Common-mode rejection ratio

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The common-mode rejection ratio (CMRR) of a differential amplifier (or other device) measures the ability of the device to reject common-mode signals, those that appear simultaneously and in-phase on both amplifier inputs. An ideal differential amplifier would have infinite CMRR; 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. An example is audio transmission over balanced lines.

Theory[edit]

Ideally, a differential amplifier takes the voltages, V_+ and V_- on its two inputs and produces an output voltage V_\mathrm{o}=A_\mathrm{d}(V_+ - V_-), where A_\mathrm{d} is the differential gain. However, the output of a real differential amplifier is better described as

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

where 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):

\mathrm{CMRR} = \left (\frac{A_\mathrm{d}}{|A_\mathrm{cm}|} \right) = 10\log_{10} \left (\frac{A_\mathrm{d}}{A_\mathrm{cm}} \right)^2 dB = 20\log_{10} \left (\frac{A_\mathrm{d}}{|A_\mathrm{cm}|} \right) dB

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 thereof.

It is often important in reducing noise on transmission lines.[citation needed] For example, when measuring the resistance of a thermocouple in a noisy environment, the 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.

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