Radio Frequency Integrated Circuit Design - Webs

A v = v o
vi
=
LNA Design
R L
R F
− g m R L
1 + R L
R f
≈ −g m R L
1 + R L
R f
155
(6.36)
Thus, we see that in this case the gain without feedback (−g m R L )is
reduced by the presence of feedback.
The input impedance of this stage is also changed dramatically by the
presence of feedback. Ignoring C� , the input admittance can be computed to
be
Yin = 1
R f
+
g m R L − R L
R F
R f + R L
Alternatively, the input impedance can be given by
Z in =
+ 1
Z�
(6.37)
Z� (R f + R L )
R f + R L + Z� (1 + g m R L ) ≈ R f ||Z� || R f + R L
g m R L ≈ R f + R L
g m R L
(6.38)
This can be seen to be the parallel combination of Z� with R f along with a
parallel component due to feedback. The last term, which is usually dominant,
shows that the input impedance is equal to R f + R L divided by the open loop
gain. As a result, compared to the open-loop amplifier, the input impedance
for the shunt feedback amplifier has less variation over frequency and process.
Similarly, the output impedance can be determined as
Z out =
R f
1 + Z ip� g m − 1
R f� ≈
R f
1 + g m Z ip
(6.39)
where Z ip = R S ||Rf ||Z� .
Feedback results in the reduction of the role the transistor plays in
determining the gain and therefore improves linearity, but the presence of R f
may degrade the noise depending on the choice of value for this resistor.
With this type of amplifier, it is sometimes advantageous to couple it with
an output buffer, as shown in Figure 6.12. The output buffer provides some
inductance to the input, which tends to make for a better match. The presence
of the buffer does change the previously developed formulas somewhat. If the
buffer is assumed to be lossless, the input impedance now becomes