CHAPTER 5. TRANSISTOR CIRCUITS87If hoeRL1 (good to about 10%) we can writeiC = hfeiB,(5.13)which is the AC equivalent of IC = βIB = hFEIB. Similarly, using the second hybridequation givesvCEvBE=−RLhfehie− RLhfehie.(5.14)If RLhfehre1 (good to about 10%) we havevCEvBE=−hfehieRL,(5.15)which is the AC voltage gain.5.1.4Ideal and Perfect Bipolar Transistor ModelsBy ignoring hoe and hre we can deﬁne a simpliﬁed AC model for the transistor (perfecttransistor) that is independent of the circuit conﬁguration:iC=hfeiBand(5.16)vBE=hieiB.(5.17)There is no PN voltage drop in these equations since it is a DC eﬀect.Since iC is typically 100 times larger than iB we can make the approximation iE≈ iC.An ideal transistor is deﬁned such that hie = 0 and hence vB = vE. When the eﬀects of hiecannot be ignored, we can use the perfect transistor model as described by the two equationsabove. On a circuit diagram hie can be added directly to the ideal transistor symbol.The ideal transistor model has the following two working rules:1. The base and emitter are at the same AC voltage (vB = vE). They diﬀer only by aconstant DC potential VPN .2. The collector current is equal to the emitter current and proportional to the basecurrent (iE = iC,IE = IC,iC = hfeiB and IC = hFEiB).5.1.5Transconductance ModelThe transconductance model provides an alternative description of transistor operation. Theforward transconductance, which has units of inverse resistance, is deﬁned as gm = hfe/hie.Using the perfect transistor model we can writeiC = gm(vB− vE)= gmvBE.(5.18)Since the transconductance is used to describe ﬁeld eﬀect transistors, it is sometimes conve-nient to apply the same parameter to bipolar transistors.