Common mode rejection

The common mode rejection ( English common-mode rejection , shortly CMR ) in are electronic , how little will change the output voltage when the two input voltages of an electrical differential amplifier to the same change amount (ie in the "common mode"). Ideally, the output voltage of the differential amplifier (such as an operational amplifier ) should not change because it only depends on the difference between the two input voltages. This goal is largely achieved by complex instrumentation amplifiers , although the two input voltages must be within specified limits so that the amplifier can form the difference.

Basics

Measurement circuit for a measurement of the common mode rejection

The voltages U in the ideal differential amplifier are given by the equation

${\displaystyle U_{\mathrm {Ausgang} }=A_{\mathrm {diff} }(U_{\mathrm {p} }-U_{\mathrm {n} })\,}$

described. Here is the differential gain ("push-pull gain"). In the case of a real differential amplifier, the components for common-mode amplification are added: ${\displaystyle A_{\mathrm {diff} }}$

${\displaystyle U_{\mathrm {Ausgang} }=A_{\mathrm {diff} }(U_{\mathrm {p} }-U_{\mathrm {n} })+A_{\mathrm {gleich} }{\tfrac {1}{2}}(U_{\mathrm {p} }+U_{\mathrm {n} })\,}$

where U _p and U _{n are} the voltages at the two inputs, A _diff the gain of the difference and A _equals the unwanted common mode gain.

The common mode rejection is defined as the ratio of the two gains and has no unit:

${\displaystyle \mathrm {CMRR} ={\frac {|A_{\mathrm {diff} }|}{|A_{\mathrm {gleich} }|}}\,}$

This ratio is often given in decibels :

${\displaystyle \mathrm {CMRR_{\ in\ dB}} =20\log _{10}\left({\frac {|A_{\mathrm {diff} }|}{|A_{\mathrm {gleich} }|}}\right)\,}$

An equally high voltage at the two inputs therefore leads to a small output voltage error if the common mode rejection is not complete. The better the common-mode rejection, the greater such input common-mode voltages can be without noticeably falsifying the output signal.

In most applications, you only want to amplify the differential voltage between the two inputs and be independent of a common mode signal (U _CM - CM for common mode ). The highest possible common-mode rejection is of practical importance, for example in symmetrical signal transmission , in order to suppress common-mode interference, for example mains hum .

Another feature similar to the feature common-mode rejection, the response to changes in supply voltage is expressed as power supply rejection ratio (English Power Supply Rejection designated PSR).

example

CMRR values ​​of up to 130 dB are common for operational amplifiers  . This means that in the circuit shown above, with a common-mode voltage of U _e  = 30 V, the output voltage only changes by U _a  = 10 µV.

literature

• Ingmar Wellach: Practice book EEG . 2nd edition, Thieme Verlag, Stuttgart 2015, ISBN 978-3-13-153922-9 , pp. 71-73.
• VS Gutnikov, A. Lenk, U. Mende: Sensor electronics. Primary electronics of measurement sensors, 1st edition, VEB Verlag Technik, Berlin 1984, ISBN 978-3-7091-9502-4 .

Web links

• Examples of amplifiers with common mode rejection, especially Fig. 5. (Real differential amplifier I, Thomas Schaerer)