The common-mode rejection ratio (CMRR) for an op amp is defined as the change in V_OS versus change in the common mode voltage of the op amp. For an ideal op amp, the common mode signal does not affect V_OS (that is, CMRR is infinite). For a practical op amp, however, the CMRR ranges from 60 dB to 170 dB. The equation for CMRR is CMRR = ΔV_CM/ ΔV_OS or 20log(ΔV_CM/ ΔV_OS) in decibels.

Figure 3-3 shows a difference amplifier in a gain of 1V/V where the inputs are connected together to force the differential input voltage to zero. The voltage source (V_IN) swings from -24 V to +24 V, which causes the common mode voltage (V_CM) to swing from -12 V to +12 V. Because the differential input is 0 V (mid-supply), the output remain near zero volts. Finite A_OL does not affect the offset (see Section 3.1). Thus, the primary factor impacting the shift in offset voltage is change in the common mode voltage.

The specifications for the OPA210 example are shown in Table 3-1. Based on the specification, you would expect the typical offset to be ±5 µV. Notice the test condition listed at the top of the table indicates that the parameters all assume V_CM = V_OUT = mid-supply. However, the common mode voltage ranges from -12 V to +12 V, and the output voltage is at 0V. The calculation for a 24V change in V_CM voltage shows a corresponding 2.4 µV change in offset (see calculation Equation 31). In this example, the simulated offset shift of 3.85 µV (CMRR = 136 dB) compares well to the calculated shift of 2.4 µV (CMRR = 140 dB). In the simulation notice that V_OS = 5 µV specification when V_CM = 0 V as you would expect based on the test condition.

In many cases, the effects of open loop gain and common mode rejection will be combined as in the case of unity-gain buffer (a follower with G = 1). From a calculation perspective the two calculations can be done separately and the results are combined. Simulation modela both effects and the output reflect the typical operation of the device. In this example, the model shows the slope of V_OS due to A_OL to be negative and the slope of V_OS vs Vcm to be positive. In general, the slope of V_OS vs V_CM can be either positive or negative, but V_OS due to A_OL will always have a negative slope. Thus, in this example the two effects are subtracted from each other.