SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

342 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS

(a)

(b)

rπ Cin

CBC

gmVBE

vBE

rb

ib

Cin

CBC

vBE

rb

Zin

ib

ib

jωT

( )ω ib

V 0

V 0 I 0

Figure 7.18: Equivalent circuit for determining (a) the input impedance and (b) the output
impedance of a BJT biased in the common emitter configuration.

In well designed transistors,fmaxis larger thanfτ, though it is possible (but undesirable) to
havefmax<fτ. Since an amplifier functions by delivering power to a load, the calculation
offmaxis carried out under conditions of the load being conjugately matched to the output of
the device. Let us calculate the input and output impedances of a BJT via its equivalent circuit
in the common emitter configuration. For these calculations, we refer to the circuit diagrams in
figure 7.18.
The input impedance (calculated by applying a test generator at the input and an open circuit
at the output as in figure 7.18a) is seen to very rapidly approachrbfor

ω>

1

rπCin

The circuit used in the output impedance calculation is shown in figure 7.18b. Here, the input
may be terminated with any impedance under the assumption that

1

jωCin

<rb

so that the current flow throughrbis negligible. Applying a test voltageVo, we can calculate the