Understanding Electronics

Urzd_wEpnfli49 ELEETRONIES 3rd Edition

R, H. Warring, Edited bg E. Randg Slone

1 Units, Abbreviations,and Slmbols whir$definewhat Inelectronicsthereareshbasicnrjb to measurcquandties srbols usedas letter i" grhg ; h a cirurit. Herese thefirst three,with tbe abbrtriatims: VAx M - Aneasneofthepotential,enl(electromotivefotec)'ot ooltagena potentialdifiereooe,enf, udvoltage dl rcalty Ct"oii. i'. practicalpurposes, meanthe samething' Anls (,0-A neasureof the currealfrowingin a circuil iittt fW -A neasgred theroreldeveloBedbytheflowd cqnentthro*b a chqdt The othertlree referto the efiectof co4ments in tbe circuit: in a circuit olzs (o)-A measul€of.rhe nsisi4,n/-or individualresistances (dc). whenthe currentflw is &ect producedby Far& (F)-AmeasrFe 6the @itancepresent in a circ{it or i.e., capacitors. individualcomponents; proftced bf n*r* fn-ineasure 4-6iln&mncepresent in a circuitor suchascoils. individualcomponents 'I\m otherinporbnt quantities,bothof wtricharemeasured in ohms,are: or individtlalresistanoes Imgqlane (A - A measnedtbeeftectiveresistance (ac)' U i circuitwhenthe currentflowis dternating in an ac andcapacitance R;*fur* (x)_Tbcombined efiectof inductance cLoit

Capital letters are also used as abbreviations for voltage and current. Strictly speaking E (for emf) is the correct symbolfor a voltage source, with V (for volts) in other parts of the circuit. V, can be used instead of E for a source voltage. The capital letter I is used for current. In some circuits lowercase letters are used to indicate voltages and currents flowing in different parts of a circuit; e.g., v and i, respectively. These may have a reference annotation attached, particularly in the case of transistor circuits; e.g., v,, describiig emitter voltage. The relationship between units is explained in Chapter 3. There are also various other units employed in electronics, the use and meaning of which will be made clear in appropriate chapters. In practical circuits, numerical values of these units may be very large, or very small. Resistance values, for example, may run to millions of ohms. Capacitor values may be in millionths or even million-millionths of a farad. To avoid writing out such values in full, prefixes are used to designate the number associated with the particular value involved. Normally, the symbol rather than the full prefix is

used, mega (M)-X 1,000,000 kilo (k)-X 1,000 milli (m)-divided by 1,000 (or 1/1,00Oth) micro (p)-divided by 1,000,000 (or 1/1,000,000th) nano (n)-divided by 1,000,000,000 (or 1/1,000,000,000th) pic0 (p) -divided by 1,000,000,000,000 (or 1/1,000,000,000,000) For example, instead of writing out 22,000,000 ohms, it is shown as 22 Mohms, or 22 MQ, using symbols both for the prefix and basic unit. Similarly a capacitor value of 0.000,000,000,220 farads is shown as 220 picoF, or, more usually 220 pF. The multipliers (M and k) are most commonly associated with values of resistors, and also for specifying radio frequencies. The lowest divisor (m) is most usually associated with the values of current typical of transistor circuits, etc. It is also used to specify most practical values of inductances. The larger divisors (p, n, and p) are most commonly associated with capacitor values. S i e capital letter abbreviations are also used for components. The main ones are:

C- capacitors D -diodes L- coils R- resistors These are all standard and universally accepted abbreviations. With other components this is not always the case. Thus transistors may be designed T, TR, Tr, VT or even Q on circuitsoriginatingfrom different sources. The use of TR, Tr, or Q is preferred, leaving the letter T as the abbreviationfor transformers. Note the abbreviation FET (or fet) is used for a field-effect transistor in text, although it may be "Q" in diagrams. In practical circuits, more than one of the same type of components are

YYr

---f-

Fhed ValueResistm

-J-- -t-

+F

Electrolytic Capacitr

Dode

lnudspeaker

I

VarbbleResistor

:

-,yE-

-+F

(

Earth Ground

Chagsis Ground

- y t-l ' T

rl

TrimmerCapacitc

-\.0..0.,1- -lF---lF coil

Variable Capacitor

),

Rteo**

-\JJrr"

-#-n+ Jr- -lrlr Cell

Battery

Fig. 1-1.Symbolsfor basiccircuit comPonents. Othcrsxntblsaregiwn in later chapters.

normallyused.Individualcomponents of the sametypearethendesignated by numbers(usuallyreading fromleft to right acrossthecircuit)associatedwith the gomrynentsymbol(Fig. 1-1).SeealsoChapterB.Thusresistorsaredesignated Rl, R2, R3; capacitorsCL,C2, C3;andso on.Thereis no correctot specific sequence in whichsuchnumbersareallocated. Theyarethereonlyto identifya particularcomponent. Here are someotler generalabbreviations that are widelyused,although againtheymaybeshownin variousdifferentways:capitalletters,or lowercase letters in uprightor italic, with or withoutperiods.Thusthe abbreviation of alternatingcurrentmayappearin five differentways: AC a.c. a.c. ac ac The generalpreferenceis that all suchabbreviations shouldbe in lowercase withoutperiods,andsothe followingabbreviations areshownthat way: ac- alternatingcurrent af-audio frequency agc-automatic gaincontrol (or amplitudemodulation) am*-amplitude modulated dc-direct current eht-extra hightension fin*-frequency modulated (or frequencymodulation) hf-high frequency ht-high tension * Thereisagoodreasonforretainingcapitallettersforthese abbreviations, sinceAJUandFMradios ugethernthiqv/ay.

3

ic -integrated circuits if -intermediate frequency(alsoi-f) if-low frequencY rf-radio frequencY uhf -ultra high frequencY vhf-very high frequencY

DC and AC A basicdirect current (dc) circuit is simple enoughto understand.A sogrceof electricalforce (suchasa battery) is connectedviawirestovarious components with a return path to the source. Cprrent then flows through the circuit in a particular direction. Figure 2-1 shows a very elementary circuit of tlis type where a battery is connectedto a dcelectric motor andis comparedwitha similar closedloop hydraulic motor in a simple recirculating system. It is obviouswhat happensin the hydraulic circuit. The pump is a sourceof pressurizedwater which impingeson tlte vanesof the hydraulicmotor to drive it. There is a flow of water aroundthe system.At the sametime, tlere is someloss of pressureenergydueto the fiction of the water flowing through the pipesand t}1emotor. This is the resistancein the circuit. But most of the pressureenergy deliveredby the pump is convertedinto power by the hydraulic motor. In the electrical circuit counterpart, the battery is a source of. electrical pres{ilre (which in simpleterms we designateooltage),This forces an electrical currentto flow through the circuit, opposd by ttre resistanceoffered by the wiringandtheelectricmotorcoils.Again,mostofthe originalelectricalenergyin the battery is convertedinto power by the electric motor. Providedthe battery voltagedoesnot change,a constantvalueof current will flow tlrough the circuit alwaysin the samedirection, and the electric motor will continue to nrn at a constantsped. Conventionally,dc current flow is regardedas beingfrom the positive to the negativeterminalsof a battery or any otler dc source(suchasa dynamo).It is a

Battery Electrical Circuit

HydraulicCircuit

circuitis similartoa hydrauliccircuil Fig.2-1.An electrieel streamflow,just like the waterflow in the hydrauliccircuit,but the streamis of sub.atomicparticlesor electrons.Unfortunately,after actuallycomposed thepositiveto negativeflowdefinition,it wasfound badestablished convention that tlis electronstreamflowwasactrullyfuon negatioetoPositioe.Thisdoes of howtransis. butfor anunderstanding not rnatterfor mostpracticalpurposes, this "reto appreciate tors andother solid-statedeviceswork it is necessary verse"working. Positivedwaysseemsstrongerthan negative,so it is difrcult to think of currentasflowingotherthanfrom positiveto negative.TVecanrelatetlis to negativeto positivebythinkingofelectronsasprticlesof electronsflowingfrom theyrepresenta reverseflow, negativeelectricity.Being"weaker"(negative), of current-from positiw to negatiae. settingup conditionsfor a Positioeflow andworkonthepracticalfacttbat* and Otlerwise,simplyforgetthedifference - are onlytermsof convenience in a circuit usedto ensuretlnt components upcorrecdy.Thisapplies whichhavepositiveandnegativesidesareconnected mainlyto batteries,transistors,diodes,andelectrolyticcapacitors. of atomsin whichthere is a stablebalanceof All materialsare composed The elements). positiveandnegativecharges(exceptin theatomsofradioactive from the of an electricalpressurecauseselectronsto be displaced application atom,leavingit with aneffectivepositivecharge.It is thenin a stateto attract anystrayelectrons.Sincethereis electricalpressurepresent,this meansthat electronsalongthechainofatomscomprisingthewiring thereis a movementof tlat constireturncircuit.It is thismovement in thecomplete andcomponent(s) tutestheelectriccurrentflowingtlrough thecircuit,thestrengthof thecurrent ontlte numberof electronspassinganyparticularpointin the beingdependent circuitin a giventime.Breaktle circuitandthe pressureis broken,socurrent So,in fact,the analogywith a hydrauliccircuitis not reallyvalidin flowceases. thisinstance(thehydraulicpumpstill deliverswaterunderpressureif its circuit is brokenuntil it hasemptiedthe fluidin the circuitbetweentle breakandthe punp). Atomsof materialslike metalswill giveupelectronsreadilywhensubiectto electricalpres$re, andsomakegoodconductorsof.electricity.Atomsof most includingplastics, arereluctanttogiveupelectronsevenunderhigh non-metals, 6

I I

Switch On

Time --.+>

Switch

off

Fig.2-2.Directcurrentfowwith constant circuit resistance. electricalpres$Ee,andso are essentiallynonconductors. If materialsare extremelyresistantto givingup atoms,they areclassified as insulators. sunmarizing,then,a dc circuitwhenconnected or switchedon providesa constantflowof currentin onedirectionthroughthecircuitasin Fig.i-2, unless somethingchangesin the circuit (e.g.,sourcevoltagechanges,or a circuit resistance valuealters).The ralueof this curent is determined by the souroe voltageandthetotalresistance in thecircuit(seeChapter3).Currentflowisalso regardedaspositive(or positivecurren$. In the caseof an ac circuit, tre sourceof electricalpressurecontinually reversesin a periodicmanner.Thismeansthatcurent flowsthroughthecircuit first Ir onedirection(positive)andthenthe other(negative). In o6er words,a simplegraphof currentflow with time will lookrikeFig. 2-3.The swingfrom naximumpositiveto maximumnegativeis knownasthe amptitudeoiaaac ctnrent.Alsoonecompleteperiodfromzeroto maximum positive,backto zero, doumto naximumnegativeandbackto zeroagainis knownasa cycle.These cyclesmayoccuratvaryingratesfrom afewtimesa second tomillionsoftimesa secondanddefnethefrequencloftheaccurrent,frequencybeingequalto the numberof cyclesper second.In the caseof the domesticmainsiupply (in Britain),for example,tbe frequencyis s0 cycles-per-second, or 60 cycles-persecondin the u.s. But "cycles-per-second" is anobsoleteterm.It is nowcalled hertz(abbreviated I{z). Thusstandardmainsfrequencyis S0c 60 Hz.

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FiS. 24. Alteraatitg currentfuu b in cycbsof positiu and regatioecurnnt.

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ru

z

Peak: + Peakto Peak RMS:0.707X Peak

I

Fig.24. Peah-ta-peah, dcfinedand conpared. fuah, ond raotmcansquaneaoltages Apart from the fact that ac is continuallyswingng from positive to negative current flow, the other differenceis that the actualcurrent valuepresentis also "average" value which can be changingall the time. It does,however,have an definedin variousways.The usualoneis the RootMeanSquare(or zzs), whichis equal to 0,707L times the ma:rimumcycle values for sine wave ac such as normally generatedby an alternator, Fig. 24. Alternating current may, however, be generatedwith other types of waveform. Anotlrer characteristicof ac is that both the voltage and qrrent are continually changingin similar cycles.Only rarely, however,do the voltageandcurrent both attain maximum andzerc valuesat exactly the sametime. In otlrcr words the current (waveform) curve is displacedrelative to the voltage (waveform) curve, Fig. 2-5. This displacementis known asa phav diference.ltis nomlally orpressedin terms of t}reratio of the actualdisplacementto a full cyclelength on t]1ezero line, multipliedby 360 (sincea full cycle represents360 degreesof ac "peak" after the working). This is calledthe plase angle.Usuallythe current will voltage (i.e., be displacedto the right of the diagram),whereuponthe current is said to be leggng and the phaseangleis referred to as angle of lag.

I

q) I

q)

db q)

z

+ Currenttageng by ] Cycleor 90 Ilegreee

Fig.2-5. Current uaul$ lagsbhind aoltagein an altcrnating curnnt circuit.

at first. It is reallyamatter Theuseof theterm "angle"canbeabit conftrsing involving calculations usefulin morecomplicated convenience, of mathematical of acit isbetterto thinkofangleas For ageneralunderstanding vectordiagrams. onefull cycle meaninga particular"numberpoint" ona linelengthrepresenting angleof30degreescanbeunderstooda Thusaphase 360divisions. dividedinto a point30/360thsalongthat line. Phasedifierence(phaseangle)canbe animportantfactorin the desigtand whena currentlags(or workingof manyalternatingcurrentcircuitsbecause are affected. of a circuit leads)the voltage,the timingaspects

3 Basic Circuits and Circuit Laws Asnotedin Ctnpter2,thecurrentwhichflowsin asimpledccircuitis dependent in thecircuit.Voltagecanbemeasured ontheappliedvoltage andtheresistance direcdyby a aoltmeterplaced acrossthe battery(or dc source)terminals;and currentbyan ammeterconnected n seiesn the circuit,asin Fig. 3-1.This in symbolicform. diagramalsoshowsthe circuitcomponents OUM'S LAW (R) is given Therelationship betweenvoltage(E),current(I), andresistance by Ohm'slaw:

.t : FE In plain language: amps:

volts resistance in ohms

or the formula can be rewritten:

volts: ampsX ohms 10

Battery

rl

Voltmetcr

L' -- ---- rl 1 v-

I

;---J

\-/ FA. 9.1.fusic dc circuitdnun in ttm ua1s,uith nwterslor ncaarhg cttrat end odtryc indicated

volts . onms-This is oneof the mostbasicandmostusefirllawsof electronics andis equally applicable to accircuitswhicharepurelyresistive(i.e.,do not haveadditional resistance effectsproduced bythecunentbeingdternatingratherthansteady). Ohn'slawmakesit possible (andthrs designltheperformance to calculate ofa simpledccircuit.Forexample, youneedacurrentof200miliamps(mA) suppose to flowin apartictlarcirorit to bepoweredbya &volt battery.Usingotrn'staw, tle correspoading circuitresistance requiredto givethis cunent caneasityle

wortecln

.

volts

tias:-:..:-

6

amps 0.200 - 30ohms

components areconnected bywires,buttheresistance ofwiringisqnatteoough to benegligible. Thusin a simpledccircuitit is theeffective totalof all the resistorraluesandothercomponents whichofrerresistance.Just whatthistotal valueis depends onhowthevarious resistors whichmaybepresentareconnected(seeChapter 4). In somecasesit is easyto caletatethe reeistance of a typicarload"Fc example, aflashlightbulbisusuallyratedbyvoltsandtheqrrentitdraws. ohm,s lawcanthenbeusedtofind itsnominalresistance. Forexample, if abulbbrated at 6 voltsand50nA" fromObm'slaw:

Resistance-#- uo obns.

