2Small-Signal Amplifiers2.1INTRODUCTIONMost amplifiers used in communications circuits can be considered small-signalamplifiers.These are amplifiers in which theinputand output signals are sufficientlysmall so that the amplifier performance is described with linear equations. In thischapter wefirstdiscussthelow-frequency small-signalmodelsforbipolarand field-effect transistor(FET)amplifiers.Thehybrid-model is usedto describe thebipolar transistor since it is the easiest to analyze.It will be shown that the samesmall-signal model canbe used for theFET.(It will be shown in Chap.5 thatthismodel canbe readily extended fortheevaluation ofhigh-frequency amplifierperformance.)The importance of push-pull and operational amplifiers wil be outlinedhere,as will theimportanceof theversatiledifferentialamplifierusedinthemajorityof linearintegrated circuits.Operational-amplifiercircuits willbediscussed, andwe will look at recent advances in integrated-circuit fabrication that have extendedthegain-bandwidthproduct(atermdefined in this chapter)oftheoperational ampli-fier to the extent that operational amplifiers now find many applications in high-frequency circuits.2.2BIPOLARTRANSISTORAMPLIFIERSEquivalentCircuitsIn the hybrid-low-frequency equivalent circuit for the bipolar transistor (Fig.2.1)terminal b' represents the base junction and b, the base terminal. The resistor rconnectedbetween thesetwoterminals is usuallyconsidered aconstant intherangeof 10to502.Theresistorris thebase-emitter junction resistance and is usually16
172.2BipolarTransistorAmplifiersr'brhoQCFIGURE2.1A small-signal,midfrequency equivalent-circuit model of abipolar transistor.much larger than rh.Auseful estimate of rw is given by the expression0.026βkTβ(2.1)r=IcqIcβ=transistorbase-to-collectorcurrentgainwhereIc=dcbiasincollectorq = charge on an electronkBoltzmann'sconstantT - the temperatureAtroomtemperatureT290K,andkT/g=0.026V.Thebase-emitterresis-tance r is inverselyproportional to the collector bias current.ExAMPLE 2.1.A2N3904 transistor has a current gain β of 100 and isbiased so thatthe quiescent collector current is 10-3A.What is the transistor base-emitter resistance?Solution.FromEq.(2.1)0.026(100)2600210-3The collector-to-emitter resistance r。and the collector-to-base resistance ruare also inversely proportional to the collector direct current. A typical value for rois 15 ks2. And ry is a large resistance, on the order of megohms, used to modelbasewidthmodulation effects in the transistor.Here ruis assumed tobe an open cir-cuit in all cases considered in this text. (It is of considerable importance in high-voltage-gainamplifiers with very large values of load impedance,but these appli-cationsare notnormaily found in high-frequency circuits.)The transistor transconductance gm is determined from the formulagml=β(2.2)qlc(2.3)~401corgmKTThetransconductance gm is directly proportional to the collector direct current.Althoughthe circuitappearsrathercomplicated,undermostconditionsthe resis.tor r, can also be neglected.The equivalent circuit is then as shown in Fig.2.2.The
18CHAPTER2:Small-SignalAmplifiers08mVbeFIGURE2.2A simplified small-signal, midfrequency cquivalent-circuitmodelofabipolartransistormodel now consists of three independent parameters gm, rw,and ro. And gm and rwaredeterminedbythecollectordirectcurrentandthecurrentgainβof thetransistor.Common-Emitter AmplifierIn order to analyze the small-signal behavior of a linear amplifier such as thecommon-emitter amplifier illustrated inFig.2.3a,thetransistorisreplaced bythe small-signal model,and thecomplete equivalent circuitbecomesas shown inFig.2.3b.If the coupling capacitor is assumed to be a short circuit, the base volt-ageVis given byRV=V(2.4)R+R,whereRis the equivalent resistanceof R,R2,and r, connected in parallel,orR,R2rR=7(2.5)R,R2+rR,+rR2TheoutputvoltageisgivenasV,=二8mRiroVRV,-gmRtro(2.6)ro+Rtro+ RR+ R.and the midfrequency voltage gain is given asRV。_gmRtroA,(2.7)ViTo+RLR+RThe phase shift of.the midfrequency voltage gain of the common-emitter amplifieris180°.Theinputimpedanceof theamplifierisbydefinitionAVZi=(2.8)AlAn increment of voltage is applied, and the change in input current is measured(assumingthatallotherindependent sourcesremainconstant)as shown inFig.2.4.In this figure, the source resistance is not included in determining the input imped-ance of theamplifier.Forthis circuitR,R27rZ; = R; =(2.9)RR2+Rr+R2r元
192.2BipolarTransistorAmplifiers2V.(a&m(b)FIGURE2.3(a)Acommon-emitteramplifier; (b)small-signal,midfrequencyequivalentcircuitoftheamplifierofFig.2.3a.IFIGURE2.4The input impedance of the amplifier circuit is defined as V/l
20CHAPTER 2: Small-Signal AmplifiersSince Fx depends on the bias direct current, the input impedance will depend on italso. The current gain is the load current l, divided by the input current, orILVo/RzR, + R;A;(2.10)IRLV./(R+R.)The currentgain from thebase to the output is -,provided that e》R.Themidfrequency currentgainalsohas a 180°phase shift.Amplifieroutput impedance is determined byapplying a voltageacross the out-put terminals and measuring the change in the output current (with all other inde-pendent sourcesheld constant).This is theThevenin equivalent impedance seen bytheload impedance:AV。Zo:(2.11)Al。The load resistance is usuallyexcluded from the definition,soZo=ro(2.12)forthecommon-emitteramplifier.Common-BaseAmplifierThe same small-signal equivalentcircuitcan alsobeusedforthecommon-baseandcommon-collectoramplifiers.Figure2.5ashowsacommon-baseamplifier,andFig.2.5b shows the midfrequency small-signal circuit.The direction of the depen-dent current source is nowfromemitter to collector, since thedependent voltageVg(a)(b)FIGURE2.5(a)Acommon-baseamplifier;(b)a small-signal,midfrequency equivalentcircuitof thecommon-baseamplifier