Thanks for your comments, they were really helpful. But a few questions:
We also do a stability analysis of the CMFB loop (i.e. we do compensation there as well). Say if there is a change at the O/P, now if the CMFB loop is unstable then the O/P would never settle back to your desired value. Treat the CMFB loop as complete separate ckt.
I didn't get it, for a CMFB like this how you can compensate it? There is also one issue with a CMFB I designed, one is similar to the one in the pic I posted before, that CMFB and the whole opamp work when I put them in a bigger circuit, but problem is when I change the Vb1 by 50 mV from the nominal value, the common mode voltage of the output would be off by like 70mV, which is not tolerable in my application. No matter how I play with the sizing of the transistors in the CMFB circuit, it won't help solving the problem.
The other CMFB I used is a single ended differential amplifier. This one can tolerate variation of the Vb1 by like 200mV and still common mode of the output is the desired one (by testing the opamp by itself). But when I put the opamp in a bigger system I see that output of the opamp has ringing. Which shows that problem is due to the CMFB circuit.
The thing is when I test the opapm by itself I use ac analysis and the CMFB part has no negative effect on the frequency response, and also by applying a small signal input I see that circuit works properly.
The other thing is, to design this CMFB I size the M12 half the M2, and the one connected to CMFB equal to the M8p. So the CMFB would work based on the current mirroring, I wonder if it's the right way or not. I couldn't find a design procedure for the CMFB part for a circuit like this please let me know if you're aware of any paper or something.
Thanks