Radio Frequency Integrated Circuit Design - Webs

334 Radio Frequency Integrated Circuit Design
some simple formulas for the image rejection they provide. For the circuit of
Figure 9.9, the gain in the stop band G SB is given by
R −
G SB =−gm1RL�R −
=−g m1RL�
R −
g m3
� 2 C 1C2
g m3
� 2 C 1C2
Isharp R −
+ 1
g m2�
� 2 C 1C2vT
Isharp
� 2 C 1C2vT
and the gain in the passband G PB is approximately
G PB =−g m1RL
+ 1
g m2�
(9.25)
(9.26)
It is assumed that the passband is sufficiently far away that the series
resonator is essentially an open circuit there. Therefore, the image rejection (IR)
provided by this filter is
IR = 20 log | G |
R −
PB
G SB | = 20 log
I sharp
� 2 C 1C 2v T
Isharp
R −
� 2 C 1C2vT |
+ 1
g m2
(9.27)
If Isharp can be tuned to perfectly cancel the loss in the resonator, this
circuit can have perfect image rejection. In practice, the accuracy to which Isharp
can be set will limit the image rejection available from this circuit.
Example 9.4 Effect of Process Tolerance on Image Rejection
Assume that the current Isharp in the circuit of Figure 9.9 can be set to an
accuracy of 1%. Determine the image rejection that can be expected from this
circuit. Assume that Q 1 and Q 2 are biased at 3 mA and that the loss in the
resonator is 5�.
Solution
In this case, we assume that Isharp will take on a value of
Isharp = � 2 C 1C2vT R �