ground - definitely an unbalanced line.

A two wire parallel line such as 300Ω TV ribbon will "behave" as balanced line only if it is installed correctly. In a TV installation, this line must be held away from metal structures such as the antenna mast, by using stand-offs. If this was not done, the metal structure would unbalance the line and alter its characteristic impedance. A correctly installed 300Ω TV feeder is twisted at least once every 150mm.

The purpose of this is to ensure that each side of the line is "influenced" to the same degree by nearby objects such as metal stormwater down pipes. Attaching 300Ω ribbon to a wall using thumbtacks driven into the centre of the dielectric is absolutely out for the same reasons (don't laugh, I have seen it done). The latter practice is commonly found in domestic TV installations and frequently leads to poor reception and interference. A balanced line is difficult to install in order to maintain the balance between each leg. Having said that, parallel balanced lines have much lower losses than coaxial lines.

WHY BE CONCERNED ABOUT BALANCE?

If a balanced line is installed correctly, then induced currents from your radio transmissions will flow in opposite directions on each leg of the TV line and be equal in amplitude, thus completely cancelling out and greatly reducing the possibility of interference (for the same reason, a parallel line does not radiate when used on a transmitter). If, however, the line is unbalanced, it will function more like a long wire antenna and funnel your signal into the TV set, greatly increasing the chances of interference.

A coaxial line is unbalanced by virtue of its non-symmetrical construction. At the transmitter, it is usual practice to connect the outer conductor to ground. The cable can be run any way you like and can even be buried in the ground (preferably in conduit). The induced voltages in the shield are conducted to earth and do not affect the shielded, inner conductor circuit.

VELOCITY OF PROPAGATION

The velocity of propagation is the speed with which an electromagnetic wave travels through a transmission line. The velocity of propagation within a line depends on the construction of the line. In particular, the dielectric used can significantly alter the velocity of propagation. Manufacturers of transmission line describe the velocity of propagation by stating the velocity relative to the velocity of light (or any other electromagnetic wave) in free space, commonly referred to as the velocity factor. The velocity factor can range from 0.56 to 0.95 depending on the type of cable. A line with a velocity factor of 0.66 means that the wave can travel along this line at 66% of light velocity (light velocity = 300,000 km per second).

Higher quality coaxial cable (unbalanced line) has excellent shielding and has a greater proportion of air as dielectric material. However, care must be taken with bending, or the cable will be crushed. Crushing upsets the physical dimensions and therefore the impedance.

The most important ones to remember for everyday use are 0.66 for coax and 0.80 for 300Ω parallel line. If you use something else look up the velocity of propagation on the manufacturer's data sheet.

There is an interesting approximation for determining the velocity factor of coaxial lines. The reciprocal of the square root of the dielectric constant (permittivity) is a close approximation to the velocity factor - 1/√ε polythene has a dielectric constant of 2.3. So a coaxial line with a polythene dielectric has a velocity factor of: 1/√2.3 = 0.659 or 0.66 rounded.

Some typical velocity factors are:

1. Parallel line, air dielectric, 0.95 - 0.975

2. Parallel line, plastic dielectric, 0.80 - 0.95

3. Coaxial, air dielectric, 0.85

4. Coaxial line, polythene dielectric, 0.66

A transmission line is not a better one if it has a higher velocity factor. Velocity factor is only important when we want to cut a transmission line to a particular wavelength. A wave travels more slowly within any cable and therefore covers less distance, in a given time, than in free space. So for example a half wavelength of coaxial cable is going to be a lot shorter than the wavelength of an electromagnetic (EM) wave in free space. Indeed, it will be about 66% of the free space length.

A LINE TERMINATED IN ITS Zo

An electromagnetic wave is travelling down a transmission line but has not yet reached the load. Remember, a wave travels at a finite velocity, a fraction of the speed of light. As it travels its current and voltage distribution, or ratio E/I, will be equal to the Zo of the line. The wave has no idea how the line is terminated until it reaches the termination. The wave has not reached the load - it is on its way down the line. The current and voltage of the wave must obey Ohm's law. When the wave reaches the load, which is equal in impedance to the Zo, it will be totally dissipated in the load or radiated if the load is an antenna. Such a line is called a flat line as it has no standing waves.

REFLECTED WAVES

An electromagnetic wave upon reaching a mismatched termination must conform to Ohm's law. You need to imagine a wave travelling in a lossless transmission line of infinite length. The voltage and current ratio (E/I) of the wave will be that of the characteristic impedance. Now let's do away with the infinite line and place a load at the end of the line. The wave has not reached the end of the line yet, so its E/I distribution is still representing the characteristic impedance (Zo). If the load is not equal to the Zo, the wave upon reaching the load must go through a current and voltage redistribution so that E/I now represents the load impedance. To do this, the wave goes through a sudden redistribution of the energies contained in its magnetic and electric fields, so that the current and voltage across the load represents the Ohm's law load impedance.

In going through a redistribution of current and voltage, an induced current and voltage wave is created (Faraday's law of induction) and this new wave opposes the wave that created it (Lenz's law). The induced wave will now begin to propagate through the line back towards the generator or transmitter. This is called a reflected wave. How much of the incident wave is reflected and how much is dissipated (or radiated) in the load is determined by the amount of mismatch between Zo and the load impedance (ZL).

Again, a wave, before reaching the termination (load), has no knowledge of the termination conditions. The wave's current and voltage distribution will be representative of the characteristic impedance of the line. As close as one micron (a millionth of a metre) away from a load, the wave is still unaware of the conditions at the load. Suddenly, upon reaching the load, an instantaneous change in impedance occurs. The voltage and current must now redistribute themselves to conform to the Ohm's law value established by the load. This rapid redistribution (of electric and magnetic fields) causes an induced reflected wave that travels back down the line from the load to the transmitter.

A line not terminated in its Zo will have an incident or forward wave and a reflected wave travelling in opposite directions.

STANDING WAVES

Standing waves are produced when reflected waves travel from the load back towards the transmitter and interact with the incident (forward moving) waves from the transmitter. The result of this interaction is called a standing wave.

Standing waves are an interference pattern caused by the interaction of incident and reflected waves. At certain points along the line, incident and reflected waves will be additive; at other points, they will be subtractive. If you throw two stones in a pond a distance apart concentric waves will radiate outward. When the two waves collide they will interfere with each other and a distinct interference pattern will be seen on the pond. This is the same effect with incident and reflected waves on a transmission line.

When incident and reflected waves interact and form a standing wave, the impedance of the line is no longer its Zo. The impedance at any point along the line is equal to the resultant and measurable E/I at that point.

Imagine placing a voltmeter at some fixed point on a transmission line which has reflected and incident waves present. At the point of attachment, the voltmeter will measure the resultant standing wave voltage. Moving the voltmeter along the line will reveal that the interference pattern exhibits a periodic pattern of maxima and minima. Common terminology refers to the resultant voltage minima as nodes and to the maxima as anti-nodes. Nodes are produced on a line where the incident and reflected waves are equal in amplitude and 180° out of phase. Anti-nodes occur when both waves are equal in phase and therefore additive.

The term 'standing wave' comes from the fact that the position of the nodes and antinodes does not move. The nodes are stationary. The distance between adjacent nodes or anti-nodes is a half wavelength.

The effect of standing waves is most dramatic when the line is terminated in an open or a short circuit. In such cases, all of the power arriving at the termination is reflected.

STANDING WAVE PATTERN ON A SHORT CIRCUITED LINE

Figure 38-5 shows the actual resultant standing wave of current and voltage on a short-circuited line. If you have trouble working this pattern out for yourself, just remember this: The voltage-current ratio E/I must represent the impedance at that point on the line. Now there is one place where you definitely know the impedance; at the load. This line is short-circuited, so the load impedance is close to zero. Can you see that at the load (the right-hand side) the current is high and the voltage is low?

Low voltage causing a high current is representative of a low impedance. If the impedance of the load was zero (short circuit), then the impedance ¼λ back from the load will be infinite. Half a wavelength away from the load the impedance will be equal to the load impedance. I have only drawn a half wavelength of the line as this pattern just keeps repeating.

STANDING WAVE PATTERN ON AN OPEN CIRCUIT LINE

Figure 38-6 shows the standing waves of current and voltage on an open circuit line. If the pattern looks familiar to you, it should, as this is exactly what happens on a dipole antenna. Again, please note how the E/I ratio represents the impedance at that point. The load is open circuit (infinite impedance). At the load, the diagram shows a very high voltage with little or no current. Is not high voltage and low current the same as a high impedance?

VOLTAGE STANDING WAVE RATIO (VSWR)

The ratio of the voltage maximum (anti-node) to the voltage minimum (node) is called the VSWR. The VSWR is an indication of the degree of match or mismatch between the line's Zo and the load impedance. VSWR means the SWR is just obtained by voltage measurement. You could, in fact, determine the VSWR by current measurement - this is called ISWR - all three are the same.

VSWR (OR SWR) FROM FORWARD AND REFLECTED POWER

Many wattmeters allow the measurement of the forward and reflected power on a transmission line. Equation 38-5 can be used to convert these forward and reflected power measurements to VSWR.

We could have used any 1 to 10 ratio and obtained the same answer. For example, if the forward power was 1 watt and the reflected power 100mW the ratio between forward and reflected power is still 10:1 so the SWR is 1.9:1.

VSWR METER

Radio stations usually have an instrument which measures the amount of reflected voltage relative to the amount of forward voltage on a transmission line. Such a device is called a VSWR meter. The forward voltage is first 'SET' to full scale and then a reading of the reflected voltage is taken. The scale on the metre is calibrated to read VSWR directly. This type of VSWR meter is, in fact, measuring the coefficient of reflection, which is just the ratio of the forward and reflected voltage. Mid-scale on these type of VSWR meters corresponds to a coefficient of reflection of 0.5 (VSWR=3) and full scale is 1.0 (VSWR = infinite). There is a simple mathematical relationship between VSWR and the coefficient of reflection (ρ-Rho), so the manufacturer (or builder) is able to calibrate the scale in terms of VSWR:

If you want to calibrate your VSWR meter in terms of coefficient of reflection, then just put a linear scale on the meter face from 0 to 1. Quarter scale would be ρ=0.25, third scale ρ=0.33, half scale ρ=0.5 etc.

A popular type of VSWR meter is the cross needle power meter. It is popular because it has no adjustments. The meter has two pointer needles one moves left to right to measure forward power and the other right to left to measure reflected power. It has a scale for forward and reflected power. Where the two needles cross the VSWR is read from a third scale.

IMPEDANCE MATCHING

For the transmitter to develop its full power and also to obtain maximum possible power transfer to the load, all components in the transmission system must be matched.

While the above statement is true, it often leads to the false conclusion that reflected power is lost power. Reflected power is not lost since it will be re-reflected at the transmitter. Reflected power does not go back into the transmitter and burn out the finals! The power amplifier may be damaged if the VSWR is high, however, this is due to the power amplifier itself creating high voltages across its components due to impedance mismatch. Reflected waves actually travel back and forth from the transmitter to the antenna - each time they arrive at the antenna a little more power is radiated. They bounce back and forth, until most of the power is eventually radiated along with some power dissipated in the transmission line due to the multiple reflections.

Generally speaking, a matched system is better because:

1. If VSWR is low, then line losses are low.

2. The transmitter will develop its full output power.

3. A flat line can carry more power than one with a standing wave present.

4. There will not be multiple reflections (and multiple attenuation) on the transmission line.

The above is particularly true of coaxial lines. Parallel open wire lines have virtually no losses even with very high VSWR.

Standing waves place the transmission line under unnecessary electric stress. Antinodes (maxima) of voltage can break down the dielectric while the anti-nodes (maxima) of current cause increased copper losses (heat loss).

The impedance of a transmission line varies along its length if it has standing waves. Look at how the impedance varies along the length of a transmission line which is terminated in a short circuit or an open circuit. By a line terminated in a short circuit, we mean there is no antenna or other load, the two sides of the transmission line are just connected together. By a line terminated in an open circuit, we mean a transmitter connected to a transmission line that goes nowhere and is just left unconnected.

The line terminated in a short circuit will be inductive for the first quarter wave, then capacitive for the next quarter wave, then inductive again and so on. Whether the line is inductive or capacitive depends on the phase of the current and voltage at that point. On short circuited lines less than ¼λ the current is increasing towards maximum at the short circuit and the voltage has already been at maximum and is decreasing. The current is lagging the voltage. Hence, the impedance is inductive.

Let's get this clear even though you may not be examined about the input impedance of a transmission line which is short or open circuited. The principles are the same for antennas.

Let's make the statement again:

A line terminated in a short or open circuit will have an input impedance which is either inductive or capacitive. Your problem is to work out what the input impedance type is, that is, inductive or capacitive. Don't memorise it, but work it out by looking at the current and voltage on the line.

Before we start, recall this:

Current LAGS voltage in an inductive circuit (think of L for inductance and L for Lag). Current LEADS voltage in a capacitive circuit.

Figure 38-7 shows a transmission line terminated in a short circuit. The short circuit is the load and the line is less than ¼ wavelength.

First, look at the load and work out what the voltage and current would be at the load. The load is a short circuit. A short circuit means high current and low voltage. That's what a short is. As we move back from the load, from right to left, the current must begin to fall since it is maximum at the load. Voltage is minimum at the load and as we move back from the load, from right to left, the voltage must rise. This is the voltage and current distribution on a short circuit line less than ¼ wavelength long.

Now the important bit. Looking into the transmission line from the left-hand side - is it inductive or capacitive? Looking into the line from the left-hand side we see current increasing and voltage decreasing. Current is on the increase and is lagging. Hence, the input impedance of this transmission line is inductive.

A length of transmission line terminated in a short circuit and less than ¼ wavelength is inductive. In fact, by changing the length, you can obtain any value of inductance you like. So if you need to add inductance to something (perhaps an antenna) you could use a shorted length of transmission line and adjust its length until you get the correct inductance.

For interest's sake, I have calculated what the inductance would be for a shorted length of transmission line at various wavelengths. These calculations are for 50Ω coaxial cable. Remember, this is the inductance you would get looking into the end opposite to the short circuit:

0.1λ= 36.327Ω (inductive reactance)  

0.125λ= 50Ω  (notice anything?)  

0.2λ=153.884Ω   

0.22λ=262.109Ω   

0.24λ=794.727Ω   

0.245λ=1591Ω   

0.248λ=3978Ω   

0.25λ=2.50197630472884x1015 Ω (infinite impedance - open circuit)  

As you can see from the values I calculated, if the length of a shorted transmission line (less than ¼ wave) is varied, its input impedance is inductive and varies with length. At 0.125 wavelengths the inductive reactance will always be equal to the characteristic impedance of the line (50 ohms in our example). A line with a Zo of 600Ω terminated in a short circuit and 0.125λ long would have an input impedance of 0j600Ω.

What happens at ¼ wavelength in figure 38-7 ? Well, that number is huge and it was the best my calculator could do to define an open circuit. A ¼ wavelength of line terminated in a short circuit (zero impedance) will have an open circuit (infinite impedance) at its input.

Let's look into the line at ½λ as in figure 38-8.

Looking into the line now (from the input) the current is high and falling and the voltage is rising. Current is ahead of the voltage, that is, current is leading. The input impedance is capacitive.

Re-capping if a transmission line is terminated in a short circuit then that line will give us an inductance between the load and a quarter wave back from the load. The same line will give us a capacitance between a quarter wave and one half wave. What we have here is the ability of a transmission line to simulate any value of inductance and capacitance. This is called a transmission line stub which has many applications. For example if an antenna is not resonant then a stub can provide the correct value of inductance or capacitance to bring the antenna to resonance.

Can you see that the current and voltage at the input (the left-hand side) is now exactly the same as it is at the load? At ½λ back from a short-circuited transmission line we again have a short circuit, or if you prefer, zero impedance.

If the load was not a short circuit but instead say 88-j20Ω, that is, the rectangular format for 88 ohms of R and 20 ohms of capacitive reactance. Then one half wavelength of line (irrespective of the characteristic impedance) the input impedance would be the same as the load. That is 88-j20Ω.

THE STUB

A stub is a length of open or short-circuited transmission line. The input impedance of such a line is reactive and the amount of reactance and its type (XL or XC) can easily be determined by equation or measurement.

Stubs are frequently used to bring an antenna to resonance. If an antenna is not resonant, it will be reactive. The reactance of a stub can be used to cancel the unwanted reactance of the antenna, thus bringing it to resonance. Short circuited stubs are favoured for this application; as open circuit stubs tend to radiate somewhat.

Figure 38-9 shows a vertical and a horizontal dipole antenna that are both electrically short. Being short these antennas are capacitive and need to have inductance added to bring them to resonance. This could be done by adding inductance in the form of loading coils. Instead we are using short circuit stubs less than a quaterwave to simulate the inductance we want. Sometimes the antenna and its stub are made from the one bent piece of aluminium tube.

THE QUARTER WAVE TRANSFORMER

A length of transmission line called a "quarter wave transformer" can be used to match an antenna's feedpoint impedance to that of the transmission line. The characteristic impedance of a quarter wave transformer is given by:

Where Zo is the impedance of the transmission line used for the quarter wave transformer. Z1 and Z2 are the two impedances to be matched.

As a practical example, suppose it was necessary to connect 300Ω transmission line to a dipole antenna which has a feedpoint impedance of 75Ω (figure 38-10).

As figure 38-10 shows, a quarter wavelength of transmission line which has a characteristic impedance of 150Ω will match the 75Ω dipole impedance to the 300Ω impedance of the transmission line. Remember that when calculating the length of a quarter wave transformer, the velocity factor (Vf) of the transmission line must be taken into account as follows:

Coaxial cable can be considered to have a velocity factor of 0.66 and parallel transmission line 0.80 unless otherwise known. The problem with quarter wave transformers is that they only work correctly on the frequency where the quarter wave of the line is indeed a quarter wave.

A ONE HALF WAVELENGTH 1:1 TRANSFORMER

In figure 38-11, we see a half wavelength of transmission line of unknown impedance terminated to a load of any impedance.

Whatever the impedance of the load, this impedance will be reflected to the input of the transmission line. Suppose the load was 72j0Ω then the input impedance will also be 72j0Ω.

Figure 38-12 shows a transmission line of any characteristic impedance terminated in a load of 72j0Ω. The termination impedance does not matter, we have just chosen the load impedance arbitrarily. The input impedance will change with the length of the line. The table shows what the impedance of the line will be at 5 points, Z1 through to Z5.

At one eighth of a wavelength from the load the impedance will be 46.85j17.5Ω. Nothing astonishing there, not yet anyway. At one quarter wavelength (Z2) from the load the impedance will be 34.72j0Ω. Now here is something worth thinking about. Did you notice something at one quarterwave from the load? There is no reactance in the line impedance. The line is resistive and equal to 34.720Ω. This would not be the case if the load had reactance. If the load was a resonant antenna though it would not have reactance.

Move on to Z3 which is three eighths of a wavelength from the load. The impedance there is 46.85j17.5Ω. Take a look Z1 and Z3. They have the same impedance of 46.85j17.5Ω. Why? Z1 and Z3 are one half wavelength apart. Any two places on a transmission line one half wavelength apart or a multiple of a half wavelength will have the same impedance. This is because the current and voltage distribution on a transmission line with standing waves duplicates itself every one half wavelength.

Z4 is one half wave from the load and therefore it has the same impedance as the load. Similarly Z5 is one wavelength from the load, which is two half wavelengths so Z1 has the same impedance as the load. I hope you can see that a half wave of transmission line is acting "as if" it was a one to one transformer.

With a half wave or multiple of a half wave transmission line whatever the impedance of the load, this impedance will be reflected to the input of the transmission line. Suppose the load was 72j0Ω then the input impedance will also be 72j0Ω.

A half wavelength of transmission line has the property of reflecting its load impedance to its input. The characteristic impedance of the line makes no difference - whatever the load impedance is, this impedance will be 'reflected' to the input of the line. So a half wavelength of transmission line acts as if it were a 1:1 transformer. Of course, the same would apply to one full wavelength of the transmission line, or in fact any multiple of half wavelength of the transmission line. This can be very useful when making antenna measurements. Suppose you are using a device called an Impedance Bridge to measure the feedpoint impedance of an antenna. Suppose it is not practical to work at the antenna. Provided you use a half wavelength or multiple thereof, of transmission line, the measurement taken at the input of that line will be as if it were taken at the antenna (neglecting the effects of losses).

Some impedance bridges allow you to measure the impedance of an antenna with any line length. To do this, you have to tell the impedance bridge the length of line in wavelengths and its loss. The bridge measures the input impedance and then computes the impedance at the load.

QUARTER WAVE NOTCH (Bandstop filter)

We have learned that a half wavelength of transmission line 'reflects' the identical impedance to its input. If you look at the diagrams showing the current and voltage distribution of an open circuit line, you will see that on a line terminated in an open circuit the impedance ¼λ back will be a short circuit. Remember that the line is only a quarter wavelength for a particular narrow band of frequencies.

AN EXAMPLE OF USING A STUB NOTCH

Suppose a TV was getting overload from a nearby radio operator on 29MHz.

To fix the problem, we need to connect a filter on the back of the TV. The purpose of the filter will be to block the 29MHz and pass all other frequencies - most importantly the VHF/UHF TV band.

A quarter wavelength of transmission line on 29MHz, terminated in an open circuit, will act as a notch filter.

Say we are using 300Ω TV cable to make our notch (we could use anything), then the length of the line is: The length of the open circuit notch is quarter of a wavelength times the velocity factor of 0.8 for 300Ω line

Length of notch= 300/29 x 0.25 x 0.8 = 2.0689 metres

In centimetres, that rounded up to 207cm. I would cut the notch a bit longer say 209cm. Remember it is open circuit and ribbon so it is going to be very easy to prune bits off the end to get it just right.

Connect 207cm of open circuit 300Ω line to the back of the TV set in parallel with the existing feeder which goes to the TV antenna. You will effectively be placing a notch of around 20-25dB on the 29MHz (approx. +/-400kHz) band for the cost of 2 metres of ribbon cable.

Please do not take this method too lightly. It is extremely useful. Notches can be made easily and cheaply for all radio bands and they really do work very well to stop overload. I would say nine times out of ten this has worked for me.

A trick if you are using 300Ω line - tape the open end up and make a sleeve of aluminium foil which you can slide on and off the end of the notch to tune it. You could solder a smaller trimmer capacitor onto the open end. The only problem with using 300Ω balanced line is your hand capacitance will alter it a bit - so adjust; let go; rinse and repeat.

