Common-mode rejection ratio
Encyclopedia
The common-mode 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 line
s.)
Ideally, a differential amplifier takes the voltages
and 
on its two inputs and produces an output voltage 
, where 
is the differential gain. However, the output of a real differential amplifier is better described as
where
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 decibel
s (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.
An operational amplifier
(op-amp) has two inputs, V+ and V-, and an open-loop gain
G. In the ideal case, the output of an ideal op-amp 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 VCM represents the common-mode voltage at the inputs, or (V+ + V-)/2.
The 741, a common op-amp 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 high-end devices may use op-amps with a CMRR of 120 dB or more.
So for example, an op-amp with 90dB CMRR operating with 10V
of common-mode will have an output error of ±316uV.
Differential amplifier
A differential amplifier is a type of electronic amplifier that amplifies the difference between two voltages but does not amplify the particular voltages.- Theory :Many electronic devices use differential amplifiers internally....
(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 line
Balanced line
In telecommunications and professional audio, a balanced line or balanced signal pair is a transmission line consisting of two conductors of the same type, each of which have equal impedances along their lengths and equal impedances to ground and to other circuits. The chief advantage of the...
s.)
Ideally, a differential amplifier takes the voltages
and on its two inputs and produces an output voltage , where is the differential gain. However, the output of a real differential amplifier is better described aswhere
is the common-mode gain, which is typically much smaller than the differential gain.The CMRR is defined as the ratio of the powers
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
of the differential gain over the common-mode gain, measured in positive decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
s (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
Common-mode signal
Common-mode signal is the component of an analog signal which is present with one sign on all considered conclusions. In electronics where the signal is transferred with differential voltage use, the common-mode signal is called a half-sum of voltages:...
will appear in your measurement. The value of the CMRR often depends on signal frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
as well, and must be specified as a function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
thereof.
It is often important in reducing noise on transmission lines. For example, when measuring the resistance of a thermocouple
Thermocouple
A thermocouple is a device consisting of two different conductors that produce a voltage proportional to a temperature difference between either end of the pair of conductors. Thermocouples are a widely used type of temperature sensor for measurement and control and can also be used to convert a...
in a noisy environment, the noise from the environment appears as an offset on both input leads, making it a common-mode voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
signal. The CMRR of the measurement instrument determines the attenuation
Attenuation
In physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
applied to the offset or noise.
Example: operational amplifiers
Operational amplifier
An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output...
(op-amp) has two inputs, V+ and V-, and an open-loop gain
Open-loop gain
The open-loop gain of an operational amplifier is the gain obtained when no feedback is used in the circuit.Open loop gain is usually exceedingly high; in fact, an ideal operational amplifier has infinite open-loop gain. Typically an op-amp may have an open-loop gain of around 10^5...
G. In the ideal case, the output of an ideal op-amp 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 VCM represents the common-mode voltage at the inputs, or (V+ + V-)/2.
The 741, a common op-amp 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 high-end devices may use op-amps with a CMRR of 120 dB or more.
So for example, an op-amp with 90dB CMRR operating with 10V
of common-mode will have an output error of ±316uV.
See also
- Signal-to-noise ratioSignal-to-noise ratioSignal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
- Balanced lineBalanced lineIn telecommunications and professional audio, a balanced line or balanced signal pair is a transmission line consisting of two conductors of the same type, each of which have equal impedances along their lengths and equal impedances to ground and to other circuits. The chief advantage of the...
- XLR connectorXLR connectorThe XLR connector is a style of electrical connector, primarily found on professional audio, video, and stage lighting equipment. The connectors are circular in design and have between 3 and 7 pins...
- Tip ring sleeve