From: Design of Analog CMOS Integrated Circuits by Behzad Razavi
This is a differential pair with a resistive load. The author derives the CMRR of the differential pair in the prescence of a gm mismatch between M1 and M2 and finite RSS. The result is Equation (4.58)
This equation suggests that if RSS were replaced with an ideal current source ISS that has infinite output resistance, then the CMRR should become infinite.
This does not make sense to me intuitively. If we assume that channel-length modulation and body effect are 0 and that M1 has a higher gm than M2 due to mismatch. Then, when the same Vin, CM is applied to the gate of M1 and M2, M1 will demand a higher current from current source ISS and M2 will receive a smaller current. Thus, the common-mode level at Vout1 will be lower than at of Vout2, hence a differential gain due to CM input and thus a finite CMRR.
Have I missed something?