Your notch can just as easily be made with a coaxial line and connected to the back of the effected receiver through a "T" connector.

Figure 38-13 shows a typical but simple television distribution system. These are used in large homes and businesses like motels where one TV antenna is connected to several TV receivers. To do this properly the TV signal needs to be amplified and distributed with the correct impedances. The television distribution amplifiers that do this are broadband amplifiers. They can amplify a very wide band of frequencies including 144-148 meter amateur band. They are easily overloaded. If overloaded from an amateur VHF signal then all TV receivers will be affected. Unfortunately many of the distribution amplifiers have poor filtering and the solution is to add rejection on the frequency that is overloading the amplifier. One method is to add a quarter wave open circuit notch filter via a "T" connector on the antenna side of the distribution amplifier.

A quarter wave notch for 146MHz will not be long. Make sure you use good quality coaxial cable when making stubs. Calculate the length: 300/146 x 0.25 x 0.66 = 340mm. It is a good idea to make the notch a bit longer than necessary and prune its length very slowly while watching the interference. The end of the notch should be open circuit. The notch can be rolled up into a small loop. This will provide around 20dB of attenuation on 146MHz and a bandwidth of approximately 1MHz. If you need more attenuation then you can use two notches spaced one quarter wave apart. With two notches you can get 30-35dB of attenuation determined primarily by the quality of the cable used.

Something to try 

If you have a radio receiver on any band, one that you can get to the antenna terminals, tune the receiver to a constant signal and make a notch for that frequency to eliminate or reduce that signal. If you try this, work out the stub length from the above equation and cut it a little long. Connect it to your receiver and then trim 2-3 mm off at a time using pliers. Watch the 'S' meter dip as you cut (tune) the stub. This is a practical way to tune any transmission line notch filter.

THE STRIPLINE

I mentioned earlier in this book that filters for UHF and above are often too difficult to make from standard capacitors and inductors. I mentioned, that filters could be made using transmission line principles. One type of filter and/or transmission line is called stripline. At UHF and higher frequencies, transmission lines become so short in terms of wavelength that half and quarter wavelength lines can easily be made of copper printed circuit board track. These printed circuit board transmission line filters are called stripline filters. They can be used to create an inductive or capacitive reactance, and act as resonant tank circuits, or filters.

The stripline for Advanced Theory is examined only to the point that you need to know stripline can be used for filters and transmission lines at UHF and above. Microstrip is not in the Australian syllabus and there is often confusion between the two, I will cover both.

Microstrip vs. Stripline 

The importance of printed circuit board (PCB) interconnect techniques increases with frequency of operation. At higher frequencies, transmission line wiring provides superior performance by minimising crosstalk, signal distortion and radiation (compared to ordinary point-to-point wiring). When implementing transmission lines on a printed circuit board (PCB), there are two options: microstrip and stripline.

Microstrip. 

A microstrip transmission line consists of a copper trace separated from a ground plane by an insulating substrate. This configuration is depicted in the image below.

Since one side of the conductor is exposed to air, these transmission lines can only exist on top and bottom PCB layers. The trace impedance is influenced by both the dielectric of the substrate material and the air above it.

STRIPLINE

Unlike microstrip, stripline transmission lines are fully contained within a substrate - which is sandwiched between two ground planes.

Due to the substrate impregnated nature of stripline, these transmission lines can only exist on internal routing layers and require a minimum of 3 board layers (2 ground planes and a routing layer).

WAVEGUIDES

Any system of conductors and insulators assembled for the purpose of directing an electromagnetic wave can be referred to as a waveguide. Ordinary coaxial cable or parallel line is a waveguide. The designation for transmission line, for example, RG8U means "Radio Guide number 8U".

It is usual though to use metallic rectangular or circular pipes as waveguides. At frequencies above 1GHz waveguides are a better alternative than coaxial or parallel lines because the latter start to become very lossy at such frequencies.

Pipe of any cross section could be used as a waveguide however it makes sense to use simple cross sections like a rectangle or a circle. Whatever cross section we choose we are going to need a system of bends, joiners and other speciality components that we can insert into the waveguide.

Figure 38.16 shows the basic construction of rectangular and circular waveguides. We can inject an electromagnetic signal into the waveguide using an antenna or a coupling loop just like we do with resonant cavities. The antenna would inject a wave that would travel down the waveguide that could eventually go to an external antenna for radiation in space to some other load.

The waveguide walls are conductors since the waveguide is often made from brass or aluminium. The walls of the waveguide are not conducting the energy. The cross sectional area of any waveguide is related to the frequencies at which it is used. Waveguides are manufactured to cover different frequencies and applications. Waveguides can be used to make the same transmission line components as coaxial cable such as stubs, transmission line transformers and directional couplers. Directional couplers are discussed in the chapter on test equipment. Waveguides can handle higher power levels and have much lower losses than coaxial line. A wave propagates down a waveguide by reflecting off the walls of the guide.

VISUALLISING A WAVEGUIDE FROM CONVENTIONAL LINES 

Some find it difficult to see how an electromagnetic wave can be guided down a metal pipe. Take a look at figure 38-17(a). Here we have a parallel transmission line with an open circuit quarter wave stub connected across it. Does the parallel transmission line "know" that this stub is present? Recall from earlier in this chapter a quarter wave short circuit stub reflects to its input an open circuit. So the short circuit at the bottom of the stub is an open circuit where it joins the parallel line. The line is not electrically affected by the stub whatsoever. This method of using short circuit stubs to support a parallel transmission line is used to provide metallic line stand-offs.

Let's get this straight. We are using metallic stand-offs to insulate and support a parallel line. As far as the parallel line is covered the metal stand-off is not even present. Suppose we were to use ceramic insulators. Ceramic is a real insulator of course. Should the ceramic insulator become covered with dust or pollution the ability to insulate the line will deteriorate. What about metallic stub insulators? If they became polluted with grime would their ability to insulate deteriorate? No, not at all, they are already conductors. In effect we are using metal DC conductive stubs to create the perfect insulator as long as we only have one frequency of operation. If we change frequency too far the stub will not be a quarter wave any longer.

In figure 38-17(b) we have added another quarter wave short circuit stub above the parallel line. Both stubs are reflecting the short circuit at the load to an open circuit at their input where the parallel line is connected. So the parallel line in figure 38-17(b) is unaware of the presence of the two stubs.

In figure 38-18 on the left we have started to get carried away with adding quarter wave stubs. Can you see that we can add as many as we like and the parallel transmission line will be unaware of the presence of the stubs?

We can add so many stubs that we have a continuous stub as shown on the right hand side of figure 38-18. What do we have? We have a fully enclosed metal pipe that we call a waveguide.

METHOD OF PROPAGATION

When an EM wave propagates in free space, coaxial or parallel line, the electric and magnetic fields are perpendicular (transverse) to the direction of propagation. This type of propagation is called Transverse Electro-Magnetic (TEM). If we tried to get a TEM wave to go down a waveguide it would not work because the electric field would be short circuited by the guide's conductive walls. Figure 38.19 shows the method of EM wave propagation we have become familiar with in free space. Both the electric and magnetic fields are transverse to the direction of propagation.

To propagate a wave down a waveguide we cannot allow the electric field to exist near a wall of the guide and also parallel to it. This must be done to prevent the wall short circuiting the electric field. The way we achieve this is to send the wave down the guide in a zig-zag fashion reflecting it off the walls creating a field that is strongest at the centre of the guide and zero at the walls.

The consequences of bouncing the wave off the wall increases the transmission path length compared to a straight line. This means the velocity of propagation is slower than we would expect. Also because the zig-zag bouncing the wave is no longer TEM. With waveguides we end up with two possible modes of propagation that are different to TEM.

In a waveguide, the electric and magnetic fields are still perpendicular to one another, but only one of these fields is perpendicular to the direction of travel. The names for the two subcategories of this type of transmission are transverse electric (TE) mode and transverse magnetic (TM) mode, depending on which field is transverse to the direction of travel.

Waveguide modes

Looking at waveguide theory it is possible to calculate if there are a number of formats in which an electromagnetic wave can propagate within the waveguide. These different types of waves correspond to the different elements within an electromagnetic wave.

• TE mode: This waveguide mode is dependent upon the transverse electric waves, also sometimes called H waves, characterised by the fact that the electric vector (E) being always perpendicular to the direction of propagation.

• TM mode: Transverse magnetic waves, also called E waves are characterised by the fact that the magnetic vector (H vector) is always perpendicular to the direction of propagation.

• TEM mode: The Transverse electromagnetic wave cannot be propagated within a waveguide, but is included for completeness. It is the mode that is commonly used within coaxial and open wire feeders. The TEM wave is characterised by the fact that both the electric vector (E vector) and the magnetic vector (H vector) are perpendicular to the direction of propagation.

Descriptions about the different types of waveguide modes often indicates the TE and TM modes with integers after them: TE m,n. The numerals represented by m and n are always integers that can take on separate values from 0 or 1 to infinity. These indicate the wave modes within the waveguide. Only a limited number of different m, n modes can be propagated along a waveguide dependent upon the waveguide dimensions and format.

For each waveguide mode there is a definite lower frequency limit. This is known as the cut-off frequency. Below this frequency no signals can propagate along the waveguide. As a result the waveguide can be seen as a high pass filter.

It is possible for many waveguide modes to propagate along a waveguide. The number of possible modes for a given size of waveguide increases with the frequency. It is also worth noting that there is only one possible mode, called the dominant mode for the lowest frequency that can be transmitted. It is the dominant mode in the waveguide that is normally used.

It should be remembered, that even though waveguide theory is expressed in terms of fields and waves, the wall of the waveguide conducts current. For many calculations it is assumed to be a perfect conductor. In reality this is not the case, and some losses are introduced as a result, although they are comparatively small. There are a number of rules of thumb and common points that may be used when dealing with waveguide modes.

• For rectangular waveguides, the TE10 mode of propagation is the lowest mode that is supported.

• For rectangular waveguides, the width, i.e. the widest internal dimension of the cross section, determines the lower cut-off frequency and is equal to ½ wavelength of the lower cut-off frequency.

• For rectangular waveguides, the TE01 mode occurs when the height equals ½ wavelength of the cut-off frequency.

• For rectangular waveguides, the TE20 mode, occurs when the width equals one wavelength of the lower cut-off frequency.

The characteristic impedance of a waveguide is very important in many areas of their use. Like other forms of transmission line, waveguides have a characteristic impedance. By matching the waveguide impedance to the source and load, the maximum power transfer occurs on each occasion.

WAVEGUIDE IMPEDANCE DEFINITION

There are several ways to define the waveguide impedance - waveguide characteristic impedance is not as straightforward as that of a more traditional coaxial line.

• To determine the waveguide impedance by using the voltage to be the potential difference between the top and bottom walls in the middle of the waveguide, and then take the value of current to be the integrated value across the top wall. As expected the ratio gives the impedance.

• Determine the waveguide impedance by measuring the voltage and the power flow within the waveguide.

• The waveguide impedance can be determined by taking the ratio of the electric field to the magnetic field at the centre of the waveguide.

Methods of determining the waveguide characteristic impedance tend to provide results that are within a factor of two of the free space impedance of 377 ohms, i.e. most results for the waveguide impedance fall between about 190Ω and 750Ω.

WAVEGUIDE CUT-OFF FREQUENCY

The exact mechanics for the cut-off frequency of a waveguide vary according to whether it is rectangular, circular, etc, a good visualisation can be gained from the example of a rectangular waveguide. This is also the most widely used form. Signals can progress along a waveguide using a number of modes. However the dominant mode is the one that has the lowest cut-off frequency. For a rectangular waveguide, this is the TE10 mode.

The TE means transverse electric and indicates that the electric field is transverse to the direction of propagation.

It is best to select the waveguide dimensions so that, for a given input signal, only the energy of the dominant mode can be transmitted by the waveguide. For example: for a given frequency, the width of a rectangular guide may be too large: this would cause the TE20 mode to propagate.

As a result, for low aspect ratio rectangular waveguides the TE20 mode is the next higher order mode and it is harmonically related to the cut-off frequency of the TE10 mode. This relationship and attenuation and propagation characteristics determine the normal operating frequency range of rectangular waveguide.

CUT-OFF FORMULA RECTANGULAR WAVEGUIDE

Although waveguides can support many modes of transmission, the one that is used, virtually exclusively is the TE10 mode. If this assumption is made, then the calculation for the lower cut-off point becomes very simple. The cut-off frequency for a rectangular waveguide can be calculated using the formula given below:

Where:

fc = rectangular waveguide cut-off frequency in Hz

c = speed of light within the waveguide in metres per second

a = the large internal dimension of the waveguide in metres

The cut-off frequency is independent of the other dimension of the waveguide. This is because the major dimension governs the lowest frequency at which the waveguide can propagate a signal.

CUT-OFF FORMULA CIRCULAR WAVEGUIDE

Where:

fc = circular waveguide cut-off frequency in Hz

c = speed of light within the waveguide in metres per second

a = the internal radius for the circular waveguide in metres

TRANSMISSION LINE BALUNS

The most popular type of balun and the type most often used by Radio experimenters is the Transmission line type. These are called "Transmission line transformers" (TLT) because they work on transmission line principles hence their inclusion here and not in the chapter on "transformers". Ordinary transformers that have a primary and a secondary are more correctly called "mutually coupled transformers." This is because they are really two or more inductors magnetically coupled and operate on the principle of Faraday's Law.

TLTs are not mutually coupled transformers. These baluns are also widely misunderstood.

In all transmission lines, the characteristic impedance depends on the physical dimensions and the dielectric used. Also all transmission lines, coaxial, parallel, waveguide, stripline and microstrip can be used to make filters and stubs.

I think that some of the misconceptions come from the fact that a transmission line balun looks similar to a transformer. That is, it looks similar to a conventional mutually coupled transformer which also can be used as a balun. Mutually coupled transformer baluns are not broadband - TLT baluns are the preferred choice for radio use.

The name is also confusing. A "Transmission line Balun" does not mean a balun used in a transmission line. Though it is used in a line, this is not what the name means. Such a balun is one that utilises "transmission line principles" for its operation.

Parallel wire (or coaxial cable) lines can be wound on to ferrite cores or even air cores to create a 1:1 balun. When a toroid or rod is wound with a parallel wire transmission line it may appear on casual inspection that it is a conventional mutually coupled transformer - it is not - it is actually a 1:1 Guanella balun though many just refer to this balun as an RF choke.

The two most common baluns used in radio are the "Ruthroff", often referred to as a "voltage balun" and the "Guanella" often referred to as a "current balun".

Figure 38-21 shows a 4:1 transmission line (Ruthroff) balun. This is one type of TLT balun. When we look closely at TLT baluns, we find some very interesting features. Firstly, the magnetic core is nearly passive when it comes to transferring energy between input and output. Ordinary mutually coupled transformers are affected by a degradation in balun action at high frequencies due to the transformer acting more like a capacitor as frequency is increased together with increased core losses. Transmission line baluns, on the other hand, have an astonishingly wide operating bandwidth. They don't appear to have enough windings on them and it seems hard to believe that such small devices can transfer so much power. The power transfer efficiency of a good TLT balun is in the order or 95-98%.

Figure 38-21 shows a 4:1 Ruthroff Balun also sometimes called a voltage balun. Wound on a ferrite toroid with a permeability (µ) of about 140.

Note: having excessive µ causes too much choking reactance and high voltages to be produced across a balun. Not having enough µ will mean that you do not have enough choking reactance.

The reason for this is that the "windings" of a transmission line balun are not windings at all! What we have wound around the toroid is a very short "transmission line". There is no reliance on inductive (magnetic) effects between what "appears" to be windings. These short transmission lines are less than 1/8A. The coiling of the very short line around a toroid has no direct electrical significance for balun action. However, if there are leakage currents down one side of the antenna through the balun, there will be a choking reactance or RF choke effect. These leakage currents are often referred to as "common mode currents". Common mode currents would cause the transmission line to radiate and significantly increase the probability of interference.

The use of a toroid also enables the transmission line to fit into a convenient small space and brings the "opposite" ends together for easy interconnection. Remember we can coil these transformers from parallel or coaxial line. It makes no difference provided the correct impedance of line (Zo) is used. If we can wind them from coaxial line, then it should be obvious that we are not relying on mutual inductance - (the linking of magnetic fields) for the operation of these devices.

The pictorial diagram of the Ruthroff 4:1 balun of figure 38-21 is shown as a construction diagram in figure 38-22.

The characteristic impedance of the coiled transmission line should be the geometric mean of the input and output impedance. (Equation 38-11) This is a 4:1 balun so it could be used to match 200Ω (balanced) to 50Ω (unbalanced). If we did this the characteristic impedance of the short length of transmission line wound around the toroid should be 100Ω as in equation 38-11. Fortunately bifilar (two wires together) of a size form 0.9 to 1.4mm gives a characteristic impedance of close to 100Ω.

What does 4:1 mean?

Now it is often wrongly thought that a 4:1 transmission line balun can be used to match any two impedances with a ratio of 4 to 1. Not so. A 4:1 balun designed to match 200 to 50Ω cannot be used to match say 100 to 25Ω. The characteristic impedance of the line wound onto the toroid is an intrinsic parameter of the design. The Zo of the line wound onto the toroid is a determining factor of the input and output impedances to which the balun can be connected.

In practice, the three impedances (Rin, Rout and Zo of the coiled line) from the equation given above can vary somewhat and the balun will still work. For example, the Zo of the coiled line in the 4:1 balun shown in figure 38-22 should be 100Ω. If you think about what determines the Zo of a transmission line you should realise you can't just wind a balun with any two wires of any diameter and with just any old insulation as it is the size of the wires and their distance apart and the type of insulation between them that determines the Zo of the line that is created.

There are some that go to great lengths to get this just right. In practice, you don't have to be too fussy.

If you look at the balun in figure 38-22, you will notice how the spacing of the line around the toroid varies slightly in a couple of spots. Well, this would mean that there is a variation in impedance at those spots. It would be better if the two wires making up the line were bound together every 10-15 mm with a narrow strip of tape 3-4 mm wide. Having said how it should be ideally, small variations in spacing (and consequent aberrations in Zo) don't seem to matter that much. The SWR of the balun figure 38-22, when terminated in 200Ω, should have an SWR of 1.5:1 or better from 2- 30MHz.

I mentioned that the type of transmission line used to make the balun is not important as long as its characteristic impedance is correct. The right hand side of figure 38-23 shows the same 4:1 Ruthroff Balun made using coaxial cable and coiled around a ferrite rod. Here it is even more obvious that the magnetic core does not influence the transmission line. The core does not participate in the transfer of energy as in a conventional transformer. This is why high power baluns can be such small devices.

Figure 38-24 shows the schematic diagram of a 1:1 Ruthroff balun. The terminals 1 and 3 represent one end of a short parallel or coaxial transmission line and terminals 2 and 4 the other end. I think it is the common use of this type of schematic which leads to the misconception that this type of balun relies on inductive transformer action.

The coil symbols are not meant to imply inductive coupling. However, we do have the property of inductance from end to end. Looking at the schematic you can see that coil (3-4) is in shunt across the output. It appears to be short-circuiting the output. There really is no short circuit because the line element (3-4) does present an ordinary reactance in shunt with the output terminals. The important thing to understand is that this shunting reactance comes from the line element's behaviour as a single conductor. The shunting reactance has nothing to do with the (3-4) element working in conjunction with the (1-2) element to form a transmission line.

This undesirable low frequency shunting action of element (3-4) is reduced if the inductance is increased. A higher inductance in element (3-4) means a greater low frequency response from the balun. How can we increase the inductance of element (3-4) without changing the characteristic impedance of the line? Well, we would wind the transmission line into a coil. If this is done on a toroid, it also brings the ends close together for easier interconnection.

The effect of a ferrite core is to make element (3-4) a more effective RF choke. So we use a core really just to extend the low-frequency response of the balun. As we go up in frequency, the length of the coiled transmission line gets longer in wavelengths. As the length of the line approaches 1/8 wavelength the high frequency response rolls off and the balun becomes ineffective.

GUANELLA BALUN

This type is commonly referred to as a "current" balun. Whatever can be done with a Guanella can be done with a Ruthroff.

I find the Guanella (current) baluns easier to construct and a little more tolerant to variations in impedance.

Guanella and Ruthroff 1:1 Baluns

We use a 1:1 balun when we don't need an impedance transformation. Figure 38-24 shows two popular and effective 1:1 transmission line baluns. I prefer the Guanella type for ease of construction and I think it is the better of the two, but you experiment for yourself. This balun is just what it looks like. It comprises of a transmission line of characteristic impedance equal to the line in which it is to be placed coiled around a ferrite rod or toroid. The coiled transmission line of the Guanella forms a choking reactance for any unwanted common mode currents. The choking reactance isolates the output from the input and only flux cancelling transmission line currents are able to flow. This is the reason why this type of balun has been in recent years referred to as a "current" or "choke balun".

MAKING A 1:1 GUANELLA BALUN 

The Guanella 1:1 balun is a short length of transmission line, of any type, usually wound on a low permeability (100-800µ) toroid or rod. The FT240-43 has a permeability of 800 and provides a very good choking reactance to limit common mode currents.

The characteristic impedance of the short line should be equal to the impedance of the system. If you're using the balun in a 50 ohm system, then the line used to wind the balun should be 50 ohms. The balun should be used in its impedance. It should not be used in a system mismatched by more than 2:1 (VSWR) for best results. As the SWR increases, there will be a higher voltage gradient along the length of the coil transmission line resulting in increased dielectric type losses.

Since the line is short, it is easy to wind the toroid with parallel line or small physical size coaxial cable.

There are two common methods of winding a Guanella 1:1 Balun. These are both shown in figure 38-25. The colours, including the toroid, are only for photographic purposes.

The winding method on the right of the photo is often referred to as a "magic crossover". Its proper name is a Reisert's 1:1 Balun. It really is just a Guanella with a crossover on the toroid. It is not a "magic" anything! Whilst it looks a bit more formidable than the previous photo, electrically these devices will work exactly the same. This method may have an advantage when using coaxial cable and you need to distribute the turns around the toroid to get your 10 turns.

USING FERRITE ROD

Ferrite rod works well, but the impedance may vary toward the upper end of HF. Ferrite rod does work well and it's even less expensive. About $4-5 at most  parts stores and has a permeability of 150. You can wind it with RG58 or similar and have connectors on each end. A popular mounting method is to place the entire assembly into a length of PVC pipe with end caps. Fill the pipe with encapsulating resin if you want to make it water and bug proof.