1l

There is just onesnagto this methodof estimatingloadresistance.Withfilament bulbs, for example,the specifiedcurrent drawn refers to the bulb in working conditionswith the filament heatedup. Its actual resistanceinitially when the filament is cold can be considerablylower, drawing more current through the bulb. This may, or may not, be a disadvantagein a particular circuit. Also, tlere are other types of loads,like dc electric motors, where the effective resistance variescondiserablywith the speedat which the motor is running.Initially, sucha motor will havea very low resistance;its effectiveresistancethen increaseswith speed. Two other basicrelationshipsalso apply in a simple dc circuit: 1. The currentvalue is tlte samethrough every part of the circuit, unlessa part of the circuit involves parallel-connectedpaths. Thus, in a circuit (A) of Fig. 3-2, all the resistorsin the circuit are connectedin seriesso that the sirmecurrent will flow through eachresistor. In circuit (B) of Fig. 3-2, the resistors are connectedin parallel. ln this case eachresistor representsa separatepath for the current andtlte valueof current flowing through eachleg dependson tlre value of tint resistor. These current valuescan be calculatedfrom Ohm's law:

throughresistort, current: throughresistorZ,currentthroughresistor3, current:

ft S $

Thecurrentflowingthroughthewiringpartof thecircuitis thesumof these tlree crrrents;Le., RT

B ResistorsinParallel A Resi$orsin Serbs Fig. &2. Current has tlrc sne oalu thrwgh all r*is&lrs cotutebd in cries, htt is difcmrt throaghcrch nslttor conncctedi; fulallcl

u

E , E E 1 . , 1 I orE Rl R2'R3 Rl-R2-R 2. Thevoltagethroughouta simpledccircuitis not constantbut suffersa drop acrosseachresistor. This canbe illustratedby the circuitshownin Fig. 3-8,wherethe voltages acrossthe individualresistorsarecalculated (or measured with a voltmeter)as VL,VZ andV3. The total resistance in the circuitis Rl * RZ+ R3. The cur:ent(whichis the samethroughoutthe circui| is givenby: .^:Rl]ft.!![ E Wethenhavethe conditions: Vl, measured acrossRl : currentX resistance :IXRl V2, measured acros{rR2 : I X R2 V3, measured acrossR3 : I X R3 Eachof thesevoltagesis lessthanE. Comparison with ahydrauliccircuitagain(seeChapter2)canhelpunderstand how a resistorworksas a voltagedropper.In a hydrauliccircuit,pressureis analogous to voltagein anelectroniccircuit.Theequivalent to aresistoris some devicerestrictingfluid flow-say a partiallyclosedvalve.Flow throughthis resistorproducesa pressuredrop.similarly,tle flow of electricitythrougha resistorproducesa voltagedrop.

,--@_,

Q

Fig. 3-3. R*istors dropooltagein a dc circuit. 13

VOLTAGE.DROPPER CIRCUIT Theaboveisnowreworkedasapracticalemmple.To ponera&volt electricd (saya &volt transistorradio)froma l2-volt battery.In this case,tlte appliance asa resistanceload.To dropthe voltagefrom 12 to 6 is considered appliance acrossthisload,adropperresistor,R,is requiredin thecircuitshownin Fig.3'4. butto dot}is it It remainsto calculatea suitablevaluefor thisdroppingresistor, of the load.(If this is not knownit to knowtlre effectiveresistance is necessary it is 100ohms. with anohmmeter.)Suppcse canbemeasured UsingOhm'slawagain,if this loadis to have6 voltsappliedacrorxlit, andits is 100ohms,the currentrequiredto 6owthroughthe circuitis: resistance 1 - : 6 100 :0.06 amps(60 millianls) the This samecurrentflowsthroughthe rest of the circuit. This, considering circuitfrom the l2-volt end: required: total resistance

# = 200 ohms

The loadalreadycontributed100 ohms,so the rnalueof droppingresistorre' quiredmustbe 200- 100: 100ohns.Afirthercalculationshowstbevoltage dropacrossthis resiston V- 0.06X 100 - 6 volts drop nrleconcerning anothersimple Thisparticularexamplealsodemonstrates ping resistors.If the voltageis to be halved,then the rnalueof the dropping resistorrequiredis the sameast}at of the load.

12 Volts I

r-O-r R€sistorto "Ilrop" 6 Volts

Fig. 34 Prutical a!flicotiut of d drofuing tesisbn

tl

POWER IN THE CIRCUIT The power developedina circuit byvirtue of theelectricalpressure(volts)and resulting current flow (amps)is given by the product of these two values,and measuredin araffs.Thus: power: watts: volts X arnps This samedefinition appliesboth to dc and ac circuits. Power is used up in producing a usr;fulresurt rn makingthe crcuit work (whether this be operatinga radio, driving an electric motor, heatingan electric element, etc.). But all componentswhich have resistance absorb a certain amountof power which is waste power normally dissipatedin the form of heat. No practical device can work without someresistancein the circuit, and thus somepower lossis inevitable.More important, the heatingeffect must not be so great that the componentis damaged.Thus componentsnormally havea power rating which shouldnot be exceeded.In specificcases,even when operating within their power rating, provisionmay haveto be madeto conductheat away from tlre component-as in the caseof heatsinksusedwith power transistors. Referringto the exampleof the droppingresistor, t}is definitelywastespower to the tune of 6 (volts) X 0.06 (amps): 0.36 watts. To be on the safi side, trerefore, tre resistor chosenwould needto havea power rating of at lqstvz watt, and would alsohave to be placedin a position where it receivesadequate ventilation to prevent heat build-upin the surroundingair. The majority of transistor circuits work on low voltages, with low current values,and so componentswith quite moderatepower ratings are usuallyade. quate.circuits carrying higher voltagesandcurrents demandthe useof components with correspondinglyhigher power ratings, and often need even more attention to-ventilation.Thus, the actualvalueof a componentis only part of its specification.Its power rating can be equallyimportant. Note that since V: IR, power can also be calculatedas: watts - (current)2X resistance P: I?R This is oftena moreconvenientforrrulaforcalculatingpowerinaparticularpart of a circuit. SHUNT CIRCTIITS A shunt circuit is usedto drop a current flowing through a particular oompG nent. It normally comprisestwo resistancesin parallel,one resistancebeingthe componentresistanceandthe other the shuntresistance.The appropriatevalue of the shunt resistanceis againcalculateddirectly from Ohm's law. A typical exampleof the use of a shunt resistanceis to adapt an ammeter movementto measuredifferent cur:mt ranges(asin a multimeter). In this case

15

is thatof thecoiloftheammeter,whichisinitiallydesignedto theloadresistance with a particularcurrentflowingthroughit (callthis deflection ruu-r.ae En". anyhighercurrentthanI, sincetlis would ir). tt " instrumentcannotmeasnre sihpry tendto carrythe pointerpastits full deflection,andvery likely cause to handlethe lowestcurrentrangereor.ag". Thus,the meteris desigrred quird, anda shuntresistor(or a seriesof shuntresistors)addedwhicttcanbe orirctt"o into the meter circuit to extendtlre range.Figure3-5 showsthis for switchingintothecircuit. withjustoneshuntresistorconnected arrangement qfient, 12, If the shuntresistoris to extendthe ammeterrangeto a higher follows resistor thentle requiredvalueof tle shunt deflection, Euingruu-sc"ru from: 1. current whichhasto flow throughthe shuntis I2-I.. This meansthat a (unless currentgreaterthanI, will neverflowtlrough themetermovement I)' exceeds meter the the actualcrrrent appliedto of the 2. Voltagedrops".t*. thuteter - I, X R- (whereR- is theresistance meter). 3. Shuntresishncerequiredis therefore: voltagedropacrossinstrument: Irt" S Iz - Ir currmt flow througbshunt Again,tlere is a simplerule to followif the currentrangeof the meteris to be dJubbd.In this casethe shuntresistancerequiredis the sameasthat of tlte meter. AMMETER INTO VOLTMETER current,canalsobe An ammeter,whichis aninstnrmentusedfor measuring a resistorin selt?swiththe meter-Fig. voltsby connecting madeto measure ofavoltagedropper.Again,if thema:rimum 3-6.This,infact,is anotlrerexample whichmustbein is 11, the fofalresistance metercurrentfor full-scaledeflection circtit is:

totalR: Ir1 whereV is the voltagerangeit is desiredto measure. (Rx) Met€trResistance

SimpleAmmeter

ShutResi*c Fig. 3-5. Ertcnding thc range of a milliamnutcr.

16

The valueof the seriesresistorrequiredis this total resistancelassthe resistance ofthemeter(thelattermaybenegligible in comparisonwith thevalue of seriesresistorrequiredandits likelytolerance-see Chapter4). Again,severalseriesresistorsmaybeused,switchedintothecircuitindividually to providedifferentvoltage-measuring rangeson ttremetermovement, as shownin the right handdiagramof Fig. 3-6. DTVIDERS A voltagedivideris yet anotherexampleof the practicalapplicationof a voltagedropper.Thebasiccircuitis shownin Fig.3-7,andsincethecurrentflow throughRl andR2 is the same,tle followingvoltagevaluesapply: Vl : sourcevoltage(e.g.,batteryvoltage) V2-VlXRl

vs:ffixnz l-..

vl

---\

is tlte currentflowingthroughRt andRZ/. \Note R-t + Rt It followsthatbysuitableselectionofvaluesfor Rl andR2,virtuallyanylower voltagethanVl canbetappedfrompointsA andB, or B andC (or both).It also hasthe advantage that it is not necessary to knowthe loadresistancebefore suitabledropperresistances canbecalculated. It couldthusbea morepractical alternativefor theorampledescribed in Fig.3-4,butconnection to aloaddoes,of course,resultin a further dropin voltage. If theresistance of theloadisknovm,tlrcnthereisnopartictlarproblemwitha fixedresistorvoltagedivider.Calculate thevalueof R2(Fig.3-Z)onthebasisof noloadresistance, tlen subtractthe actualvalue oftheloadresistancefromthis to arriveat therequiredvaluefor R2.(In thecomplete tap@ circuit,R2andttre loadresistance is effectivelyin series.)

Anmeter Moqeoeot

snlle Voltnetcr

Voltmeter with Five Ranges

Fis.34.C.onoertingan dmmcteriilo a ooltmcbr. 17

R1

B

'Droeeea' Voluge Ortput

Fig.&7. tusic fuobntialdiilder circtit.

BASIC AC CIRCUITS in Chapter2, the voltageandcurent flow bothalternatein ac As e:rplained circuits,with the possibilityof oneleadingor laggingthe other.Also,it was offeredbyresistancecomponentsrnaybe intimatedthat theeffectiveresistance by reactiveeffects.Theseeffectsbecomeincreas. modified(usuallyincreased) are inglymarkedas thefrequencyof theacincleases,andat radiofrequencies thanpureresistance. morepronounced It is possibleto obtainanac circuitwhichis purelyresistive,particularlyat in whichcaseOhm'slawisequallyvdid for suchcircuitsasit is lowerfrequencies, for dc circuits.Ohm'slaw canalsobe appliedto ac circuitsin whichreactive effectsare present,but in slightlymodifiedform. Thesereactiveeffectsare as reactanceandimfedance, describedspecifrcally loadingeffectproducedby cafocitors andin&rc' is circuit the Reactance by thesymbolL Its actqal in ohmsanddesignated is measqred trt tances(atrs). the frequencyof tlte ac. value and component tlrc both on is dependent value (usually designated&) is reactance capacitive capacitors, of the case In givenby:

\:L^ in farads,aadTt: 3.L4L2. wheref is theacfrequencyin llz, Cis thecapacitance )&,) is ind*ctioe reactatre(usuallydesignated In the caseof inductances, givenby: Xa:ZnfL in hen4n whereL is the inductance 18

If the ac circuit contains only reactance(i.e., does not have any separate resistance),then x takes the placeof resistance(R) in the ohm's law forrrula:

-I : Ex In practice,reactancepresentis alsousuallyassociated with resistance,the resultingcombination representingthe impedance (Z) of.the circuit. If reactance andresistancearein series:

2:lfrpl If reactanceand resistanceare in parallel:

"-

[r

! RtR

Again, impedance(Z) takes the placeof resistancein the Ohm's law formula:

I:2 Theseare the basicformulasfor accircuitcalculations. POWER FACTOR Powerfactoris something specificto accircuits,althoughit is onlytheresistancein suchcircuitsthat actuallyconsume power.Thispowerconsumed canbe calculatedas tle productof the squareof the current flowingthroughthe resistance andthevalueof theresistance; i.e.,IzRwatts.Theapparentpowerin the circuitis the productof acvoltageandcurrent,correctlyspecifiedasvoltamps. The ratio of tlre powerconsumed to the apparentpoweris calledthepower asa percentage. If the circuitis purelyresistive,then factor,usuallye:rpressed thepowerfactoris 100percent(sincealltheapparentpoweris consumed in the resistance). Reactance power,soin a purelyreactivecircuit doesnot consume tlte powerfactoris zero.TVhen a circuitcontainsbothresistance andimpedance (i.e.,reactance), thent]tepowerfactoris alwayslessthan100percent,its ralue present. depending on tlte resistance DC and AC in the SameCircuit It is quitepossibleto havebothdcandacflowingin the samecircuit.In fact, this is theprincipleonwhichmostradioandsimilarcircuitswork.Thedcis the basicsourceof electricalsupply,onwhichrrarious accurrentsaresuperimposed. Theoneessential differenceisthatdccanonlyflowthrougha continuous circuit,

ac+dc ac+dc

+

*l

ac+dc

€

c

Fig. 3{.. Flow of ac and dc in a circuit.

suchascapacitors whereasac canpassthroughcomponents whichpresenta breakinthecircuittodc.Theseeffectscanbeusedtoadvantagetoisolatestages in a circuit. In the type of circuitshownin Fig. 3-8,for example,aninputcomprisinga mixtureof dcandacis appliedto the left-handsideof ttrecircuit.If onlythe ac component of thesignalis required,thedccontentcanbeblockedby acapacitor (C1).Meantime,thenextpart of the circuitwhichhasto dealwith that signalis poweredby dcfromthesourcesupply(saya battery),probablyviaresistorsRl andR2actingasdividersto getthevoltagescorrectfor thatstage(otler stages mayneeddifferentworkingdcvoltages,all comingfromthesamesource).The outputsigrralfromthisstagetlen consists of amixtureof dcandac.If onlytheac (C2)isagainusedasa contentis wantedfor passing to thenextstage,acapacitor blockfor dc.

n

Supply Voltage

Resistors Resistors,as the nameimplies,are designedto providesomedesirable,or necessary, amountof,resistance to currentflow in a circuit.Theycanalsobe usedto dropvoltages,as explainedin chapterB. As such,t.heyare the nain elements usedincircuitdesignto arriveat thedesiredcurreotflowsandvoltages tlat work the circuit.Resistorsdo not generateelectricalenergy,but merely absorbit. This energyis dissipated in tbe form of heat.The perforrnance of a resistorisnotaffectedbyfrequency, soit behaves in thesamewayinbothdcand ac circuits.(Thereareexceptions, asnotedlater.) Resistorsare specifiedby (a) resistanceralue in ohms;(b) toleranceas a percentage of the nominalvalue;and(c) powerratingin watts.Theyare also categorized by the typeof construction.

COLOR CODE Resistance ralueandtolerancearenormallyindicated by a colorcodeconsisting offour coloredrings,startingat, or closeto, oneend(FiS.4-1).Theseare readasfollows: lst ring givesfust digit 2ndring givesseconddigit 3rd ring givesnumberof zerosto put afterfrst two digits

21

i ---

Black-0 Brown-l Red-z Orange-3

Yellow-'l Green-S Blue-6

Violet-7 GreY-8 White-g

Fig. Ll. Stsndarit tesistor color cdc marhing.

The fourth coloredring gives t}re tolerance: silver- 10% toleranceeither side of the nominalvalue gold-5% toleranceeither side of the nominalvalue toleranceeither side of the nominalvalue iA-ZW brown-1% toleranceeither side of the nominalvalue BramPle;Resistor color coderead as brown, blue, orange'

Valuereadas

Brown 1

Blue 6

Orange 000

i.e.,16,000Q or 16 kQ (kilohms). Absnce of a fourth ring implies a toleranceof 20 percent' Certain types of modirn resistors of larger physicalsizemay haveletters and on tle body instead of colored rings. With this coding, tle numbers "*f"a numbers indicate the numerical value and the following letter tle multiplier, where: E:Xl K: X 1,000 (or kilohms) M - X 1,000,000(or megohms) A secondletter then gives the tolerance: M: 20% toleranceeittrer side of the nominalvalue K - 10% toleranceeither side of the nominalvalue J - 5% toleranceeither side of ttre nominalvalue H:2.5oti toleranceeither sided the nominalvalue G:2% toleranceeither side of tle nominalvalue F : 1% toleranceeither side of the nominalvalue The actual range of (nominal)resistancevaluesto which resistors are madeis basedon stepsthat give an approximatelyconstantPercentageclnnge in resistancefrom oneralue to the ne:rt-not simplearithmeticalstepslike 1, 2, 3, etc. These are basedon tle preferred numbers:

22

t, 1.2,1.5,1.E, 2,2r2,7,,3.3, 3.9,4.?,5.6,6.E,E.Z, 10,12,15,lE,etc. Thus,for example,a typicalrangeof resistorvalueswouldbe: L0,12,15,19,22,27,33,39, 47,56,69,92, and100ohms 120,150,180,220,270,330,390,470, 560,680and820ohms L,1.2,1.5,1.8,2.2,2.7,3.3, 4.7,5.6,6.8,and8.2kilohms). L0,12,etc.kilohms 1, 12,etc.megohms As a generalrule, resistorswith a l0 percenttoleranceare suitablefor averagecircuituse.Theactualresistance valueof,say,a 1kilohmresistorwould thenbeanythingbetween900and1,100ohms.For morecriticalwork,suchas radiocircuits,resistorswith a 5 percenttolerancearepreferred.Closertolerancesarenot normallyrequired,exceptfor very criticatcircuits. POWER RATING The physicalsize(or strape)of a resistorprovidesno clueto its resistance value,butcanbearoughguidetoitspowerrating.physicalsizes (Fig.4-2)range fromabout4 mmlongby 1 mmdiameterupto abouts0 mmlongand6 mmor morediameter.Theformerwouldprobablyhaveapowerratngof.Ll2}watt and the latter possibly10 watts.More specifically, however,the powerratingis relatedto typeaswell assize.A generalrule that doesapplyto powerrating, however,is that while this figurenominal$representsa safemaximumthe resistorcantoleratewithoutdamage, it is usuallybestto operatea resistorwell belowits powerrating-say at b0 percent-particularly if components are crowdedonacircuitorthe circuitisenclosedin acasewithlittle ornoventilation. VOLTAGE RATING Maximumoperatingvoltagealsocanbespecified for resistors,butsincetlis is usuallyof theorderof 250voltsor more,thisparameteris not importantwhen choosingresistorsfor batterycirctits. Resistorsusedon mainscircuitsmust, however,havea suitablevoltagerating. Tpes of Construction Resistorfy'asclassified by construction follow.

^----

-

-

l-l

-

Fig, tL2. Eramplesof mdern resistoroutlinx (actualsie).

23

Carbon Resistors (alsocalledcarbon-composition,molded-carbon,andcarbonrod). Carbonresistorsare in the form of a smallrod moldedfrom carbonand a binder, with wire connectionsat eachend.The rod is usuallyprotected with a paper or ceramic sleeve,or a lacquer coatin$. Carbon resistors are the most common(andcheapest)type of resistor, andare availablein valuesfrom 10 ohms to 22 megohms.Standardtypesare usuallyavailableinl/a,Vt,Yz, L,and?watt ratings. It is a generalcharacteristicof carbonresistorsthat their valueremainsstable at normal temperatures,but above60"C their resistanceincreasesrapidly with increasingtemperature. Carbon-film Resistors (alsoknown as high-stability carbonresistors). To makea carbon-filmresistor, a thin film of carbonis depositedon a smallceramic rod. The rod is fitted with metal end caps,to which wire leadsare attached.The body of the resistor is usually protected by a varnish, paint, or siliconeresin coating, but some types may be encasedin a ceramic, plastic, or glass outer coating. Carbon-filmresistorsare little affectedby temperaturechanges(theirstability is usuallybetter than 1 percent)andare alsocharacterizcdby low noise.They are availablein sub-miniaturesizes(U20 and U10 watt power rating, andin larger sizesup to 1 watt power rating. They are a preferred type for radio circuits, particularly as they have excellenthigh-frequencycharacteristics. Metal-film Resistors. To makea metal-filmresistor, a metallicfilm (usually nickel-chromium)is depositedon a glassor ceramicrod. A helical track is then Metallicendcatsarethen cutin the filmtoproducethe requiredresistancevalue. protected is by a lacquer,paint, or wire leads, the body fitted, carrying the and plasticcoating.Stability characteristicsare similar to thoseof carbon-filmresistors, but they are more e:rpensive.They are generally producedin miniature sizeswith power ratings from 1/10 watt upwards. Metaloxide Film Resistore. Constructionis similar to that of a metal-film resistor except that the coating used is a metallic oxide (usually tin oxide), subsequentlycovered with a heat-resistant coating. This type of resistor is virtually imperviousto accidentaloverheating(e.g.,when makingsolderedconnections)andis alsonot affectedby dirmpness.Stability is very high (better than 1 percent), and the power ratings are higb for their physicalsize. Metal-glaze Resistors. In this type, tlre resistive film depositedon the rod is a cermet (metal-ceramic);otfierwise, construction is similar to metal-film resistors. Film-resistors also can be classifiedas thich-film or thin-rth. As a general rule, individualresistors of this type are thick-fiIm. Thick-film resistors are also madein groupson a smallsubstrateandencapsulatedinintegradedcircuitchips. Thin-film resistorsare madein a similar way, but on a considerablysmallerscale for use in the manufactureof integrated circuits. 24

Efiect of Age All resistorscanbeexpected to undergoa changein resistance is mostmarkedin thlgse of carbon-colnporiu*resistors, with age.This wtrerethe change mightbeasmuchas2O-percent in a yearor so.In the caseof carbon-firm and met'llic-fiknresistors,trrechanges"ido. will be,ooi" tu- " ril pur."nt. Efiect of High Frequencies The generaleffectof increasingfrequencyin ac circuitsis to decrease the apparentvalueof ther:y:torland thehighertheresistor ,.ru" ii"-i""ter this changeis likelyto be.This effectis mosimarked with carbon+omposition and wire-roundresistors.carbon-filmanametar-nr,n-resiriil,iirr"""it'ure high_ frequencycharacteristics. WIRE.WOUNDRESISTORS A wire-roundresistorismadebywrappingarengthof resistance wirearounda ceramiccoil.The wholeis thencoveredwilh a protectivecoatingor film. The offeredby wireresistorsarethat a wiaerange';varues :p".i6g advantages can (tyeicallyfrom i ohmto sookitohms)*ith po;;;;; eroduced !: from 1 to 50 watts (or up to 225 watts-in"power" types)and tolerancesas closeas 1 percent.Theyalsohaveexgelelt stability andlow noise.Thea disadvantages arethat trey aremostcostryandalso*.uit"ut" for usein,. "i.JL carrying highfrequencies because their effectivevaruechanges. physicary,theyneedbe no biggerthanfilm-typeresistorsfor the samepower rating. VARIABLE RESISTTVEDEVICES Themostcommontlpe ofvariabreresistive deviceusedinmodernerectronics il calleda potentiomefar. A potentiomet"iisa three.leadresistivedeviceconsistingof a fixedresistiveerementtrratcanbesweptby a wiperarm.The6xed resistiveelement,or trach,may b" circurar r".u"uv r zi6J"g* arc) or a straightline,circulartypesbeingthe morecommon. Theresistiveelementmaybe-wire-wound, carbon-composition, carbon-fiIm, or metallic-fiIm.The former tlpe is knownas a wire.wbundpotenuometer. carbon-trackpotentiom€ters. are the cheapest(with the samelimitationsas carbon-composition resistors),but are availableonly with ,nJ"ot" power ratings-e.g.,Yr wattforlowresistance ralues-reducingwith higherresistancevalues.wire-woundpotentiometers usualyhavehigG po","i'oting, .no arealsoavailablein lowerresistance varuesttrancarbonrtraclpotentiometers. Tolerances areusuallyontheorderof r0 percentof 20percent,futo'"v u",*r, closerwith precisionpotentiometers. connections shouldbeobviousfromFig.4-3.Thus,with connections to endr the.tryckandthe wiper,length1 to ck the resistivetrack 9f is in the circuit. Actualcircuit resistancethus can be variedby moving the wiper towards3 (increasing resistance), or toward1 (decreasing resistance). The changein resistancecal occurpropoiionanyto the actuarrengtrrof track involved,or rogarithmeticafu,*n*u trrereis a logarithmic increasein

Potentiometetr

Wipet (Turnedby lhob)

rr"*

Fig. H. Potentiometershown in vhematic form (lefr). Correspondingtcrminal positions are sluun on thc symbols(ight).

moretrack(similarto tlte "stegs" uncovering resistance with wipermovement adoptedfor standardresistorvalues).Theformeris knownasa linearpotenttPotentiometers canalsohavecharacometerandthelattera logpotentiometer. teristicsbetweentlre two. Note that linear in this descriptionhasquite a To avoidconfirdifferentmeaningto a linearphysicalshapeof potentiometer. sion,it is bestto refer to the latter asa slide-typepotentiometer. Thereis alsoaclassofvariableresistorsintendedtobeadjustedtoapartiodar Theseareknownas trim Potentiresistance settingandthenleft undisturbed. ometers, or just trim pots.Theyaresmallin sizeandmorelimitedin maximum resistancevalue-typically from 100 ohmsto 1 megohm.They are usually by a screwdriverappliedto the centralscrew. for adjustment designed Anothertypeofvariableresistivedeviceis calleda rheostat.A rheostatis a endof canbecreatedby simplybrpingone twoleadvariableresistor.Rheostats its associatedtap. Thus,thepotentiomofapotentiometerto thefixedresistance resistor.Otler tlpes of rheqstatsareawila two'leadadjustable eter becomes Theyconsistof a able,whichare usuallyintendedfor highpowerdissipation. powerresistorwith atrackoftheresistiveelementexposed. An fixedwirewound lockedat any ring makescontactwith this trackandis permanently adjustable valuealongtlre traclc desiredresistance in a circuitin whichit is necessary to be Potentiometers areusedspecifically ableto adjustresistance.A typicalexampleis the volumecontrolin a radio sothat at oneendof the canbedesigned circuit.In this casethe potentiometer track the wiperrunsright off the track to breakthe circuit.Thusthe volume up to work asanon-offswitch,usingtlis ortra controlcanalsobe connected facilityprovided. of fixedresistorsin a voltage Anotherpracticalexampleis the replacement potentiometer make circuit variablein performance. to the by a single divider Thus,t}re circuit previouslydescribedin Fig. 3-7 (Chapter3) alwaysgivesa

26

Fig. tU. A Practicaladjustablepotentialdioider.

predetermined voltageat the tappingpoints(providedthe supplyvoltagere(Fig.4-4), mainsconstant). Replacing resistorsRl andR2with a potentiometer wittr the tappingpointtakenfromoneendof tle potentiometer andthe wiper, willgiveatappedvoltagethatisfullyvariablefromthefullsupplyvoltagedownt zero,depending on tle positionof the wiper. In practice,in a variable'voltage circuitof this type,it maybe necessary to leavea fixedresistorin serieswith thepotentiometer to limit theorrent being drawnin ttreeventthat the potmtiometerhasbeenadiusted to zeroresistance andthe tappedcircuit is brokenor switchedoff with the originalsupplystill connected. Witlout thefixedresistor,thesupplyis shorted.Thevalueof afixed resistoris calculated to limit the currentdrawnin sucha caseto a safelevel Withafi:redresistorinserieswiththepotentiometer, of course,tie maximum voltagethatcanbetappedfromtle potentiometerisequal tothe supplyvoltage lessthe voltagedroppedby the fixedresistor. The mainthing to watchin sucha circuit is that the powerrating of the potentiometer is adequate to accommodate thevoltageandcurrentdrainin the tappedcircuit.But it hasonefurther advantage overa 6xedresistorpotential divider:Whena loadis addedto the tappedcircuit,it addsresistancein that circuit,causing afurthervoltagedrop.Unlessthisisallowedfor in calculating the valuesfor thefi:redresistorsin a potentialdivider,theloadwill receivelessthan the designvoltage.With a potentiometer replacingthe two fixedresistors,its positioncanbeadjusted (Fig. to bringtheloadvoltage backto therequiredfigure 4.5).Thisconsiderably simplifiesthedesignof a potentialdividerwheretheload resistance is knownonlyapproximately, or not at all

Fig. +5. Tltcfotzntiometcrcan b adjustztltogiaerequiredooltageacrosstlu load.

