Inelectronics, thecommon mode rejection ratio (CMRR) of adifferential amplifier (or other device) is a metric used to quantify the ability of the device to rejectcommon-mode signals, i.e. those that appear simultaneously andin-phase on both inputs. Anideal 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 strongelectromagnetic interference (EMI). An example is audio transmission overbalanced line insound reinforcement orrecording.

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

${\displaystyle V_{\mathrm{o}}=A_{\mathrm{d}}(V_{+}-V_{-})+\frac{1}{2}{A}_{\mathrm{c}\mathrm{m}}(V_{+}+V_{-})}$

where${\displaystyle A_{\mathrm{c}\mathrm{m}}}$ is the "common-mode gain", which is typically much smaller than thedifferential gain.

The CMRR is defined as the ratio of thepowers of the differential gain over the common-mode gain, measured in positivedecibels (thus using the20 log rule):

${\displaystyle \mathrm{C}\mathrm{M}\mathrm{R}\mathrm{R}=\left(\frac{A_{\mathrm{d}}}{|A_{\mathrm{c}\mathrm{m}}|}\right)=10{\log }_{10}{\left(\frac{A_{\mathrm{d}}}{A_{\mathrm{c}\mathrm{m}}}\right)}^2\text{dB}=20{\log }_{10}\left(\frac{A_{\mathrm{d}}}{|A_{\mathrm{c}\mathrm{m}}|}\right)\text{dB}}$

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 unwantedcommon-mode signal will appear in the output, typically a measurement of some quantity. The value of the CMRR often depends on signalfrequency, and must be specified as afunction thereof.

It is often important in reducing noise on transmission lines.^{[citation needed]} For example, when measuring the voltage of athermocouple in a noisy environment, theelectrical noise from the environment appears as an offset on both input leads, making it a common-modevoltage signal. The CMRR of the measurement instrument determines theattenuation applied to the offset or noise.

CMRR is an important feature of operational amplifiers, difference amplifiers and instrumentation amplifiers, and can be found in the datasheet. The CMRR often varies with the frequency of the common-mode signal, and is often much higher at higher gain settings. The key to achieving a high CMRR is usually the use of very precisely matched resistors (better than 0.1%) to minimise any difference in the amplification of the negative and positive sides of the signal. Single-chip instrumentation amplifiers typically have laser-trimmed resistors to achieve a CMRR in excess of 100 dB, sometimes even 130 dB.

The design of a microwavebalun (single-ended to differential conversion circuit) defines the CMRR as the ratio of differential gain to common-mode gain inS-parameters, as follows:^[1]

${\displaystyle \mathrm{C}\mathrm{M}\mathrm{R}\mathrm{R}=|\frac{S_{\mathrm{D}\mathrm{S}}}{S_{\mathrm{C}\mathrm{S}}}|=|\frac{S_{21}-S_{31}}{S_{21}+S_{31}}|}$

Here, port1 is a single-ended input, and ports 2 and 3 are differential outputs. The CMRR of the balun represents the smallness of the gain and phase error between the differential outputs. If the phase difference between the differential outputs of the balun is close to 180° and the amplitudes are equal, the CMRR will be high.

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