Lots of ferrite rods and other shapes can be scrounged from scrapped electronic equipment for free. Don't be afraid to try these. If you want to know the permeability just wind a small inductor on to the unknown ferrite and measure the inductance. Then remove the ferrite and measure the inductance again. The amount by which the inductance drops is the permeability of the ferrite. If you measured 2mH and the inductance dropped to 0.01mH when you removed the ferrite then the permeability of the ferrite is 2mH/0.01mH = 100.

The 1:1 Guanella balun is a basic building block for a range of baluns. It is easy to use two 1:1 Guanella baluns to produce a 4:1 (or 1:4) impedance transformation. You can coil two 1:1 baluns on to each side of a toroid. At the low impedance end you connect these two transmission lines in parallel and at the high impedance end (four times higher) the lines are connected in series. This will be obvious if you look at the schematic diagram of the 4:1 Guanella balun in figure 38-26.

In figure 38-26, we simply have two short transmission lines. One line is formed by elements 1-2 and 3-4. A second line is formed by elements 5-6 and 7-8. Each of these lines taken in isolation from a 1:1 Guanella balun.

Each of the two transmission lines has a characteristic impedance of 100Ω. On the low impedance side, they are connected in parallel and give a net impedance of 50Ω and on the high impedance side they are connected in series giving 200Ω. This gives a 200:50 or 4:1 impedance transformation. The two 1:1 baluns can be wound on separate cores for very high power use or for most purposes on each side of a single toroidal core will be fine.

Figure 38-27 is a photograph showing two 1:1 baluns configured to produce a 4:1 transformation. The optimum impedance of the line used to wind this balun is as before the geometric mean of the input and output impedances. So if our 4:1 balun is matching 50 to 200Ω the line impedance making up the balun should be; Zo =√ (200x50)= 100Ω.

We have seen how two simple 1:1 Guanella baluns parallel connected on one side and series connected on the other side can make a 4:1 impedance ratio. By using more parallel series connections other impedance ratios are possible.

With a Guanella balun we are not limited to using two transmission lines. Use your imagination. We could use 3 x 100Ω lines. On one side we series connect to get 300Ω. On the other side we parallel connect to get 100/3 = 33Ω. We then have a 300:33 or for practical purposes a 10:1 balun.

If we had two 200:50 (4:1) Guanella baluns, we could series them one side to get 250Ω and parallel connect them to get 40Ω as shown in figure 38-28. This would give us a balun of 250:40 or 6.25:1.

Many other impedance ratios are possible just by using different series parallel combinations. You can make the balun from different impedance lines and you use multiple baluns as in figure 38-28. You could even try using 300Ω ribbon cable. If you end up with an output or input that is balanced and you want unbalanced then place a 1:1 Guanella balun at that point.

39 - Test Equipment & Measurements

CATHODE RAY TUBES

Figure 39-1 shows a cathode-ray tube (CRT) showing all the important parts.

The CRT is in many respects similar to the ordinary electron tube. The differences arise from the different uses which are made of the electron beam that is attracted to the anode. A controlled beam of electrons was originally called a cathode ray, hence the name "cathode ray tube." Like the ordinary electron tube, there is a heater and cathode to create a space charge, an anode to attract electrons and a control grid to adjust the flow of these electrons. The anode current of a CRT is quite small, typically no more than 1 milliampere. The anode voltage is typically between 10 and 25kV.

The anodes, as shown in figure 39-1, have a small hole, in the end, to allow the electron beam to pass through to the fluorescent screen.

It may seem that the electron beam should be attracted to the anode instead of passing through it. The reason this doesn't happen is that throughout most of its journey the electron beam is surrounded by the anode, so there is no difference of potential sideways across the tube to deflect the beam. The flanged sides of the CRT are coated with a conductive Aquadag coating which is at the same potential as the anode. This serves to keep the beam on track and drain off electrons once they have struck the screen and emitted a photon of light.

The focusing electrode enables the beam to be concentrated into a narrow beam by creating an electrostatic lens (magnetic fields are used in older CRT TV receivers). Two pairs of deflection plates enable the beam to be deflected to any position on the screen by the electric field created between them from an applied deflection voltage (see figure 39-2).

Figure 39-3 shows a drawing of the first cathode ray tube made by J.J. Thompson. The process by which photons of light are emitted when an electron strikes the atoms within the phosphorus coating is called fluorescence. However, there is also another effect called phosphorescence, which has a continuance of the glow after the collision. This characteristic, together with the persistence of human vision, enables waveforms and TV images to be displayed without flicker on a cathode-ray tube.

THE OSCILLOSCOPE

The oscilloscope is basically a graphing voltmeter, it draws a graph of an electrical signal (figure 39-4). In most applications the graph shows how signals change over time: the vertical (Y) axis represents voltage and the horizontal (X) axis represents time. The intensity or brightness of the display is sometimes called the Z axis. This simple graph can tell you many things about a signal.

• You can determine the time and voltage values of a signal.

• You can calculate the frequency of a signal.

• You can see the wave shapes of a circuit represented by the signal.

• You can see if a signal is modulated and determine the depth of that modulation.

• You can tell if timing pulses have occurred at the right place in a signal.

• You can tell if a signal is being distorted.

• You can tell if a signal has a DC bias or if it is pure AC.

• You can tell if the signal has noise in it.

An oscilloscope's front panel includes a display screen and the knobs, buttons, switches, and indicators used to control signal acquisition and display. Front panel controls normally are divided into Vertical, Horizontal, and Trigger sections, and in addition, there are display controls and input connectors. Take a look at figure 39-4 that shows a generic oscilloscope and take note of the three sections Vertical, Horizontal and Trigger.

Oscilloscopes are used by everyone from electronic repair technicians to physicists. They are indispensable for anyone designing or repairing electronic equipment. The usefulness of an oscilloscope is not limited to the world of electronics. With the proper transducer, an oscilloscope can measure all kinds of phenomena. A transducer is a device that creates an electrical signal in response to physical stimuli, such as sound, mechanical stress, pressure, light, or heat. For example, a microphone is a transducer that converts sound to an electrical signal.

An automotive engineer uses an oscilloscope to measure engine vibrations. A medical researcher uses an oscilloscope to measure brain waves.

ANALOGUE, DIGITAL STORAGE AND DIGITAL PHOSPHOR OSCILLOSCOPES 

Electronic equipment can be divided into two types: analogue and digital. Analogue equipment works with continuously variable voltages, while digital equipment works with discrete binary numbers that may represent voltage samples.

Oscilloscopes also come in analogue and digitising types.

Fundamentally an analogue oscilloscope works by applying the measured signal voltage directly to an electron beam moving across the oscilloscope screen (usually a cathode-ray tube, CRT). The back side of the screen is treated with a coating that phosphoresces wherever the electron beam hits it. The signal voltage deflects the beam up and down proportionally, tracing the waveform on the screen. The more frequently the beam hits a particular screen location, the more brightly it glows. This gives an immediate picture of the waveform.

The range of frequencies an analogue scope can display is limited by the CRT. At very low frequencies, the signal appears as a bright, slow moving dot that's difficult to distinguish as a waveform. At high frequencies, the CRT's "writing speed" defines the limit. When the signal frequency exceeds the CRT's writing speed, the display becomes too dim to see. The fastest analogue scopes can display frequencies up to about 1GHz.

In contrast, a digitising oscilloscope uses an analogue-to-digital converter (ADC) to convert the voltage being measured into digital information. The digitising scope acquires the waveform as a series of samples. It stores these samples until it accumulates enough samples to describe a waveform, and then reassembles the waveform for viewing on the screen. The conventional digitising scope is known as a DSO - Digital Storage Oscilloscope. Its display doesn't rely on luminous phosphor; instead, it uses a raster-type screen.

Recently a third major oscilloscope architecture has emerged: the Digital Phosphor Oscilloscope (DPO). The DPO is a digitising scope that faithfully emulates the best display attributes of the analogue scope and provides the benefits of digital acquisition and processing as well. Like the DSO, the DPO uses a raster screen. But instead of a phosphor, it employs special parallel processing circuitry that delivers a crisp, intensity-graded trace.

For both DSOs and DPOs, the digital approach means that the scope can display any frequency within its range with equal stability, brightness, and clarity. The digitising oscilloscope's frequency range is determined by its sample rate, assuming that the probes and vertical amplifiers are adequate for the task.

For many applications either an analogue or digitising oscilloscope will do. However, each type has unique characteristics that may make it suitable for specific tasks.

People often prefer analogue oscilloscopes when it's important to display rapidly varying signals in "real time" (as they occur). The analogue scope's chemical phosphor based display has a characteristic known as "intensity grading" which makes the trace brighter wherever the signal features occur most often. This makes it easy to distinguish signal details just by looking at the trace's intensity levels.

Digital storage oscilloscopes allow you to capture and view events that may happen only once - "transient" events. Because the waveform information is in digital form (a series of stored binary values), it can be analysed, archived, printed, and otherwise processed within the scope itself or by an external computer. The waveform doesn't need to be continuous; even when the signal disappears, it can be displayed. However, DSOs have no real time intensity grading; therefore, they cannot express varying levels of intensity in the live signal.

The digital phosphor oscilloscope breaks down the barrier between analogue and digitising scope technologies. It's equally suitable for viewing high frequencies or low, repetitive waveforms, transients, and signal variations in real time. Among digitising scopes, only the DPO provides the Z (intensity) axis that's missing from conventional DSOs.

HOW OSCILLOSCOPES WORK

To better understand the oscilloscope's many uses, you need to know a little more about how oscilloscopes display a signal. Although analogue oscilloscopes work somewhat differently than digitising oscilloscopes, some of the internal systems are similar.

ANALOGUE OSCILLOSCOPES

When you connect an oscilloscope probe to a circuit, the voltage signal travels through the probe to the vertical system of the oscilloscope. Figure 39-5(A)is a simple block diagram that shows how an analogue oscilloscope displays a measured signal.

Depending on how you set the vertical scale (volts/div control), an attenuator reduces the signal voltage or an amplifier increases the signal voltage. Next, the signal travels directly to the vertical deflection plates of the cathode ray tube (CRT). Voltage applied to these deflection plates to move the electron beam draw a vertical trace where this beam hits the phosphor on the inside of the CRT.

The signal also travels to the trigger system to start or trigger a "horizontal sweep." Horizontal sweep is a term referring to the action of the horizontal system causing the glowing dot to move across the screen. Triggering the horizontal system causes the horizontal time base to move the glowing dot across the screen from left to right within a specific time interval. Many sweeps in rapid sequence cause the movement of the glowing dot to blend into a solid line. At higher speeds, the dot may sweep across the screen up to 500,000 times each second.

Together, the horizontal sweeping action and the vertical deflection action traces a graph of the signal on the screen. The trigger is necessary to stabilise a repeating signal. It ensures that the sweep begins at the same point of a repeating signal, resulting in a clear picture.

In summary, when using an analogue oscilloscope (or any type of oscilloscope), you need to adjust three basic settings to accommodate an incoming signal:

• The attenuation or amplification of the signal. Use the volts/div control to adjust the amplitude of the signal to the desired measurement range.

• The time base. Use the sec/div control to set the amount of time per division represented horizontally across the screen.

• The triggering of the oscilloscope. Use the trigger level to stabilise a repeating signal, or for triggering on a single event.

In addition, analogue scopes have focus and intensity controls that can be adjusted to create a sharp, legible display.

DIGITAL STORAGE OSCILLOSCOPES

Some of the systems that make up DSOs are the same as those in analogue oscilloscopes; however, digitising oscilloscopes contain additional data processing systems (figure 39-5(B)). With the added systems, the digitising oscilloscope collects data for the entire waveform and then displays it.

The first (input) stage of a DSO is a vertical amplifier, just like the analogue oscilloscope. Vertical attenuation controls allow you to adjust the amplitude range of this stage.

Next, the analogue-to-digital converter (ADC) in the acquisition system samples the signal at discrete points in time and converts the signal's voltage at these points to digital values called sample points. The horizontal system's sample clock determines how often the ADC takes a sample. The rate at which the clock "ticks" is called the sample rate and is expressed in samples per second.

The sample points from the ADC are stored in memory as waveform points. More than one sample point may make up one waveform point.

Together, the waveform points make up one waveform record. The number of waveform points used to make a waveform record is called the record length. The trigger system determines the start and stop points of the record. The display receives these record points after being stored in memory.

Depending on the capabilities of your oscilloscope, additional processing of the sample points may take place, enhancing the display.

Note that the DSO's signal path includes a microprocessor. The measured signal passes through this device on its way to the display. In addition to processing the signal, the microprocessor coordinates display activities, manages the front panel controls, and more. This is known as a "serial processing" architecture.

DIGITAL PHOSPHOR OSCILLOSCOPES 

The digital phosphor oscilloscope (DPO) offers a new approach to oscilloscope architecture. Like the analogue oscilloscope, its first stage is a vertical amplifier; like the DSO, its second stage is an ADC. But after the analogue-to-digital conversion, the DPO looks quite different from the DSO. It has special features designed to recreate the intensity grading of an analogue CRT.

Rather than relying on a chemical phosphor as an analogue scope does, the DPO has a purely electronic digital phosphor that is actually a continuously updated data base. This data base has a separate "cell" of information for every single pixel in the scope's display. Each time a waveform is captured (in other words, every time the scope triggers), it is mapped into the digital phosphor database's cells. Each cell representing a screen location that is touched by the waveform gets reinforced with intensity information. Others do not. Thus intensity information builds up in cells where the waveform passes most often.

When the digital phosphor database is fed to the oscilloscope's display, the display reveals intensified waveform areas, in proportion to the signal's frequency of occurrence at each point - much like the intensity grading characteristics of an analogue oscilloscope (unlike an analogue scope, though, the DPO allows the varying levels to be expressed in contrasting colours if you wish). With a DPO, it's easy to see the difference between a waveform that occurs on almost every trigger and one that occurs, say, every 100th trigger.

Importantly, the DPO uses a parallel processing architecture to achieve all this manipulation without slowing down the whole acquisition process. Like the DSO, the DPO uses a microprocessor for display management, measurement automation, and analysis. But the DPO's microprocessor is outside the acquisition/display signal path (figure 39-5), where it doesn't affect the acquisition speed.

SAMPLING METHODS 

Digitising oscilloscopes - DSO or DPO - can use either real-time, interpolated real-time, or equivalent-time sampling to collect sample points. Real-time sampling is ideal for signals whose frequency is less than half the scope's maximum sample rate. Here, the oscilloscope can acquire more than enough points in one "sweep" of the waveform to construct an accurate picture. Note that real-time sampling is the only way to capture single-shot transient signals with a digitising scope.

When measuring high frequency signals, the oscilloscope may not be able to collect enough samples in one sweep. There are two solutions for accurately acquiring signals whose frequencies exceed half the oscilloscope's sample rate:

• Collect a few sample points of the signal in a single pass in real-time mode and use interpolation to fill in the gaps. Interpolation is a processing technique to estimate what the waveform looks like based on a few points.

• Build a picture of the waveform by acquiring samples from successive cycles of the waveform, assuming the signal repeats itself (equivalent time sampling mode).

REAL-TIME SAMPLING WITH INTERPOLATION

Digitising oscilloscopes take discrete samples of the signal which can be displayed. However, it can be difficult to visualise the signal represented as dots, especially because there may be only a few dots representing high frequency portions of the signal. To aid in the visualisation of signals, digitising oscilloscopes typically have interpolation display modes.

In simple terms, interpolation "connects the dots." Using this process, a signal that is sampled only a few times in each cycle can be accurately displayed. However, for accurate representation of the signal, the sample rate should be at least four times the bandwidth of the signal.

Linear interpolation connects sample points with straight lines. This approach is limited to reconstructing straight-edged signals such as square waves.

The more versatile sin(x)/x interpolation connects sample points with curves (figure 39-6). Sin(x)/x interpolation is a mathematical process in which points are calculated to fill in the time between the real samples.

This form of interpolation lends itself to curved and irregular signal shapes, which are far more common in the real world than pure square waves and pulses. Consequently, sin(x)/x interpolation is the preferred method for most applications.

DISPLAY CONTROLS

Display systems vary between analogue oscilloscopes and digitising scopes, including both DSOs and digital phosphor oscilloscopes (DPOs). Common controls include:

• An intensity control to adjust the brightness of the waveform. As you increase the sweep speed of an analogue oscilloscope, you need to increase the intensity level.

• A focus control to adjust the sharpness of the waveform. Digitising oscilloscopes may not have a focus control.

• A trace rotation control to align the waveform trace with the screen's horizontal axis. The position of your oscilloscope in the earth's magnetic field affects waveform alignment. Digitising oscilloscopes may not have a trace rotation control.

• On DPOs, a contrast control.

• On many DSOs and on DPOs, a colour palette control to select trace colours and intensity grading colour levels.

• Other display controls may let you adjust the intensity of the graticule lights and turn on or off any on-screen information (such as menus).

VERTICAL CONTROLS

Use the vertical controls to position and scale the waveform vertically. The oscilloscope also has controls for setting the input coupling and other signal conditioning, described later in this section.

The vertical position control lets you move the waveform up or down to exactly where you want it on the screen.

The volts per division (usually written volts/div) setting varies the size of the waveform on the screen. A good general purpose oscilloscope can accurately display signal levels from about 4 millivolts to 40 volts.

The volts/div setting is a scale factor. For example, if the volts/div setting is 5 volts, then each of the eight vertical divisions represents 5 volts and the entire screen can show 40 volts from bottom to top (assuming a graticule with eight major divisions). If the setting is 0.5 volts/div, the screen can display 4 volts from bottom to top, and so on. The maximum voltage you can display on the screen is the volts/div setting times the number of vertical divisions. (Recall that the probe you use, 1X or 10X, also influences the scale factor). You must divide the volts/div scale by the attenuation factor of the probe if the oscilloscope does not do it for you.

INPUT COUPLING

Coupling means the method used to connect an electrical signal from one circuit to another. In this case, the input coupling is the connection from your test circuit to the oscilloscope. The coupling can be set to DC, AC, or ground. DC coupling shows all of an input signal. AC coupling blocks the DC component of a signal so that you see the waveform centred at zero volts.

The ground setting disconnects the input signal from the vertical system, which lets you see where the zero-volt level is on the screen. With grounded input coupling and auto trigger mode, you see a horizontal line on the screen that represents zero volts. Switching from DC to ground and back again is a handy way of measuring signal voltage levels with respect to ground.

MATH OPERATIONS 

An oscilloscope may also have operations to allow you to add waveforms together, creating a new waveform display. Analogue oscilloscopes combine the signals while digitising oscilloscopes create new waveforms mathematically. Subtracting waveforms is another math operation. Subtraction is possible with analogue oscilloscopes by using the channel invert function on one signal and then using the add operation. Digitising oscilloscopes typically have a subtraction operation available.

HORIZONTAL CONTROLS 

Use the horizontal controls to position and scale the waveform horizontally. Using the power of their internal processors, digitising oscilloscopes offer many advanced math operations: multiplication, division, integration, Fast Fourier Transform, and more.

Position and Seconds per Division 

The horizontal position control moves the waveform left and right to exactly where you want it on the screen.

The seconds per division (usually written as sec/div) setting lets you select the rate at which the waveform is drawn across the screen (also known as the time base setting or sweep speed). This setting is a scale factor. For example, if the setting is 1ms, each horizontal division represents 1ms and the total screen width represents 10ms (ten divisions). Changing the sec/div setting lets you look at longer or shorter time intervals of the input signal.

TIME BASE SELECTION

An oscilloscope has a time base usually referred to as the main time base and it is probably the most useful. Many oscilloscopes have what is called a delayed time base - a time base sweep that starts after a pre-determined time from the start of the main time base sweep. Using a delayed time base sweep allows you to see events more clearly or even see events not visible with the main time base sweep alone. The delayed time base requires the setting of a delay time and possibly the use of delayed trigger modes and other settings not described in this book. Refer to the manual supplied with your oscilloscope for information on how to use these features.

Modern oscilloscopes have many more features than those discussed here. However we have covered the main features of most oscilloscopes. Oscilloscopes today are not expensive but if you do not need one often you may still not be able to justify the cost. This is where many clubs and enthusiast's organisations can often play a big role by purchasing equipment for members and loaning it out.

SPECTRUM ANALYSER 

The oscilloscope measures the amplitude of a signal against time. A spectrum analyser measures the amplitude of a signal against frequency. Figure 39-7 shows various waveforms as they would be seen on an oscilloscope and the same signal on a spectrum analyser. A spectrum analyser is somewhat like a sophisticated scanning receiver with the output display on a graph of the frequency of and amplitude of the signal being received.

The spectrum analyser can be set to scan between two frequencies. For example you might want the analyser to scan the entire FM broadcast band in which case you would set the frequency span to go from 88 to 108MHz and connect an antenna to the analyser input. What you would see on the display would be spikes representing all the broadcast transmitters in the area. The height of each spike would represent the amplitude or strength of each station received. The IF bandwidth of the analyser is very adjustable. Narrow bandwidth widths increase the sensitivity of the analyser just as it does in any superheterodyne receiver. How fast the analyser scans a range of frequencies can also be adjusted. The amplitude on the display is calibrated in dBm, i.e. decibels relative to a milliwatt.

When you find the particular FM station you are looking for on the analyser you can then then zoom in on that station by reducing the start and end frequencies (span) to include just that station. Then by adjusting the IF bandwidth and gain you can then see the FM signal in more detail. Figure 39-7(b) shows an FM signal seen on an oscilloscope and a spectrum analyser. The analyser signal on the right shows a carrier null and the side frequencies of an arbitrary FM signal. Can you see how the frequency domain gives us useful information that the time domain does not?

There is some confusion when looking at the modulation envelope of an AM (DSB) signal about what the carrier is doing (figure 39-7(c)). It does appear on the oscilloscope as if the carrier is rising and falling in amplitude. This, as we have learned, is not the case. The carrier in a DSB signal is constant and what changes power is the sidebands. Look at the analyser display of the same signal. If you could see this in real time the amplitude of the carrier in the centre would be constant and the amplitudes of the upper and lower sidebands would vary with modulation.

Parasitics, harmonics, intermodulation and other non-linearity problems are much easier to find and identify on an analyser. Figure 39-7(d) shows a 1MHz square wave on both devices. A square wave is rich in harmonics and you can see these harmonics easily 1MHz apart on the analyser.