27

R4

R3

R2

RT

- Rl * R2+ R3+ R4 TotalResistance in vriesFig.tt6. Resrsfors CIRCUIT RULES FOR RESISTORS '' in in series(Fig.4-6),thetotalresistance connected Ifr thecaseof resistances circuitwill be tle sumof tle variousresistorvalues;i.e., :Rl * R2+ R3+''' totalresistance In the caseof resistorsconnectedin parallel(Fig. 4-7)' the total effective resistanceis givenby: 1

1

1

1

n-Rt-R2-85T"' whereR is the total resistance. In tle caseof two dissimilarresistors: K - -

Rl R2

Rl+R2

as: or remembered total resistance

productof resistorvalues sumof resistorvdues

I _ 1 .' 1 * ' l totA nesistance Rl R2 R3

in Parallel. Fig.+7. Resistors

%

F

o

Capacitors A capacitoris basicallya devicewhich storesan eJytric charge.physicary, it consistsof two metarplates-ora*troa.. ."p"oted by aninsurati'gmateriaror dielectric.Apprication of.. a. r"rig" .-"Jirrg napacitorprodu.ur-, a"fi.iun.y of electronson tre oositiygpr.r" ria "-ilt'of erectronson tre negativeprate (Fig. 5-l). This diffLrenua...rrut"tioi}"r".t onsrepresentsan erectricar up

ffii,ft"Yr1*rt$:i

acertain tuvet tJepenoing "" t[";;il6

andthen

As far asdc is concerned, the insulatoractsasa bluhing deienfor current flow(atthoughtrrereis a certaintt-.luni.rr.rging current which stops assoon asthe capacitoris frrtv charged).rn trr"-.iJorac appliedto thecapacitor, trre upduringone r,"[.y.r"u"."i".

reversed

lfo-ry:so that effectively ontrrcsecond harfoftre cycle' the capacitor "onou.6 current through it as if the f$y.

didnotexist.fhus,..i;;;.;;;cerned,

"."p."ito?i.acoupring

Therearescarcelyanyelectroniccircuits carryingacwhichdonotincorporate oneor more capacitors,ei_ther for coupringor shapingtrr" o'.on-i"qu"n"y responseof the netwolk. In the tattei?i,-a capacitoris associated with a resistorto form an RC cornbination GJtiiapter.6). The charge/discharge phenomenon associated_wittr *pr.i-t-")" *.],"* be usedin otfr", typ"* or circuits(e'g', trrephoto-graphic "r*troni"il'.r, is-operatedby the chargeand subsequent dischargeof a capacitorttiggurJat the appropriatemoment).

a ?

to a dc ktikls up d chargewlpn connected Fig.5-1.Illustratinghowa capacitor ttochingcurrentfow. ooltage, to havefixedvaluesor berrariable maybedesigrred Likeresistors,capacitors arethe mainbuildingblocksof a circuit(together in capacity.Fixedcapacitors aremainlyusedfor adjustingtunedcircuits. witl resistors).Variablecapacitors FD(ED CAPACITORS and non-polarizdcapacitors, fall into two maincategories: Fixedcapacitors thetypeof polarized Themainthingwhichdetermines or electrolyticcagacitors. capacitoris the dielectricmaterialused. Non-polarized capacitorsconsist,basically,of metallicfoil interleaveswitlt sheetsof soliddielectricmaterial,or equivalentconstruction.The important it As a consequence, thingis that the dielectricis readymadebeforeassembly. positive plate in The capacitor works or negative. is made doesnotmatterwhich just thesameway,whicheverwayit is connected in a circuit,hencethedescrip "non-polarized." butthisformof construction is convenient, This obviously tion in a single accommodated which can be doeslimit ttre amountof capacitance physicalsize.Up to about0.1 microfarads, the package packageof reasonable tle valuesmuchaboveI microfarad, canbemadequitesmall,butfor capacitance large in physicalsizeof a non-polarized become excessively capacitortendsto in the same circuit. likelyto be used with othercomponents comparison This limitationdoesnot applyin the caseof anelectrolyticcapacitor.Here, by a thin film of elecfuo separated initialconstruction consistsof two electrodes a voltageis appliedacrossthe electrodes bte. Fs a finalstageof manufacture, producing metallicoxide averythinfilmof nonconducting whichhastheeffectof plate of a to formthe dielectric.Thefactthat capacitance onthe surfaceof one much capacitorincreasesthe thinnerthe dielectricis mademeansthat very canbe producedin smallerphysicalsizes.The onlydisadhighercapacitances vantageis that an electrolyticcapacitormadein this waywill havea polarity to theoriginalpolaritywith whichthedielectricwasformed,tlis corresponding tbe correctpolaritybeingmarkedon tlre bodyof the capacitor.If connected wrongwayin a circuit,the reversedpolaritycandestroythedielectricflm and permanently ruin the capacitor. whichappliesto anelectrolyticcapaciThereis alsooneothercharacteristic electrolyteremainsafterits initialforming.This tor. A certainamountof unused 30

acts as a conductorand canmakethe capacitorquite leakyas far as dc is concerned. This mayor maynot beacceptable in particularcircuits. NONPOLARZED CAPACITOR TI"ES varioustypesof constructionareusedfor nonpolarized capacitors, mostof whichareeasilyidentifiedby theshapeof thecapacitor-seeFig. s-2.Thereis noneedto gointodetailabouttheactualconstructions. Theirspecificcharacteristicsareimportant,though,astlese candeterminethe besttpe to usefor a particularapplication. Paper Dielectric capacitors. Generallyrecognizable by their tubular form,arethelestexpensive but generallybulky,valuefor value,compared with moremoderntypes.Theirothermainlimitationis that tley arenot suitablefor useat frequencies muchabove1 MHz,whichvirtuallyrestrictstheirapplication to audiocircuits.Theyaregenerallyavailable in varuesfrom0.0bpF upto I or 2 pF, withworkingvoltagesfrom200to 1,000volts.Plastic-impregnated paper dielectriccapacitors mayhavemuchhigherworkingvoltages. ceramic capacitors. Nowwidelyusedin miniaturized audioandrf circuits. Theyarerelativelyinexpensive andareavailable in a widerangeofvaluesfrom 1 pFto 1 pF with highworkingvoltages,andalsocharacterized byhighleakage resistance. Theyareproduced in bothdiscsandtubularshapes andasmetallized ceramicplates. silver-mica capacitors. Moreorpensivethanceramiccapacitors buthave excellenthigh-frequency response andmuchsmallertolerances, soaregenerally

H ^mmf/ "fr N s n -r'x c ' \l-M f t

A-Ceramic Dsc B-Gramic Ptate C-SilveredMca D-Polystyrene E-Polycarbonate

H

F

I

F-Tantalum Bead G-Electrolytic(Polarizcd) H-Non-PolarizedElectrolytic J-Plug-InType(Sienens)

Fig, &2. Erample^sof modern capacitors

31

regardedas superior for critical applications.They can be madewith very high working voltages. Polystyrene Capacitors. Madefrom metallicfoil interleavedwitl polystyrene film, usuallywith a fusedpolystyreneenclosureto ensurehigh insulation resistgrce. They are noted for their low lossesat high frequencies(i.e., low induptafce and low seriesresistance),goodstability andreliability. Valuesmay range from l0 pF to 100,000 pF, but working voltage generallyfalls substantially with increasingcapacitance(e.g., as low as 60 volts for a 100,000 pF polystyrenecapacitor). Polycarbonate Capacitors. Usually producedin tlte form of rectangular slabswith wire end connectionsdesignedto plug into a printed circuit board. They offer high values(up to I pF) in very smallsizes,with the characteristicsof low lossesand low inductance.Like polystyrene capacitors,working voltages becomemore restricted with increasingvalue. Polyester Fitm Capacitors. Also designedfor use with printed circuit boards,with valuesfrom 0.01 1B up to 2.2 pF. Valuefor valuethey are generally larger in physicalsizethan polycarbonatecapacitors.Their low inherent inductancemakesthem particularly suitablefor couplinganddecouplingapplications. Valuesof polyesterfilm capacitorsare indicatedby a color codeconsistingof five color bands(seeFig. F3). Mylar Film Capacitors. A general-purposefilm type, usually availablein valuesfrom 0.00f pF up to 0.22 1$, with a working voltageup to 100 volts dc. ELECTROLYTIC CAPACITORS The original material used for electrolytic capacitorswas aluminium foil, together with a pasteelectrolyte, wound into a tubular form with an aluminum outer cover, characterizedby dimpledrings at one or both ends.The modern form of aluminum electrolytic capacitor is basedon etched-foil construction, enablinghigher capacitancevaluesto be achievedin smaller can sizes.Values availablefrom I pF up to 4,700 lE (or even larger, if required). Working voltagesare generallylow, but may range from 10 volts up to 250 or 500 volts dc, lstDigit

-

ffi_2dDisit Multiplier W Tobrance rc vort"g" n"tiog l:'l\

l

-

Black*OR-20% whiter oR- lolo

E:fr?'rKB

l FA. 5-?.C;olorcodefor poly.stercafuibr*

z

Capacitancein pF

1QOLOR Black Brown Red Orange Yellow Green Blue Violet Grey White

Ring

Ring

1 2 3 4

0 1 2 3 4

O

D

6

6

t

t

8 9

8 9

Working Voltage

3rd Ring dc and Multiplier

x 1.00 x

Color

Voltage

White Yellow Black Green Grey Pink

3 6.3 10 16 25 35

x 0.01 x 0.10

Fig. 54, C,olorcdc for tantalumbad capacitors. dependingon valueand construction.A singleleademergesfrom eachend,but singleendedtypes (both leadsemergingfrom oneend), andcan-t1peswith rigid leadsinone endfor plugginginto a socketare alsoavailable.single-endedtypes are preferred for mounting on printed-circuit boards. The other main types of electrolytic is the tantalum capacitor. This is produced both in cylindrical configurationwith ddal leads, or n tantalumhead configuration.Both (anathe latter type particularly) can offer very high capacitance valuesin small physicalsizes,within tlre range 0.1 to 100pF. voltage ratings are generallylow; from 35 volts down to less than 10 volts dc. All electrolytic capacitorsnormally have their value marked on tlre body or case,togetler with a polarity marking (* indicatingthe positive lead). Tantalum-beadcapacitors,however, are sometimescolor codedinstead of marked witr values.This color codingis shownin Fi g. s-4,while other codeswhich may be found on otfier types ofnon-polarizedcapacitorsare given in Fig. F-b.

' : MultiplierTolerance

2ndDgit Multiptier \ rst Digit

Murtiprie.53{'"**

q"/ iTffi: w

}}J1

Toterancell tr*'r*u .^,.-..-l I lst Digit 2nd Digit Multiplier i

i

l

l

|

|

Fig. 5-5. Aher codingsysbmsuvd on capacitars.

3:)

Tolerance of Fixed Capacitore As a generalrule, only silver-micacapacitorsare madeto closetolerances is (plusor minus1 percentis usrul).Thetoleranceonothertypesof capacitors (as as 50 much higher percent even may be and 20 10 and usuallybetween Because of thewidetolerances percent)in thecaseof alurrinumfoilelectrolytics. is seldom criticat value actual choice of norrralwith electrolytics, VARIABLE CAPACITORS setsof metalplates,onesetbeing arebasedoninterleaved Variablecapacitors by a dielectricwhichmay Theplatesareseparated fixedandtheothermovable. area onesetofplatesdterstheeffective Movementof beairorasoliddielectric. present. plates, ralue capacitance the of and thus the of for fre' Thereis alsoa generaldistinctionbetweentuning capaa;i/airsv*d quentadjtstment(e.g., to tute a radio receiverto a partiorlar station)and of a hmedcircuit.Tuningcapacifor initialadiustment trimmer caprciforsused generallyof airdielectrictype. and robust in constnrction more larger, tors are dielectricwitha smaller mica orfi}n ona based are usrully Trimmercapacitors a ceotralscrewto rary trrning plates, by adjusted being capacitance numberof Becausetheyaresmallerinsize,however, thepressurebetweenplatesandmica. onasubminiabeusedasahmingcapacitor a trimmercapacitormaysometimes are made,decapacitors hning miniature ture radiocircuit, althougbspecial printed*ircuit board" signedto mountdirectlyon a themanner determines theshapeof tbernanes In thecaseof tuningcapacitors, cbaracteristics Tbese movemeot" with spindle charryes in whichcapacitance usully fall underoneof the followingdescriptions: anequalchangein e Linear-where eachdegreeof spindlerotationproduces Tbis is the mostusualtne chosenfor radioreceivers. capacitance. poducesa constant o Logaithmic-where eachdegreeof spindlemovement circuil a hmed of n change frequncy fercentage -Ewn p&rcs m equal o freqtuncyI whseeachdegreeof spindlemovement circ'uit. in a tuned frequency in change ispropodionalto thequare of' o Squirelaw- wherethechangeintapacitance movemeot. spindle of the angle BASIC CIRCUIT RI'LES FOR CAPACITORS of capacitorsin series andin paralleltare The rules for total capacitance connectednseria (Fig.5-6)' the For capacitors resistors. for to that opposite given (C) by: is capacitance totaleffective

-l a

HHI-Fig.ffi. &Pcitors itsriss

I

-i-'1,-A ' '

TotalCapacitance Cl

C2

Ci!

