Engineering and technology

Common-mode rejection ratio – Wikipedia

Jovan Stosic March 20, 2018

The common mode rejection ratio (CMRR) of a differential amplifier (or other device) is a metric used to quantify the ability of the device to reject common-mode signals, i.e., those that appear simultaneously and in-phase on both inputs. An ideal differential amplifier would have infinite CMRR, however this is not achievable in practice. A high CMRR is required when a differential signal must be amplified in the presence of a possibly large common-mode input, such as strong electromagnetic interference (EMI). An example is audio transmission over balanced line in sound reinforcement or recording.

Theory
Ideally, a differential amplifier takes the voltages, V+ and V- and produces an output voltage

V_{\mathrm {o} }=A_{\mathrm {d} }(V_{+}-V_{-})

where Ad is the differential gain. However, the output of a real differential amplifier is better described as

{\displaystyle V_{\mathrm {o} }=A_{\mathrm {d} }(V_{+}-V_{-})+{\tfrac {1}{2}}A_{\mathrm {cm} }(V_{+}+V_{-})}

where {\displaystyle A_{\mathrm {cm} }} A_{\mathrm {cm} } is the common-mode gain, which is typically much smaller than the differential gain.

The CMRR is defined as the ratio of the powers of the differential gain over the common-mode gain, measured in positive decibels (thus using the 20 log rule):

{\displaystyle \mathrm {CMRR} =\left({\frac {A_{\mathrm {d} }}{|A_{\mathrm {cm} }|}}\right)=10\log _{10}\left({\frac {A_{\mathrm {d} }}{A_{\mathrm {cm} }}}\right)^{2}{\text{dB}}=20\log _{10}\left({\frac {A_{\mathrm {d} }}{|A_{\mathrm {cm} }|}}\right){\text{dB}}}
differential gain should exceed common-mode gain, this will be a positive number, and the higher the better.

 

Source: Common-mode rejection ratio – Wikipedia