When a spectrum analyser is used on an antenna to look for interference it is important to remember that it is a receiver and like any other receiver, susceptible to overload, blocking, distortion and intermodulation. Often one or more cavity filters are connected to the analyser to keep out or reduce the level of unwanted signals and prevent erroneous measurements.

SPECTRUM ANALYSER WITH TRACKING GENERATOR

Most spectrum analysers today come with an inbuilt tracking generator. We explained how the analyser sweeps or scans between two frequencies determined by the operator. Suppose we had an oscillator that was synchronised with the spectrum analyser so that when the analyser was tuning through 140MHz the oscillator outputs a signal on 140MHz. As the analyser scans the oscillator follows it. When the analyser is on 141MHz so is the oscillator. As the analyser moves from 140-150MHz (or whatever chosen span) the oscillator moves with it. Such an oscillator is called a Tracking Generator.

Suppose the tracking generator was set to have an output power of 0dBm (one milliwatt), what would you see on the display of the spectrum analyser? No matter what frequency the analyser is scanning through the tracking generator is sending to the analyser input, a constant signal level of 0dBm. You would see a straight line on the display.

Figure 39-8 shows the arrangement just discussed. We have connected the RF input of the spectrum analyser to the tracking generator output using a patch lead. We will presume the output of the tracking generator is set to 0dBm. Let's call this our reference level.

What we see on the analyser display is a straight line as shown and it is at a power level of 0dBm. Does not seem like we have achieved much yet. What if we were to remove the patch lead and connect a frequency selective device like a filter? The filter would attenuate some of the frequencies going between the tracking generator and the analyser. We would know how frequencies were being attenuated as we would no longer see a straight line on the display. The display would now show a selectivity graph of the device under test (DUT).

This setup is shown in figure 39-9. The tracking generator has been connected to a pair of notch filters allegedly tuned to 145MHz. The notch (bandstop) curve can be seen on the display. The centre frequency to which the notch is tuned can be seen on the middle of the display which is 145MHz. If the notch was off frequency we would just have to adjust the tuning rods while looking at the display to move the curve to the centre.

We know the maximum depth of the notch from the reference level of 0dBm. The graticule is calibrated in 10dB divisions, though this can be changed with the controls. The insertion loss outside the notch can be read directly off the display.

Using a spectrum analyser with an inbuilt tracking generator is the best way to tune cavity filters, diplexers, isolators and any other frequency tuneable device. This has by no means been an exhaustive treatment of oscilloscopes and spectrum analysers. To do so would be a book in itself. Many radio clubs have test equipment for use by the members, though they will probably want to know that you can safely use it before loaning it out. Some measurements like the latter are very safe. It is impossible to damage the equipment, but when performing transmitter measurements great care must be taken not to exceed the test instrument's maximum input power. Excessive power, even for a fraction of a second, can do very expensive damage to test equipment. The best way to learn is to use the test equipment and ask for guidance if needed.

SSB MEASUREMENTS

The two-tone test signal comprises of two non-harmonically related sinusoidal audio tones of equal amplitude.

These tones are used to modulate an SSB transmitter and conduct linearity and power measurements.

Why use a two-tone test signal?

The two-tone test signal is the standard modulating signal used when conducting tests on an SSB transmitter. If an SSB transmitter is voice modulated then the output waveform, as seen on an oscilloscope, would be unpredictable and dependent on the voice characteristics of the operator. The peak power measured in this way would vary from one operator to the next. The two-tone signal overcomes this problem by providing a standard test modulating source which produces a predictable wave shape on an oscilloscope, enabling tests to be repeated.

Because the two audio tones are not harmonically related then any mixing products of the tones are due to non-linearity in the SSB system.

Figure 39-10(A) is a correctly adjusted SSB transmitter as would be seen using a two tone test modulating signal and an oscilloscope. Notice the sharp crossover "X", for this reason this modulation envelope is sometimes a called a Bow-tie.

Figure 39-10(B) is the result of cross over distortion caused by incorrect bias on a push pull amplifier. Lastly figure 39-10(C) shows flat topping which is a result of overdriving the linear SSB amplifiers. Flat topping produces splatter interference on adjacent frequencies and of course is to be avoided.

When a two-tone signal is used to modulate an SSB transmitter and the output of the transmitter checked with a spectrum analyser, then only those radio frequencies representing the two tones should be present if the transmitter is perfectly linear. In practice other signals will be present in the output - these will be the result of the two discrete tones mixing due to some non-linearity within the transmitter. The level of these mixing products is shown on specifications as intermodulation distortion products (IMD). The frequencies of the two-tone signal are not important provided they are sinusoidal, equal amplitude, not harmonically related and fit within the audio passband of the transmitter under test.

POWER MEASUREMENTS

Measurement of RF power is perhaps not as simple as it should be as often power measurement is defined by radio regulation. Let's start out with an unmodulated carrier wave. Now this could be a straight carrier wave from a CW or FM transmitter or it could be an SSB transmitter modulated with a single tone. All of these would produce a radio frequency sinewave shown in figure 39-12. This would be the display shown on an oscilloscope. Where is the envelope of this wave? The envelope is the extreme excursions that the signal, in this case, a sinewave takes. So the envelope is the top and bottom lines drawn above and below the carrier wave. In this example we have set the peak carrier voltage to 100V as shown.

If we were to zoom in on this carrier wave so as to see just a couple of cycles we would see the drawing at the bottom of figure 39-12. The waveform has a Peak, Peak-to-Peak and RMS values. What if we wanted to calculate the peak envelope power? To calculate power with AC we always have to use the RMS value. The RMS value as we have learned is the effective value of a sinewave that does the real work as if it was DC. Since radio systems usually have an arbitrary impedance of 50Ω we can use that as resistance in P=E2/R.

With this waveform the peak envelope power will be the same no matter where we measure it as the peak envelope power does not change.

P= (Ex0.707)2/50Ω = 99.96 watts or close enough to 100W PEP.

To be clear here, this is the PEP of the carrier wave not the mean power.

What if we were to amplitude modulate the carrier wave (AM or DSB)?

At 100% modulation the voltage peaks of the envelope will double to twice their unmodulated value and fall theoretically to 0V. We have to be careful not to hit zero volts so we do not cause distortion. So what is the peak envelope power (PEP) of our 100% AM (DSB) modulated carrier wave?

As before P= (Ex0.707)2/50Ω = 400W PEP

So an AM (DSB) transmitter with a 100W carrier has a PEP power of 400W. We are not used to thinking of DSB as peak power but usually refer to such a transmitter as mean power. Obviously the mean power must be much less than the peak. Just take a look at the waveform in figure 39-13. Most of the time the peak power is not present and power often falls to zero. The mean power for DSB is 37.7% of the peak. This can be checked by using the equation for the power distribution in a DSB wave.

Pt=Pc+0.5m2Pc

Where

Pt = the total mean power transmitted

Pc= the carrier power

m = the modulation from 0-1 (0-100%)

Inserting the values in the equation we get:

Pt= 100 + (0.5 x 1 x 1 x 100) = 150 watts mean.

So a 100W carrier has a total PEP of 400W and 150W mean power. 

Please be aware that you only have that 400W PEP for a very brief instance on voice peaks if at all. It is time to look at single side band where we do use PEP to measure power.

Figure 39-14 shows an SSB signal fully modulated. How do we know for sure that it is fully modulated? Well we don't and we will come to that shortly. This is an SSB signal modulated with voice modulation as seen on an oscilloscope. The peak envelope voltage is shown as 200V. The same as we had earlier with DSB.

It is obvious that with voice modulation we do not get the peak power very often. It only occurs on voice peaks. We could improve this slightly by compressing the audio prior to modulation but this would not change how often the peak power reached a peak by much at all.

The PEP power of this SSB signal, using Ohm's Law and 50 ohms impedance:

PEP= ERMS2/R = (200 x 0.707)2/500 = 400W PEP

This the same PEP that we got with a 100V carrier DSB modulated. So when are you actually transmitting 400W? It is not that often is it?

So if you are using a mean reading power meter on SSB and say you are expecting 100W PEP the mean reading power meter is going to read very much less as it cannot follow the rapid and brief excursions to 100W PEP. If you have a power meter with a "Peak Hold" capability it will read much higher - close to what should be the peak power. If you have such a meter are you really transmitting any more power? No, peak power is very transient. The other problem with looking at the waveform of figure 39-14 is knowing when you have adjusted the audio modulating power to achieve 100% modulation. A better method is to use a two-tone test modulating signal.

Using a two-tone test signal the Peak Envelope Power PEP is twice the mean power. 

We have already discussed the two-tone test signal but I have placed it here again to emphasise its usefulness in power measurement. When you have a two-tone modulated signal correctly adjusted you can measure the power with a mean reading power meter and simply double that reading to get the peak envelope power (PEP).

The modulation shape also tells you easily if you have flat topping or cross-over distortion. If you already own an oscilloscope and it does not have a built in two-tone generator I would encourage you to build or otherwise obtain one to add to the versatility of your oscilloscope.

THE VSWR METER

The following description of the operation of a VSWR meter is given for sake of completeness and is not required for examination purposes. However, you may be required to identify the schematic diagram.

Refer to figure 39-16. A forward moving RF wave travelling through the VSWR meter from the transmitter to antenna will induce small forward-moving waves into L1 and L2.

The forward wave induced into L2 will arrive at R2 and be totally dissipated, since R2 is equal to the characteristic impedance formed by the centre conductor in the VSWR meter and L2. However, the forward moving wave induced into L1 will be rectified by Dl and this rectified current will produce a DC voltage across C1. The level of the voltage across C1 is directly proportional to the forward voltage.

If the transmission line is not terminated in the correct impedance, then a reflected wave will be present which will travel through the VSWR meter from antenna to transmitter and induce currents into L1 and L2.

The reflected wave induced into L1 is absorbed by R1, but the reflected wave induced into L2 is rectified by D2 and a DC voltage is developed across C2, which is directly proportional to the voltage of the reflected wave.

So it can be seen that the upper circuit consisting of L1, C1 and D1, is only responsive to forward waves while the lower circuit consisting of L2, C2 and D2, will only respond to reflected waves.

The switch S1 enables the operator to switch between the forward and reflected voltage readings. Meter M1 will read the voltage across C1 and C2, being the forward and reflected voltages respectively.

Though this meter could be calibrated to measure forward and reflected voltage, it is more commonly used to only measure VSWR and the operator is frequently unaware that it is, in fact, a forward and reflected voltage meter.

For VSWR measurements, the operator switches S1 to the forward position and, while transmitting, adjusts R3 for full scale deflection on M1. The forward voltage is now referenced to full scale. S1 is then switched to the reflected position and the pointer on M1 will directly read the coefficient of reflection (K). If the forward voltage and reflected voltage are equal (open or short circuit termination), then the reflected reading will be full scale, indicating a K of 1. If there is no reflected voltage (perfectly matched system), then there will be no deflection of M1, indicating a K of zero. If 50% of the forward voltage wave is reflected, then M1 will indicate half scale deflection or a K of 0.5.

Therefore, you see, the most common type of VSWR meter really measures the coefficient of reflection. However, there is a simple relationship between K and VSWR:

For example, suppose the reflected voltage came to half scale or K=0.5. What is the VSWR?

This explains why all (non-amplified) VSWR meters have '3' calibrated at centre scale. If you want to make your VSWR meter more useful, just calibrate the scale from 0 to 1 using rub on lettering and it will now double as a coefficient of reflection meter.

THE REFLECTOMETER

In the schematic diagram of the VSWR meter (figure 39-16), the section of the circuit consisting of the two pickup inductors (L1 and L2) and their associated terminating resistors, is, in fact, a dual reflectometer since it has two loops for simultaneous measurement of forward and reflected voltage.

A reflectometer can be made or purchased as a stand-alone test device. To use a reflectometer, a level indicating device such as a power meter or RF voltmeter must be added. Some instruments have a moving coil meter calibrated in watts connected to each port of a dual reflectometer.

VSWR METER (BRUENE BRIDGE)

The Bruene bridge is often used in directional wattmeters. The bridge is able to sense the forward and reflected waves proportionately, and indicate the corresponding power levels. It does this by using the important fact that forward voltage and current (EF and IF) are always in phase, everywhere along the line, while ER and IR are always 180° out of phase.

Figure 39-17 shows a simplified Bruene bridge directional sensor. The sampled RF voltages proportional to the mainline voltage and mainline current (EV and EI) can be either added or subtracted. The diode detector displays the resultant voltage.

If the instantaneous voltage on the line is V, and the instantaneous current is I, the capacitive voltage divider C1 and C2 takes a sample of the voltage (EV) and the current transformer T1 takes a sample of the current, developing a voltage EI across the load resistor R. The reversing switch 'S' allows us either to add the two instantaneous RF voltages EV, and EI or to subtract them. A diode detector detects the amplitude of the resultant RF waveform.

When EI and EV are added in phase, we are sensing the forward wave in the transmission line. When EI and EV are added in antiphase we are sensing the reflected wave.

To satisfy the condition that there is no reflected wave from a matched load, the circuit needs to be proportioned to make EV = EI under these conditions, so that they subtract to zero. That is how a directional coupler is made, initially by designing the capacitor ratio and transformer turns ratio to make EV and EI approximately equal, and finally by adjusting C1 or C2 to equalise them exactly.

The meter can be calibrated for forward and reflected power or VSWR. Figure 39-17 is not a very practical form of the Bruene bridge. The double pole double throw switch floating at RF potential is not desirable. This design was used to make the explanation of the circuit operation clearer. This design, "as is" of the Bruene bridge will work but you will find other designs in construction handbooks and articles that do away with the need for the switch.

THE DIP OSCILLATOR

A dip oscillator is just a portable hand held oscillator. The operating principle works as follows. The dip oscillator is set to oscillate at a known frequency, say 14MHz. Now suppose the dip oscillator is moved close to a circuit resonant on 14MHz. Remember when we talked about bringing a vibrating tuning fork close to another non-vibrating tuning fork on the same resonant frequency? Energy is transferred from one tuning fork to the other. A dip oscillator running on 14MHz and brought close to a tuned circuit on 14MHz will result in RF power being transferred from the dip oscillator to the resonant circuit under test. The resonant circuit under test could be an antenna or an LC circuit. So, the dip oscillator then is ideal for finding the resonant frequency of an antenna or an LC circuit. Energy is not transferred from the dip oscillator to an external circuit unless the external circuit is mutually resonant with the dip oscillator. The dip oscillator has a meter - a current dip on the meter indicates mutual resonance.

Refer to figure 39-18. When the circuit is oscillating, an RF voltage will appear across the resistor between the gate and ground. Because of the rectifying action of the gate-source junction, a DC current will flow through this resistor and indicate on the meter. In a free running oscillator, the gate voltage is high and therefore the current is high. When the coil of the resonant circuit is coupled to an external resonant circuit, power will be transferred when the two circuits are mutually resonant. This will be indicated by a dip in the gate current meter. The calibrated dial will indicate the frequency of the external circuit.

A dip oscillator only measures resonant frequency. However, if one component of a resonant circuit is known (L or C) then the resonant frequency can be measured and the value of the unknown component worked out mathematically.

I have often seen an exam question which tests for the function of a dip oscillator. One of the answer options might be to 'measure capacitance' or 'measure inductance'. Don't get caught here; a dip oscillator only measures resonant frequency. Capacitance or inductance may be calculated from knowing the resonant frequency, but the dip oscillator does not measure L or C directly.

RADIO FREQUENCY PROBE 

An RF probe enables a DC Voltmeter to measure RF voltages. It an also allows oscilloscope and  to measure RF voltages exceeding its bandwidth. An RF probe is very simple to make, inexpensive and small in size. An RF probe can be built into a metal pen case or something similar. It is desirable to shield the circuit but not essential. The schematic diagram of an RF probe is shown in figure 39-19.

The RF probe consists of a simple half wave rectifier and filter. The probe is designed not to excessively load the circuit being measured. For the best frequency response, a point contact diode should be used (IN34 or similar). For improved RF immunity the circuit should be in a shielded case and the lead to the meter or oscilloscope should also be shielded. However this is only necessary when the probe is to be used in a place where there are energetic electromagnetic fields such as the output of a radio transmitter.

By measuring the voltage developed across a known load (say a dummy load of 50 ohms), the output power can then be calculated from P = E2/R, where E is the RMS voltage and P the average power. Power levels as low as a few milliwatts at frequencies up to several hundred megahertz can be measured using an RF probe

The probe should enable your multimeter or oscilloscope to read voltage from several millivolts and at frequencies well into VHF. You make a calibration chart if you want more accuracy, though when reading RF voltages, you are not always concerned with the exact value of a voltage. For example, when peaking a tuned circuit in a transmitter you are looking for the peak voltage only.

You may have already noticed that the probe is simply an RF detector or half wave rectifier. The RF probe could be in a shielded box with its own microammeter and used as a relative field strength meter. The probe tip could then be replaced with a telescopic antenna.

If you have an oscilloscope or digital multimeter you are really missing out on some functionality if you do not have an RF probe.

FUNCTION GENERATOR

A function generator is a type of signal generator that is able to generate waveforms with common shapes. High end function generators are sometimes called Wave Generators. Unlike RF signal generators and some others that only create sinewaves, the function generator is able to create repetitive waveforms with a number of common shapes.

Typically a function generator may be able to vary the characteristics of the waveforms, changing the length of the pulse, i.e. the mark space ratio, or the ramps of the different edges of a sawtooth waveform, but it will only be able to create the waveforms that are built into the function generator. Another capability of most function generators is to produce modulated signals such as DSB, SSB, FM, PSK, FSK. Professional function generators can produce IQ and QAM signals.

Function generators vary in price from under $AUD100 to $AUD20K. For experimenter and hobbyist purposes a very useful function generator can be obtained for under $AUD200. Models around this price range have enough in-built waveforms, voltage output and frequencies up to about 60MHz making them very useful for repairers, experimenters and hobbyists. The author uses a function generator that cost $AUD120 and the features of that generator will be described here.

Any device deserving of the name "function generator" will at the very least be able to produce the waveforms shown in figure 39-20. You would also expect to be able to vary the amplitude in the order of some volts. The frequency range will depend on your budget but you can and should expect up to 60MHz for a hobbyist model. There should be two channels so that you can produce two separate waveforms at the same time. Most function generators will allow simple modulation of the waveforms. With square and pulsed waveforms you should be able to adjust the duty cycle or the mark-space ratio. Every function generator should have the ability to make the signal produced sweep between given start and stop frequencies. Some generators may allow you to ramp a signal up or down in amplitude over a given time. Today even budget generators allow you to program your own "arbitrary" waveforms. You will have in most cases a USB interface between your function generator and your computer for use with its accompanying software.

DIRECT DIGITAL SYNTHESIS

Most modern, even budget, function generators use direct digital synthesis (DDS). As the name implies these generators use digital technology to generate the waveforms.

DDS uses a phase accumulator, a look-up table containing a digital representation of the waveform, and a digital to analogue converter (DAC). The phase accumulator moves to another position each time it receives a clock pulse. The next position in the look-up table is then accessed giving the digital value for the waveform at that point. This digital value is then converted into an analogue value using a digital to analogue converter, DAC.

Digital function generators are able to offer high levels of accuracy and stability because the clock for the system is crystal controlled. Also digital function generators provide a high spectral purity and low phase noise. A DDS based digital function generator can also can be swept over a much wider frequency range than an analogue function generator. It can also perform a number of other functions such as phase continuous frequency hopping because of the action of the direct digital synthesiser.

SWEEP FUNCTION GENERATOR

A sweep function generator is simply one that can sweep its frequency. Typically the more versatile sweep function generators utilise digital technology, but it is also possible to use analogue versions as well.

Sweep function generators may be able to sweep over ranges of up to 100:1 or more, although this is very dependent upon the actual generator type in question. Speed of the sweep may also be important. Another feature that may be of importance is whether the sweep is linear or logarithmic. Some function generators may have a switch for this.

OUTPUT LEVEL

The output level on most function generators will be continuously variable. Often it will be able to easily adjust so that it is (Transistor-Transistor-Logic) TTL compatible. However maximum limits will vary from generator to generator. Typical maximum levels may be in the vicinity of 10 volts peak-to-peak.

As the frequency is increased you can expect the output voltage amplitude to fall. This is normal for most generators.

MODULATION

The ability to modulate the waveform is extremely useful for RF fault finding in radio transmission and reception. Almost all function generators will produce the common modulation types. Receiver and transmitter alignment as well as fault location is made easy by injecting a signal into an IF amplifier on the correct frequency and using the appropriate modulation type.

OUTPUT IMPEDANCE 

In many instances the load that can be driven by the function generator is of importance. The figure is measured in ohms, and is typically 50Ω. Any output level readings will assume this, and at this impedance the output will drop by half from its no load value.

DC OFFSET

Many RF signals are not alternating voltage. Most RF amplifying devices do no amplify AC. Adding DC offset bias to an AC signal we produce varying a DC. Most function generators will allow you to apply a DC offset to the generated signal. Again this is very useful when testing or fault finding.

FREQUENCY RANGE

For a budget function generator at the time of writing you can expect a sinewave frequency range up to 60MHz. If you want a higher frequency range you will need to invest more. I find 60MHz high enough when you consider the intermediate frequencies used in radio communications. With the sweep function it is easy to check filters and IF stage bandwidths and adjustments. You can expect the highest frequency to be less when using waveforms other than a sinewave.

This has been an overview of function generators for the general hobbyist. A function generator really is a useful tool to have. It is also a very useful learning tool and well worth an investment of less than two hundred dollars. It was not long ago when such an instrument was economically out of bounds for most hobbyists. The cost of electronic test equipment has truly plummeted and the instruments are feature rich.

DIGITAL MULTIMETER - DMM

Next to basic tools the piece of test gear that is an absolute "must have" is a digital multimeter (DMM). Choosing the right DMM for you requires thinking about what you will be using it for. Evaluate your basic measurement needs and job requirements and then take a look at special features/functions built into many DMMs. Think about whether you need it for basic measurements or for more advanced troubleshooting options. You can get very inexpensive DMMs (that can be dangerous; we will discuss that) for less than $AUD10 and a very good meter that is safe and will do most measurements very well for $AUD80. Then you can get professional meters that are extremely accurate and perhaps made for use in explosive environments for many hundreds of dollars.

