Radio Frequency Integrated Circuit Design - Webs

144 Radio Frequency Integrated Circuit Design
f T =
g m
2� � (C� + C� )
(6.7)
It is also useful to note that above the pole frequency, we could ignore
r� and just use C� in the transistor model with little error. This simplified
model is shown in Figure 6.4.
Example 6.1 Calculation of Pole Frequency
A 15x transistor, as described in Chapter 3, has the following bias conditions
and properties: IC = 5 mA, r� = 500�, � = 100, C� = 700 fF, C� = 23.2 fF,
g m = IC /vT = 200 mA/V, and r b = 5�. IfZL = 100� and R S = 50�. Find
the frequency f P1 at which the gain drops by 3 dB from its dc value.
Solution
Since g m Z L = 20,
C A ≈ C� g m Z L = 23.2 fF � 20 = 464 fF
Thus, the pole is at a frequency of
f P1 =
1
= 2.76 GHz
2��500||(5 + 50)��700f + 464f �
Example 6.2 Calculation of Unity Gain Frequency
For the transistor in Example 6.1, compute f� and f T .
Solution
Using (6.6) and (6.7), the result is
f� =
1
2�r� (C� + C� ) =
1
= 440 MHz
2� � 500�(700 fF + 23.2 fF)
Figure 6.4 Simplified small-signal model for the transistor in the common-emitter amplifier
above the dominant pole frequency.