Radio Frequency Integrated Circuit Design - Webs

LNA Design
Figure 6.3 C� is replaced with two equivalent capacitors C A and C B in the common-emitter
amplifier.
v�
1
C B = C�� 1 − = vo� C�� 1 + ≈ C� (6.4)
g m Z L�
There are now two equivalent capacitors in the circuit: one consisting of
C A + C� and the other consisting of C B . This means that there are now two
RC time constants or two poles in the system. The dominant pole is usually
the one formed by C A and C� . The pole occurs at
f P1 =
1
2� � �r� ||(r b + R S )��C� + C A�
143
(6.5)
where R S is the resistance of the source driving the amplifier. We note that as
the load impedance decreases, the capacitance C A is reduced and the dominant
pole frequency is increased.
When calculating f T , the input is driven with a current source and the
output is loaded with a short circuit. This removes the Miller multiplication,
and the two capacitors C� and C� are simply connected in parallel. Under
these conditions, as explained in Chapter 3, the frequency f� , where the current
gain is reduced by 3 dB, is given by
f� =
1
2� � r� (C� + C� )
(6.6)
The unity current gain frequency can be found by noting that with a
first-order roll-off, the ratio of f T to f� is equal to the low-frequency current
gain �. The resulting expression for f T is