Radio Frequency Integrated Circuit Design - Webs

142 Radio Frequency Integrated Circuit Design
Figure 6.1 Simple transistor amplifiers.
Figure 6.2 The common-emitter amplifier with transistor replaced with its small-signal model.
A vo = vo r�
=−
vi r b + r� g m Z L ≈ Z L
(6.1)
re where re is the small-signal base-emitter diode resistance as seen from the emitter.
Note that r� = �re and g m = 1/re . For low frequencies, the parasitic capacitances
have been ignored and r b has been assumed to be low compared to r� .
The input impedance of the circuit at low frequencies is given by
Z in = r b + r�
(6.2)
However, at RF, C� will provide a low impedance across r� , and C� will
provide a feedback (and feedforward) path. The frequency at which the lowfrequency
gain is no longer valid can be estimated by using Miller’s Theorem
to replace C� with two capacitors C A and C B , as illustrated in Figure 6.3,
where C A and C B are
C A = C�� 1 − vo v�� = C� (1 + g m Z L ) ≈ C� g m Z L (6.3)