Radio Frequency Integrated Circuit Design - Webs

f T =
LNA Design
1
2�(C� + C� ) =
1
= 44 GHz
2� � (700 fF + 23.2 fF)
Knowing the pole frequency, we can estimate the gain at higher frequencies,
assuming that there are no other poles present, with
A vo
A v ( f ) =
f
1 + j
f P1
Example 6.3 Calculation of Gain of Single-Pole Amplifier
145
(6.8)
For the above example, for A vo = 20 with f P1 = 2.76 GHz, calculate the gain
at 5.6 GHz.
Solution
With f P1 = 2.76 GHz, at 5.6 GHz, the gain can be calculated to be 8.84, or
18.9 dB. This is down by about 7 dB from the low-frequency gain.
vo
vs
The exact expression for vo /vs (after about one page of algebra) is
=
C� R ′ S� s 2 + s� 1
C� R S� +
s − g m
C�
1
+
C�� Z L′
g m
C�� +�
1
C� R S� C� Z ′ L�� (6.9)
where: R ′ S = R S + r b , R S� = R ′ S ||r� , C�� = C� in series with C � , and
Z ′ L = Z L ||ro .
As expected, this equation features a zero in the right-half plane and real,
well-separated poles, similar to that of a pole-splitting operational amplifier [1].
Example 6.4 Calculation of Exact Poles and Zeros
Calculate poles and zeros for the transistor amplifier as in the previous example.
Solution
Results for the previous example: 15x npn, 5 mA, Z L = 100�, C� = 23.2 fF,
C� = 700 fF, R S = 50�, r b = 5�. Using (6.9), the results are that the poles
are at 2.66 and 118.3 GHz; the zero is at 1,384 GHz. Thus, the exact equation
has been used to verify the original assumptions that the two poles are well
separated, that the dominant pole is approximately at the frequency given by