Radio Frequency Integrated Circuit Design - Webs

186 Radio Frequency Integrated Circuit Design
Figure 6.34 LNA with transformer coupling collector to emitter.
[6]. This circuit has all the same useful properties as the previously discussed
LNA but adds some additional benefits. From [6], the gain of this circuit is
given by
where
S21 =
A BJT + g m Z L� 1
n
−g m Z L
1
+ j�rbC�� n + 1� − � 2 L iC�� 1
+ 1�� n
(6.100)
A BJT = 1 + j�r b (C� + C� ) − � 2 L i (C� + C� ) (6.101)
At low frequencies the gain is given by
S21 ≈
−g m Z L
1 + g m Z L� 1
n�
(6.102)
Under many circumstances, g m Z L is large and the gain is approximately
equal to n, the turns ratio. This means that there is very little dependence on
transistor parameters.
Considering the redrawn circuit in Figure 6.35, a simplistic description
of this circuit can be provided. The transistor acts as a source follower to the
input of the transformer. A transformer by itself cannot provide power gain,
since, if the voltage is increased by a factor of n, the current is decreased by a
factor of n. However, in this circuit, the transistor feeds the primary current