Radio Frequency Integrated Circuit Design - Webs

Bopt =
LNA Design
− v T
(�C� )
2IC
v T
2IC
+ r b
163
(6.59)
Thus, Gopt will vary with the size of the device used (through C� and
r b ) as well as the bias current. At some point, it would equal 1/50�. Thus,
for a device of that size, matching to 50� would also give the best noise figure.
The expression for Bopt can be simplified if r b is small compared to 1/2g m .
This would be a reasonable approximation over most normal operating points:
Bopt =−�C�
(6.60)
Thus, it can be seen that the condition for maximum power transfer
(resonating out the reactive part of the input impedance) is the same as the
condition for providing optimal noise matching.
Hence, the method in the next section can be used for matching an LNA.
6.3.3 Input Matching of LNAs for Low Noise
Since the LNA is the first component in the receiver chain, the input must be
matched to be driven by 50�. Many methods for matching the input using
passive circuit elements are possible with varying bandwidths and degrees of
complexity, many of which have already been discussed. However, one of the
most elegant is described in [2]. This method requires two inductors to provide
the power and noise match for the LNA, as shown in Figure 6.16.
Starting with (6.35), the input impedance for this transistor (assuming
that the Miller effect is not important and that r� is not significant at the
frequency of interest) is
Figure 6.16 LNA driver transistor with two inductors to provide power and noise matching.