Environmental Engineering Reference
In-Depth Information
This representation can be particularly useful when the complex poles derive
from two indented feedback loops (such as in three-stage amplifiers with
nested-Miller
4
compensation). In this case, term is the gain-bandwidth
product of the inner loop-gain and is the ratio between the second pole
and the gain-bandwidth product in this inner loop. The phase margin of the
whole amplifier is given by
hence from (4.55) we get
and we can determine the gain-bandwidth required for a fixed phase margin
when the higher poles are fixed
Like the case of three separate poles, now we can define an equivalent
second pole and, if the quantity within the square roots is close to one, which
means
the equivalent second pole is approximated by The frequency and
time domain behaviour of the closed loop amplifier are hence equal to those
of the closed loop amplifier whose open loop transfer function is
4
See Sec. 5.5 of this topic.