- C1+ C2+ Ci| TotalCapacitance

FA. e7. Cafacitorsin parallel.

'c2 lc: : + c ll + l +' c 3 or, in tle caseof hro dissimilarcapacitors clcz A ar:f,ffi In words : total capacitance '

product-ofcapacitances sumofcapacitances

Fc capacitorsconnected in parallet(FiS.$Z):

C - C l + C 2 + C 3 +. . . Thiscapacitance efrect,of course,isonlyapparentin anaccircuiLIn adccircuita capacitorsimplybuildsup a chargewithoutpassingcurrent.In a practicalac circuit,a capacitoralsoorhibits reactance(seeChapter2), andbecarceof its ao$itruction,mayalsoexhibita certainamountof.indrctance(seeCbapterZ).

ffi

6

capacitorand RC Circuits capable ofpassing Oneofthe principalusesofa capacitoris asa couplingdevice practical In any circuit, tlere will be some but acting as a block to dc. ac in serieswith the capacitor(e.g.,tle resistiveloadof the resistance connected circuit beingcoupled),This resistancelimits the currentflow andleadsto a certaindelaybetweentle applicationof a voltageto the capacitorandthe build-upof chargeon tle capacitorequivalentto tlnt voltage.It is this charge of of dc. At the sametime,tbe combination voltagewhichblocksthe passage generallyabbreviated to RC,actsasafilterapprbb resistance with capacitance, onthechargedischarge timeof thecapaciof passing acfrequencies, depending tor, or the time consfuntoftheRCcombination

TIME CONSTANT the time constant(t) is quitesimple: The formulafor calculatirrg

t -R C where: t : time constantin seconds in ohms R - resistance in farads C: capacitance fi

raluefor T is givenif R is in ohmsandC 0t canbenotedthatthesamenumerical in farads,but megohmsandmicrofaradsare usully muchmore convoient units.) The time constantis actuallythetime for thevoltageacrossthecapacitorin an RCcombination to reach63 percentof the appliedvolt4ge(this63 percent is chosen as mathernatical a ThevoltageacK)ssthe capaciconvenience). foure tor goeson buildingup to almost(butneverquite)100percentof the applied roltage,as shonmin Fig. Gl. T\e time+onstantfadorrcfersto the durationof timein termsof the time ftctor; e.g., at I (whichrs the time factorof the RCcombinations) 63 percent full voltagehasbeenbuilt up, in a time equalto 2 timesthe time consbnt,80 percentfull rcltage;andso on. After a time constantof 5 the full (almost100 percenDvoltagehasbeenbuilt up acrossthe capacitor. The dischargecharacteristics of a capacitortakeplacein essentially the b yercemantrer;e.g.,aftera periodof timeequalto tle timeconstanttbevoltage acrossthecapacitorbasdropped100- 63 - 37 percentof thefull volt4geand so orl" In theory,at least,a capacitorneverchargesup to full appliedvoltage;nor doesit fully discharge. In p'ractice,full charge,or completedischarge, canbe considered as beingachievedin a periodof time equalto five time constants. Thus,in the circuit identifiedwith Fig. G2, closingswitctr1 producesa fdl chargeon ttre capacitorin 5 timestime constantseconds. If $ritch 1 is now opened, thecapacitorthenremainsina conditionof storingavoltageequiralent to the originalappliedvoltage,holdingthis chargeindefnitelyif there is no internalleakage.In practice,it very slowlylosesits charge,as no practical capacitoris perfect,but for someconsiderable time it remainseffectivelyasa potentialsourceof full*tnrge voltage.If the capacitoris part of a high-voltage circuit,foroanple, itisreadilycapable of givinganelectricshoc.kif touc.hedfor sometime afterthe circuithasbeenswitchedoff. To completethecycleof chargedischarge asshownin theseconddiagramof Fig.&1, switch2 is closed, whenthecapacitor discharges throughtheassociated resistance, tahng a finiteamountof time to completeits discharge.

0

1 2 3 { 5 0 1 2 3 4 5 Tim Coostatrt Fact6 Tiuc CosteatFactc FA. eL. Penentageodtageaclor*calacitor nlated to tittu ubn bing cluryed(W anddialurge (ighil.

tr

TimeConstantFactor

TLncCortrnt Frctr

Fig.62 Closingwihh 1allouscaluitor b clwrgcigltt upin a tisu c.qulb 6 ritu a similarpriod todinluryefil$ throrgha ld rcifur tfrcs cmstantsIt thcntahos witch2isclovd. Figure&3 showsavery simplecircuitthatworksonthisFinciple.It coosists ddcvoltage.Ar seriestoasource of aresistor(R)andcapacitor(C)connectedin a visualindicationof ttre workingof the circtit, a neonlampis connectedin parallelwith thecapacitor.Thelamprepresentsavirtully opencirctit until its thresholdvoltageis applied,whenit imnediatelyconductscurrentlike a low resistance andglows(seeChapter10for moreaboutneons).Tbevoltagesouroe for this currentmustthereforebe abovetbat of the neontum-onvolt4ga ata Whenthiscircuitis switchedon,the capacitorstartstobuiH upa c.harge on tle time constantof R andC. Tbe lampis fed by voltage rate dependfuig acr$s the capacitor.Oncethis reachesthe turnon voltqged ttre developed tlrowb the hmp, the lampswitcheson andcausesthe capacitorto disc.harge nom6€ qrrrent neongas,causingit to glow.Orcethecapacitorhasdischarged, flowsthroughthelampandsoit switcbesoffagainutil thecapacitorhasbuiltup throwh the to theturnon voltage,whenit dischargea anotherchargeequivalent by lamp,andsoon.In otherwords,theneonlampwill flashat a ratedetermined R and C. the time constantof valuesshown,tbe time constaotfor tle cirqdt iss Usingthe component

x 0.1(niaoftrads) t - 5 (megohms) - 0.5seconds

Fig. ffi. Sinpleneonfoshcr circuit (notctheqnbl lor a ,wrr lanfu). Ttu oalucEof the rcsisbr (R) and ca!rcitor (C) detemiw thcfoshing rate. I

theactualflashingrateof thecircuit.It maytakeaperiod Thisisnot necessarily of morethanonetime constant(or less)for the capacitorvoltageto buildupto the neonturn-onvoltage-more if the turn'on voltageis greaterthan 63 percentof thesupplyvoltage;lessif theturn'onvoltageislessthan63percentof the supplyvoltage. It atsoiollowsthattheflashingratecanbealteredby alteringthevdueof R or C, either by substitutingdifferentvaluescalculatedto give a differenttime asimilar resistoror capacitor.Connecting constant,oi wittra paraUit-connected valueresistorin parallelwith R, for example,woulddoublethe flashingrate Connecting (sinceparalleting iimitar resistorvalueshalvesthetotalresistance). rate. flashing the parallel halves c with in capacitor value a similar This type of ctcuit is knownas a relaration osillator. Usinga variable for aspecificflashingrate.It candsobeextended resistorfor R it canbeadiusted aseriesofRCcircuits,each in theformof anoveltylightingsystembyconnecting with a differenttimeconstant eachRCcombination with a neonlampin cascade, neonsin tle completecircuit. -Fig. &4. Thi; produces randomflashingof t11e CAPACITORSIN AC CIRCUITS thefactthattheappliedvoltageis alternatingmeans Asfar asacis concerned, that duringone half cyclethe capacitoris effectivelybeingchargedanddischargedwith onedirectionof voltage;andduringthesecondhalfof t]1eaccycle, with oppositedirectionof voltage.Thus,in effect,ac ctrarieaanddischarged maybe restrictedonlybysuchlimitationsas uottaie.pass*noughttrecapacitor, proportion applied of the what determines appffr UvtfreRCtimeconstantwhich the time, At the same t}rough the capacitor. niit"g" is Uuittup anddischarged (see reactance passage through ac of to the ."p.Jitot offersa certainopposition power.Its maininfluenceis Ciiipt* 3), althoughthisdoesnot actuallyconsume of RCcircuits. on frequencyresponse SIMPLE COUPLING Couplingonestageof a radioreceiverto the next stagevia a capacitoris onitsown, isapparentlyused Althoughthecapacitance commondesignpractice. loadofthe by the represented with aneffectiveseriesresistance it is associated

thiswayand will fash in Fig. &4. Randomcasadefla.slprcircuit. Any numfurof lampscanbeconnecbdin rardomorfur.

stagebeingfed-Fig. &5. This, togetherwith the capacitor,forms an RC whichhasa particulartimeconstant.It is importanttlat this time combination from of theacsignalfrequenclbing passed therequirements constantmatctres to the other. onestage In the caseof AM radiostage,the ma:rimumsignallikely to be presentis How10 kIIz. The cycletime of sucha signalis U10'000- 0.1 milliseconds. funcpass two charge/disc;harge cycle represents frequency each this ever,to positive negative. one andone concerned, tionsasfarasthecouplingcapacitoris functionis 0.05milliseconds. Thusthetimeperiodfor a singlecharge/discharge this application mustbea to accommodate The RCtime constantnecessary preferably percent passing 63 of the appliedacvoltage-and valuecapableof moretlnn 63 percentof the appliedvoltage. Thesefigres cangiveyou a clueas to the optimumralue of the coupling capacitorto use.For example,the typicalinput resistanceof a low power transistoris of the orderof 1,000ohms.The time constantof a matchingRC (seeabove),givingthe requirements: couplingwouldbe 0.05milliseconds f

t:RC.'.C:= t(

-9W

1X ld :0.05 x 10-5 :0.05 pF (or higtrer,sincethis wouldensuremorethan63 percentvoltagepassed). wlue wouldnormallybeused;evenas In practice,a muchhighercapacitance higb as lpF or more This usuallygivesbetter results,at the expenseof (Anapparentcontradiction, but it efficiencyof ac(in tlis caserf) transrnission. the loadis reactiteratherthanpurely happensto work out that waybecause reistive.) Whatthe simplecalculationdoesshowis that capacitivecoupling frequencyof acsignalwhen lessefrcientwith decreasing increasingly becomes usedfor couplingduties. with practicalvaluesof capacitors associated FILTER CIRCUITS usedasafllarcirczitis shownin Fig. &6. Fromthe A basicRCcombination reutance,witha a resistorin serieswith a capacitive inputside,thisrepresents

acSigld Gcocntcd

SuScf

EficcrivcRceicrncc

Copling C.Fcit6

is b W o signalsad tlu* dc Fig.ffi. fusicf*tution of a couflingcapacitor signals dc uwlulating dgnals.It ab lases 4)

FiS.6$. fusiefilter circuit.It Huhsrcfnquncieshighcrtlvn theilbtfnq.cnct of ofR andC, thccoabination If the reactanceof the capacitor()b) is voltagedropacrosseachcomponent. acrossthecapacitorand muchgreaterthanR,mostof tle inputvoltageappears is the input voltagein value.Reactance tlus the outputvoltageapproaches to frequency, however,andsowith increasing frequency inverselyproportional andso doesthe outputvoltage(an the reactanceof the capacitordecreases, hcreasingproportionof tbe inputvoltagebeingdroppedby the resistor). tlere is a criticalfrequeocyat As far aseffectivepassage of acis concerned, in valuetlat suchacircuit component becomes sodegraded wbichthereactance Le.,tle ratioofvoltqd/volt% st rts to become blockingratherthanconductive; formin Fig. C7. startsto fall rapidly.This is shom in simplifieddiagrammatic point, point knownastheroll-off Thecritical or catotrfreqaenq(4),is givenby: f ..

I

2nRC

where: R is in ohms C is in farads z- 3.1416 0dB

gd

\

-t* ! -uorE

\

I

g

-r* .E I -o*F

\

I

g

\

g

\

0.rE

0.125 0.09 h0

a

-$dB! \ I

-"*$ -21 dB>

t/to -rfirqu4t

[

1&f,

FA.e7. Sinllifieddiagramoflnw thcratioof ooltsinl ooltsnt dnhsralidb u the cntoffteWenqofafiltq b e,rualcd. All Ebrrole Uorr tb cubt Inryenq an lM sitho*t attenuatio*

previously, ButRC,asnoted isegual tothetimecmskntdtheRCombinatio. Ilence:

\. : mt whereT irsthe time constant,in seconds. Theperforrnance of suchafilter is definedby its cutofrfrequencyandtherate at whichthe volts5/volts"nratio fallsabovethe cutofffrequency.Thelatter ic normallyquotedas(somany)dBperoctave(or eachdoublingdfrequency)(see Fig. e8) whichshowstherelationship betweendBandvoltqbfrcttsdratio,and alsothe tnre form of thefrequencyresponse ctree. IOW.PASS FILTDRS Circuitsd this type are ealledlowlass filtersfuu* they passsg siguts belowthe @crrt-off frequencywith little or no loss or atbntutios e Jgnal streryth" with signls abovethe cutoftfrequency,thereis increasingatteotntim. suitablecomponent rnalues are readilycalcnlated" For examplga typical sratch filbrassociatd with a recordplayeror amplifierwonHbedesigned to attmuatefrequencies above,say,l0 kHz-Fig. Gg. Thisraluerepresenrts the oilofr frequencyrequired;i.e.,Anycombination d R (in obns)ad C (inhrads) giyingthis prodrctrnalue couldbe r$ed. EIGtr.PASS FILTERS High-passfilters work the other way around.They attenuatefrequencies belowthe ortoff frequency,but passfrequencies at andabovethe cutofrfre

>.

