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1. I am afraid I do not understand that your signal "theoretically output should be all over 0"?
2. how do you generate you bias. are they ideal vdc or?
3. I have never used this kind of cmfb.
4. How does you vcc look like?
5. did you check your tb? initial conditions etc..
I am sorry that I...
I was just thinking if this is a large signal phenomena. to have a the ota stable at smal signal doesn't necessary mean that you have a stable large signal ota. also i noticed that your input signal freq is quite high compared to unity freq. Try to lower your swing and also the freq??
I think you should simulate the cmfb loop together with the rest of ota. Try to find a good spot were to open the cmfb loop and analyze(loopgain, phasemrgin). Have you tried to decrease the input/output swing?
Well, there is almost no different between positive feedback and unstabled negative feedback? This depends on the Phase margin in your feedback loop. You could read about this in any control theory book.