Common-mode rejection ratio

In electronics, 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, formula_1 and formula_2 on its two inputs and produces an output voltage formula_3, where formula_4 is the differential gain. However, the output of a real differential amplifier is better described as :
where formula_6 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):
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. 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.