0dB -3 dB -6 dB .9 E

\

I Ro[offpointor cutofftrequency \

-edB

& $ -udB

\ \

-15 dB

\

-18 dB -2r dB

Vl00

V10 Frequency

t

\ r0 x i

Fig.ffi Theoctr.olrollof fodntot ttu fnqrercy nsfurt* crtw of a fiItet is mt *r-tV defr,ten"Theilbt fnqunq b nallXa nninaifigun andgeturalgtthtn as tlelrcwcaq at uhichtlun iso J biM loss ora cr/lts inl ,dltsmt itu ofi.mz rhiEie qtiulest b a 50pncnt las offuwt

c

(R) Resistor

low-PassFilter

Fig.&9. simplcvrahhfiltcrcitcuit.Anycombination ofcomfionent giainga aarues lraductofRC- 7ffi0will worh. quencywith no attenuation. To achievethis modeof working,the two compo-' (Fig.6-10). interchanged nentsin the circuitare This typeof filter is againcommonlyassociated with recordplayercircuits, incorrporated to eliminatelow-frequencynoiseor "rumble" which may be present.The desigltcutofffrequency mustbe lowenoughnot to interferewith bassresponse, andso the valuechosenis usuallyof the orderof 15 to 20llz. Exactlythe sameformulais usedto determinethe cutofffrequency,hence, usinga desigrralueof 20llzz

,r-#'.,Ji RC: 125 Again,anycombination of R (in ohms)andC (in farads)grvinsa productof.l'25 wouldwork. Capocitor(C)

High-Pass Filtctr

FA. 6n. Rteh[ High-tdssor ntmblefilters cut of lowlreqrenciesfut passhigh A typicalaalrcfor thelroduct RC in thiscav wouldb 125. frequencies.

ln practical circuits, such filters are normally inserted in the preamplifier stage,or in tlre amplifierimmediatelyin front of the tone control circuit. For hi-fi systems,the type of filter circuits usedare considerablymore complicatedthan the onesdescribed. For more advancedfilter designs,seethe appendix.

tU

Coils and Inductances magneticfield.Thiscreationof magneticenergyrepresents a powerlossduring thetimethatfieldis beingcreated,whichismeasurable in termsofavoltagedrop to thevoltagedropproduced 9r bachemf,Thisis quitedifferent(andadditional) by the resistance of the conductor,anddisappears oncestabli conditionshave beenreached.Thus,in a dc circuit,the backemftendsto preventthe curent risingrapidlywhenthecircuitis switchedon.oncea constantmagneticfieldhas beenestablished, tre backemf disappears sinceno further "n*gy is being extractedfrom the circuitandtransferredto the magneticfield. In thecaseof anaccircuit,thecurrentis continuallychanging, creatinga back emf whichis alsochangrngat a similarrate. The valueof the backemf is dependentboth on tlre rate of changeof current(frequency)andto a factor dependent on the form of tle conductorwhichgovernsits inductance.Inductanceis tlus anotherformof resistance to ac,generated in additionto the pure resistance. Every conductorhasinductance whencarryingac, althoughin the caseof straightwiresthis is usuallynegligible(exceptat very highfrequencies). If the wireiswoundin theformofacoil,however, itsinductanceisgreatlyincreased.If thecoilisfittedwith anironcore,thenits inductance is evenhigheifor tlresame numberof turnsandcoil size. TViththe acflowingthrought}recoil,tlre "resistive"conditionestablished is notasdrasticasmayappearat first sight.Thepolarityof thebackemfis always

suchasto opposeanychangein current.Thuswhilethe currentis increasing, workis beingdoneagainstthebackemfby storingenergyinthernagnetic field. On the next part of the currentcyclewhenthe curent is falling,tle stored energyin tlte magneticfield returnsto the circuit, tlrus tendingto keepthe current flowing(seeFig. 7-1). An inductance,in fact, may be a very good conductorof ac,especially whencombined with a capacitorrn a tunedcircuit (seelater).Onthe otler hand,it maybedesigned to workasa resistivecomponentot chohe. Theinductance ofasingle-layer coil,woundwith spacebetweenadjacent turns canbecalculated from the formula: L-

R2 N2

9R + 10L

where: L is the inductance in microhenrys R is the radiusof the coilin inches N is the numberof turns L is the lengthof the coilin inches. Written as a solutionfor the numberof turns requiredto producea given inductance with R andL predetermined:

' - : 1 @lo[,)xL -lThisformulaappliesregardless of the actualdiameterof the wire used(also,it doesnot matterwhetler barewire or insulatedwire is used),providedttrecoil diameteris muchlargerthanthewire diameter. Forpracticalsizesof wiresused for coilwinding,this meansa minimumcoildiameterof at least1 inch(25 mm).

+

I E

a (J

switchoo

Time -*

SwitchOn

Time*

Fig. 7'1. fuch emfinducedin a dccircuit onxtitching on eristson\t momcntarig.In an accircuit, thcfuchemfis continuallychanging.

/to

For smallerdiametercoils,thewiresizehasanincreasing modifyingeffecton the actualinductance, andeventhe lengthof leadsat the endsof the coil can upsetthe calculation. Thussuchcoilsarenormallydesigned on empiricallines (i.e.,basedona specifiednumberof turnsofagivensize ofwireknowntoproduce a giveninductance whenwoundona specificforrr diameter). In practice,smallcoilsarenormallywoundona formintendedto takeaniron core. The positionof this core is adjustable, relativeto the woundcoil, by screwingin or out.Thust}e actnalvalueof inductance canberariedfor tuning (Fig. 7-2, left). purposes Alternativelya pot coremaybe usedwherethe coil is woundon a form or bobbin,subsequently in aniron housing.Providedthesiecific inilucenclosed tanceof.the pot coreis known(it is usuallyspecified by the manufacturer), the numberof turns (p) to be usedfor the windingcanbe calculatedwith good accuracy fromthe formula N:

t=

-/3

YA"

whereL is the inductance required,andA" is the quotedspecificinductance of . the pot corein the sameunitsasL. Practicalvaluesof inductanceusedin electroniccircuitsmay rangefrom microhenrys(in mediumand high frequencycircuits)to millihenrys(in low frequencycircuits),up to severalhenrysfor chokesin powersupplycircuits. Normally,aninductance will bewoundfromthelargestdiameterenameled wire it is convenient to use(andstill gettherequirednumberof turnsontlte formor bobbin),because this will minimizeobmicresistance andtlus improvetle efficimcy or &factarof.the coil RESONANTCIRCUITS A coil(inductance) anda capacitorconnected in seriesacrossanacsupplyhas theveryimportantcharacteristic that it is possible for thereactiveeffectof one to cancelouttle reactiveeffectsof theother.Thusin thedemonstration circuit shownin Fig. 7-3,L is the inductance, andC the capacitorconnected acrossa sourceof ac,the frequencyof whichcanbe varied.A resistor(R) is shownin serieswith L andC, asaninevitablepart of a practicalcircuit. If theacsupplyis adiusted to a lowfrequency, thecapacitive reactance will be verymuchlargerthanR, andttreinductivereactance will bemuchlowerthanR

E

g

ffi

g E ffi

Fig. 7-2 Coilform (lcfi) and tot con^c(rieht)47

PracticalEqrdnkrt

Th€oreticalCirqrit

Fig. 74. Components whichmahea resnantcircait. (andthusalsoverymuchlowerthanthecapacitive reactance). SeeCbapter3 for the formulasfor capacitiveandinductivereactance,andhowtlese valuesare on frequency. dependent If the ac supplyis adjustedto a highfrequencythe oppositeconditionswill lower reactance muchlargerthanR,andcapacitive apply-inductive reactance thanR andL. Somewhere betweenthesetwo e:rtremesthereis anacfrequency areequal,andthis is andinductance of the capacitance at whichthe reactances the really interestingpoint.I[hen inductivereactance(X") equalscapcitive (Xc),thevoltagedropsactosstiese two components will beequalbut reactance 7& degrees out of phav. This meansthe two voltagedropscanceleachotler to currentflow.In out,with theresultthat onlyR is effectiveastotalresistance onlybythe currentflowsthroughthecircuit,determined otler words,maximum valueof R andthe appliedacvoltage. ![orking undertheseconditions, thecircuitis saidto be resnant.Obviously, resonance occursonlyat a specificfrequency,whichis thuscalledthe resonant frequency.Itsvalueis givenby the simpleformula: . l ':ffiLC where: f: resonantfrequencyin IIz L - inductance in henrys C - capacitance in farads. formulato useis: A moreconvenient

'.

? : -

106

2nJfr,

wbere: f - resonantfrequencyin kilohertz(kIIz) tt8

L - inductance in microhenrys(pH) C: capacitance in picofarads(pF). Notethattlreformulafor resonant frequency isnotaffectedbyLy resistance (R) in thecircuit.Thepresence of resistance does,however,affecttheeualityfactor or 0 of the circuit.Thisis a measureof how sharfgthecircuit canbetunedto resonan@, thehighertlle valueof Qthebetter,in thisrespect.Theactualvalue of Q is givenby:

o:* whereX is thereactance in ohmsof eitherthe inductance or capacitance at the resonantfrequency(theyareboththe same,soit doesnot matterwhichoneis taken)andR is the valueof the seriesresistance in ohms. The practicalresonantcircuit (or tuned circuit) is basedon just two - aninductance components andacapacitor.Someresistance isalwayspresent, however.At lowto moderately highfrequencies, mostof tltis resistance comes fromthewirefromwhichthecoiliswound.At verymuchhigherfrequencies, the najority of the resistancemay comefrom the frequencyenergylossin the capacitor. TUNED CIRCUITS The combination of an inductance andcapacitance in seriesis the standard Iormof.tunedcircuitu#nalmost everyradioreceiver.Figurez-4illustratesa tunedcircuit with the inductorandcapacitorin a parallelconfiguration. The (Z) of thiscircuitis oppositein effectto thecircuitshownin Fig.Z-3. impedance As previouslydiscussed, whentlte resonantfrequencyis appliedto ttre circuit shownin Fig.7-3,thecircuitcurrentis at its highest(meaning its impedance isat minimum).Thecircuitillustratedin Fig.7-4presentsits highestimpedance at its pointof resonance.

TheoreticalCircuit

PracticalEquivdent

Fig. 74 TheoreticaQ, on$ a capacitor and indrctance are inoobed in a resnant circuit. In practice, snc resistanceis alway frexnt as uell.

To make the circuit tunable over a range of resonant frequencies,either componentcan be a variable type. The usualchoicefor antennacircuits is to maketlre capacitorvariable.In practice,tlte coil may alsohavevariablecharacteristics. It is usudly wound on a sleevefitted on a ferrite rod, and capableof being moved up and down the rod, providing a meansof varying tlre effective inductance.Oncean optimumpositionhasbeenfoundfor the coil, it is cemented to the rod. ln other words,the variablecharacteristicsof the coil areusedonlyfor initial adjustment.After that, all adjustmentof resonantfrequency,or tuning, is doneby the variablecapacitor. To assist in selecting suitable componentvalues, the resonant frequency formula can be rewritten:

LC:

1012 4n2 f2

where L is in mictohenrys,C is in picofarads,and f is the frequencyin kIIz. Maximum valuesof variablecapacitorusedare normally 300 pF or 500 pF. The working formula for calculatinga matchinginductancevalue is:

L(microhenry n: # thetunedcircuitistobedesignedto coverthemedium Asanexample, suppose from500to 1,600kHz;anda 500pFtuningcapacitor waveband, or frequencies is to be used.It followsfrom the resonantfrequencyformulathat ma:rimum will correspondto the lowestresonantfrequency(with a fixed capacitance inductance), whichin thiscaseis 500kHz.lnsertingtlese valuesin tle working formula:

L(microhenrysr:Z;#,

*

:200 the capacitoris turnedto its miniNowcheckthe resonantfrequencywhen (which pF, associated probably will be about 50 with this valueof mumvalue inductance:

FM 4nzX200X50

: 1,600kIIz

This showsthat a 50-500 pF variablecapacitorwill tune the circuitfrom 50

Fig. 7-5.A series-rennantcircuit. Tlv impedance acrosstlrctcrminab of tlu circuit b wry lou at thefrequencyof rennance;at thcconnection btween tlv capacitorand inducta4 the imfodanceis wry higrL Thc cafrcitor is usual$ theoariablcelcmentin thisanangement

T

1500kHz (the highestfrequency),downto 500kIIz satisfactorily.In other words,it coversttrewholeof the mediumwavebroadcast band. If the finalresultsachievedin the circuitdo not providequitetlre coverage required(for example, a stationnearoneendof the bandis not pickedup)then thereis stillthe possibilityofshiftingthefreguencyooverage inonedirectionor (i.e.,slidingthecoilupor downtheferrite the otherby adjustingtheinductance rd). Thereareotler typeof tunedcircuitswhichnormallyrequireadjustment only wheninitiallysettingup.Thesenormallyemployatunableinductance (e.g.,acoil powdered-iron woundona formwith anadjustable core).Suchcircuitsmayalso be tunedby a trimmer capacitor,or both a trimmer capacitorand tunable inductance. providesdoubletuniqg. The latter combination

SERIES.RESONANTCIRCIIITS Anottrerarrangement of the coil-capacitor combination is to connectthemin series(Fig.7-5).Thisproducesaseries-resonantcraitwherein thereactances of the coil andcapacitorare againequalbut opposite.The differenceis that it presentsa lowimpedance at the terminalsof the circuit(topandbottom).This lowimpedance hastheeffectof shuntingtheacfrequency of resonance outofthe circuit.Frequencies otherthanthe resonantonearenot affectedby the tuned circuit,asthe off-resonance impedance is undisturbed. A common usefor thistypeofcircuitis to remove,or reducein amplitude, any unwantedsignals,whileallowingall othersto pass.A popularapplication of the series-resonant circuitisin theantenna or rf-amplifierstagesofreceivers,where it is oftencalleda waoe-trap.Itcanalsobeusedquiteeffectivelyin transmitter power-amplifier (harmonics) stagesto trapunwantedmultiples oftlefundamental frequencyof operation. RADIO.FREQUENCYCHOKES A radiofrequencychoke(rfc) is a coilor inductance sodesigned that it hasa relativelylowohmicresistance buta veryhighreactance at radiofrequencies. It

Fig. 74. ?ypicalapfuaranceof clnhx woundon a ferrite core. can thus passdc but blockshigh frequencyac when tlte two are present in the samecircuit (Fig. 7-6). ln other words,it really works the oppositeto a capacitor as a circuit element in this respect. The characteristicsof any rfc vary with frequency.At high frequenciesit has characteristicssimilar to that of a parallel-resonantcircuit; and at low frequencies characteristicssimilar to that of a series-resonantcircuit. At intermediate frequencies,it has intermediate characteristics.The actual characteristicsare relatively unimportantwhen an rfc is usedfor seriesfeedbecausethe rf voltage acrqss the choke is negligible. If used for parallel feed (where the choke is shuntedacros{ra tank circuit), it must have sufficienfly high impedanceat the lowest frequenciesand no series-resonancecharacteristicsat the higher frequenciesin order to reduce power absorption to a suitable level. Otherwise, there is a danger of the chokebeing overloadedand burned out. Chokesdesigred to maintain at least a critical value of inductanceover tlre likely range of qrrent likely to flow through them are calledswinging chohes. They are usedas input filters on power suppliesto reduce riiple, or residualac content. Chokesdesignedspecificallyfor smoothingripple, and having a sub stantially constantinductance,independentofcbangesin current, are known as snmthing ch&es.

