x Preface With this brief apology for a style which some my colleague and friend of more than a quarter of will undoubtedly find leisurely to the point of a century's standing, Mick G. Thanks also to Dave boredom, but which will I hope materially assist Watson who produced the 'three-dimensional wire others, it only remains to mention two minor grid' illustrations of poles and zeros in Appendix 4 points before passing on to the main body of the and elsewhere. For permission to reproduce circuit book. First, I must apologize to British and many diagrams or other material, supplied or originally other non-US readers for spelling 'analog' published by them, my thanks are also due to all throughout in the North American manner: they the following: will in any case be used to seeing it spelt thus, whereas 'analogue' looks very quaint to North C. Barmaper Ltd American eyes. Second, the following pages can EDN be read at different levels. The technically minded Electronic Design adolescent, already interested in electronics in the Electronic Engineering early years of secondary or high school, will find Electronic Product Design much of practical interest, even if the theory si not Electronics Worm (formerly Wireless World) appreciated until later. Technicians and students ETI at technical colleges and polytechnics will all find Ever Ready Company (Great Britain) Ltd the book useful, as also will electronics under- Hewlett-Packard Journal graduates. Indeed, many graduates and even post- Maplin Electronic Supplies Ltd graduates will find the book very handy, especially Maxim Integrated Products UK Ltd those who come into electronics from a different Microwave Journal background, such as a physics degree. Microwaves & RF Writing the following pages has turned out to be Motorola Inc. a not inconsiderable task. My sincere thanks are New Electronics due first to my ever-loving (and long-suffering) Philips Components Ltd (formerly Mullard Ltd) wife, who shared the typing load, and also to Practical Electronics those who have kindly vetted the work. In par- Practical Wireless ticular, for checking the manuscript for howlers and for many helpful suggestions, I must thank my Ian Hickman colleagues Pete C., Dave F., Tim .S and especially Eur. Ing retpahC 1 Passive components The passive components used in electronic circuits by ),.(/.-, ,,.,I all make use of one of the three fundamental l phenomena of resistance, capacitance and induc- tance. Just occasionally, two may be involved, for where P (lower-case Greek letter rho) is a property example delay cable depends for its operation on of the material of the wire, called resistivity. In the both capacitance and inductance. Some com- case of copper the value of P is 1.55 (cid:141) 01 -80m in ponents depend on the interaction between an other words, the resistance between opposite faces electrical property and, say, a mechanical prop- of a solid cube of copper of 1 m side is 0.0155 ~f~. erty; thus a piezoelectric sounder operates by The term (//A)p is called the resistance of the wire, virtue of the small change in dimension of certain denoted by R. So one may write types of ceramic dielectric when a voltage is applied. But most passive components are simply l resistors, capacitors or inductors. In some ways R -~p (1.2) inductance is the most subtle effect of the three, since with its aid one can make transformers, Combining (1.1) and (1.2) gives I= E/R, the form which will be described later in this chapter. in which most people are familiar with Ohm's law (see Figure 1.1). As mentioned earlier, when current flows through a resistance, energy is dis- sipated as heat. The rate at which energy is Resistors I )serepma( Some substances, for example metals (particularly 0.1 copper and aluminium- also gold, but that's a bit expensive for everyday use), conduct electricity well; these substances are called conductors. 15~ t 0.5- / i ' They are distinct from many others called insulators, such as glass, polystyrene, wax, PTFE -r jl 5.w0__ ~ , , v ---~, E )stlov( -1.5 5.0 1 5.1 etc., which in practical terms do not conduct electricity at all. In fact, their resistivity is about 1018 or a million million million times that of metals. Even though copper, say, conducts elec- -1.0 tricity well, it exhibits some resistance to the flow of electricity and consequently it does not conduct ehT slope fo eht line si given yb .Eg/lg nI this noitartsulli lg = 1 A and Eg = 1 ,V os eht conductance G = 1 .S ehT S perfectly; energy is lost in the process, appearing in sdnats rof siemens, eht unit fo conductance, ylremrof dellac the form of heat. In the case of a wire of length 1 eht mho. G = .R/1 metres and cross-sectional area A square metres, Figure 1.1 Current through a resistor of R ohms as a the current I in amperes which flows when an function of the applied voltage. The relation is linear, electrical supply with an electromotive force as shown, for a perfect resistor. At DC and low frequen- (EMF) of E volts is connected across it is given cies, most resistors are perfect for practical purposes. 