Radio Frequency Integrated Circuit Design - Webs

174 Radio Frequency Integrated Circuit Design
where
The following can be found:
x = b 1 y + b 2 y 2 + b 3 y 3 + ... (6.81)
b 1 = 1
a 1
b 2 =− a2
a 3 1
b 3 = 1
a 3 (2a
1
2 2 − a1a3)
(6.79) can now be rewritten as a function of ic :
ic =
vs
R E + re
+ 1 re vs
2IC� R E + re��RE + re� 2
+� 1
2I 2
re
R E + C� re� 2
− 1
3I 2
re vs
R E + C� re���R E + re� 3
(6.82)
(6.83)
Now the third-order intercept voltage can be determined (note that this
is the peak voltage and the rms voltage will be lower by a factor of √ 2):
k 1
v IP3 = 2√ 2√ =
3k 3
1
2
1 6IC 3�|R E + re |� �|RE + re |�5 re |2R E − re |
= 2√ 2v T
|R E + r e | 2
√ r 3 e |2R E − r e |
(6.84)
This very useful equation can be used to estimate the linearity of gain
stages. An approximation to (6.84) that can be quite useful for hand calculations
is
v IP3 = 2√ 2v T� R E + re
re � 3/2
(6.85)