Inexpensive meters are great for training. Particularly if you have had no experience with measurements. Get a cheap one for a few dollars to play with and make simple low voltage, current and resistance measurements. The cost is less than a magazine and you will learn a lot and you may damage it but these lessons are worth the price you paid. However, I advise that under no circumstances should you use these meters anywhere there are high voltages such as household electricity. If you are not sure ask a competent person for advice. Some of the cheap DMMs have incorrect information printed on them. Don't trust any low cost meters for use on voltages above 50VDC. A good set of meter leads for a good meter can cost more than a cheap meter with leads. Good meters meet standards that we will talk about. No meter, even a good one, can prevent you from getting an electrical shock or worse.

There are a lot of different requirements for a DMM used by a motor vehicle mechanic, electrician, auto electrician and a radio technician, to name just a few. A meter used in a mechanical workshop probably needs to be able to deal with some physical abuse as though it did not matter. Accuracy to within a small fraction of a volt will most likely do but it still needs to be a sturdy well made meter. A laboratory technician may need very high accuracy. A radio technician might need high accuracy and RF immunity.

So it is worth taking your time and working out what you need and it should also last you for many years.

I purchased my first DMM almost 50 years ago. Then it was one of the first ever made. It cost an arm and a leg to buy. It just measured voltage, current and resistance. It was accurate by standards of the day. However I have not used it for decades. I still have it though and it still works! I did not destroy it but I think that was more good luck than skill.

Figure 39-22 shows an average but good DMM. The DMM we will discuss is what you can expect and what you should look for when choosing a DMM for basic electrical and radio work. The price of all test equipment varies with time and it always seems to be coming down. At the time of writing $AUD80 buys you a very good DMM that, if you look after it, will last a lifetime.

DMM FIRST LOOKS

So you have decided to buy a DMM. Pick the DMM up and hold it firmly in each hand and give it a flex test to determine how robust the case is. It should feel firm and not twist much at all and certainly make no sounds as if the top and bottom covers were loose. Take a look or more to the point have a touch feel of the plastic case. You can usually tell if a case is hard and brittle just by feeling it. A brittle case means it is not going to withstand being dropped.

All DMMs have a continuity test and usually an audible alarm when there is continuity. An audible alarm for continuity for me is a must as I do not want to be looking at the meter display to know if I have continuity between the probes. Insert the probes, usually into common (COM) and Ω and touch the probe tips. You should hear an audible tone. Tap the tips rapidly and the audible tone should stop and start cleanly. If this does not happen then the probes may be of poor quality. The leads should be soft and not feel stiff. The ends of the leads that plug into the meter should have no exposed metal as is the case with banana type plugs. Better plugs are fully insulated, you will see no metal.

Meter leads have some resistance. Does the meter have an automatic method of "zeroing" out lead resistance? The REL button usually does this. The same goes for capacitance, if the meter has provision for capacitance measurements, you will want to zero out the lead capacitance particularly when measuring very low values of capacitance.

Do you have a requirement for a back-lit display? If you use the meter in low light conditions you may not be able to see an LCD display clearly if it is not back-lit. Check the meter stand. Does it hold the meter at a good angle and is the meter stable when on the stand?

The meter should be fused with quality fuses. Specially designed "high-energy" fuses are designed to keep the energy generated by excessive current short within the fuse enclosure, thus protecting the user from electric shock and burns. These high-energy fuses are designed to limit the length of time the energy is applied and the amount of oxygen available for combustion. Fuses can not only be designed to open at a specified constant current, but at an instantaneous high current as well.

IEC CATEGORIES

There are four categories (figure 39-23) defined by International Electrotechnical Commission (IEC) that all manufacturers of DMMs are required to mark their products with. These are CAT I, CAT 11, CAT Ill and CAT IV. With these markings one can easily identify what the maximum transient voltage is that the meter can safely withstand.

SAFETY INDICATORS

Responsible manufacturers of DMMs obtain safety certifications from independent third party testing agencies. These marks can usually be found at the back of the devices.

Digital multimeter (DMM) probes should also be marked with a logo of a third party safety-testing agency. You can check out some such marks in Figure 39-24.

RESOLUTION AND ACCURACY

Resolution of a DMM is expressed in the number of digits the unit can display. For example, a 4½ DMM has four full digits that display values from 0 to 9 and the fractional digit, which is the most significant digit in the display. A fractional digit is either 0 or 1. Such a meter shows positive or negative values from 0 to 19,999.

Accuracy of a DMM is different from display resolution. It is the maximum allowable limit of error in readings. All DMM manufacturers express accuracy specifications as ±(% of reading+number of least significant digit).

TRUE RMS

Basically there are two types of DMMs: average responding and true-rms. The latter is a consistent and standard way to measure and compare dynamic signals of all shapes and sizes, whereas the former is calibrated for sinewave inputs only. Average responding meters normally work well for linear loads (standard induction motors, resistance heating, incandescent lights and more), but if non-linear loads (electronic/electric-discharge lighting, adjustable-speed drive systems and so on) are present, errors occur, which could make the readings lower than expected. If you want to measure non-linear loads such as those found at electronic controls, you should choose true-rms.

INPUT IMPEDANCE

I would be surprised to find a DMM today that did not have a high input impedance. You should expect an input impedance of several Megohms and 10MΩ is not an unreasonable expectation.

TYPICAL ACCURACY MID-RANGE DMM

Measurements like, capacitance, frequency and temperature are not essential functions of a DMM. Often these measurements can be done as well or even better with low cost devices. For example a LASER thermometer is not expensive and can give you very accurate measurement of a single spot on a heat sink, component or circuit board. There are low cost component testers for capacitance, inductance and semiconductor devices such as FETs, BJTs, SCRs and the like.

MEASUREMENTS

A basic DMM measures AC/DC voltage, AC/DC current and resistance, checks continuity and diodes, and includes an auto-ranging feature. More expensive DMMs also measure capacitance, frequency, temperature and pressure. Before purchasing one, you should first identify the type of testing you need to perform, establish which features are important and determine the required tolerance range for those tests.

Auto-ranging is an essential feature in my view however it is also useful to be able to choose manual mode. For radio work a high DC current range is very useful. Most meters have a 10A range, I don't have it but 20A would be more useful. As I have a maximum of 10A when I have had to make higher current measurements I have resorted to an external shunt to increase the meter's range.

AUTO-OFF

Auto shutdown is an essential feature. A DMM that does not shut down after a certain time of no use will discharge the battery. Though less likely with good dry cells today's batteries still do leak and can damage the DMM.

DATA LOGGING

Many DMMs will record data internally or allow you to connect the meter to a PC and log measurements over time. This is a feature you have to pay for and if you have no use for it I would not spend the extra just to get it. I have only used data logging myself when trying to determine if mains voltage variation through the day was causing an appliance such as a television to have problems.

Today there are many low cost component testers that will automatically test and measure transistors, inductors, capacitors and resistors and they do it better than a DMM though it may be likely that component testers may become integrated into DMMs in the future. We will discuss component testers later in this chapter.

FIELD SENSE

Some modern DMMs have a feature called "Field Sense" this means that you can take measurements of voltages and currents without breaking or making direct physical electrical contact with the circuit under test. The DMM senses the electric or magnetic field relative to ground. If there is no ground you can connect a ground wire to earth. This feature can be very useful but should be used with caution. The ground connection is by capacitive coupling between your body and ground. If you think you have capacitive coupling to ground but do not you could get a no voltage reading, trust it, then touch the metallic connection with you hands and get a shock or worse. If you are going to come in direct electrical contact it is best to do so with power OFF and absolute verification that the power is indeed OFF.

ANTENNA IMPEDANCE ANALYSERS

Antenna impedance analysers also called "vector network analysers" or just an "impedance meter" are, next to a DMM, one of the most useful tools in a radio experimenter's kit. Prices range from $AUD150 to several hundred dollars. The feature you will be most concerned about is the frequency range. Most radio amateurs want antenna analysers to work in the HF range 3-30MHz and anything above that is a bonus.

Antenna analysers measure the impedance where they are connected. They only have one port for the connection of usually an antenna or the input of a transmission line going to an antenna.

Impedance as we have learned cannot be expressed as a single value unless that impedance is purely resistive. Impedance can be expressed in rectangular form with two numbers, real and imaginary, or in polar form as two numbers, magnitude and angle. When working with antennas the most useful form is rectangular.

If an antenna has an impedance in rectangular form of 85j20Ω then this means the antenna impedance comprises of 80 ohms resistance and 20 ohms of inductive reactance. Such an antenna would not be resonant because its impedance contains 20 ohms of inductive reactance. To be resonant an antenna should have a very low value of reactance, theoretically no reactance but we can settle for just a few ohms. If the impedance was 85j-20Ω then the -j20Ω would indicate 20 ohms of capacitive reactance.

An antenna analyser tells us what the impedance of the antenna (or input to the transmission line) is in terms of its resistance and reactance. Some analysers provide the impedance in polar and rectangular form but rectangular is more useful.

If an antenna is too short then it will be capacitive and this usually means lengthening it to increase inductance or physically adding inductance such as a loading coil. If an antenna is too long it will be inductive. This means we have to counteract that inductance using a capacitance or an easier way it to just shorten the antenna.

What an impedance measurement does is tell you immediately if the antenna is too short or too long. The there is no guess work, you know immediately if you need to shorten or lengthen the antenna.

If you connect an antenna tuning unit (ATU) to an antenna and an impedance analyser to the transmitter side of the ATU then set the frequency of the antenna analyser to the frequency of the antenna then, if the ATU has tuned the antenna to the correct frequency you would expect to measure an impedance close to 50j0Ω. If you do not get this measurement then you can just adjust the controls of the ATU until you do get 50j0Ω. Don't be too fussy about getting exactly j0Ω, a few ohms of reactance is okay. When done remove the antenna analyser and connect the transmitter and you are ready to transmit with an SWR close to 1:1. This is an excellent way of tuning up off air as tuning on air can sometimes produce interference.

Most antenna analysers just have controls to adjust frequency and sometimes a bandswitch for different frequency ranges. There is one connection and that is for the antenna or the device under test (DUT).

All antenna analysers have a digital readout which will usually tell you the impedance being measured in rectangular and polar forms. Rectangular form is the important one with R being the resistance and X being the reactance. Usually SWR and on some of the better meters a graph of SWR versus frequency.

Antenna analysers can be used to cut coaxial cable to different wavelengths and to make stubs either quarter or half wave and not to forget phasing harnesses.

I am yet to meet a person who has purchased an antenna analyser and regretted it. They are a very useful tool and almost an essential one next to the DMM.

If you are measuring the impedance at the input of your transmission line you are not measuring your antenna impedance. You can mathematically extrapolate line input impedance to antenna impedance if you know the length of your transmission line and an estimate of its loss. Though you still have to do some maths that you may not be pleased about. Modern antenna analysers allow you to tell the analyser what the length of your line is, usually in wavelengths and the estimated loss then automatically convert the line input impedance to the true antenna impedance.

Pictured in figure 39-31 is a high end graphing antenna analyser of exceptional accuracy and a quality instrument. There are less expensive models available that may suit your purposes. The most important aspect affecting price is the frequency range required. A HF only analyser may cost as low as $AUD150. If you need VHF then the cost will be greater and UHF even higher. Do you need graphing or not? There is a price to suit just about every budget.

COMPONENT TESTERS

Component testers started to appear on the market in about 2017. At first they were thought of as a bit of a novelty and regarded by many as not a serious testing device. I have to say that is no longer the case. These devices are very low cost, some under $10. I am not recommending any particular component tester but to ignore their existence and usefulness would be an injustice to the reader. They are available online in the usual public trading markets. I am not aware of any commercial outlet at the time of writing.

Many are available as a completed circuit board and while they work like this you have to supply or make your own box. Other component testers come boxed in a purpose made enclosure. Figure 39-32 shows a typical low cost component tester.

The component to be tested is inserted in the ZIF (zero insertion force) socket and then the button pressed. The display shows the schematic symbol of the component and its relevant values. These testers can work for semiconductors, capacitors, resistors and inductors. I have tested a number of them and found them to be sufficiently accurate. If the tester cannot recognise what the component is or it is untestable because it is faulty or unknown, a question mark is displayed. Figure 39-33 are some readouts from a typical component tester.

40 - Other Operating Modes

Apart from the usual voice modes of AM, FM and SSB, amateur radio operators can experiment with dozens of different modes of operation. Different digital modes are introduced every year. There are literally dozens of special modes and protocols. The change is so fast that regulatory authorities in some countries have difficulty keeping up with them all. The answer for many regulators is to permit any mode as long as the maximum permitted bandwidth or power density is not exceeded.

This chapter then, out of necessity, will be a brief overview of some of the many 'extra' modes that an amateur station may use. Amateur radio communication has progressed in many ways since its beginning in the early 1900s. General communications has progressed from spark CW to tuned CW then voice communications from AM to FM and SSB. Similarly, data communications as a mode of experimenter communications have progressed from CW to (frequency shift keying) FSK and from (radio teletype) RTTY to more 'modern' modes of data communications utilising data packets with error correction.

Amateurs now communicate using both fast and slow scan television. An exciting developing area is high-speed wide bandwidth point to point links on the microwave bands.

I would like to encourage you to broaden your baseline in amateur radio once you have acquired your license. Thinking that it is all too hard sometimes stops the beginner. It is not hard, have a go and you will be surprised. There is a wealth of information available for free from special interest groups and the internet and other radio amateurs are usually only too happy to help having been where you were once themselves.

RADIO TO COMPUTER INTERFACE 

Some VHF and UHF transceivers come with purposed designed inbuilt coders/decoders (CODECS) for a specific digital modes. Yaesu Fusion and D-Star are typical examples. On HF the encoding and decoding is generally performed by a computer connected to a conventional HF SSB transceiver.

Basically what you want to do for HF digital modes is to interface the audio output of your computer to the audio input of your transceiver and the audio output of the transceiver to the computer. You also need to key the transmitter ON and OFF using PTT control. Many transceivers have custom ports for this purpose. If your transceiver does not then all is not lost as it is it very simple to either build a computer to radio interface or to purchase one.

You will find many easy circuits for an interface on the internet and some specific for your radio. The are many commercial interfaces, two that I have used with good success and no issues, are the Signalink USB interface and the MFJ USB interface MFJ-1204. There are many user groups on platforms such as FaceBook for just about any specific radio and for using that radio with digital modes.

Some radios do not require any interfaces at all. You should check your user manual. Many transceivers today have a Computer Aided Control or CAT port for totally controlling your radio from your computer with free or proprietary software. The programs can change frequency, control modulation levels, virtually full control of your radio by the computer. In addition sometimes there is an accessory port to switch the radio between transmit and receive. On my HF transceiver I have a USB port which means everything can be done with one USB cable connection between the radio and the computer. I expect this type of connection will be commonplace with all transceivers now and into the future.

TRANSMITTER DUTY CYCLE

Most HF digital modes are done using an SSB transceiver. A 100W SSB transmitter is not designed to transmit 100 watts all the time. SSB does not drive a transmitter hard. The peak power of 100 watts is reached very occasionally on voice peaks, This means for the rest of the time the transmitter is not being driven very hard at all. SSB is a low duty cycle mode. Compare that to a 50W FM transmitter. During transmission the transmitter is producing 50 watts all of the time. The duty cycle of FM is then 100% or 1.

Duty cycle varies from 0 to 1 or 0% to 100%. RTTY and FM have a 100% duty cycle because "during transmission" the transmitter is operating at full power. CW or Morse code transmitted with an interrupted carrier has a duty cycle of about 44%. This is because the transmitter while transmitting is getting lots of rests between the dits and dahs and between words.

Most digital modes, which we will discuss in more detail shortly, have a duty cycle of 1. So if your are using such modes with an SSB transmitter you must reduce the power. For example a 100W SSB transmitter using a digital mode with a duty cycle of 1 should have the output power reduced to 10-20W maximum. If you do not do this you will cook the transmitter very quickly.

BINARY

Binary is a method of representing numbers with only two states - ON/OFF or HighVolts/Low-Volts.

Using the characters 0-9 forms all decimal numbers. If electrical circuits were to use 10 states like this, they would be very complex indeed. In the binary system, all numbers can be represented by a combination of 1s and 0s. Thus, it is very easy to represent any number of characters as a string of high and low voltage states. Figure 40-1 shows the binary representation of the decimal numbers from 0 to 15.

For example, a square wave digital data stream consisting of 1010 could represent decimal 10.

Binary data can be represented with many different types of modulation. For example, FSK (frequency shift keying). The secret to the lower bandwidth and higher quality of digital modes is that only two states a "1" and a "0" have to be transmitted. Analogue and Digital signals are subject to the same noise. The difference is that a noisy 1 or 0 is still a 1 or 0. Digital signals can be restored to noiseless provided the signal level is good enough. Algorithms can also be used for error checking. In sophisticated systems, much like an internet modem, full handshaking and error correction is implemented.

PSK31

PSK or Phase Shift Keying has become a very popular digital mode. There is a wealth of information on the web regarding BPSK (Binary PSK) and QPSK (Quadrature PSK). Because PSK31 has a bandwidth of only 31Hz, many signals can fit into the same bandwidth that would be occupied by an SSB signal (2.8kHz approx.).

Peter Martinez G3PLX created the mode in 1999 and released software for Windows to use the mode. In those days computers had 16 bit sound cards and this was how PSK was generated by using the sound card as analogue to digital converter and in the received direction as a digital to analogue converter.

PSK31 transmits two states, a "1" and a "0" by using a 180° phase shift. A "0" is no phase shift whereas a "1" is a 180° phase shift. Since PSK31 uses two phase conditions to transmit information it is sometimes referred to as BPSK which stands for Binary Phase Shift Keying. PSK31 audio used to modulate an SSB transmitter will produce a very narrow bandwidth of 31.25Hz. Every PSK31 transmission starts with a string of zeros and this allows the receiver software to "get ready" for the data information that is to follow. As PSK31 is so simple - just two phases - even if the signal is lost for a second or more due to fading then the receiver software can quickly re-synchronise with the transmitted signal.

PSK31 is not perfect, copy can be lost, but is a very good weak signal mode that has remained popular since its introduction in about 2000.

QPSK (Quadrature Phase Shift Keying) is similar to PSK31 but now we have four phase shift states rather than 2. BPSK and QPSK are discussed in this book in the chapter on digital modulation. There are other variants of Phase Shift Keying that are faster but the down side is the faster the speed the wider the bandwidth so the signal becomes more susceptible to noise.

RADIO TELETYPE - RTTY

Radio teletype has been around for a very long time but it is still very popular today. It is especially popular for contests and DX-expeditions. RTTY copes with crowded conditions very well while supporting a character speed of 60 words per minute which is faster than most people can type.

RTTY uses the Baudot code. While many use the term Baudot code, others use the term Murray code. These two names acknowledge two important telegraph pioneers, both of whom made major contributions in this field. However, the correct term is CCITT International Alphabet No. 2. The differences between code types in practical systems are apparent in punctuation characters and would not be noticed between two operators unless they used punctuation such as !:%@ etc. Baudot is sent at different speeds in different areas. Early transmission speed in Australia was mostly much standardised at 45 baud.

These days, computers have completely taken over from the mechanical teleprinter, so baud rate changes are no longer the problem they once were.

The code comprised of marks and spaces which much like the 1s and 0s of PSK. Each code character is 5 bits long. The "1" called a "mark" is represented by a tone of 2125Hz and the "0" bit a 2295Hz tone - the difference being 170Hz. Also every bit string has a start and a stop pulse. The most common speed is 45 baud or 60WPM.

FT8 AND JT65A

These modes started out in the software suite by Dr. Joe Taylor called WSJT. The WSJT modes were originally used for moon bounce. Dr. Joe Taylor is an astronomer and a Nobel Prize recipient and because of his scientific work he is very keen on weak signals.

One of the WSJT modes JT65A when tried in the HF amateur bands, quickly became very popular out shining PSK31. Then in 2017 the software now called WSJT-X released FT8. Radio amateurs embraced FT8 like no other HF digital mode before it - it was faster and very much automated. Some radio amateurs do not like the automation but regardless FT8 has become one of the most popular HF digital modes. WSJT-X also contains the WSPR beacon mode.

If you want to have a ragchew or any conversation then don't use FT8 or JT65A. All you will be doing with these modes is making a contact, exchanging grid squares and a signal report. These modes meet the requirements for ARRL DX Century Club and other awards.

JT65A is intended for extremely weak but slowly-varying signals, such as those found on troposcatter or Earth-Moon-Earth (EME, or "moon bounce") paths. It can decode signals many decibels below the noise floor, and often allows amateurs to exchange contact information successfully without signals being audible to the human ear. Like the other digital modes, multiple-frequency shift keying is employed. However, unlike the other digital modes, messages are transmitted as atomic units after being compressed and then encoded with a process known as forward error correction (FEC). The FEC adds redundancy to the data, such that all of a message may be successfully recovered even if some bits are not received by the receiver. (The particular code used for JT65A is ReedSolomon.) Because of this FEC process, messages are either decoded correctly or not decoded at all, with a high probability of success. After messages are encoded, they are transmitted using MFSK with 65 tones. Operators have also begun using the JT65A mode for contacts on the HF bands, often using QRP (very low transmit power usually less than 5 watts). While the mode was not originally intended for HF use, its popularity has resulted in several new programs being developed and enhancements to the original WSJT in order to facilitate HF operation.

MFSK

MFSK is similar to the commercial Piccolo system. MFSK is very good under poor propagation conditions. The usual variant of MFSK is MFSK16, but other types such as MFSK 8 are in development, along with other similar modes to MFSK (such as Domino). MFSK is sideband dependant, so you must have your receiver set to the correct sideband in order to decode it properly. Tuning is quite critical, although automatic frequency control (AFC) helps somewhat.

The most common form of MFSK uses 16 tones, sent one at a time at 15.625 baud. The tones are spaced 15.625Hz apart. Each tone represents four binary bits of data. The transmission is a bit wider than RTTY at 316Hz. To take advantage of this narrow band mode a narrow filter should be used. A 500Hz CW filter will work for RTTY and MFSK16.

OLIVIA

Olivia is an amazing performer under weak signal and noise conditions. It is a conversational mode. Signals can be decoded that are 10-12dB below the noise floor which is really quite remarkable. Olivia uses a number of formats with the differences being the number tones used. It can use 2, 4, 8, 16, 32, 64, 128 or 256 tones. They correspond to an operational bandwidth of 125, 250, 500, 1000, and 2000Hz. The trade off the Olivia has for its amazing performance is that it is slow. However in very bad conditions slow is better then nothing.

Olivia is available in a number of software packages such as MixW and Fldigi and others. Olivia was developed by Pawel Jalocha SP9VRC and named after his daughter.