2 Analog Electronics B bR R _- R2 R- 2/R A C A . . . . C 2R Star or eyw ,h, Delta or mesh A AtoA AtoA, 1 RbRc R2R 3 R1 1 1 R 1 = R b+ R c+ aR Ra= R 1 + R 2+ R 3 = R2 = R R1 2 RaR c R1R 3 2R 1 + 2R R 1 + R 2 R2=Ra+ Rc+ ~---"R Rb= R 1+ R 2+R 3 RaR b R1R 2 R3=Ra+ Rb+ ~-"---R Rc= R 1+ R 2+R 3 (a) )b( For resistors in series, total For resistors in parallel, resistance si 1 1 1 1 n, = + + n_ = + + Figure 1.2 Resistors in combination. )a( Series parallel (also works for impedances). )b( The star-delta transformation (also works for impedances, enabling negative values of resistance effctively to be produced). dissipated is measured in watts, where one watt 1 Mf~ (one million ohms) were available, but were equals one joule per second. If a current of I expensive owing to the vast number of turns of amperes flows through a resistance of R ohms, very fine wire needed to achieve this resistance. the power dissipated is given by W = IZR. Using Nichrome (an alloy of chromium and nickel) is Ohm's law it also follows that W=EI=EZ/R, used for high-power resistors designed to dissipate where E is the EMF necessary to cause the current several or many watts, whilst precision wirewound I to flow through the resistance R. Clearly from resistors may use constantan or manganin (alloys (1.2), if a second identical wire is connected in of copper with nickel or manganese respectively). series with the first (doubling l) the resistance is Such resistors have an extremely low temperature doubled, whilst if it is connected in parallel (dou- coefficient of resistance; they are available manu- bling A) the resistance is halved (Figure 1.2 also factured to a tolerance of better than 0.05% and shows the useful 'star-delta' equivalence). are stable to within one part per million 1( PPM) Electronic engineers use resistors from a frac- per year. Such resistors are used as reference tion of an ohm up to millions of ohms. Low-value standard resistors in measurements and standards resistors up to a few thousand ohms are often laboratories. In many electronic circuits, resistors wirewound, although pure copper wire is seldom with a tolerance of ,1 2 or 5% are entirely used owing to its high temperature coefficient of satisfactory; indeed, in the era of thermionic resistance, namely +0.4% per degree centigrade. valves 20% was the norm. At one time, wirewound resistors with values up to In the interests of economy, most low-power Passive components 3 resistors up to 1 W rating are not wirewound, and Resistors are mass produced in certain preferred indeed the resistive element is frequently non- values, though specialist manufacturers will supply metallic. Carbon composition resistors have a resistors of any nominal value, at a premium. cylindrical resistance element made of an insulat- Appendix 1 shows the various E series, from E6 ing compound loaded with carbon, usually which is appropriate to 20% tolerance resistors, to protected by a moulded phenolic covering. Such E96 for 1%. resistors were universally used at one time and are Resistors of 1% tolerance are readily available still widely employed in the USA. The resistance in metal film and metal glaze construction. Metal tends to rise as the resistor ages, owing to the glaze resistors use a film of glass frit and metal absorption of moisture: the effect is less powder, fused onto a ceramic core, resulting in a pronounced where the resistor is run at or near resistor with good surge and short-term overload its rated dissipation and operates for long periods. capability and good stability even in very low and Carbon composition resistors not only are in- very high resistance values. Metal film resistors expensive but also behave very well at radio have a conducting film made entirely of metal frequencies, unlike wirewound resistors and to a throughout and consequently offer a very low lesser extent spiralled film resistors. noise level and a low voltage coefficient. The next big improvement in resistor technology The latter