26CHAPTER2: Small-SignalAmplifiersFIGURE2.13(a) An emitter-follower; (b) asimplified equivalent circuit10009.1koftheemitter-follower.12V501OV500(a)50.0261000500(b)bias current Ic = 40 × 10-3, and r is[Eq. (2.1)]26(40)262240The voltage gain is [using Eq. (2.27) and neglecting the 9.1-k 2 bias resistor]BRL40(50)A==0.94R,++(I+β)RL50+26+41(50)The current gain is [Eg. (2.31)]A,~B+1=41The input and load impedances are real, so the voltages and currents are in phase andthepowergain isAp=A,A,=38.54Theamplifieroutputimpedanceasseenbythe50-2resistor is26 + 50Zo=1.8541
2.3Field-EffectTransistorAmplifiers272.3FIELD-EFFECTTRANSISTORAMPLIFIERSEquivalent CircuitsSymbolic representations ofthreetypes of field-effecttransistors (FETs)aregiveninFig.2.14.Figure2.14a illustrates aJFET(junction field-effect transistor).Theoff-centerlocation of the arrowisused if thedrain-to-sourcechannel of thepartic-ular device is asymmetric so that the drain and source cannot be interchanged.ManyJFETs dohavea symmetric channel.Adepletion-typeMOSFET (insulated-gateFET)is illustrated inFig.2.14b,and an enhancement-typeMOSFET is illus-trated inFig.2.14c.Theadditional terminal U referstothe substrate(body)of thedevice and is usually connectedto the source.If the gate arrowpoints towardthe device, it is an n-channel device, while in p-channel FETs the arrow points out.The important signals are the gate, source, and drain currents (Ig,Is,and la,respec-tively); the gate-to-source voltage Vs; and the drain-to-source voltage Vds. Thesmall-signal,midfrequency model of this device (ignoring the dc components)isshowninFig.2.15.For all practical purposes, the input impedance of an FET is so large that theinput can be considered an open circuit in the midfrequency range, and the gatecurrent I,=O.The small-signal model then consists onlyofavoltage-dependentcurrent source whose value is proportional to thedifferencebetween the gate andODGCGCosos(a)(b)OUGOos(c)FIGURE2.14Circuit models for field-effect transistors: (a)a JFET; (b) a depletion-typeMOSFET;(c)anenhancement-typeMOSFET
28CHAPTER2:Small-SignalAmplifiersODFIGURE2.15Asmall-signal low-frequencyequiv-alent circuit for a field-effectOGtransistor.ossource small-signal voltages and a drain-to-sourceresistance rd.The same modelisusedforboth junction and insulated-gateFETs.Only the relationbetween gmandthe dc biasing varies for the different devices. By definition, the transistor's trans-conductance relates the change in drain current to the change in gate-to-source volt-age,Thatis,dla(2.33)gmdVgsForJFETsitis reallyshownthat1/2(2.34)gm=where gmois the transconductance when gate-to-source bias voltage is zero.2Ip isthe drain direct current, and Ipss is the drain current when the gate-to-source volt-age is zero.The transconductancegm is often referred toby theyparameter symbolYfs on data sheets. For an MOS transistor, gm is given by1/2Ip(2.35)gm=gmRIDRwhere gmr is the transconductance at some specified drain bias current Ipr. In bothtransistor types, the drain current varies proportionally to the square root of the biasdirectcurrent.Common-Source AmplifierThecommon-sourceamplifier issimilartothecommon-emitteramplifier.Themid-frequencyequivalentcircuitofthecommon-sourceamplifier shown inFig.2.16aisgiveninFig.2.16b.Normally R》R,so V,Vg.Thedependent current sourcegm Vgs depends on both the gate and the source voltages. The gate voltage is known(V,=V),but the sourcevoltage must be determined from the following equa-tions:V。-V,Vo2+gmVgs=0(2.36)RzrdV. +V, - VoandgmVgs(2.37)R,ra
292.3Field-EffectTransistorAmplifiersFIGURE2.16(a)Acommon-sourceamplifier;(b)anequivalentcircuitforthecommon-source amplifier.(a)oV,V(b)The sourcevoltage,interms ofthe output voltage,is-V.R,Vs(2.38)RLandthevoltagegain isVo-gmRird(2.39)ViRL+rd+R(1+gmrd)If the transistor output resistance ra is much larger than R, and RL, as it nor-mallywill be,thevoltage-gainexpression simplifiestoV。--gmRL(2.40)V,=1+gmRandifgmR,》1,V。_-RL(2.41)ViR
30CHAPTER2:Small-SignalAmplifiersThecommon-sourceamplifier with a source resistance canbeusedtodesign an inverting amplifierwhosegain is independentof thetransistor(providedgmR,》1)This is a particularly valuable design procedure since it eliminates the costly pro-cessofhavingtocarefullyselectatransistor.Since the input impedance of the amplifier is very large, the current gain is alsovery large (for practical purposes, it is infinite).If R,=O, the output impedance isgiven by(2.42)Zo=rdIt is left as an exercise to calculate the output impedance for a nonzero R..EXAMPLE 2.4.Figure 2.17a contains an FET amplifier, and Fig.2.17b is the small-signal, midfrequency equivalent-circuit model.The coupling and bypass capacitors areassumed to act as short circuits in this frequency range. The manufacturer's data sheetfor the 2N5486 gives thefollowing minimumparameter values for Vps =15 V:Ipss =8mA, gmo= 4×10-3S,and ra =13ks2.And R,is selected so that theamplifier is biased with Ip=2.0 mA.What is the midband voltage gain of theamplifier?Solution.Fromtheequivalentcircuit we seethat106V, = V,=V106+5×103C5k0WW2N54862keMO(a)5koVo30(b)FIGURE2.17(a)Acommon-sourceamplifier;(b)an equivalentcircuitfortheamplifiershown in (a)