212.2BipolarTransistorAmplifiershas beentaken from emitterto base rather than from base to emitter.Since the sumof the currents leaving the emitter junction is zero,VV- VeV-VigmV=0(2.13)RsroTrV.v-V。(2.14)Also8mVRLroIf the dependent voltage Vis eliminated from these two equations, we obtain anexpression for the voltage gain of the common-base amplifier.This equation israther complicated,and usually little accuracy is sacrificed by assuming that rislarge compared with Rs,rr,and Rz.The voltagegain is thenBRLV.gmRirm(2.15)A,==R,++gmRgr元=元+R(1+p)(Note that there is no phase inversion in the voltage gain of the common-baseamplifier.)Ifthesource impedanceissmall,r》R,(1+β),themagnitudeofthevoltagegain willbethe sameas that ofthe common-emitter amplifier.The input impedance of the common-base amplifier is determined using thesimplified circuitofFig.2.6.SinceV,(2.16)Ii=+gmVr元1rar元(2.17)thenZi=1+gm元1+βgmTheinput impedanceof the common-baseamplifier is smallerthanthat of thecommon-emitter amplifier. Since it is inversely proportional to gm, it is inverselyproportional to the collector direct current.This property is found useful in settingthe amplifier impedance to a desired level forimpedance matching.Also,since(2.18)IL=gmV,=gml,Zthe current gain isβgml元(2.19)Ai:1 + β1+gm元8mViFIGURE2.6The input impedance of this common-base ampli-fierequivalent circuits isV,/lj.R
22CHAPTER2:Small-SignalAmplifiersFIGURE2.7Asimplifiedcircuitmodelforcalculat-ing the output impedance of thecommon-baseamplifier.emlwhich is slightlyless than 1.The output impedance can be determined from thetwonode equations (see Fig.2.7)V- V.-l。=gmV+(2.20)roVVVand8mV=0(2.21)RroTaRR=where(2.22)ra+RsTherefore,the outputimpedanceis(2.23)Z。=r+R(1+gmr)which is larger than that of the common-emitter amplifier.EXAMPLE 2.2. Calculate the midband voltage gain, the current gain, and the inputimpedance of the common-baseamplifiershown inFig.2.8.The collectorbias currentis10-3A,andthetransistorβ=100.Solution.The small-signal,midfrequency model is shown in Fig.2.9.The collector-emitter resistance is assumed to be infinite. Since Ic -1 mA,-8m=40lc=40×10-3sFIGURE2.8Acommon-base amplifier.≥ 4 k0820k0V.3k012
232.2BipolarTransistorAmplifiersFIGURE2.9A small-signal equivalent cir-cuit of the amplifier illustratedRin Fig.2.8.00V4k0B25002andgmTherefore, from Eg. (2.15), the voltage gain is given by100(4×103)52.98Au:2.5 ×103+50(101)and the current gain is [using Eq. (2.19)]100=0.99A;101TheinputimpedanceiscalculatedusingEq.(2.17):1Z.~252gmThe common-base amplifier has a voltage gain, but the current gain is less thanunity.This amplifier is used in applications in which it is desired to build a non-inverting amplifieror an amplifierwithalow-input or a high-output impedance.Itdoes havemuch betterhigh-frequencyresponsethan the common-emitter amplifierand is often used in high-frequency circuits. An application of this amplifier isdescribed in the section onmultistageamplifiers,and additional examplesarepro-vided in Chap. 5.Emitter-FollowerThe common-collector amplifier,betterknown as an emitter-follower,has variousapplications.It will be shown thatthis amplifierhas anoninvertingvoltagegainofless thanl,anda currentgain approximately equal to the β of thetransistorused.Although it has a voltage gainless than 1,it can be combined with anotheramplifi-er stage,such as acommon-emitterstage,torealize agreater combined voltagegainthan could be achieved from the use of a common-emitter stage alone.This is par-ticularlyuseful when a low-impedanceload is used.An emitter-follower amplifier is illustrated in Fig.2.10, and the small-signalmidfrequency equivalent circuit is given in Fig.2.11. It is normally the case thatthe base-biasing resistor R, is much larger than the source resistance R,and can
24CHAPTER2:Small-SignalAmplifiersFIGURE2.10An emitter-follower(common-collectoramplifier).FIGURE2.11A small-signal equivalent cir-cuit of the emitter-followerillustrated in Fig,2.10.+VoRttherefore be neglected. If this is the case, the equivalent circuit is as shown inFig.2.12. The voltage gain is determined from three equations:V,=l(R+r)+V。(2.24)V=lr(2.25)ToRLandV。=（+gmV)(2.26)o+RLIf Vand l, are eliminated, thevoltage gain is found tobeVo(1 +)Er。RL/(r。+ Rz))Anr=(2.27)V,=R,+r元+(1 +β)[r。RL/(r。+Ri))The voltage gain is noninverting (positive)and less than 1. As R, increases, thegain approaches i.The emitter-follower input impedance can be found fromEgs.(2.24)and(2.27)byeliminatingV。andsettingR,=0.Theinput impedance is+(1+β)roRZi=(2.28)ro+ RtIf risverylarge,Z,~r+(1+β)RTheinput impedanceof theemitter-follower isthelargestofthethreetransistoramplifierconfigurations.Actually,itisthesameasthatofthecommon-emitterampli-fier if the samevalueof emitter resistance is usedforboth,but the additional resis-tanceusedforthecommon-emitteramplifierwillcreateadditionalpowerdissipation
252.2BipolarTransistorAmplifiersLFIGURE2.12A simplified small-signalequivalentcircuitoftheemitter-follower.VThe output impedance is determined by applying a voltage to the output ter-minalsand measuring the current Ig.The output current is determined fromtheequationV.V.Tn(2.29)Ve+1.+mR,+r元ra+RsroTheoutputimpedanceisV.ro(rw+R,)(2.30a)Z.I。+R,+ro(I+p)Zo~'x+R(2.30b)Then1+βThe output impedance of the emitter-follower is the lowest of the threetransis-tor amplifier configurations. Low output impedance is a requirement in manyamplifier applications.The emitter-follower is used when a low output impedanceis neededTheemitter-followercurrentgainisILVo/RLV.R.+Z(2.31)Ai=ViI.IRLand by using Eqs.(2.27)and (2.28), the current gain is found to be(1 +gmrw)r。2~1+β(2.32)A:ro+RLAlthough the emitter-follower has a voltage gain less than l, it has a large currentgain, It is also frequently used as a power amplifier for low-impedance loads.ExAMPLE2.3.Calculatethepowergainof thecommon-collectoramplifiershown inFig.2.13a.The transistor is a 2N5901 with β=40.The transistor output impedance islarge and can be neglected.The collector direct current is 4O mA.Solution. The small-signal,midfrequency equivalent circuit is shown in Fig.2.13b(rhas been neglected). Since the 100-s2 resistor, which is used for biasing,is in serieswith the dependent current source, it has no effect on the output signal.The collector