 Commonmode rejection ratio

The commonmode rejection ratio (CMRR) of a differential amplifier (or other device) is the tendency of the devices to reject the input signals common to both input leads. A high CMRR is important in applications where the signal of interest is represented by a small voltage fluctuation superimposed on a (possibly large) voltage offset, or when relevant information is contained in the voltage difference between two signals. (An example is audio transmission over balanced lines.)
Ideally, a differential amplifier takes the voltages V _{+} and V _{−} on its two inputs and produces an output voltage V_{o} = A_{d}(V _{+} − V _{−} ), where A_{d} is the differential gain. However, the output of a real differential amplifier is better described as
where A_{cm} is the commonmode 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 commonmode gain, measured in positive decibels (thus using the 20 log rule):
As differential gain should exceed commonmode 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 commonmode 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 commonmode voltage signal. The CMRR of the measurement instrument determines the attenuation applied to the offset or noise.
Example: operational amplifiers
An operational amplifier (opamp) has two inputs, V_{+} and V_{}, and an openloop gain G. In the ideal case, the output of an ideal opamp behaves according to the equation
This equation represents an infinite CMRR: if both inputs fluctuate by the same amount (while maintaining a constant difference V_{+}  V_{}), this change will have no bearing on the output. In real applications, this is not always the case: the lower the CMRR, the larger the effect on the output signal, following the general equation
Where V_{CM} represents the commonmode voltage at the inputs, or (V_{+} + V_{})/2.
The 741, a common opamp chip, has a CMRR of 90 dB, which is reasonable in most cases. A value of 70 dB may be adequate for applications which are insensitive to the effects on amplifier output;some highend devices may use opamps with a CMRR of 120 dB or more.
So for example, an opamp with 90dB CMRR operating with 10V of commonmode will have an output error of ±316uV.
See also
 Signaltonoise ratio
 Balanced line
 XLR connector
 Tip ring sleeve
External links
Categories: Electronics terms
 Engineering ratios
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