52

Transformers A transformerconsistsof two coilssopositionedthat theyhavemutualinductance.Thismagrretic couplingeffect canbefurtherenhanced bywindingthetwo coilson a commoniron core(seeFig. &1). The coilwhichis connected to tlrc sourceof supplyis calledthey'rimary,mdtheothercoilis calledthewcondary. In orderto transferelectricalenergrfromprimaryto secondary, the magretic fieldmustbe continuallychangrng; i.e.,the supplymustbe ac. Oneof the mostusefulcharacteristics of a transformeris its abilityto step down(orstepup)acvoltages.Thestepdown(orstepup)ratioisproportional to the numberof turnsin eachcoil: V,=NNrx% where: V. : secondary voltage N, : numberofturns on secondary \ : numberof turnsonprimary V, -prinaryvoltage. Thecurrentsffowingin theprinaryandsecondaryfollow a similarrelationship, but in oppositeratio:

L:Nn/N,x t 53

Iron Core

".,.71IF:.'** Secondary

Fig. 8-1. Thesimpleiron+oredtransformcr. where: l: secondarycurrent - nrimaw current | ln other words, a stepdown in voltage producesa step-upin current, and vice versa. In practice,there are alwayssomelossesdueto the resistanceof tlte coilsand energy lost in hysteresisand eddy currents in the core (in the caseof an ironcoredtransformer),andalsofrom reactancecausedby a leak of inductancefrom both coils.Thus, the powerwhich canbe takenfrom the secondaryis alwaysless than the power put intothe primary, the ratio of the two powersbeingameasure of.the eftciencyof the transformer. Typically, efficiencymay rangefrom 60 percentupwards,but is not necessarily constant.A transformer is usuallydesignedto haveits maximumefficiencyat its rated power output. Its actual efficiency figure decreasesif the output is higherorlower.This lossofpowerappearsintheformofheat.Thus,overloading a transformer can both reduce its efficiency and increasethe heating effect. Operatingat reducedoutput hasno harmfuleffect, exceptforreducing efficiency becausethe actual power loss (and thus heating effect) is lowered. TRANSFORMERS AS POWER SUPPLIES By selecting a suitable turns ratio, a transformer can be used directly to convert an ac supply voltage into a lower (or higher) ac output voltage at efficiencieswhich may be as high as 90 percent lpig. 8-2). There are also applicationswhere a I : 1 turns ratio transformer is used,providingthe sameac output voltage astlte ac input voltage,where it is desirableto isolatetlte supply from the output circuit. All transformersdo, ofcourse, provide physicalseparation of input and output circuits, but the degreeof isolationsafety is very muc.h dependenton the actual constructionof tlte transformer. The more usualpower-supplyapplicationof a transformer is to stepdown an ac voltage into some lower dc voltage output. The transformer only provides voltage conversion.Additional componentsare neededin the output circuit to transform the convertedac voltage into a dc voltage. Two basiccircuits for doingthis are shownin Fig. 8-3. The first usesa single diodeandprovideshalf-waaeratification,passing onehalf of eachaccycleasdc 51

Power loss 10 Percent or More

ac ln

StepDownTransformer

StepUp Trandormer

Fig.&2 stct4owrr ard step-uptransformersdefined,In fractice, transfotztcrsare oftcn drawn in slmbolic fottl uith bth coilsof tlv vme length,regardless of actual turns ratio.

andsuppressing theotherhalfcycle.Thepurposeof thecapacitoris to maintain the dc voltageoutputasfar aspossibleby discharging on eachsuppressed half cycle,andfor this a largevaluecapacitoris required.Althougha very simple circuit,it hasthe inherentdisadvantage of generatingttrgh peahvolkgesand currents,especiallyif ahighcurrentisdrawnfromtheoutput.Also,thedcoutput is far from smooth.It hasa rippleat tlre acfrequency. Muchcanbedoneto smooththeoutputbyaddinganinductance or chokeanda secondcapacitor,asshownin theseconddiagrarn.Thesetwo components work as a filter (seealsochapter 6). The designof the chokehasto be specially matchedto tlte requirements, offeringlow resistanceto dc withoutbecoming saturated, whichcouldreduceits inductance. In particularcircuitstheinductance maybea swingingchoke,whenit is possibleto eliminatethereservoircapacitor

c1.

Thefirst diagramof Fig.84 showsa sinplefulr-wau rectifiercircuitaddedto tlte transformer(thesecondary of whichmustbecentertapped).For the same secondary voltageasthehalf-wave rectifier,thedcoutputvoltageis nowhalved, but the currentwhichcanbedrawnfor a givenrectifierratingis doubled.The reservoir capacitorchargesand dischargesalternately.This producesa smootherdcsupply,butrippleis still presentandin tlis caseisequalto twicethe acfrequency. Themoreusualformof full-waverecffier isthe bridgecircuit,shownin the seconddiagramofFig.8-4.Thisgivesapproximately thesameno-loadvoltageas a half-waverectifier with the advantage of full-waverectificationandbetter smootldng.

*l Vob r

2!l0 Volts ac

Fig. &3. Half-wau rectificationof ac.

55

Fig. 8.4. Full-waaenctifuation of u.

A practicalcircuit of this type is shownin Fig. &5. A singlehigh ralue electrolyticcapacitoris usedfor smoothing.Additionalsmoothingbetrreen stagesfedfrom sucha powersupplymaybeprovidedby a resistor,associated with a decoupling capacitorQikeFig.8-3).Theresistorrraluecandsobechosen to dropa specificamountof voltageif thepreviousstage(s) donotrequirethefrdl power-supply outputvoltage. TRANSFORMERSAS COUPLING DEVICES Transformersare very usefulcouplingelementsfor ac circuits.As well as providingcouplingtheycanstepupa voltageor current,andevenmoreimpormatching.By choosingthe properturnsratio,the impedtant for imPedance anceofafixedloadcanbetransfornedto anydesiredhigherorlowerimpedance, within practicallimits.This canbe a particularlyimportantrequirementwhen couplingtransistorradiostages. For impedance matching,the followingrelationshipapplies:

*-,8 where:

Altmat'w! Symbda f6 BridS! Rccdfa

@ Fig. &5. Practicalpower-svpfl1circuit. A hiSh wluc capacitoris usd. Thefur singlecom|oneil calleda bridgerectifer. 56

diodesdreboaght a 8 a

ac Output

FiS,e4. Theaubtransformer is a singlcfuil-lcrgthcoilwitha tallittg loint Znis the impedance of the tran$ormerlookinginto ttre primaryterminats z. is the impedance of the loadconnected to the secondary of tle trandormer For impedance matching,it is thereforenecesvry to designthe primaryto providethe requiredZo^d selectthe turnsratio to satisfythe equation AUTOTRANSFORMERS An autotransforzarisa one.winding coilwith anintermediate tappingpoinl The full lengthof the coil (usually)formsthe primary,andthe lengthof coil betweenthe tappingpointandoneendof tlre coilsenesastlre secondary (Fig. &6). It worksonoractlythesameprincipleasa conventional transformer,with the voltagedeveloped acrossthe outputproportionalto the turnsratio of this lengtl ofcoil to thefull lengthofcoil.Thebiggestdisadvantage ofanautotrans" formeris that it doesnot provideisolationbetweenthe primaryandsecondary windings.This canbe critical(or evendangerous) in somehigh-powerapplications.

57

9 Semiconductors Deare knownas passiu components. Resistors,capacitorsandinductances in circ'uitconditions by reactingto appliedsignals viceswhichproducechanges The majorityof activecomponents usedin are knownas actioecomponents. modernelectroniccircuitsue smiconductors,or morecorrectlyput, devices materials. basedon semiconductor materialis onewhichcanbegivena predomiVery simply,a semiconductor nanceof mobilenegativechargesor electrons,or positivechargesor holes. of bothelectronsand Currentcanflowthroughthematerialfromthemovement holes.This is quitedifferentfrom the behaviorof a normalconductor,where clrrrentflow is the resultof electronsthroughthe material(seeChapter1). propertiescanbe givento a strictly limitednumberof mateSemiconductor rials by dopingwith minutetracesof impurities.The two mainsemiconductor or "semimetals").Doping materialsaregermaniumand silicon(bothnon-metals of .fusitivecharges(holes) canproducea materialwith eithera predominance of l\>ive charges resultingn a P-tyfe material;or with a predominance (electrons),knownasm N-$pematerial. This doesnot becomeparticularlysignificantuntil a singlecrystal(of gerrnaniumor silicon)is treatedwith botha P-typedopeandanN-typedope.In this regionsareformed-a P-regionandanN-region.Sincetlese case,twoseparate regionshaveoppositechargesthereis a tendencyfor electronsto miratefrom theN-zoneto theP-zone,andholesto migratefromtheP-zoneintotheN-zone. of chargesin the regionof thejunctionof the P- and Theeffectis a cancellation N-zones,formingwhatis calleda dePtetionlayr(Fig.9-1). This layer,which 58

P-Dope

ffi.w

in theconstntction ofa xmiconductor dide, slnut in simplc lis. s't. Fourstages diagrammatic form.

containsnofree electronsorholes, tlenactsasabarrierbetweenthep-zoneand t.heN-zone,preventinganyfurther migrationof either erectronsor holes.In effect,the barrieror depletionlayersetsup a potentialdifferenceberweenthe two regionsandthe deviceremainsin a stablestateuntil anexternalvoltageis appliedto it. Figure9-2 showswhathappenswhenan qrternalvortageis appriedto tle device.In thefirst diagram,the * voltageis connected to the p-zone.provided this voltageis sufficientlyhighto overcomethepotentialdifferencesetupin the construction of thedevice(whichmaybeonlya fewtentls of a volt (it willrepel holesin theP-zonetowardstheN-zone,andattractelectronsin theN-zoneinto theP-zone.Effectively,thebarrieror depletionlayerwill disappear andcurrent will flowthroughthedevice.Voltageappliedthiswayis knownas/orward bias. If theexternalvoltageis appliedtheotherway,asin tre seconddiagram,t.he oppositeeffectiscreated;i.e.,thetlicknessofthedepletionlayerincreases, tlrus buildingupa higherpotentialin thedevice,opposingtheexternal voltage.The backvoltagedeveloped is equalto thatof theappliedvoltage,sonocurrentflows throughthe device.Voltageappliedthis wayis knownas negatioebias, Thedevicejust described is a semiconductor diode.lttnsthebasiccharacteristic of actingas a conductorwhenconnected to an externalvoltageonevxay Gorwardbias),andasaninsulatorwhenconnected theotherway(reversebias). Diodecharacteristics are describedin somedetaillater on, but tle same principlescanbe appliedto e:rplainthe worki4gof a transistan

Fonrard Bias

ReverseBias

Fig.92 Thctw mdes in whicha diodecan b operated. 59

TRANSISTORS Basically, atransistoris twodiodesplacedback-to-back with acommon middle layer,tlre middlelayerin thiscasebeingmuchthinnerthanthe otjrertwo.Two confgurationsare obviouslypossible,PNPor NPN (Fig. g-3).Thesedescrip tionsareusedto describethetwobasictypesof transistors. Because atransistor junctions,it is referredto as a bipolar containstwo seperatesemiconductor device,or bifolar transistor, A transistorhasthree elements,andto operatein a workingcircuit it is connectedwith two externalvoltagesor polarities.one externalvoltageis workingeffectivelyasa diode.A transistorwill, in fact,workasa diodeby using justthisconnection andforgettingaboutthetophalf.Anexample is ttresubstitution of a transistorfor a diodeasthe detectorin a simpleradio.It worksiust as well asa diodebecause it is workingasa diodein this case. The diodecircuitcanbegivenforwardor reversebias.connectedwith forward bias,as in the first diagramof Fig. 9-4, drawnfor the PNP transistor, currentflowsfromP to thebottomN. If asecond voltageis appliedto thetopand bottomsectionsof the transistor,with the samepolaityappliedto thebottom, the electronsalreadyflowingthroughthe bottomN sectionpromotea flow of currentthroughthe transistorbottom-to-top. By controllingthe degreeof dopingin the differentlayersof the transistor duringmanufacture, this abilityto conductcurrentthroughthe secondcircuit throughtle resistorcanbe very marked.Effectively,whenthe bottomhalfis forwardbiased,the bottomsectionactsasa generoussourceof freeelectrons (andbecauseit emitselectronsit is calledthe emitter).Theseare collected readilyby the tophalf,whichis consequently calledthe collector,butthe actual amountofcurrentwhichflows throughthisparticularcircuitiscontrolledbytle biasappliedat tle centerlayer,whichis calledthebase. Effectively,therefore,trere aretwoseparate workingcircuitswhenatransistor is workingwith correctlyconnected polarities(Fig. 9-S).Oneis the loop formedby the biasvoltagesupplyencompassing the emitterandbase.This is calledthe 04s,circuitor inlut arcwt Thesecondis the circuitformedby the

PNPTransistor

NPNTransistor

FA.A?.ConstnrctionofPNPand NPNtransistors,shownin simplediagrammatic form,

ffi

shoundiagrammaticalll taa PNPtransistor Fis,94. Biasandsvpfll connections (neht). (lcfi)andin symbol form ofthetransistor.Thisis calledthe supplyandallthreeelements collectorvoltage (Note: appliesonlywhenthe this description outputglrcJjlt collectoretrqitor as commonemittcr circuits-known to both is common emitter connection transistors,but of connecting used way widely most This is tlte configuration. andcommon base configurations-common alternative there are two other in eachcase.) the transistor principles of in the working apply collectonT\esame srnallbase relatively is that a circuit particular by this offered advantage The (or,more current collector much larger very instigate a and cgrrentcancontrol producing larger output much power a of is capable input correcdy,a small power).In otherwords,tle transistorworlrsasanamplifier. circuitis the inputside,andthe Withttrismodeof working,the base-emitter Althoughthesehavea outputside. to collectorcircuitisthe emitterthroughbase are effectivelysepatwo circuits path the and emitter, throughbase common tle base polarity is concerned, circuit the base of far as ratedby thefacttlat, as Hence biased diode. reve6e as a are connected andupperhalfof the transistor circuit. collector into the basic circuit thereis no currentflowfrom the For the circuitto work, of course,polaritiesof both the baseandcollector circuitshaveto be correct(forwardbiasappliedto the basecircuit, andthe collectorsupplyconnectedso tbat the polarityof the commonelement(the

O{put Cirsuit

FtS.g44,. Trtctw cparatc citeuitsinoolutt in olerating a transisbr. Ditz.ctianol curnnt fuw is for a PNP tlarrsis/lor..