can be a very important consideration was the carbon film resistor, popularly known in in critical measurement or very low-distortion the early days as a Histab resistor owing to its applications. Ohm's law indicates that the current improved ageing characteristic. It was available in through a resistor is directly proportional to the 5, 2 and 1% tolerances, and the 5% variety is still voltage across it; in other words, if the current is widely used in the UK and Europe as a general plotted against the voltage as in Figure 1.1, the purpose low-wattage resistor. Manufacture is result should be a perfectly straight line, at least if highly automated, resulting in a low-cost resistor the rated dissipation is not exceeded. Hence a that is very reliable when used within its rated resistor is described as a 'linear' component. It voltage and power limits. (Note that for resistance can more accurately be described by a power series values much above 100 kf~, it is not possible in the for current as follows: case of a carbon film resistor to dissipate its rated I - (E + E~0 2 + E3 3 + 7E 4 +-..) power without exceeding its rated working (1.3) R voltage.) The carbon film is deposited pyrolytically on a ceramic rod, to a thickness giving an end-to- If ,ta ,3 7 and the coefficients of higher powers of end resistance of a few per cent of the required E are all zero, the item is a perfectly linear resistor. final value. End caps and leads are then fitted and In practice, t0 is usually immeasurably small. a spiral groove is automatically machined in the Coefficient 3 will also be very small, but not carbon film. The machine terminates the cut when necessarily zero. For instance, the contact resis- the required resistance is reached, and a protective tance between individual grains of carbon in a insulating lacquer is applied over the film and end carbon composition resistor can vary slightly caps. Finally the resistance and tolerance are with the current flowing, i.e. with the applied marked on the body, usually by means of the voltage, whilst with film resistors the very small standard code of coloured bands shown in contact resistance between the film and the end Appendix .1 caps can vary likewise. A quality control check Metal oxide resistors are manufactured in much used in resistor manufacture is to apply a pure the same way as carbon film, except that the sinusoidal voltage of large amplitude across resistive film is tin oxide. They exhibit a higher sample resistors and check the size of any third- power rating, size for size, than carbon film, and harmonic component generated- indicating a when derated to 50 or 25% of maximum they measurable value of .3 Contact resistance varia- exhibit a degree of stability comparable to Histab tion can also be responsible for the generation of or semiprecision types respectively. an excess level of random noise in a resistor, as can 4 Analog Electronics ragged edges of the spiral adjustment cut in a film deciding whether it is worth achieving a particular resistor. nominal value by the above means. It is sometimes convenient to connect two or Variable resistors are available in various more resistors in series or parallel, particularly technologies: wirewound, carbon film, conductive when a very low or very high resistance is required. plastic, cermet etc. Both ends of the resistive track It has already been noted that when two equal are brought out to contacts, in addition to the resistors are connected in series, the resultant 'slider' or 'wiper'. When the component is used resistance is twice that of either resistor alone, purely as a variable resistor, connections are made and if they are connected in parallel it is half. In to one end of the track and the wiper. It may be the general case of several resistors of different useful to connect the other end of the track to the values, the results of series and parallel combina- wiper since then, in the event of the wiper going tions are summarized in Figure 1.2a. So, for open-circuit for any reason, the in-circuit resis- example, to obtain a resistance of 0.33 ft (often tance will only rise to that of the track rather than written as 0R33) three 1 ~f (1R0) resistors in go completely open-circuit. When the component parallel may be used. Not only does this arrange- is used as a potentiometer, the wiper provides a ment provide three times the power rating of a signal which varies between the voltage at one end single resistor, it also offers a closer initial of the track and that at the other- usually