= Common-mode rejection ratio
{title2=$\mathrm{CMRR}$}
The <common-mode rejection ratio> compares a receiver's differential gain $A_d$ with its gain $A_c$ for <common-mode voltage>. In a linear small-signal model,
$$
V_o=A_dV_d+A_cV_c,\qquad\mathrm{CMRR}=\left|\frac{A_d}{A_c}\right|,\qquad\mathrm{CMRR}_{\mathrm{dB}}=20\log_{10}\mathrm{CMRR}.
$$
A high value means that equal disturbances on the two inputs have relatively little effect on the output. It does not specify the maximum common input range before saturation.<A Practical Review of Common Mode and Instrumentation Amplifiers by Eamon Nash>[Equations (1)–(2), common-mode output error]{ref}
For $A_d=100$ and CMRR $=80$ dB, the ratio is $10000$ and $|A_c|=0.01$. A 1 V common disturbance then creates 10 mV of output error, equivalent to 0.1 mV at the differential input. A measurement applies equal input changes while keeping their difference fixed, subtracts the initial output, and compares the measured common gain with a separate differential-gain measurement. Both gains depend on frequency, so a DC specification alone does not describe rejection of a rapidly changing disturbance.
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