61

emitter) is the samefrom both voltagesources).This alsomeansthat the polarity of the voltagesmust be correct for the type of transistor. In the caseof a PNP transistor, asdescribed,the emitter voltagemustbe positive.It followsthat both tlte baseandcollectorare negativelyconnectedwithrespecttothe emitter. The symbolfor PNP transistor hasan uurowon the emitter indicatingthe direction of.current flow;i.e.,alwaystowardsthe base.(P for pcsitive,witl a PNP transistor.) In the caseof anNPN transistor,exactlythe sameworking principlesapplybut the polaritiesof both suppliesarereversed,Fig. 9-6. The emitter is alwap made negative relative to baseand collector. (N for negative in the caseof an |rIPN transistor). This is also inferred by the reverse direction of the arrow on the emitter in tlre symbolfor an NPN transistor; i.e., cgrrent flow away from the base. PRACTICAL DIODES The typical appearanceof a semiconductordiode is shown in Fig. 9-7. The cathodeend is usuallymarked by a red dot or color band,or a * sign, and also usuallywith a type numberconsistingof oneormore lettersfollowedbyfigures. This identifiesthe diodeby manufacturerandspecificmodel.Specifict1ryenumbers are usuallyquotedfor specificcircuit designs,but many circuits are fairly noncritical as regardsthe type of diodeused. Diodesmay also be describedin more generalterrrs by the crystal material (germaniumor silicon), and by construction.Here, choicecan be more important. C"tt oiurn diodesstart conductingat lower voltagest}an silicon diodes (about 0.2 to 0.3 volts, as comparedwith 0.6 volts), but tend to have higber leakagecurrents when reverse biased,this leakagecurrent increasingfairly substantialwith increasingtemperature. Thus, the germaniumdiode is inherently less efficient as a rectifier than a silicon diode, especiallyif reverse bias ctrrent is high enoughto produceappreciableheatingeffect. On the other hand, a gerrnaniumdiode is preferred to a silicon diode where very low operating voltagesare involvedbecauseit starts to conductat a lower forward voltage. The constnrction of a diode governs both its curent{arrying capabilities

diqramnaticalll toan NPNtransistor,sltoum Fig. 94. Biasand wpp$ connections (lefi) and in syttrlu,lic form (right).

e

.r'.;.-i

Dodes AiF

@

m F

Volts ReverseBias Volts Forward Bias

-.....---

Forward Voltage Needed to Overcome

Fig.97. AlerationalcharactzrMics ofa ffiical vmiconductor diode. whenconducting, andits capacitance effect.Thelargertheiunction areaof.a diode,tlte highertlrecurrentit canpasswithoutoverheating-for example, tltis characteristic is desirable in high-power rectifiers.Ontlte otherhand,increasing thejunctionareaincreases the readiness with whicha diodewill passacdueto inherentcapacitance effects.To reducethiseffectto a minimum,a diodecanbe madefromasingledopedcrystal(usuallyN-type),onwhichthepointof apieceof springwire rests.The endof this wire is givenoppositedoping(P-type).This reducesthe junctionareato a minimum,suchas a diodebeingknownas a point+ontacftype.It is afavoredtlpe for usein circuitscarryinghighfrequency ac signals,andfor this reasonis sometimes calleda signal diode. Thetypicalcharacteristics of a diodearealsoshownin simplegraphicformin Fig.9-7.Biasis represented by thevoltageappliedto thepositiveside,referred to asanodewltage.Currentflowingthroughthe diodeis referredto asanode current. With forwardbias(positivevoltageappliedto the anodeendof the diode), ttrereis at first no anodecurrentuntil the inherentbarriervoltagehasbeen overcome(0.3 volts for a germaniumdiode,0.6 volts for a silicondioderegardlessof the constructionof either tne). Any further increasein anode voltageproduces asteepriseof anodecurrent.In practice,it isnecessary to limit this currentwitl a resistoror equivalentresistiveloadin thecircuitto prevent the diodebeingoverheated andthejunctiondestroyed. Withreversebias(negativevoltageappliedto theanodeendof thediode),tlre only currentflowingwill be a very smallleakagecurrentof the order of microampsonly, and normallyquite negligible.This leakagecurrent doesnot increase appreciably with risein (negative) anodevoltage,onceit hasreached its saturationvalue. It will beappreciated thatadiodewillworkin bothadcandanaccircuit.Inadc circuit,it will conductcurrentif connected with forwardbias.If connected the opposite way,it will actasastopforcurrentflow.Anexample ofthistypeofuseis wherea diodeis includedin a dc circuit-say the outputsideof a dc power

supply-to eliminateanypossibilityofreversepolarityvoltage surgesoccurring which could damagetransistors in the samecircuit (seeFig. 2&1). In an accircuit a diodewill "chop" the appliedac,passinghalf cycleswhich are positive with respect to the * end of the diode, and stoppingthose half cycles which are negativewith respect to * end of the diode.This is rectifieractton, widely usedin transforming an ac supply into a dc output. The sameaction is requiredof a detector in a radio circuit. Here the current appliedto the diodeis a mixture of dc andac.The diodedetector transformsthis mixedinput signalinto a varying dc output,the variationsfollowingthe form of ttre ac contentof the signal. BASIC TRANSISTOR CIRCUITS The transistor in common-emitter configuration works as an amplifier, as previouslyexplained.It needstwo separatesupplyvoltages-one for bias and the ot}rer for the collector-but tlese do not necessarilyhave to come from separatebatteries.Theycanbeprovidedbyasinglesupply(battery)takentothe commonconnection(the emitter) and the collector, and tapping t}te collector sideto applythe necessaryforward biasvoltageto the base,droppedthrough a biasresistor. A basicamplifiercircuit then lookslike Fig. 9-8. To makethe circuit do useful work, tie collector current hasto be fed through an output load, suchas a load resistor. These two diagramsalso show clearly input and output as separate entities, andcan clarify the point about amplification.The power derived in the output is far greater than that put into the input. This very simplemethodof supplyingboth collector andbiasvoltagesfrom a single source is known as current biasing. It needsonly one resistor, and it works.The resistor valueis chosento give a base-emittervoltageof the order of 0.1 to 0.2 volts for germaniumtransistors; and about 0.6 to 0.7 for silicon transistors.It is not asstableasit shouldbe for manycircuits, however,particularly if a germaniumtransistor is used,so voltage bias is often preferred (Fig.

e-9).

Fig. 98. Simfle current biascircuitsfor transistaroforation, fl

FA. 9-9. Voltage biascircuitsfor transistor oferation. Withvoltagebias,two resistors(Rl andR2)areusedto workasa divider.A resistor(R3)is alsoaddedin tlre emitterlineto provideemitterfeedback auto matically,to controlthe biasvoltageundervaryingworkingconditions.This latterresistorisalsousuallyparalleledwith acapacitortoprovidefurtherstabili(but zation this maybeomittedwitl silicontransistors). Determination of suitablecomponent valuesis nowmorecomplicated since tlree resistorsareinvolved.Theactualbasevoltagecanbecalculatedfromthe followingformula: basevoltage:

R2 X supplyvoltage (R1+ RA

The emittervoltageis equalto this lessthevoltagebetweenbaseandemitter (acrossthe transistor).ln mostcases,a voltagedropof I volt in the caseof germanium transistorsand3 voltswith silicontransistorsis thedesignaim.The emitter resistor(R3) alsoneedsto be quite largeso that there are minimal changesin emitter currentwith anyvariationin the supplyvoltage.This can causea little re-thinkingaboutsuitablevaluesfor R1 andR2, for tlre voltage developed acrossR3 mustbevery muchgreaterthanthe voltagedeveloped by tlte basecurrentacrosstlte sourceresistance formedbytheparallelcombination of Rl andR2. TRANSISTORCONSTRUCTION Theoriginaltransistorsweremadefromgermanium crystalswith point FrequencY

FA. 48. fund.tto/filtcrefat onfnqtercy.

f,igh-Pass Filters flter. fite ralueof Figrre A-10illustratesa commonformd activehigh-pass q$ofrfrequency ({,) into 10.Theresult the desired by dividing is determined Q C1 Nsrt, multiplytheralueof inmicrofarads. this calculationistheralueof of Q factor. product This result is the scale into 159. this fc and divide with thedesired of theremainingcomponents The scalefactoris neededto calculatethernalues from tle followiqgtable:

Component

For Gain of 2

Cz0n/F) Cs(inpF) Rr (in k0) Rr (in kO)

0.500X valueof C1 f .000X valueof Ct 0.566X scalefactor 3.536X scalefactor

190

For Gain of l0 0.100X ralueof C1 1.000X ralueof C1 0.673X scalefactor 14.849X scalefactor

Fig.A-10.High-|a$filtcr.

Exarple: fc - 50llz; Gain:2 Desired to

Q:fr -o'02 tE

Cc: (0.02)0.500:0.01p1t - 0.02tE Cc: (0.02)1.000

scalefrctor-H-f;- ts.e : 8.99k0 &: (0.566)15.9 f,r: (3.536)15.9:56.22ka BandpassFilter FigureA-11illustratesa cornmon formof activebandpass filter. Thevalueof (fo)into 10.Theresult Cris determined bydividingthedesiredcenterfrequency dthiscalculationisthevalueof Cl inmicrofarads.Next, multiplytderalueof C1 with thedesiredfo anddividethisproductinto 159.Theresultis tle scalefactor, usedto calculatethe raluesof the renainiqgcompooents from tle followiag tabte:

Cmpooent

For Gain of 2

FcGalnof 10

Cr(tnpF) &(ro kO) RrGnkO) Rr(in kO)

1.000XwhedCg 1.000X scalefactc 0.333X scalefrctm 4.000X scalefactc

2.000XvaluedQ 0.200X scalehctc 1.000X scalefrcttr 3.000X scalefrctor p1

Fig.A-11.tundlassflt /. Example: Desiredfo: 500IIz; Gain: 10 10

Ct:Bii':0.02#F : 0.0apF Cc: (2.000)0.02 factor:g - 119: rb.9 scale lu tU, Rr: (0.200)15.9:3.18kO Rr: (1.000)15.9:15.9kO : 47.7kA f,r: (3.000)15.9

a higherQ valueis required.Theraluesof R1,R2, For a narrowerbandpass, andRscanbeadjustedby multiplyingthemby thefactorsgivenin thefollowing table: For Gain of 1O

For Gain of 2

DeeiredValue ofQ

Rl and R3

1 6 8 10

2 3 4 5

Rr 0.400 0.258 0.189 0.153

Rt aodRg

2 3 4 5

R, 0.105 0.06r 0.0/t4 0.034

Dxample: maintainingthe calculationswhile Desirea Qof 8 fromthepreviousbandpass gainat 10. 1%

Rr - 3.18kQ X 4 : L2.72lc-Th ruGgT TRIANGI,E (1)fta-* (2)cc A-*

(3)tano-l (4)sec0-*

(5)cot0-8 (6) csc0-

H

O ROOTIIIEAN SQUARE (SINE WAVE SHAPEONLY) (1) rms- 0.707Geakvalue) (2) rns: 1.111(avsagevahre) SECANT

(1)sec A-x tg

otf,^

(2) sec0- cosecant (90- d) (3) sec0- I = CGI U

SINE

(1)sinA:i

o

(2)sin0- cos(90- d) ( 3 ) s i-n Q - ' ' . > cosecant A 1

SUSCEPTANCE x.

(1)B,-pft (2 )B- .:i r \

t c

(3)Bmmr:Br+Bs+Bs . . . etc, TANGENT o

(1)tan0_i

(2 )tm0 :o t(9 0 -d ) 1

(3)tan?-;i.re TEMPERATTIRE (1 )C :0 .5 5 6 F -1 7 .8 (2)F: 1.8C + 32 (3 )K : C +2 7 3 TRANSISTORS, BIPOIITR (1)I"-Iu f (2) I"= 1" (3) B" - Eu- 0.7(silicontransistors) (4) E. - Eu- 0.3(gernaniuntransistors) F

(5)I":ff

I\G

19

(6) 4-R.F A i+ - F Wh€res of a comnmco[ectcemi$radm &is tle porvergain TRANSISTORS, FISII) EFFECT "- --AIoAVcr Wbere: ralue Gbis thetransconductance rroltage in gateto source AVcsi8a change in &ab curreot change AIDiEa suhequent INANSFONUERRATIO

N ' E t - t { rT- ,

-----

N

WAVEI,ENGTg

m

E. t

lz,