tolerance. In values down to 1R0, resistors are maximum and zero respectively (Figure 1.3). available with a 1% selection tolerance; whereas Thus the voltage at the output depends upon the for values below 1R0, 5 or 10% is standard. This position of the wiper. But what about the effect of would be an inconveniently large tolerance in the resistance of any circuit we may wish to many applications, for example the current sensing connect to the wiper? Well, this is as convenient shunt in a linear laboratory power supply. The a point as any for a digression to look at some of parallel resistor solution may, however, involve a the corollaries of Ohm's law when connecting cost penalty, for although three IR0 resistors sources of electricity to loads of one sort or will usually be cheaper than a higher-power another, e.g. batteries to bulbs or whatever. 0R33 resistor, the assembly cost in production is Figure 1.4a shows an ideal battery or voltage higher. source, and Figure 1.4b a more realistic one with a Series resistors may be used likewise either to finite 'internal resistance'. It would clearly be obtain a value not otherwise readily available (e.g. imprudent to short-circuit the ideal battery, since 200M); or to obtain a closer tolerance (e.g. two Ohm's law indicates that with a resistance of zero 1% 750K resistors where a 1M5 resistor is only ohms between its terminals the resultant current available in 5% tolerance); or to gain twice the would be infinite- smoke and sparks the order of working voltage obtainable with a single resistor. the day. To be more precise, the foregoing scenario Unequal value resistors may be combined to give a must be fictional: for if the voltage source really value not otherwise readily obtainable. For ex- has zero internal resistance there must always be E ample, E96 values are usually restricted to resistors volts between its terminals, however much current above 100R. Thus a 40R resistance may be it supplies; whereas if the short-circuit really has produced by a 39R resistance in series with 1R0, zero resistance there can be no voltage between the a cheaper solution than three 120R resistors in source's terminals, however much current flows. parallel. Likewise, a 39R 1% resistor in parallel Shades of the irresistible force and the immovable with 1K0 is a cheaper solution for 37R5 at 2% object! In practice a source, be it battery or power than two 75R 1% resistors in parallel, as the 1K0 supply, will always have some internal or source resistor may be 5 or 10% tolerance. If you don't resistance, say Rs. In principle one can measure Rs believe it, do the sums! In addition to its initial by noting the open-circuit voltage E and measur- selection tolerance, a resistor's value changes with ing the short-circuit current csI through an am- ageing, especially if used at its maximum dissipa- meter. Then Rs = E/Isc. In practice this only works tion rating. This must be borne in mind when approximately, for the ammeter itself will have a Passive components 5 retemoitnetoP desu sa elbairaV srotsiser f Potentiometer a elbairav rotsiser i i = .----q _ Y or Ril l ~ss---" lt jf 11~'~ c."" / /i ,," / /I detaunettA ~-1 signal si .~ / / i / / ", I : ,, / / ,/ I I I / / ,," i I i / / / I / "//" I Rm/5 -4--- __Z. . . . . . . / i'"-----.-.__l _U , / ,,/f 1 i 0 05 001 egatnecreP noitator of repiw )A( Linear law. )B( Log law (20% log shown; some potentiometers have a 10% log law). Used for volume controls. )C( Reverse log law. Figure 1.3 Variable resistors and potentiometers. small but finite resistance: nevertheless you can, in common or garden primary (i.e. non-rechargeable) the case of a dry (Leclanch8 primary type) battery, battery such as the zinc-carbon (Leclanch6) variety get a reasonable estimate of its source resistance. is set by the rise in internal resistance rather than (It is best not to try this with batteries having a low by any fall in the battery's EMF as measured off internal resistance, such as lead-acid or Ni-Cd load. (Measuring the open-circuit voltage and the types.) Naturally it pays to short-circuit the bat- short-circuit current to determine the internal tery through the ammeter for no longer than is resistance is even less successful in the case of a absolutely necessary to note the reading, as the laboratory stabilized power supply, where sR may procedure will rapidly discharge the battery. be zero or even negative, but only up to a certain Furthermore, the current will in all probability rated output current.) be gradually falling, since with most types of The observant reader will not fail to notice that battery the internal resistance rises as the battery the current flowing in the load resistance in Figure is discharged. In fact, the end of the useful life of a 1.4c must also be responsible for dissipating 6 Analog Electronics Rs + )(+) O o (a) )b( R+sR2=v R L J 4 E 1 ~ I = Rs ~ LR + Load ,.