Common mode rejection ratio (cmrr) and the operational amplifier

Common Mode Rejection Ratio
(CMRR) and The Operational
Amplifier

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Common Mode Rejection Ratio (CMRR)
and The Operational Amplifier
Introduction:
 The CMRR(Common Mode Rejection Ratio) is the most important
specification and it indicates the how much of the common mode signals will
present to measure. The value of the CMMR frequently depends on the signal
frequency and the function should be specified. The function of the CMMR is
specifically used to reduce the noise on the transmission lines.

 The CMRR in an operational amplifier is a common mode rejection ratio.
 Generally, the op amp as two input terminals which are positive and
negative terminals and the two inputs are applied at the same point.
 It will give the opposite polarity signals at the output.
 Hence the positive and the negative voltage of the terminals will cancel
out and it will give the resultant output voltage.
 The ideal op amp will have the infinite CMRR and with the finite
differential gain and zero common mode gain.
What is a CMRR

What is a
CMRR
 The ideal op amp will have the infinite CMRR and with the finite
differential gain and zero common mode gain.

Common-mode Rejection Ratio Formula
 The common mode rejection ratio is formed by the two inputs which will
have the same sign of DC voltage.
 If we assume one input voltage is 8v and the other 9v here
 The 8v is common and the input voltage should be calculated through
the equation of V+ – V- .
 Hence the result will be 1v but the common DC voltage between the two
inputs has a non-zero gain.

Common-mode Rejection Ratio Formula
 The differential gain Ad magnifies the difference between the two input
voltages.
 But the common mode gain Ac magnifies the common mode DC voltage
between the two inputs.
 The ratio of two gains is said to be as a common mode rejection ratio.
 The value of the format is in dB. The formula of a common mode
rejection ratio is calculated by the following equation.
• CMRR = 20log|Ao/Ac| dB

Power Supply Rejection Ratio
 The power supply rejection ratio is defined as the changes in input
offset voltage per unit changes in the DC supply voltage.
 The power supply is also calculated in the format of dB.
 The mathematical equation of the power supply rejection ratio is given
below.
• PSRR= 20log|ΔVDc/ΔVio| dB

Common Mode Rejection Ration of Op Amp
 The common mode rejection ratio is a differential amplifier and the op
amps are amplified in with the differential input.
 Hence the CMMR ratio can be applied to the operational amplifier.
 Using the condition of common mode rejection ratio, i.e.
 When both the input of the amplifier has same voltage.
 Then the output of the amplifier should be zero or the amplifier should be
rejecting the signal.

 The following image shows the amplifier of MCP601 of common mode
rejection ratio.

Offset Error of a CMRR of The Op-Amp
 The CMRR can build parallel out offset voltage in op amps configured in
 The non-inverting amplifier which is shown in the below figure.

Offset Error of a CMRR of The Op-Amp
 The non-inverting operating amplifier will have a small amount of
CMRR error because both the inputs are connected to ground.
 There is no presence of CM dynamic voltage.

Offset Error of a CMRR of the Op-Amp
 Error (RTI) = Vcm / CMRR = Vin / CMRR
 Vout = [1 + R2/R1] [ Vin + Vin/ CMRR]
 Error (RTO) = [1+R2/R1] [Vin/CMRR]

 There are different ways to measure the common mode rejection ratio.
 In the below figure we will discuss the four precision resistor to configure
the op amp as a differential amplifier.
Measuring Common Mode Rejection Ratio

 A signal is applied to the both inputs.
 Changes in the output are measured and an amplifier with infinite CMRR
also no changes in the output.
 The inherent difficulties of this circuit are that the ratio match of the
resistors is important as the CMRR of the op amp.

 The 0.1% mismatch is between resistor pair and the result will be in
CMR of 66 dB.
 Hence the most of the amplifiers will have a low frequency of CMR
is between the 80dB to 120Db.
 In this circuit, it is clear that there is only marginally useful for
measuring the CMRR.
ΔVout = ΔVin / CMRR (1 + R2/R1)

CMRR without Using Precision Resistors
 The following circuit is more complicated by comparing with the above
circuit and it can measure the CMRR by without using a precision
resistor.

 By switching the power supply voltage the common mode rejection
ratio is changed.
 Practically, the circuit can be implemented easily and by using the same
circuit.
 We can apply different power supply voltages to measure the power
supply rejection ratio.

 In this circuit, the power supply is from the +-15 DUT op amp with the
common mode voltage range of +-10V.
 From this circuit, the integrated amplifier A1 should have high gain.
 Low Vos and low IB and the op amp is 097 devices.

 The common-mode rejection ratio (CMRR) of a differential amplifier (or
other device) measures the ability of the device to reject common-
mode signals, those that appear simultaneously and in-phase on both
amplifier inputs. An ideal differential amplifier would have infinite
CMRR; 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.
Conclusion

Common mode rejection ratio (cmrr) and the operational amplifier

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Common mode rejection ratio (cmrr) and the operational amplifier