View source for Common-mode rejection ratio

In [[electronics]], the '''common mode rejection ratio''' ('''CMRR''') of a [[differential amplifier]] (or other device) is a [[wiktionary:metric#Noun|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 [[sound recording|recording]].

== Theory ==

Ideally, a differential amplifier takes the voltages, <math>V_+</math> and <math>V_-</math> on its two inputs and produces an output voltage <math>V_\mathrm{o}=A_\mathrm{d}(V_+ - V_-)</math>, where <math>A_\mathrm{d}</math> is the differential gain. However, the output of a real differential amplifier is better described as
:<math>V_{\mathrm{o}} = A_\mathrm{d} (V_+ - V_-) + \tfrac{1}{2} A_\mathrm{cm} (V_+ + V_-)</math>
where <math>A_\mathrm{cm}</math> is the common-"mode gain", which is typically much smaller than the [[differential gain]].

The CMRR is defined as the ratio of the [[Power (physics)|powers]] of the differential gain over the common-mode gain, measured in positive [[decibel]]s (thus using the [[20 log rule]]):
:<math>\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}</math>

As differential gain should exceed common-mode gain, this will be a positive number, and the higher the better.

The CMRR is a very important specification, as it indicates how much of the [[common-mode signal]] will appear in your measurement. The value of the CMRR often depends on signal [[frequency]] as well, and must be specified as a [[function (mathematics)|function]] thereof.

It is often important in reducing noise on transmission lines.{{Citation needed|date=October 2014}} For example, when measuring the resistance of a [[thermocouple]] in a noisy environment, the [[signal noise|noise]] from the environment appears as an offset on both input leads, making it a common-mode [[voltage]] signal. The CMRR of the measurement instrument determines the [[attenuation]] applied to the offset or noise.

== See also ==
* [[Balanced line]]
* [[XLR connector]]
* [[Tip ring sleeve]]

==External links==
* [http://pages.emerson.edu/faculty/O/Owen%5FCurtin/Audio_Connectors.htm Powerpoint presentation on audio connectors]

[[Category:Electrical parameters]]
[[Category:Engineering ratios]]