~2V LR 0V 0 1"- 0.5 1 (cid:12)9 1.5 2 V (volts) )c( )d( Figure 1.4 The maximum power theorem. )a( Ideal voltage source. )b( Generator or source with internal resistance .sR )c( Connected to a load .LR )d( E = 2 V, sR = I .~f Maximum power in the load occurs when LR = sR and V = E/2 (the matched condition), but only half the power si supplied to the load. On short-circuit, four times the matched load power is supplied, all dissipated in the battery's internal resistance .sR energy in the internal resistance of the source itself. 50%. This result is usually dignified with the title Figure 1.4d shows the power (rate of energy) of the maximum power theorem. The matched dissipation in the source resistance and the load condition gives the greatest possible power in the for values of load resistance from zero to infinity. load, but only at the expense of wasting as much It can be seen that the maximum power in the again in the internal resistance of the source. In load occurs when its resistance is equal to the many cases, therefore, the source is restricted to internal resistance of the source, that the terminal load resistances much higher than its own internal voltage V is then equal to half the source EMF E, resistance, thus ensuring that nearly all of the and that the same power is then dissipated in the power finishes up where it is really wanted - in source's internal resistance as in the load. This is the load. Good examples of this are a radio called the matched condition, wherein the effi- transmitter and a hand flashlamp; an even more ciency, defined as the power in the load divided telling example is a 660 MW three-phase turbo- by the total power supplied by the source, is just alternator! Passive components 7 Now Ohm's law relates the current through a won't in fact correspond to midtravel, as a volume resistor to the applied EMF at any instant and control is designed with a non-linear (approxi- consequently, like the maximum power theorem, mately logarithmic) variation of track resistance. applies to both AC and DC. The AC waveform This gives better control at low volumes, as the ear shown in Figure 5.1 is called a sinusoidal wave- does not perceive changes of loudness linearly. form, or more simply a sine wave. Preset potentiometers for circuit adjustment on It is the waveform generated across the ends of a test, on the other hand, almost invariably have loop of wire rotating in a uniform magnetic field, linear tracks, often with multiturn leadscrew op- such as the earth's field may be considered to be, at eration to enable very fine adjustments to be made least over a localized area. Its frequency is meas- easily. Potentiometers for user operation, e.g. tone ured in cycles per second or hertz (Hz), which is and volume controls, are designed for continued the modern term. As a necessary result of Ohm's use and are rated at greater than 100000 opera- law, not only is the current waveform in a resistive tions, whereas preset controls are only rated for a circuit the same shape as the voltage waveform, few hundred operations. but also its peaks and troughs line up with the voltage waveform as shown in Figure 1.5. The sine sroticapaC wave shown contains alternating energy at one frequency only, and is the only waveshape with Capacitors are the next item on any shopping list this important property. An audio-frequency sine of passive components. The conduction of elec- wave reproduced through a loudspeaker has a tricity, at least in metals, is due to the movement of characteristically round dull sound, like the flue electrons. A current of one ampere means that pipes of a flute stop on an organ. In contrast, a approximately 6242 x 1014 electrons are flowing sawtooth waveform or an organ-reed stop con- past any given point in the conductor each tains many overtones or harmonics. second. This number of electrons constitutes one Returning to the potentiometer, which might be coulomb of electrical charge, so a current of one the volume control in a hi-fi reproducing organ ampere is alternatively expressed as a rate of music or whatever, to any circuitry connected to charge movement of one coulomb per second. the