Radio Frequency Integrated Circuit Design - Webs

48 Radio Frequency Integrated Circuit Design
doped buried layer in the collector. The base resistance r b is the source of several
problems. First, it forms an input voltage divider between r b , r� , and C� , which
reduces the input signal amplitude and deteriorates high-frequency response. It
also directly adds to thermal noise.
3.5 Small-Signal Parameters
Now that the small-signal model has been presented, to help determine appropriate
values for model parameters at different operating points, some simple
formulas will be presented.
First, the short-circuit current gain � is given by
� =
i c
i b
�
noting that currents can be related by
Transconductance g m is given by
=
�I C
�I B
�
small-signal �large-signal
ic + ib = ie
g m = ic IC
= =
v� v T
Ic q
kT
(3.3)
(3.4)
(3.5)
where IC is the dc collector current. Note that the small-signal value of g m in
(3.5) is related to the large-signal behavior of (3.1) by differentiation.
At low frequency, where the transistor input impedance is resistive, ic and
ib can be related by
ic = �ib = g m v� = g m ib r�
(neglecting current through ro ), which means that
VA :
� = g m r�
(3.6)
(3.7)
Also, the output resistance can be determined in terms of the early voltage
ro = VA
I C
(3.8)