AMTOR - AMATEUR TELEPRINTING OVER RADIO

One common problem with direct printing RTTY (such as Baudot and ASCII) is errors in reception. If there is any slight disturbance to the received signal, it is quite likely that an incorrect character will be printed. This is not a major problem in the average amateur conversation, as the rest of the sentence will usually fill in the gaps. However, on all but the best contacts, important details (e.g. frequencies) must be repeated a couple of times to ensure that the other station gets what you want to say. This form of operation may be satisfactory for amateurs, but it is not satisfactory for commercial operations such as ship to shore teletype.

AMTOR can be thought of as a more advanced form of RTTY, which includes automatic acknowledgement of each group of characters sent, or a request for a repeat. This results in error free communication (at the expense of speed, especially in poor conditions). The protocol is very specific, so there is no variation in the transmission speed of 100 baud. As this mode requires more sophisticated equipment able to handle the error checking functions and a relatively fast receive/transmit changeover in the radio, the number of operations are slightly less than on the more simple modes.

The main feature of AMTOR is that it uses the Moore code, which is made up of seven unit characters (bits), but utilising a select few of the possible combinations, thus allowing a receiving station to tell if a received code is correct or not. AMTOR operation involves the transmitting station sending three characters, then waiting for a response from the receiving station. The response will either be "roger, go ahead", or "no go" (or perhaps nothing at all if the path has faded out). The transmitting station then either repeats the last three characters or sends the next three. This operation is a form of ARQ (Automatic Repeat ReQuest) known as AMTOR Mode A.

By sending text in bursts of three characters, awaiting a one-character reply, then sending three more, AMTOR requires radio equipment which can change from transmit to receive in a very short time. On-air AMTOR has a characteristically fast "chirp-chirp" sound.

There is another version of AMTOR (Mode B) which also uses the Moore code (i.e. has the ability to detect errors), but is an FEC (Forward Error Correction) system, rather than an ARQ system. Instead of a transmit and wait acknowledgement system, Mode B simply transmits every character twice, three characters apart. This allows the receiving station two goes at getting it right. As a result, Mode B AMTOR is more reliable than RTTY, but not as reliable as Mode A AMTOR. Mode B, as it does not require acknowledgement responses from the receiving station, is used for news broadcasts and CQ calls. Mode A is also limited by propagation timing to short-path HF contacts, due to radio propagation time intervals for around the world contacts.

PACKET RADIO

Packet Radio is another error-free mode which has the added advantages of higher speed (if good radio signal is available) and increased economy of spectrum space by time-sharing a channel with other users.

Transmitted text is collected into "packets" before sending. Within this packet is the callsign of the packet destination, the source (sender's) callsign, information on the type of packet being sent (control, acknowledgement, etc.), data (where applicable) and a CRC (Cyclic Redundancy Check) which enables the receiver to determine whether there are any errors in the received packet. The exact format of the packet is laid down by an agreed protocol (a full explanation of packet radio can be found in recent editions of the ARRL Handbook and other such publications).

The first protocol widely used by amateurs was known as the VADCG V1 protocol. While this protocol facilitated early experimentation, it had a number of limitations. These limitations were overcome by a new protocol called AX.25. AX.25 is based on X.25, a commercial computer communications protocol.

Packet radio requires the use of a computer to handle the protocol and the exchange of data. This may be done by either programming a personal computer, or by using a dedicated computer called a TNC (Terminal Node Controller) connected between a computer/terminal and the radio. The TNC approach leaves the operator's computer free to handle application activities. A hybrid system that uses software and a computer  I/O card is another alternative that has the benefits of both the programming and TNC approach.

Packet Radio has traditionally been used at data rates of 1200bps using AFSK modulation. With advances in applications and technology, this has become a rather limiting factor and 9600bps operation is becoming more common. Higher speeds are also being used on higher bands for networking applications and speeds of 19200bps through to 2Mbps are not uncommon.

Packet radio, like the commercial X.25 packet switched systems, allows several simultaneous point to point connections to share the same frequency.

In packet radio, whenever we send a message to another station, our TNC builds a packet (like an envelope) around our message, adding details such as the callsign of the station this message is addressed to. Then, if the frequency is clear, the packet is transmitted into the airwaves.

Our TNC listens to the audio coming from the radio receiver and, if there are any other packet radio stations using the frequency, waits until there is a lull in the transmissions before transmitting our packet. At first, you might wonder how long it has to wait, thinking the other stations might be going for hours! However, in practice, a packet might take only a fraction of a second to transmit - a relatively short burst of time compared to the time it takes us to type a message. Unless the frequency is really busy, you might not even notice the delay!

The packet radio frequency in use carries messages for many people at the same time. When receiving, your TNC looks at every packet received, checks the address of each packet and identifies any packets addressed to you.

Any packets not intended for you may be ignored by your TNC, so you see on your screen only those messages addressed to you. This way you need not concern yourself with all the other information flowing around on the frequency and are free to concentrate on your contact with the other station.

If you wish, you can ask your TNC to display everything it receives. This is called monitoring. Every packet contains an AX.25 header ("envelope") which identifies the station who sent it and the station it is addressed to. The header contains other information too, but we won't get into that just now. When monitoring, your TNC will send to the computer the header and content of all the messages, so you can see who sent what to whom. Then you will see how the AX.25 systems are able to handle lots of different conversations on the same frequency at the same time. The other modes do not offer this capability.

PACTOR

Pactor is a hybrid between packet and AMTOR techniques to try to provide a faster and more robust protocol for HF data links.

PACTOR transmits either 12 or 24 characters, depending on the baud rate which is either 100 or 200 respectively. Four characters are used for control including two checksum bytes. Errors are detected at the receiver by comparing the checksum with the accompanying data. PACTOR uses the AX-25 checksum (CRC-16). The receiver requests new data, a retransmission of data, or a change in system baud rate.

PACTOR has become a popular HF mode, as it is more efficient than AMTOR or Packet in most situations. It is readily available in commercial data controllers and is also available in software form for simple modem designs.

Pactor was developed in 1991 by Hans-Peter Helfert, DL6MAA, and Ulrich Strate, DF4KV in 1991. It remains to this day the most popular of the HF burst modes. There are four versions of PACTOR, PACTOR I, PACTOR II, PACTOR III and PACTOR IV. PACTOR I is considered obsolete and is little used. PACTOR II and III are in current use, primarily to connect to automated stations such as the Winlink 2000 network.

There is no sound-device software method for sending and receiving PACTOR. The only way to get on the air with PACTOR is to use a stand-alone hardware controller (also referred to as a Multimode Communications Processor) that connects between your computer and an SSB transceiver. Pactor modems range in price from $AUD1500 to $AUD2500 at the time of writing.

Rather than sending a continuous stream of data like RTTY, PSK31, MFSK16 or Olivia, PACTOR transmits bursts of information that take the form of short data blocks. When the data is received intact, the receiving station sends an ACK signal (for acknowledgement). If the data contains errors, a NAK is sent (for non acknowledgment). In simple terms, ACK means, "I've received the last group of characters okay. Send the next group." NAK means, "There are errors in the last group of characters; send them again".This back-and-forth data conversation sounds like crickets chirping. In the case of PACTOR, the long chirp is the data and the short chirp is the ACK or NAK.

In less sophisticated burst modes such as AMTOR or Packet, a data block must be repeated over and over if that's what it takes to deliver the information error-free. This results in slower communication, especially when conditions are poor. PACTOR handles the challenge of "repairing" errors very differently. Each data block is sent and acknowledged with an ACK signal if it's received intact. If for any reason data is lost a NAK is sent and the block is repeated.

When a PACTOR controller receives a corrupted data block, it analyses the parts and temporarily memorises whatever information appears to be error free. If the block is shot full of holes on the next transmission as well, the controller quickly compares the new data fragments with what it has memorised. It fills the gaps as much as possible and then, if necessary, asks for another repeat. Eventually, the controller gathers enough fragments to construct the entire block.

Most PACTOR activity involves connecting to automated systems, so you can still occasionally enjoy a real conversation. You'll tend to find these in the same frequency segments used for RTTY.

WINLINK 2000

The internet has become the messaging method medium of choice for everyone , this includes radio amateurs. How do you send an email when you are at sea, or in any other isolated geographical regional where there is no internet? A high frequency (HF) digital radio network is a way to achieve email communications with no internet.

There are many HF digital stations worldwide that have formed a remarkably efficient internet information exchange network, including e-mail and binary file transfers. Running Winlink 2000 software and using mostly PACTOR II or Ill, these facilities transfer information between HF stations and the internet. They also share information between themselves using internet forwarding.

The network evolved in the 1990s from the original AMTOR-based APLink system, authored by Victor Poor, WSSMM (SK). APLink was a network of stations that relayed messages to and from each other and the VHF packet network. As computers became more powerful, and as PACTOR and Clover superseded AMTOR, a new software system was needed. That need brought about the introduction of Winlink, authored by Victor Poor, WSSMM, with additions from Peter Schultz, TY1PS.

Winlink itself evolved with substantial enhancements courtesy of Hans Kessler, N8PGR. To bring the internet into the picture Winlink stations needed an e-mail "agent" to interface with cyberspace. To meet that requirement Steve Waterman, K4CJX enlisted the help of Jim Jennings, WSEUT and Rick Muething, KN6KB, to add Netlink.

Early in 2000 the system took the next evolutionary leap, becoming a full-featured Internet-to-HF gateway system known as Winlink 2000 or "WL2K." Jim Corenman, KE6RK, developed software called RMS Express, which is the end user portion of Winlink 2000. Winlink 2000 is a network of participating stations known as RMS radio gateways, all connected to a central server that functions as the "hub" for connectivity to internet e-mail and position reporting.

Thanks to these developments, an HF digital operator at sea can connect to a Winlink 2000 participating network station using RMS Express software and their PACTOR controller and exchange internet e-mail with non-amateur radio friends and family. He can also exchange messages with other amateurs by using the Winlink 2000 network stations as a traditional global "mailbox" operation.

Most Winlink 2000 participating stations scan a variety of HF digital frequencies on a regular basis, listening on each frequency for about two seconds. By scanning through frequencies on several bands, the Winlink 2000 stations can be accessed on whichever band is available to you at the time.

FEATURES Of RMS EXPRESS, WINLINK 2000

· Text-based e-mail with binary attachments such as DOC, RTF, XIS, JPG, TIF, GIF, BMP,etc.

· Position inquiries accessible from both the internet graphically via APRS and YotReps (position reporting), e-mail or radio to track the mobile user.

· Graphic and text-based weather downloads from a list of over 400 weather products, covering the entire globe.

· Pickup and delivery of e-mail regardless of the participating station accessed. · End-user control of which services and file sizes are transmitted from the participating stations, including the ability for each user to re-direct incoming email messages to an alternate e-mail address.

· The ability to use the internet via Telnet instead of a radio transmission.

· The ability to use any Web browser to pick up or deliver mail over Winlink 2000.

WINMOR (WINLINK MESSAGE OVER RADIO)

WINMOR does not require a hardware dedicated PACTOR controller. WINMOR is sound-card based. This relatively new software offers a solution to those who want to access the Winlink 2000 network but don't own or want to pay the high cost of a PACTOR controller. WINMOR works perfectly with RMS Express as the Winlink email client.

WINMOR will operate with just about any sound-device-based station and SSB transceiver. If you are set up to operate PSK31 or any similar mode, you are also setup to run WINMOR by simply downloading and installing the software. See the WINMOR page on the Winlink 2000 website at www.winlink.org/WINMOR

In most digital modes the transmitting station sets the speed and the receiving station must set its speed to match. In WINMOR it is the receiving station that determines the speed and lets the transmitting station know what speed it is accepting automatically. The speed you set in setup only comes into effect if someone calls your station in peer-to-peer mode. One of the reasons for this is the RMS stations operating unattended on amateur radio frequencies are limited to a 500Hz bandwidth. MARS stations are not subject to the same restriction so all the Winlink MARS* stations will accept a 1600Hz bandwidth when using WINMOR.

Within each bandwidth there are a number of different modes that may be operating. These choices are not under the operator's control and are determined by the signal strength, propagation conditions, multipathing, noise and interference and the bandwidth set by the receiving station. In other words, the program shifts gears to get the best throughput under changing conditions.

A map of the WIN MOR network can also be found at: https://winlink.org/RMSChannels

* The Military Auxiliary Radio System (MARS) is a United States Department of Defense sponsored program, established as a separately managed and operated program by the United States Army, and the United States Air Force. The United States Navy-Marine program has been closed. The program is a civilian auxiliary consisting primarily of licensed amateur radio operators who are interested in assisting the military with communications on a local, national, and international basis as an adjunct to normal communications. The MARS programs also include active duty, reserve, and National Guard units; Navy, Marine Corps, and National Oceanic and Atmospheric Administration ships, and Coast Guard cutters and shore stations. (Source:https://en.wikipedia.org/wiki/Military_Auxiliary_Radio_System)

WSPR

WSPR is an acronym for "Weak Signal Propagation Reporter". It is often referred to as "Whisper". WSPR does not support two way radiocommunications. WSPR can receive signals that most other digital modes would find undetectable. An extremely weak signal may appear as very faint trace on the waterfall and WSPR will decode it. WSPR is included in the WSJT-X software and Windows. Linux and MacOS is supported.

Each WSPR transmission includes your;

Call sign.

Power Output in dBm.

Maidenhead grid square.

A transmission is about 110 seconds long and begins one second after an even minute. A WSPR tone on air sounds like a single warbling tone. It may sound as if there is no modulation because the WSPR symbol rate is less than 2 baud. This makes a WSPR signal very narrow - about 6Hz.

WSPR signals are usually transmitted at very low power and certainly 5 watts or less is recommended. It is not uncommon to see WSPR decode power levels of a few milliwatts. WSPR does not require much power at all and can be received at great distances.

WSPR REPORTS

WSPRnet.org is the website that gathers all the WSPR signal reports for around the world. You can see on this site who is receiving your signals and at what level they are being received. The WSPR reports can be filtered for the ones that you are interested in and displayed in graphical or text format.

Go to WSPRnet.org and click on MAPS and have a look at the WSPR signal reports for yourself. Many operators just leave their WSPR running for long periods of time in receive mode, whether or not they are present. This contributes to the global WSPR signal reports and is helpful to other operators.

There are three ways to use WSPR.

1 . You can use a WSPR transceiver which means you are both transmitting and receiving. This requires a transceiver, a computer and WSJT-X software.

2. As a receive only station. This means you are only receiving WSPR signals and uploading WSPR reports to WSPRnet.

3. As a transmitting station only. There are many low cost dedicated QRP transmitter kits to construct or you can buy ready made units.

PROJECT 25 (P25 OR APCO-25)

P25 is a suite of standards for digital radio communications for use by federal, state, province and local public safety organisations in many countries enabling them to communicate with other agencies and mutual aid response teams in emergencies. In this regard, P25 fills the same role as the European Terrestrial Trunked Radio (TETRA) protocol, but the two are not interoperable. The major difference between the two is that P-25 is expected to work jointly with existing analogue systems. Therefore, it uses "simulcast" method for control. "Simulcast" refers to the use of the same set of control channels throughout a given area, which are "simultaneously broadcast, or simulcast" in the region. In contrast, TETRA uses "Multicast," which means the control channel is embedded. Therefore there is no need to use a separate channel to broadcast control signals. TETRA provides 4 slots per channel, which means four voice calls can be handled on one channel. This is similar to the GSM cellular system, which allows eight slots or eight users per channel.

DSTAR

DSTAR (Digital Smart Technologies for Amateur Radio) is a digital voice and data protocol specification for amateur radio. The system was developed in the late 1990s by the Japan Amateur Radio League and uses frequency-division multiple access and minimum-shift keying in its packet-based standard. There are newer digital modes (Codec2, for example) that have been adapted for use by amateurs, but DSTAR was the first that was designed specifically for amateur radio.

Several advantages of using digital voice modes are that it uses less bandwidth than older analogue voice modes such as amplitude modulation, frequency modulation, and single sideband. The quality of the data received is also better than an analogue signal at the same signal strength, as long as the signal is above a minimum threshold and as long as there is no multipath propagation.

DSTAR compatible radios are available for HF, VHF, UHF, and microwave amateur radio bands. In addition to the over-the-air protocol, D-STAR also provides specifications for network connectivity, enabling DSTAR radios to be connected to the internet or other networks, allowing streams of voice or packet data to be routed via amateur radio.

DSTAR compatible radios are manufactured by both lcom and FlexRadio Systems. The system today is capable of linking repeaters together locally and through the internet utilising callsigns for routing of traffic. Servers are linked via TCP/IP utilising proprietary "gateway" software, available from lcom. This allows amateur radio operators to talk to any other amateurs participating in a particular gateway "trust" environment. The current master gateway in the United States is operated by the KSTIT group in Texas, who were the first to install a DSTAR repeater system in the U.S.

DSTAR transfers both voice and data via digital encoding over the 2M (VHF), 70cm (UHF), and 23cm (1.2 GHz) amateur radio bands. There is also an interlinking radio system for creating links between systems in a local area on 10GHz, which is valuable to allow emergency communications oriented networks to continue to link in the event of internet access failure or overload.

Within the DSTAR Digital Voice protocol standards (DV), voice audio is encoded as a 3600 bit/s data stream using proprietary AMBE encoding, with 1200 bit/s FEC, leaving 1200 bit/s for an additional data "path" between radios utilising DV mode. On air bit rates for DV mode are 4800 bit/s over the 2M, 70cm and 23cm bands. In addition to digital voice mode (DV), a Digital Data (DD) mode can be sent at 128kbit/s only on the 23cm band. A higher-rate proprietary data protocol, currently believed to be much like ATM, is used in the 10 GHz "link" radios for site-to-site links. Radios providing DV data service within the low-speed voice protocol variant typically use an RS-232 or USB connection for low speed data (1200 bit/s), while the lcom ID-1 23 cm band radio offers a standard ethernet connection for high speed (128kbit/s) connections, to allow easy interfacing with computer equipment.

DMR

Digital mobile radio (DMR) is an open digital mobile radio standard defined by the European Telecommunications Standards Institute (ETSI) Standard TS 102 361 parts 1-4, and used in commercial products around the world. DMR, along with P25 phase II and NXDN are the main competitor technologies in achieving 6.25kHz equivalent bandwidth using the proprietary AMBE+2 vocoder. DMR and P25 II both use two-slot TDMA in a 12.5kHz channel, while NXDN uses discrete 6.25kHz channels using frequency division.

The primary goal of the standard is to specify a digital system with low complexity, low cost, and interoperability across brands, so radio communications purchasers are not locked into a proprietary solution. In practice, many brands have not adhered to this open standard and have introduced proprietary features that make their product offerings non-interoperable.

The DMR standard operates within the existing 12.5kHz channel spacing used in land mobile frequency bands globally but achieves two voice channels through two-slot TDMA technology built around a 30ms structure. The modulation is 4-state FSK, which creates four possible symbols over the air at a rate of 4,800 symbols/s, corresponding to 9,600 b/s. After overhead, forward error correction, and splitting into two channels, there is 2,450 b/s left for a single voice channel using DMR, compared to 4,400 b/s using P25 and 64,000 b/s with traditional telephone circuits.

DMR covers the RF range 30MHz to 1GHz. The DMR Association and manufacturers often claim that DMR has superior coverage performance to analogue FM. Forward error correction can achieve a higher quality of voice when the received signal is still relatively high. In practice, however, digital modulation protocols are much more susceptible to multipath interference and fail to provide service in areas where analogue FM would otherwise provide degraded but audible voice service. At a higher quality of voice, DMR outperforms analogue FM by about 11 dB. But at a lower quality of voice, analogue FM outperforms DMR by about 5dB.

YAESU SYSTEM FUSION

Yaesu System Fusion integrated digital voice and analogue FM system. The system switches the user automatically between C4FM digital voice and conventional analogue FM. Automatic modes select (AMS) switches the user's radio, working into a fusion repeater, from digital to analogue based on what is detected by the repeater's receiver. If you were using digital and communicating with someone on analogue through a Fusion repeater, the repeater would convert your outgoing signal from the repeater to analogue.

System Fusion has four communications modes. In the voice data or V /D mode half of the 12.5KHz channel bandwidth is used for digital voice and the other half for data. Voice F/R mode uses the full 12.5kHz to transmit high quality digital audio. Data F/R mode uses the full 12.5kHz bandwidth for higher speed data. This can be used for transmitting images or pictures.

The fourth mode is Analogue FM. Yaesu claims greater distance at lower power consumption in analogue mode.

C4FM digital group mode notifies you when members registered to a group are within communication range. Also providing you with the distance and bearing of other group members. Group members can send text messages and images when they are within simplex range. In digital DV mode, your position and bearing is shared with group members in real time.

Fusion transceivers have an SD card and an optional microphone with an inbuilt camera for taking and transmitting photographs. Some Fusion transceivers have a built in GPS. I suspect these features will become very much the standard for all transceivers even those not using the fusion system.

SLOW SCAN TELEVISION (SSTV)

Slow scan television produces a very slow scan frame rate (no moving pictures with SSTV). Slow scan TV is popular because its narrow bandwidth requirement means that it can be used on the HF bands, enabling long distance communication. The pictures sent back from many space probes are in slow scan.

For slow scan, the camera outputs a variable frequency audio tone. High tone is for bright picture information, and low tone is for dark areas. SSTV is not difficult to produce with computer software. All that is needed is some way of getting the image you want to transmit into the computer from an external camera.

This can be done with a video capture card and a simple web camera. It is easy for computer software to scan this image and produce the audio tones which are simply used to modulate the transmitter. At the receiver the demodulated audio tones can be fed into the computer's sound card and software will reconstruct the image on the remote computer monitor. It is a simple matter to transmit colour pictures in SSTV.

With colour SSTV the frame rate is slower.

With computers, SSTV is one of the easiest 'extra' modes to use with very limited cost. In fact, even if you do not have a camera you can transmit and receive images just using free software and your computer's sound card (and a radio transmitter of course). SSTV can be received just by audio-coupling your transceiver's speaker to your computer sound card.

You can audio-couple for reception of many digital modes. Download software and you can be receiving in a few minutes. A low noise audio coupler between your sound card and the transceiver is recommended for transmission. Radio sound card interfaces are easy and inexpensive to construct yourself, or you can purchase a manufactured interface including cables for your transceiver.