wiper of the potentiometer it will appear as a In a piece of metal an outer electron of each source of an alternating EMF, having some inter- atom is free to move about in the atomic lattice. nal resistance. When the wiper is at the zero Under the action of an applied EMF, e.g. from a potential (ground or earth) end of the track, this battery, electrons flow through the conductors source resistance is zero. At the other end of the forming the circuit towards the positive pole of track, the source resistance seen 'looking back' the battery (i.e. in the opposite direction to the into the wiper circuit is equal to the resistance of conventional flow of current), to be replaced by the track itself in parallel with the source resistance other electrons flowing from the battery's negative of whatever circuit is supplying the signal to the pole. If a capacitor forms part of the circuit, a volume control. If this source resistance is very continuous current cannot flow, since a capacitor much higher than the resistance of the track, then consists of two plates of metal separated by a non- the resistance looking back into the wiper simply conducting medium- even a vacuum, for example increases from zero up to very nearly the track (Figure 1.6a). If a battery is connected across the resistance of the potentiometer as the volume is plates, its EMF causes some electrons to leave the turned up to maximum. In the more likely case plate connected to its positive pole or terminal and where the source resistance is much lower than the an equal number to flow onto the negative plate, track resistance - let's assume it is zero - then the as indicated in Figure 1.6c. A capacitor is said to highest resistance seen at the wiper occurs at have a capacitance C of one farad 1( F) if an midtrack and is equal to one-quarter of the end- applied EMF of one volt stores one coulomb to-end track resistance. If the potentiometer is 1( C) of charge. The capacitance is proportional indeed a volume control, then midtrack position to A, the area of the plates in Figure 1.6a, and 8 Analog Electronics $g V -.I I ER A 0 rotareneG daoL v )stlov( )a( --1 enO elcyc 1_. " v m )tot(nis mV -- -- 2~~~-'~3~ 4~/0 )snaidar( Is I,. )b( i )serepma( ml --- mI )tot(nist 2~ r73 4~ rI 0 "- -I m - )c( w )sttaw( V m nis )tot( I m )tot(nis aerA 1 - lmV m 2/1 1( - ))tot2(soc Vmlml ~ Area 2 ~ 1 I " I "- )d( One cycle corresponds to 360 ~ (or ~r2 radians), e.g. I revolution of a loop of wire in a magnetic field. If the wave- form has a frequency off Hz then each cycle lasts I/f seconds. Thus there are ot = 2~f radians per second. Note that there are two power peaks per cycle of the applied voltage, so the angular frequency of the power waveform is 302 t radians per second. Peak power load = Vmlm--Vm2/RL--Im2RL, occurs at 0=rc/2,3rc/2 radians etc. Power in load at 0 = tot = 0,1t, cr2 etc. is zero. Since area 1 equals 2, average power in load is (1/2)(vmZ/RL) = VZ/RL, where V = Vm/v/2. V is called the effective or root mean square (RMS)voltage. Figure 1.5 Alternating voltage and power in a resistive circuit. Passive components 9 (-) indicates electrons which have flowed away from eht + positive metal plate Area A I .I I , __ , .... Ill muucaV d t , t _-i irtce!.e, c , . . r . ::_ --I- I _ _ (a) (b) )c( Switch closed Switch closed att=0 +sv~ _~=0 5f~ 5 o o~ + F3T T "~ 1.8 ..... f~at t=O OV 0 51 Time )sdnoces( VO )d( (e) )f( 5 //I " etalP 3.15 ........ noitcennoc # I llA foil strips , )setalp( 0 51 Time )sdnoces( Polystyrene )g( smlif )h( )cirtceleid( Figure 1.6 Capacitors. inversely proportional to their separation d, so As mentioned earlier, an insulator or dielectric that C = k(A/d) (provided that d 2 is much smaller is a substance such as air, polystyrene, ceramic etc. than A). In vacuo the value of the constant k is which does not conduct electricity. This is because, 8.85 x 01 -12 F/m, and it is known as the permit- in an insulator, all of the electrons are closely tivity of free space .o~ Thus ni vacuo C = eo(A/d). bound to the respective atoms of which they More commonly, the plates of a capacitor are form part. But although they cannot be completely separated by material of some kind- air or a detached from their parent atoms (except by an solid substance- rather than the vacuum of free electrical force so great as to rupture and damage space. The permittivity of air is for practical the dielectric), they can and do 'give' a little (as in purposes the same as that of free space. Figure 1.6c), the amount being directly propor-