pole splitting with miller compensation

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So I always read that basic vanilla miller compensation splits the VAS pole and the input stage pole, and that this is good. I think the notion is starting to click for me, and just want to have you guys tell me if I'm on the right/wrong track here.

If I understand, the input stage signal see's the pole of the IPS and miller cap as being the same as 2 caps in series, making for a smaller net capacitance. This raises the pole at the IPS. Is this the correct way to interpret this?

Of course the miller cap lowers the pole at the VAS. I understand completely how this happens, and why its good.

What I am maybe a little foggy on is why raising the pole at the IPS is desirable. The best I can come up with is that by putting the pole at a higher frequency, its phase lag doesn't become a problem at freqs low enough to be trouble.

Is that what's going on?
 
not really. I am talking about the pole splitting that occurs in simple miller compensation. In Self's book in the chapter on compensation, the first paragraph on standard single pole miller compensation talks about how it has the added advantage of splitting the poles of the IPS and VAS, raising the IPS pole as it lowers the VAS pole.

On my own I came to the conclusion that the IPS Cbc pole is in series with the VAS/miller cap pole, and being two caps in series makes the "cap" seen at the base of the IPS to be smaller, this raises the pole freq at the IPS. Is this indeed what is meant by "pole splitting"?
 
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