5.1.4 Ideal and Perfect Bipolar Transistor Models

Chapter 5.1.4 Ideal and Perfect Bipolar Transistor Models

Physics Lecture Notes – Phys 395 Electronics Book
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Physics Lecture Notes – Phys 395 Electronics Book

  • 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.