Many digital-mode software programs used for modes such as PSK and RTTY (i.e. MixW and DM780) have support built in for receiving SSTV pictures. The most commonly used program for amateur SSTV transmission and reception is the dedicated SSTV program MMSSTV written by Makoto (Mako) Mori JE3HHT.

Analogue SSTV transmissions can be found on HF frequencies around 3.640MHz LSB, 7.170MHz LSB, 14.230MHz USB, 21.340MHz USB and 28.680MHz USB. On 2m and 70cm transmissions are commonly found around 145.625MHz (USB and FM) and 433.775MHz (USB and FM).

DIGITAL SSTV 

Digital SSTV is a recent innovation whereby multi-carrier orthogonal frequency division multiplexing (OFDM) techniques, based loosely around the digital radio mondiale (DRM) broadcasting protocols as used for commercial digital radio transmissions in Australia, are used to digitally encode and broadcast images and simple data files. The DRM protocol has been adapted to fit within a voice-spectrum bandwidth (up to 2.5kHz) that can easily be modulated and received by standard SSB and FM transceivers.

The most common program in use today is "EasyPal". See figure 40-3.

Analogue slow scan builds up a picture progressively - line by line - until the image is complete. Digital SSTV works on building up enough received digital data from mathematically compressed images to begin rendering pictures. A huge advantage of digital SSTV is the ability to request re-transmission of data segments that have not been received properly in order to build up a high resolution picture. As a result pictures received by digital transmission tend to be far superior in quality than those received via analogue transmission.

Digital SSTV transmissions are usually conducted between 3-6kHz higher on HF bands and on the same frequencies as analogue transmissions on VHF and UHF. A considerable number of groups that operate across Australia are experimenting with this mode, often using FM on 2m and 70cm.

HF DIGITAL VOICE FREEDV

FreeDV is an open source digital voice system designed particularly for HF Radio. FreeDV software is available for PC, Linux and Mac computers.

FreeDV is a digital voice mode for HF radio. You can run FreeDV using a free GUI application for Windows, Linux and OSX that allows any SSB radio to be used for low bit rate digital voice. FreeDV uses forwarded error correction (FEC). There have been reports of the new FreeDV 700D mode outperforming SSB at low signal to noise ratios (SNR). At high SNRs FreeDV 1600 sounds like FM, with no annoying analogue HF radio noise.

FreeDV can be done without a computer using the SM1000 which allows you to run FreeDV without a PC. Connect the SM1000 to your SSB radio, and you now have digital voice (DV). You don't have to buy a new radio to run digital voice! It's based on a STM32F4 micro-controller, with a built in microphone, speaker amplifier, speaker, and transformer isolated interfaces to your radio. It's just 80 x 100mm, and can be held in your hand and used like a regular PTT microphone. Or it can sit on your bench and work with your favourite headset.

The SM1000 was developed by David Rowe VK5DGR and Rick Barnich KA8BMA. It is being manufactured, tested and shipped from Shenzhen, China.

The SM1000 is completely open - hardware and software - including the Codec 2 vocoder. The licenses encourage you to modify the software and hardware, under the condition that you share your modifications. You can purchase the SM1000 adaptor online.

A Google search of FreeDV will quickly reveal the location of the free GUI software to download and tips on getting started with FreeDV.

IRLP

Figure 40-5 shows an IRLP mode system. IRLP is an acronym of Internet Radio Linking Project created by David Cameron VE7LTD (Canada). IRLP uses the Voice over Internet Protocol (VoIP) to provide a voice service between amateur radio stations via the internet. As can be seen in the above diagram IRLP entry from the amateur station is via a repeater, which acts as a communication node, and thence into the internet system to reappear at a remote amateur repeater and to any listening amateur stations. The system is usually accessed by VHF or UHF radios working to a repeater equipped to handle IRLP traffic. The calling station, after checking the channel is free, enters the DTMF codes for the station being called and the IRLP system directs the call to that station. There are already more than 1400 nodes across 7 continents in the IRLP network and hence the amateur has no shortage of locations to call other amateurs around the world.

IRLP requires nothing special. You just need a VHF or UHF radio that can reach a repeater with IRLP capabilities. Most VHF and UHF radios today have DTMF coded buttons on the microphone. You use these buttons to type in the IRLP node number of the repeater to which you want to be connected. When you successfully connect to an IRLP repeater a stored message will announce that a connection has been established. Now when you transmit to your local repeater you will be using the remote node in parallel. That is you will be heard and communicate with radio amateurs locally and at the remote node location. At the beginning of each transmission through a node it is best to press the push to talk (PTT) and wait about two seconds before talking into the microphone. This is to allow the necessary switching to be made. When an IRLP connection has finished one of the stations at either node will transmit the DTMF code "73". This disconnects the link and when done successfully you will hear an announcement.

IRLP is quick and easy to get into. For more information and a list of nodes look at www.irlp.net

ECHOLINK

Echolink is a computer-based amateur radio system distributed free of charge that allows radio amateurs to communicate with other amateur radio operators using Voice over IP (VoIP) technology on the internet for at least part of the path between them. It was designed by Jonathan Taylor, a radio amateur with call sign K1RFD.

The system allows reliable worldwide connections to be made between radio amateurs, greatly enhancing amateur radio's communications capabilities. In essence it is the same as other VoIP applications (such as Skype), but with the unique addition of the ability to link to an amateur radio station's transceiver. Thus any low-power handheld amateur radio transceiver which can contact a local echolink node (a node is an active echolink station with a transceiver attached) can then use the internet connection of that station to send its transmission via VoIP to any other active echolink node, worldwide. No special hardware or software is required to relay a transmission via an echolink node.

Before using the system, it is necessary for a prospective user's callsign to be validated. The echolink system requires that each new user provide positive proof of license and identity before his or her callsign is added to the list of validated users. There is no cost for this service, and it ensures that this system is used only by licensed amateur radio operators.

The software is written to run on 32-bit and 64-bit versions of Microsoft Windows. Another edition of the software runs on Apple mobile devices (iPhone, iPod touch, and iPad), and is available from the Apple App Store. An android version is available on Google Play and several other android app repositories.

Echolink is one of the easiest global modes to set up and use quickly. You do not even need a radio. You can go into the echolink radio network from your computer or a smartphone.

For more information and software go to http://www.echolink.org/

41 - Mathematics - AC Circuits

Throughout this book the mathematics required for amateur radio exams has been used and explained. The purpose of this chapter is to go a little further with the mathematics for radio and electronics. This will by no means be an exhaustive treatment of mathematics but is for those readers who just want to go a few steps further. This chapter is not required learning for any amateur radio examinations.

RIGHT ANGLE TRIANGLE TRIGONOMETRY

A right angle triangle is any triangle on a flat surface where one of the angles is 90°.

All triangles have three sides and three angles. If one of those angles is 90° then we call it a right angle triangle. In the triangle above the square at the bottom left corner represents the right angle. The angle opposite the right angle is called "theta" the Greek letter θ.

The bottom (base) of the triangle is referred to as the Adjacent side. The side opposite the right angle is the longest side and is called the Hypotenuse. The side opposite the angle θ is called the Opposite side.

If we know any two sides of a right angle triangle we can easily work out the unknown side. The method is called the Theorem of Pythagoras.

Pythagoras of Samas (570-495BC) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samas. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated for complete vegetarianism.

Now Pythagoras is attributed with the theorem of solving right angle triangles. He allegedly said that the "square of the hypotenuse is equal to the sum of the squares of the other two sides".

I am sceptical that Pythagoras was the first to discover this. I am sure the Egyptians and many other civilizations before 530 BC knew about right angle triangles.

I remember when I first heard this in school I had no idea what it meant. So what does it mean?

To square something means to multiply it by itself - 2 squared (written 22=4). Let us see what this would look like if we squared all sides of a right angle triangle.

To square a side means just to make a square out of it. So we have made three squares out of the three sides of the triangle in figure 41-2.

The area of the Opposite Square plus the area of the Adjacent Square equals the area of the Hypotenuse Square.

For example if these were paddocks with the maximum number of sheep in them, then the sum of the sheep in the A square and the O square would be equal to the number of sheep in the H square. That is all the theorem of Pythagoras amounts to.

We write this mathematically as;

If we want H and not H2 we simply take the square root of each side. Giving;

If the length of the unknown side is not H but instead O or A we just have to transpose the formula for the side we want.

Suppose we want to find the length of the Hypotenuse in figure 41-3.

THE BASIC TRIGONOMTRIC FUNCTIONS 

Suppose however we do not know the length of 2 sides. Suppose we know the angle θ and the length of one side.

If more than one right angle triangle has the same angle θ then the ratio of the sides of those triangles will have the same ratio. Look at the triangles in figure 41-4.

We have three triangles all with the same angle θ (the angle opposite the right angle in this case but it could be any common angle) of 45°. All are right angle triangles.

The ratio of any two sides of one triangle is the same as the ratio of the same two sides of any of the other triangles.

Suppose triangle 1 had the sides H1=5; 01=3; and A1=4.

Then the second triangle could have the sides H2=10; 02=6 and A2=8. We could nominate the length of the sides for the third triangle but let's not bother, I think you have the idea.

What is the ratio of the Opposite to the Hypotenuse of the first two triangles? In other words what is the ratio O/H of the first two triangles as real numbers?

Triangle 1 gives O1/H1 = 5/3 = 1.6667 (rounded)

Triangle 2 gives O2/H2 = 10/6 = 1.6667 (rounded)

As you can see the ratio of O/H is the same. It is the same for all three triangles no matter what their actual size.

This is because all triangles in figure 41-4 are right angle triangles and they share a common angle other than the right angle, in this case opposite the right angle, of 45°.

We say that the trigonometric function sine (usually written as just sin) is equal to O/H. Or sinθ = O/H. So if we knew what sinθ was and we only knew the length of either O or H we could find the length of the unknown side.

So how do we find out sinθ? In bygone days we would look it up in a book of sine tables. Or perhaps use a slide rule. Today we would just use the "sin" key on a calculator.

You might be asking how is sinθ calculated and then placed in sine tables?. How does the calculator work out sinθ?. I will explain that shortly. Fortunately we don't have to use tables and we can just use a calculator but I will ask you to trust me and I will show how sinθ is calculated later. You will never have to calculate sinθ (the hard way) as you will always use a calculator. In the past we used lookup tables. Also there are an infinite number of values for θ and therefore sinθ.

For now sinθ=0/H.

There are 3 basic trigonometric functions. They are; sine, cosine and tangent. Usually abbreviated to sin, cos and tan.

Each of the three functions (you have already seen sine) relate to the ratio of two sides of any right angle triangle.

Here is a way to easily remember which is which. Simply remember the memory aid SOH-CAH-TOA. Best is to say it as one word SOHCAHTOA.

We can find sin, tan, and cosθ by using the calculator as long as we know the angle θ.

AN EXAMPLE USING TAN

We have a tower or any other object, and we want to know its height.

We use a tape measure to measure out from the base of the tower 40 metres. This does not have to be 40 metres. We can measure any distance out from the base within reason until the curvature of the earth begins to matter.

At the 40 metre mark we measure the angle (θ) between the ground and the top of the tower.

You need a protractor or some other angle measuring device to measure the angle from 40 metres out to the top of the tower. You need to measure the angle from ground level. If you don't that's okay you will just have to add the amount that the protractor was above ground to your answer.

In this instance the angle θ is 45 degrees. This makes the height of the tower obviously 40 metres but we do this to make sure our method works. We know the length of the adjacent side (A) and we know the angle θ. We want to find the length of the opposite side (O) so we can use tanθ=O/A.

What is the ratio for tanθ?

SOHCAHTOA 

tanθ=0/A

Transposing tanθ=0/A for the opposite "O" is easy as we just multiply each side of the equation by A and get;

O(the height of the tower)=tanθxA

O=tan(45°) x 40

O=40 metres.

I have drawn the triangle to scale so you might be able to see the answer for yourself. Any right triangle with a 45° angle opposite the right angle must be half of a square. The other angle above the right angle would also have to be 45° because all the angles of a flat triangle add up to 180°

The tan of 45° = 1. (1x40=40)

On most calculators, to find tan you just have to make sure the calculator is in degree mode (unless you are using radians) and it usually is by default. Type {tan}{45}{=} and you will get the answer 1 in the display.

However it does not matter that I have drawn half a square. This just means that intuitively you can probably see the answer yourself without any trigonometry. It also means that if you really want to know the height of anything and you can walk out from the base to where the angle between the ground and the top of the object is 45° then the adjacent (base) is the same length as the height. Such a triangle is called an isosceles triangle. That is, two sides opposite the hypotenuse are the same length.

Using one of these you can find everything about a right angle triangle if you know the length of one side and either of the other two sides plus the angle opposite the right angle.

There are quite a few other trigonometric functions but these are all we have to deal with for our purposes and for that matter most fundamental trigonometry. I know I have not yet revealed why we need to know this but I will give you a hint:

"Trigonometry has a lot to do with describing waves".

HOW DOES THE CALCULATOR FIND SINθ?

This is a question that always gets asked and usually not answered. I am going to answer it. There is more than one method. Similar methods are used for tan and cos.

A calculator could be looking up a sine table stored in read only memory (ROM). This may have been the case with the early electronic calculators. However even if I said this is how it is done you would ask the obvious follow up question: how is the sine table made?

The calculator uses an algorithm that gives a very close approximation to sine. There are several such algorithms that use only the four basic operations (+,-,X,+) to find the sine, cosine and tangent. All of these are an infinite series. However after a few terms of the series the answer can be considered so close that it is precise enough.

One such algorithm is the "Taylor Series". It can be used to find sin(x).

sin(x)= x-x3/3! + x5/5! - x7/7! ... ,

3! (3 factorial) Means 1 x 2 x 3 which is 6. 5! Means 1 x 2 x 3 x 4 x 5 = 120. I am going to do this for one angle (30 degrees) and we are lucky there is a factorial key on every scientific calculator {!}. See bottom page 584.

FINDING THE INSTANTANEOUS VALUES OF A SINEWAVE

The trigonometric function sine describes a sinewave. If we were to plot the sine of all angles from zero to 360 degrees we would get the sinewave shown in figure 41-6.

Notice in the first half cycle the sines are positive numbers. Sin(30°) is 0.5, sin(45°) is 0. 707 and the sin of (90°) is 1. The sine values duplicated themselves for the corresponding angles from 90° to 180°. For example sin(45°) and sin(135°) are both 0.707. On the second half cycle the numbers for the sine values are the same but they are negative. It is easy to see that the sine function fully describes one cycle of alternating voltage or current. Knowing this we can use the sine function to calculate the instantaneous values of voltage or current at any angle on a sinewave.

Figure 41-7 shows one cycle of an AC sinewave. The instantaneous voltage at 45° is 240VAC. You probably recognise this as the approximate RMS voltage of the household mains supply in Australia and some other countries. Calculate the maximum or peak voltage and also the instantaneous at 210°.

We know from figure 41-7 that:

sin (45°) x Emax = 240VAC.

By dividing both sides by sin(45°) we get:

Emax = 240VAC / sin(45°)

Solving we get:

Emax = 339 volts

Which I hope you recognised as the peak household mains voltage.

Calculate the instantaneous voltage at 210°

e=sin(210°)xEmax

e=sin(210°)x339

e=-169 volts

Notice how the voltage on the second half cycle of the sinewave is negative. This tells us that when the sinewave is representative of voltage it has a polarity reversal.

THE RADIAN

We say that a circle is 360°. Why? We could just as easily define a circle as 100°. The 360° is totally arbitrary and goes back to the Babylonians having a base 60 numbering system. While we work in degrees and are familiar with them in daily life it really is a silly way to define angles on culture rather than on the circle itself.

A better way to define angles is to use a unit of angular measure called the radian. A radian is a better method because it uses the circle itself to define angular measure rather than some historical arbitrary division like degrees.

A radian is how many times the radius of a circle will fit into its circumference. We know the circumference of a circle is C=2πr where r is the radius. So there are 2π radiuses (or radii) in the circumference of a circle. You cannot fit an even number of radiuses into the circumference of a circle. There are 2π or roughly 6.2831853' radiuses in a circle - each radius is called a radian. 2π is called "Tau" after the Greek letter that looks like a small "t". This is not used much but some argue it would be easier if we did.

So 2π radian is 360°, then π radians (or rads) is 180°.

The first thing we must do is convert our 360° to radians.

Convert 360° to radians.

Radians (rads)=degrees x π/180 so 30° is 30 x π/180 = 0.523598775 radians or rads.

To be clear, we are starting from sin(30°) or sin(0.523598775 rads).

We are now going to use the Taylor series to find the sine of the angle 30° or 0.523598775 radians.

Let B = 0.523598775 rads (store in Memory/Variable B)

sin(B)= B-(B3/3!)+(B5/5!)-(B7/7!)... , 

You can enter this equation just as written above into an algebraic calculator in conventional math mode (COMP). I only did it to three terms as above and pressed "=" which gives the answer.

sin(B) = 0.499999991 

More precise (with more terms) is sin(30°)=0.5

Now perhaps you can see why we do not work out the sines of angles manually as we would have long strings of decimal numbers and would have to go to 4 to 5 terms to get the precision we need. So be content, having seen one way it is done, to use your calculator to find sinθ, tanθ or cosθ.

DEGREES, RADIANS AND GRADIANS

These are all units of angular measure. Though we normally abbreviate them to "deg or °", rad, or grad.

In electronics and radio communications we will use degrees and radians a lot. A common mistake when using a scientific calculator is not to have the calculator set to one of these three modes and the mode you wish to use. If you are working in degrees then the calculator mode must be set to degrees.

We will not use the grad. I believe this is mostly used by surveyors. The gradian is a unit of angular measure in which the angle of an entire circle is 400 gradians. A right angle is therefore 100 gradians. A gradian is sometimes also called a "gon" or a "grade".

The inverse of the three basic trigonometric functions is as follows:

Inverse means (1/x or x-1)

1/sin θ = cosecant θ or just csc θ 

1/cos θ = secant θ  or just sec θ 

1/tan θ  = cotangent θ or just cot θ 

On your calculator cos, sec and cot may be written as Sin-1, Cos-1 and Tan-1, respectively.

Most of the time though we will just be using sin, tan and cos - remember SOHCAHTOA.

Since this tells us that sinθ=O/H , cosθ=A/H and tanθ =O/A, then the inverse trigonometric functions are found just by swapping the denominators and numerators:

cscθ=H/O

secθ=H/A

cotθ=A/O

Try this for yourself. Find the sin, cos and tan of 26° (make sure your calculator is in degree mode).

I have set my calculator to FIX 4 which means to 4 decimal places.

sin(26°)=0.4384

cos(26°)=0.9888

tan(26°)=0.4877

Now find the csc, sec and cot of 26°.

You could find cot by the inverse of your answer for sin, sec is the inverse of cos, and csc the inverse of tan in your last answers.

So;

csc(26°) = 1/sin(26°)= 1/0.4877 = 2.2812

sec(26°) = 1/cos(26°)= 1/0.9888 = 1.1126

cot(26°) = 1/tan(26°) =1/0.4384 = 2.0503

What if we know the sine of an angle (in degrees); say sin(30°)=0.5 - we know the sin is 0.5 but we do not know the angle (30°) - how do we get it back? On some calculators to get the angle back we use arcsin(0.5) = 30°. Your calculator may have sin-1 in which case if we go sin-1(0.5) we will get our angle back; that is 30°.

ANGULAR VELOCITY

I often get asked why π keeps coming up in many of our equations. Simple Harmonic Motion can be graphed as a circle or a sinewave. Pi (π) is directly related to both. Have a look at figure 41-9.

The motion of a point around a circle is simple harmonic motion. This motion plotted against time would produce a sinewave. By convention we say the starting point of a rotation around a circle is at the 3 o'clock  position.

Suppose a point on the circumference did one revolution per second. This is the same as saying "one cycle per second" or a frequency of 1Hz. 10 revolutions per second would be 10Hz. However there is another way to describe the rotation of a point around a circle. We know there are 2π radians in a circle. We can then say that one full circle is 2π radians or one cycle per second is 2π radians per second.

A frequency of 1Hz, 1 cycle per second= 2π radians/sec. 

When the rotation is expressed in radians per second we call it the angular velocity. The symbol for angular velocity is lower case Omega (ω).

To convert frequency in Hz to radians per second we would multiply whatever frequency we have by 2π since there are 2π radians per cycle.

ω=2πf(rads/sec).

No doubt you have seen 2πf in many equations used in electronics and radiocommunications?

How about XL=2πfL for inductive reactance? The 2πf part is us converting frequency to radians per second. We could write XL= ωL and it means exactly the same thing; we have just gotten rid of the f by converting it to angular velocity (ω). Likewise the equation for capacitive reactance; XC=1/2πfC would become XC=1/ ωf

Angular velocity is just a different way of describing harmonic motion or rate (speed) of motion just like frequency.

You will come across angular velocity used in place of frequency. You should be able to work with either or both.

RLC CIRCUITS

The effects of inductance, capacitance and resistance.

It is worthwhile remembering that current lags voltage in an inductive circuit and if the inductance is pure (no R or C) then the lag of current behind the voltage is 90°. So we say that the phase angle θ between current and voltage in an inductive circuit is 90° lagging.

In a purely capacitive circuit the current leads the voltage by 90°. So we say the phase angle between current and voltage in a purely capacitive circuit is 90° leading.

Since the lag is 90° behind the voltage in an inductive circuit and the lead is 90° in front in a capacitive circuit then the phase angle between these two currents in an LC circuit is 180° (or π: radians - since there are 2π: radians in a circle).

Purely Inductive circuit 

1. Inductance is the electrical property of a circuit that opposes change in current.

2. Produces a magnetic field around itself where it stores and discharges (returns) energy.

3. Inductors have a property called inductive reactance XL (measured in ohms) that reduces the amount of current flowing in a circuit.

4. Passes a DC current with no losses.

5. Produces a phase difference of 90° with the current lagging the voltage.

Purely capacitive circuit

1. Is the electrical property of a circuit that opposes change in voltage.

2. Produces an electrostatic field where it stores and returns energy.

3. Capacitors have a property called capacitive reactance XC (measured in ohms) that reduces the amount of current flowing in a circuit.

4. Blocks DC current flow.

5. Produces a phase difference between current and voltage of 90° with the current leading the voltage.

Purely resistive circuit

1. Is the electrical property that opposes current flow (measured in ohms).

2. Does not store energy at all but converts electrical current into heat.

3. Does not change the phase of the current and voltage.

4. Resistance is the only electrical property that produces power, does work or dissipates heat.

To bring the big difference between reactance i.e. how a capacitor XC or inductor XL reacts in an AC circuit consider the circuit in figure 41-10. The inductor in this circuit is a pure inductor (in fact that is always the case when no resistance is shown).

