When designing a multi-stage operational amplifier, people usually use butterworth polynomial to set closed loop pole location of the op amp in feedback configuration, and then back calculate to open loop pole locations.
For one example, in this particular compensation scheme, http://repository.ust.hk/ir/bitstream/1783.1-2351/1/200409TCASI_AFFC.pdf, the author states that,
The stability of the AFFC amplifier is achieved by following Butterworth frequency response to arrange the location of poles.
Requires p3=2p2=4ωun for stability (Butterworth response)
, or in countless other literatures. It seems it is a common sense that butterworth placement is the assumption, no matter what compensation you are doing.
In butterworth's original paper, he certainly didn't envision people in the future that is going to generalize his idea into multi-stage op amp design.
My question is why use butterworth? how is this generalization done? How is this filter design theory generalize to multi-stage op amp stability design?
For most people that is familiar with two stages design, we do the placement like: based on how much phase margin and how much unity-gain bandwidth we want, we will place the open loop non-dominant pole a cetain factor larger than the unitiy-gain frequency.
For three stages or more stage op-amp, for an amateur like me, I can imagine I will place the poles/zeros like I do in two stage amp recursively, by treating the already-compensated amp as another single-stage, although the phase margin for the intermediate steps may be somehow done in an ad-hoc way.
So I cannot understand why butterworth pole placement strategy is preferred. It would be nice if this can be explained in comparison to other compensation strategies in terms of power, bandwidth, transient overshoot/phase margin or other metrics of interests analytically.