Environmental Engineering Reference
In-Depth Information
effectively achieved only in one-pole amplifiers. However, these are
somewhat an abstraction, since real architectures -even single-stage ones-
exhibit multiple poles. Bandwidth extension is, therefore, not such a general
and effective property as commonly reported. Actually, amplifiers with the
highest frequency performance (e.g., RF amplifiers) all adopt open-loop
topologies.
4.3
TWO-POLE FEEDBACK AMPLIFIERS WITH A POLE-ZERO
DOUBLET
The loop gain of real amplifiers can include a pole-zero doublet beside
two significant poles. Usually, a doublet arises from imperfect pole-zero or
feed-forward compensation due to process tolerances [KM74], [BAR80],
[PP95], or is caused by the frequency limitation of current mirrors when they
are used to provide a differential-to-single conversion [GPP99].
The degradation in the settling performance of a one-pole amplifier with
a pole-zero doublet was first discussed in [KMG74]. The effect of the
doublet in a class AB one-pole amplifier was then analysed for both the
settling and slewing time periods in [S91], [SY94]. However, extending the
results in [KMG74] to two-pole amplifiers is not as straightforward as
sometimes reported [GM74], [LS94], [EH95]
.
A simpler representation of a two-pole amplifier with a pole-zero doublet
was proposed in [PP992]. The approach is based on the consideration that, in
practice, the pole and the zero forming the doublet are often very close. In
addition, they are usually located at a frequency around or greater than
Thus, such a doublet leaves the loop-gain unity-gain frequency almost
unchanged, but can considerably alter the phase margin. We now
demonstrate that a two-pole amplifier with such a pole-zero doublet can be
modeled by an
equivalent
pure two-pole amplifier with a modified second
pole.
Consider an amplifier whose loop-gain transfer function includes two
poles and a pole-zero doublet
as given below
Without loss generality, assume to be the lowest frequency pole
(remember that a dominant-pole behavior is mandatory to achieve stability).
Phase margin evaluation of (4.25) gives
