Paul
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Hi,
as Raul already mentioned, the input CM range is delimited by the voltage levels, where one of the devices goes out of saturation. For lower input CM, it is the current source which will enter triode region, on the upper end it may either be the diff pair or the active loads. If you have a differential output, this will depend on your output CM setting.
Plotting the DC open-loop gain while sweeping the input CM should reveal both limits. Is this what you describe in your post? I don't exactly understand what operating point you select. In any case, in the middle of the obtained range, the gain should be maximum and the CMRR should be good. Don't go to close to either border in the typical case as this value somewhat varies with the transistor's threshold voltages.
Paul
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