vivkr
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Hi Zhonghan,
I think my reply was not clear enough. The second pole is fixed. The pole location cannot depend on the frequency. It is a characteristic of the system, otherwise the whole idea of linear systems would become unworkable.
What I meant was the following:
While computing the second pole, you always make an assumption that the opamp is reasonably well-designed, which means that the second pole is expected to be a bit beyond the unity-gain frequency. Then, you compute the location of this pole with this assumption. This allows you to simplify the circuit by assuming that the cap Cc is effectively a short, and creates a drain-gate short at high freequencies, giving you the simple expression of Gm2/Cl for the second pole.
Note that you can go ahead and derive the second pole location without this assumption, and you will get a number very close to Gm2/Cl (detailed analysis can probably be found in Gray&Meyer or Johns&Martin).
It is not the pole location that changes with frequency, but the output impedance of the 2nd stage that does. So, it is relatively high at low frequencies, giving you DC gain, and at high frequencies, it starts to roll off, causing the gain to fall. However, since the 2nd pole must be beyond the unity-gain bandwidth, the effect of this rolloff will not dominate the opamp's gain vs. frequency curve.
This is why the 2nd pole is called the "non-dominant pole".
Hope this helps. Vivek
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