With 240V across 240Ω this current will draw 1 ampere from the supply. The current in this circuit will lag the voltage by 90°. We could have used a capacitor of 240Ω reactance and current would be the same but the current would lead the voltage by 90°.

How much power in watts is dissipated in this circuit?

Since there is no resistance, no power is dissipated in the circuit! Only resistance can dissipate power. The inductor will charge energy into and out of its magnetic field, taking it from the mains and giving it back.

A capacitor would do the same thing. If you connect such an inductor to your power point (don't - this is a mind experiment) you could leave it there for a year and your power meter would never register any energy consumed. This is presuming the electrical conductors to your power point have no resistance. If there is no R shown on the circuit then there is no R.

Say you did not know there was an inductor. It is in a black box. You then put an ammeter in series with the circuit and measure 1A. It would be easy to presume that the power dissipated then is P=EI = 240 x 1 = 240W. However you would be wrong as the power formulas only work when there is R in the circuit. You cannot use, for example, P=E2/XL. 240W is the apparent power but in fact there is no power in this example. Electrical supply authorities do not like reactive loads as they draw current but this current does not register on your energy meter. Reactive loads do register a little because of the tiny amount of ohmic losses in the conductors between your power meter and the power point.

Now something to think about. Is the 1A of current flowing real? Well we can measure it so it must be real. However there is no power. How would we plot such a number for the current on a number line?

Figure 41-11 is a number line and I have plotted positive and negative 6 on it.

This could be 6 amps DC in one direction and 6 amps DC is the opposite direction. Where would we plot the 1A in our inductive circuit? There is nowhere on the number line! It is pretty obvious then that we are going to need something more than a simple number line to plot reactances and/or their currents.

CARTESIAN COORDINATES

Here is a way that we can expand the number line to show the lagging current of the inductor. I can add another vector  90° down from the number line and I can mark on that line 2A like this.

Using this modified number line we can show a current lagging (negative)  90° out of phase with resistive current (if there is any).

What if we had used a capacitor of the same reactance instead of an inductor? What if we had used both?

We could plot the capacitive current (2A) in cartesian (also called rectangular) coordinates as shown in figure 41-13.

Using two extra coordinates in the Y axis that are not part of the normal number line I can now show a leading and a lagging current. The extra Y coordinate contains what we call imaginary numbers. Such numbers are usually (in electronics) denoted as 'j'. So the inductive current would be -j2A and the capacitive current +j2A or just j2A. The letter "i" for imaginary is often used instead of "j" and sometimes it is written +2Ai however in this course and most electrical/electronic courses the letter "j" is the convention.

The reason why the numbers on the Y axis are called "imaginary numbers" is that we cannot perform normal arithmetic on them. All the numbers on the X axis are real numbers. We can do all normal arithmetic operations on real numbers on their own but we cannot do the same to imaginary numbers or when imaginary numbers and real numbers are combined. Then they are called complex numbers.

For example the Y axis going down from the origin "0" zero are negative imaginary numbers. Suppose we marked it off just like the number line.

On the real number line (the x axis is not marked) we have all real positive numbers to the right of the origin and all negative real numbers to the left. On the imaginary axis (y) we have almost the same. Positive imaginary numbers going up and negative imaginary numbers going down.

We are going to be doing some trigonometry on these cartesian coordinates later. If we just worked with the real number line then we would use normal math. In normal math √(-1) is not permitted. Try it. Get your calculator and try to find the square root of (-1). Your calculator will have a dummy spit. We do not do this on the real number line but we do need to do it (as you will see) on the imaginary number line. -1 is set to the value of "j" or "i". If your calculator has a complex mode (cmplx) then set to this mode and try again √(-1) you will this time get an answer. Not a number (because there is no number for the √(-1) ). Instead your calculator will return the answer "1i".

Are imaginary numbers real or imagined? Well they are not called "real" numbers because we cannot express them the way ordinary real numbers are defined on the number line. However we use imaginary numbers to be able to combine real things like reactance and resistance to get "real world" answers. The imaginary numbers are real numbers in the sense that they allow us to obtain real answers using complex numbers. Radio amateurs use complex numbers even if they are not aware of it. For example, a radio amateur might measure the impedance of their antenna using an impedance bridge and normally get and an answer R+/-X. Suppose R = 100 and X = -50. Then the radio amateur, if asked what the impedance of their antenna was, would say it is 100 ohms of resistance and 50 ohms of capacitive reactance. A better way of expressing this is to say the impedance is 100-j50Ω.

They know their antenna is not resonant because it has 50 ohms of capacitive reactance. Their antenna is too short and needs inductance (to cancel that capacitive reactance out). If the antenna was 100j50Ω then it has 100Ω of R and 50Ω of inductive reactance (it is too long or needs C to cancel out the L).

Do you notice how the radio amateur cannot give you the impedance as a single number? They have to express the impedance as two parts; real+/-imaginary. They are using complex numbers in what is called rectangular form. There is another form called "polar" which we will get to shortly.

The only time an impedance can be expressed as a single number is when j=0, in other words, when the reactances cancel. The j0 is still there. We just don't "say it" because j0 is the same as the real number 0. A resonant dipole has impedance (which varies a bit with the environment) of about 72j0Ω. Since there is a real part (72) and no imaginary part (j0) we usually just say 72Ω. However, change frequency off resonance and watch the real part change and "j" increase to a higher value either positive (inductive) or negative (capacitive).

Let us not get too far ahead of ourselves. Let's have a look at a circuit with just R and L and we will work with reactances and resistance. Working with reactances is the same as working with L and C. Because we will be working with reactances XL and XC the inductive reactance is plotted as j and the capacitive reactance as -j.

INDUCTANCE AND RESISTANCE IN SERIES

When an inductance and resistance are in series with an RF AC source an alternating current will flow in the circuit. If the inductor was not there the phase between the current and voltage (called the phase angle) would be zero. In other words without L the current and voltage are in phase. Without an inductor all the power would be converted to heat. The current could be determined by simply l=E/R.

If this circuit just had inductance alone, the current and voltage would be 90° out of phase. The current would lag (or be lagging in phase) the voltage by 90°. No power would be dissipated in the circuit. Whatever the inductor took, in the way of energy from the supply, would be returned on the next half cycle. Current would flow in the circuit and be equal to l=E/XL.

With both R and L as shown there is often a need to work out what the current is and the voltages are across L and R and the amount of real power dissipated in the circuit.

If the frequency of the RF source is known and the L is known then the reactance of the inductor can be found from:

The current in an LR circuit will be opposed by L (opposing changes of current) and R opposing current. However the opposition of L is 90° out of phase with the opposition of R.

We can draw this on cartesian coordinates as shown in figure 41-16:

The total opposition to current flow is the combined effects of L and R. This is called Impedance (Z) in ohms. If we draw a line between XL and R we produce a right angle triangle whose hypotenuse is equal to Z or the impedance of the circuit. Being a right angle triangle we can work out the value of Z by using the Pythagoras Theorem.

Hang on a minute. Now we are expressing the impedance as a single number. We cannot do this unless there is no reactance (such as in a resonant circuit).

We cannot express impedance as a single number. In this case we have to say what the phase angle is of this LR circuit.

PHASE ANGLE

The current in a purely inductive circuit lags the current by 90°.  In a resistive circuit alone the phase angle is 0°. When both resistance and inductance are in the circuit the phase angle will be between 0° and 90°.

It is time to do an example. Take a look at figure 41-17.

This could be the circuit of anything. It could be the resistance and inductive reactance in a vertical antenna and that is what we will call it. What is the impedance of this circuit in rectangular, complex number form?

The antenna has an impedance of 10+j20Ω < this is a complex number where 10 is a real number and +j20 is an imaginary number plotted on the imaginary number line discussed earlier.

Let's plot this in the upper right quadrant of the complex and real plane.

Figure 41-18 shows XL and R approximately to scale. XL is 10 ohms upwards from the origin on the positive imaginary line. R is 20 ohms drawn from the origin on the real number line.

First let us work out the impedance (using Pythagoras).

So the impedance is 22.36Ω. We cannot describe impedance as a single number if there is reactance present. So we need to find the phase angle of this current.

We know the three sides of a right angle triangle and we want to find θ, the angle opposite the right angle. We could use any of the basic trigonometric functions but let's suppose that we did not find (Z) the hypotenuse first and all we then knew was adjacent (XL) and opposite (R).

What trigonometric function could we use? SOHCAHTOA 

Well, tanθ=O/A, pops into mind.

Or

Phase angle=tanθ=XL/R so tanθ=10/20 = so tanθ=0.5

We need to find the arctan (or inverse tangent) of 0.5.

On most calculators we do this by going inverse, 2nd, or shift tan then entering 0.5 and pressing = gives 26.565°.

So the full description of this impedance is then:

 Z = 22.36/26.565°Ω 

So now we have expressed the impedance comprising of a resistor of 20Ω in series with an inductive reactance of 10Ω two ways.

For this circuit the impedance can be expressed (using two numbers) as either.

1. Z=20+j10Ω (this is a complex number in rectangular form)

2. Z=22.36/26.565°Ω (this is the same complex number in polar form)

In rectangular form (1) we have the REAL part + the IMAGINARY part.

In polar form (2) the 22.36 is called the "MAGNITUDE" and the 26.565 is called the ANGLE (or in our case the phase angle)

Both methods describe the same impedance but using different methods. A modern impedance meter will give you either or both.

If the reactance was capacitive we would plot that on the negative imaginary number line.

How about we do another circuit?

This could be an antenna. The R in the circuit would be the antenna radiation resistance + the antenna losses. We would normally show these as two separate resistances but let us assume there is no loss resistance and that the 7Ω is the radiation resistance.

What is the total impedance of this circuit in ohms?

How much current will flow and how much power is dissipated or radiated?

Here is the vector diagram using cartesian coordinates.

Now the reactances as a complex number are 0+j8Ω for the inductance and 0-j18.95Ω for the capacitance. The resistance is 7+j0Ω.

Using complex number arithmetic we can add (0-j18.95) + (0+j8) and we get the difference which is 0.-j10.95Ω.

Now you have been doing that all along haven't you? Before you knew about complex numbers you knew that opposite reactances in series cancel each other.

So the impedance of the circuit in rectangular form is.

Z=7-j10.95Ω 

Now on a calculator (in complex mode; this allows me to enter complex numbers and do operations with them) I am going to enter this value and ask it to convert to polar form, I get:

Z=12.996/-57.4107°Ω 

[Note. We could have used Pythagoras and tanθ to get to this last result. We just jumped this by using the calculator to convert rectangular coordinates to polar form i.e.(magnitude and angle)]

That step of using the calculator was very quick and easy. Now I could use either of these same impedances (just in different form) to do further calculations.

Suppose we were told that 100V (100j0V) rms was applied to this circuit how much current will flow?

We have 100j0V (we don't know the frequency but we do know the complex impedance) applied across 7-j10.95Ω.

l=E/Z=(100j0)÷(7-j10.95)

Using the calculator again I get.

I=4.1444+j6.4830 amperes

I get a complex current because there is reactance in the circuit. I could easily (with a calculator or by hand, but why do it by hand) convert this to polar and I would get the magnitude and phase angle of the current.

I=7.6945/57.4105°A

[note: We could have used the magnitude of the total impedance to find the magnitude of the total current i.e. l=E/Z = 100/12.996 =7.694A]

We have nearly 7.7 amperes but there is a phase shift between current and voltage of approximately 57.4°.

What if we calculated the power dissipated or radiated by the circuit by the applied voltage and the magnitude of the impedance?

We have 100V rms applied.

We have 7.6945A flowing.

P=l2Z

P=(7.6945)2xl2.996=796 watts* (Or is it!. This is wrong.)

Or we could have done the same thing using P=E2/Z

P=(100)2/12.996 = 796 watts!*(still wrong)

This cannot be the true power dissipated in the circuit because the circuit has reactance. We call this the "Apparent power" and it is measured in VA (volt-amperes)

*The power we calculated here is the apparent power in volt-amperes (VA) not watts.

We know there is 7.6945/57.4105°A flowing in the circuit. This current flows through all components in a series circuit. So this is the current flowing through our R which is 7Ω.

What if we calculated the power dissipated (or radiated) in R?

P=l2R

P=(7.6945)2x7Ω 

Now the magnitude of the current regardless of its phase is 7.6945A. These are real coulombs moving around here. Real electrons or 7.6945 coulombs/sec through the resistance so we can drop the phase angle. The power radiated by the resistance is only determined by the current through that resistance.

P=(7.6945)2x7=414.4373W or 414W

The true power is a lot less than the apparent power calculated earlier. Apparent power is 796VA while true power is 414W.

We do not use the term power factor (PF) in radio. PF is just the ratio between true power ÷ apparent power. When the PF=1 the true and the apparent power is the same. At least that is what electrical engineers use. What radio engineers say (when PF=1) is "we have resonance" - there is no reactance in the circuit.

PERFORMING CALCULATIONS WITH COMPLEX NUMBERS 

Complex numbers can be added, subtracted, multiplied and divided along with other operations provided the rules for using complex numbers are followed. However, using complex numbers manually is not hard but it is cumbersome and as such prone to errors. Most modern scientific calculators will perform complex number arithmetic. There is computer software for using complex numbers and even website based calculators.

My choice for doing complex number arithmetic is the scientific calculator. Some calculator brands and models are better than others in terms of ease of use and price. The calculator that I recommend to students is the CASIO FX-991ES-PLUS or any similar model. This a low price range calculator and unless you are a very advanced mathematician you are unlikely to out grow it.

Performing complex arithmetic on the calculator is easy to learn. Once you set the mode of the calculator to CMPLX (complex) using the mode switch you can, with a couple of simple rules, just key in the complex numbers and perform operations on them returning a complex result.

WHY LEARN HOW TO USE COMPLEX NUMBERS? 

Most of the radio circuits we use in radiocommunications require complex numbers to describe them. You are probably already using complex numbers if you have an antenna analyser. Most antenna analysers will give you an impedance in rectangular form R+/-X.

The rules for finding total impedance in series and parallel circuits are the same as for resistance.

For example, resistances in series, the total resistance is given by:

Rt=R1+R2+R3...n

Impedances in series, the total impedance is given by:

Zt=Z1+Z2+Z3...n

The total resistance of resistors in parallel is given by the reciprocal of the sum of the reciprocals:

Rt=1/(1/R1+l/R2+1/R3 .. n)

Similarly, total impedance of impedances in parallel is given by:

Zt=1/(1/Z1+1/Z2+1/Z3...n)

Antennas, transmission lines and tuned circuits are just some examples that you can learn to understand more if you learn how to use complex numbers. Later in this chapter we will do some complex number calculations to explain how an antenna tuner works. I will be using a Casio FX-991ES. Just about all modern scientific calculators will work in a similar way but try not to go overboard and purchase a calculator that is too complex to learn as you may never use many of the other advanced functions.

Have a look at figure 41-21 and ask your self what is the impedance of this series RLC circuit? You can probably work it out and using complex numbers without realising you are using complex numbers.

The first step to determine the impedances is to find the reactance of the inductor (XL) and that of the capacitor (XC).

XL=2πfL=1256.64Ω=0j1256.64Ω

XC=l/2πfC = 318.31Ω=0-j318.31Ω 

XL and XC can now be shown on the circuit:

USING A CALCULATOR

The instructions are for the Casio FX-991ES or similar. To do complex operations the calculator must be set in complex mode. Press the mode button and then press "2" for CMPLX.

MEMORY STORAGE 

Often when doing complex number calculations you will get an intermediate answer that you need to use again in the calculation. An easy way to do this is to store the complex number in one of the calculator's memories. The 991ES (and most other calculators) have memories A-F and numbers can be stored in complex form with SHIFT STO A-F, where A to F is the required memory location. If you want to recall a number from memory A to include it in a further calculation you only have to press RCL A.

Find the impedance of figure 41-22. This is a series circuit with three impedances so we must sum the three impedances in complex form.

Zt=Z1+Z2+Z3

Zt=(0+1256.64i)+(0-318.31i)+(1000+0i) (written the way it is keyed into the calculator).

Press=

Display shows 1000+938.33i

We normally write this as 1000+j938.33Ω 

This means: 1000 ohms of resistance in series with 938.33 ohms of inductive reactance. This is the impedance of the circuit shown in 41-22 in rectangular form.

If we wanted polar form we can force the calculator to polar with SHIFT SETUP then 3 for CMPLX and 2 for polar and we get 1371.23/43.17°.

This means the magnitude of the impedance of figure 41-22 is 1371.23 ohms with a lagging phase angle of 43.17 degrees.

That was fairly easy and you may have guessed the answer knowing that when you have two opposite reactances in series the net reactance is simply the difference between the reactances or X=938.33-318.31 = 938.330 and that the R of 1000 is just tagged on to give 1000+j938.33Ω 

What if the three impedances in 41-22 were in parallel? See figure 41-23

With the three impedances now in parallel we cannot just sum them. We have to calculate the reciprocal of the sum of the reciprocals of each impedance.

CASIO calculators working in complex mode receive a complex number input as (real +/-imaginary). For example 10-j24Ω would be entered (including the brackets) as

(10-24i). When doing the calculations on this page I used memory functions to store intermediate operations and recall them for later use.

This shows us that the circuit diagram if figure 41-23 can be reduced to a single resistance of 153.8 ohms and a series capacitance with a reactance of 360.7 ohms.

HOW DOES AN ANTENNA TUNER WORK?

The purpose of an antenna tuner is to match impedances between a source and a load. The source could be a radio transmitter and the load either the antenna or the input of a transmission line. Matching source to load ensures maximum power transfer to the load. Antenna tuners do this by using a combination of adjustable capacitors and inductors. The following problem (figure 41-24) was requested by a student of RES. The request was to prove using complex maths that the "L" high pass filter matches the complex load impedance of 28j208Ω to a 50Ω source impedance. In other words the antenna has a complex impedance of 28j208Ω, does the L-match convert this to 50j0Ω at the transmitter to give near 1:1 VSWR?

This L-match has been adjusted for low SWR and then the values of L and C read with an LCR meter. Can we prove using complex number arithmetic that the L-match is converting the antenna impedance of 28j208Ω to 50j0Ω as seen by the transmitter?

The first step is to convert the 67.47pF capacitance and the 0.87uH inductor to their respective reactances so that we can re-draw the circuit with impedance only.

XC= 1/2πfC

XC= 1/2π x 10.1MHz x 67.47pF

XC= 233.55Ω and we write this as 0-j233.55Ω 

XL= 2πfL

XL= 2π x 10.1MHz x 0.87uH

XL = 52.21Ω  and we write this as 0+j52.21Ω 

Next we re-draw the circuit and update the L and C with their equivalent impedance at 10.1MHz.

The capacitor and the load are in series. (figure 41-26). First we can find the total impedance of this circuit.

We can now redraw the circuit of figure 41-25 and replace the capacitor and the load in series with 28-j25.8Ω 

Now in figure 41-27 we are left with the inductor and the series RC circuit in parallel. If we calculate the impedance of these two in parallel we will arrive at the impedance that the transmitter sees. For this parallel impedance calculation we find the reciprocal of the sum of the reciprocals.

There you have it! The antenna is an LR circuit of 28j208Ω. So the antenna is not resonant since it has inductive reactance. The L-match converts the antenna impedance to 51.75+j0.8Ω at the transmitter. The transmitter sees a very low almost perfect SWR. The transmitter then will develop full power into the load (the antenna system). Where does all this power go? The L-match is made of reactive components L and C. Reactance does not dissipate power. In practice the L and C of the L-match will have a very small amount of resistance but none worth worrying about. For practical purposes all the power is being delivered to the antenna.

On receive the antenna is the source of power and the receiver is the load. The source impedance of the receiver is 50j0Ω by design. Let's work out what the antenna sees as a load when the antenna is acting as a source.

Looking from the antenna's perspective towards the load we need to first calculate the load (the receiver) source impedance of 50j0Ω in parallel with the inductor of 0+j55.21Ω 

Now (as always) we can re-draw the circuit replacing the receiver and the parallel inductor with the equivalent impedance calculated above.

Now work out the equivalent impedance of 24.46+j24.87Ω in series with O-j233.55Ω

Again we re-draw the circuit.

The source impedance of the antenna sees a load equal to its conjugate impedance. Conjugate impedance means the real part of the impedance is the same (or close enough as calculated here) and the imaginary or reactive part is the opposite sign. Maximum power transfer from a source to a load will occur when both the source and the load impedance are resistive and equal. When the source or load have reactance, they are complex, and maximum power transfer will occur when the load impedance is equal to the complex conjugate of the source impedance.

That is how our antenna tuner works. It alters the impedance of the load so that the source sees a complex conjugate and this enables maximum power transfer to occur. Here we used an L-match but it matters not what the configuration of the tuner's matching circuit is as the principle is exactly the same.

This match on receive explains why you can adjust an antenna tuner on receive for maximum signal or noise. On receive you are finding an approximate conjugate match. Then on transmit you are making final small and more accurate adjustments for a conjugate match which also coincides with an SWR of 1:1.

Table of Contents

RADIO THEORY HANDBOOK

Contents

1 - Basic Electricity - I

2 - Basic Electricity - II

3 - Basic Electricity - III

4 - Ohm's Law

5 - Series Circuits

6 - Parallel Circuits

7 - Series Parallel Circuits

8 - Magnetism

9 - Alternating Current I

10 - Alternating Current II

11 - Capacitance - I

12 - Capacitance - II

13 - Capacitive Reactance

14 - Inductance

15 - Meters

16 - Electric Cells & Batteries

17 - Microphones

18 - Transformers

19 - Resistive, Inductive & Capacitive Circuits

20 - Power Supplies

21 - Electron Tubes

22 - Decibels

23 - Electromagnetic Radiation

24 - Semiconductors I

25 - Semiconductors II

26 - Amplifiers

27 - Oscillators

28 - Propagation

29 - Amplitude Modulation

30 - AM Transmitters & Receivers - I

31 - AM Transmitters & Receivers - II

32 - Filters in Radio Communications

33 - Interference

34 - Frequency Modulation

35 - Digital Modulation

36 - Transmitter Faults

37 - Antennas

38 - Transmission lines

39 - Test Equipment & Measurements

40 - Other Operating Modes

41 - Mathematics - AC Circuits