Radio Frequency Integrated Circuit Design - Webs

LNA Design
The gain of either amplifier at the resonance frequency of the tank in the
collector, ignoring the effect of C� , is found with the aid of Figure 6.10 and
is given by
vout
v in =
−g m R L
�1 + Z E
Z� + g m Z E� ≈−R L
Z E
153
(6.31)
where Z E is the impedance of the emitter degeneration. Here it is assumed that
the impedance in the emitter is a complex impedance. Thus, as the degeneration
becomes larger, the gain ceases to depend on the transistor parameters and
becomes solely dependent on the ratio of the two impedances. This is, of course,
one of the advantages of this type of feedback. This means that the circuit
becomes less sensitive to temperature and process variations.
If the input impedance is matched to R S (which would require an input
series inductor), then the gain can be written out in terms of source resistance
and f T . v out in terms of i x in Figure 6.10 can be given by
vout =−g m v� R L =−g m i x Z� R L
(6.32)
Noting that ix can also be equated to the source resistance R S as ix =
v in /R s :
vout
v in
= −g m Z� R L
R S
assuming that Z� is primarily capacitive at the frequency of interest:
Figure 6.10 Small-signal model used to find the input impedance and gain.
(6.33)