Common-Mode Rejection Ratio

Common-mode rejection ratio is a measure of how well a differential measurement rejects a voltage that appears on both input terminals. It is usually abbreviated CMRR and reported as a ratio or in decibels.

CMRR matters because many useful sensor and biomedical signals are small differential voltages riding on much larger common-mode voltages. An ECG front end may need to resolve hundreds of microvolts while the body, cables and environment carry mains-related common-mode voltage. A bridge sensor may produce millivolts of differential signal while both amplifier inputs sit near half the bridge excitation voltage.

Engineering Meaning

For a differential input, the wanted signal is:

The common-mode voltage is:

A real amplifier responds mostly to V_d, but a small part of V_{cm} can leak into the output. If A_d is differential gain and A_{cm} is common-mode gain, then:

Higher CMRR means better rejection of common-mode voltage.

Decibel Form

The decibel form is:

The inverse conversion is:

For:

the ratio is:

Every 20 dB of CMRR is a factor of 10 in voltage rejection. Losing 20 dB can therefore turn a harmless residual into a visible error.

Input-Referred Residual

A useful screening estimate is:

If an ECG front end sees:

and:

then:

If the input-referred residual limit is 20\ \mu\text{V}_{RMS}, this first-pass screen passes. The same situation with only 80\ \text{dB} CMRR gives:

and:

which would fail the same residual limit.

System CMRR versus Data-Sheet CMRR

Data-sheet CMRR is not automatically system CMRR. It may be measured with shorted, balanced inputs, a particular gain, a particular frequency, a clean supply, a stated common-mode voltage and a narrow temperature range. The installed system adds source impedance imbalance, electrode impedance, cable motion, shield currents, protection components, filter tolerances, PCB leakage, input bias current and amplifier headroom limits.

For system review, the relevant value is the CMRR achieved at the measurement boundary that supports the decision: electrode-to-display, bridge-to-ADC code, sensor connector-to-software value or calibration fixture-to-report.

Frequency Dependence

CMRR usually changes with frequency. A front end may reject slowly varying common-mode voltage well but reject mains frequency, switching noise or RF pickup poorly. The relevant value is therefore:

not only a single headline number. If a data sheet gives 110\ \text{dB} at low frequency but the installed residual is judged at 50\ \text{Hz} or 60\ \text{Hz}, the test should use the rejection available at that frequency. Cable capacitance, protection components, input filtering and electrode impedance can all reduce practical AC CMRR.

Source Imbalance

Even a high-CMRR amplifier can perform poorly when the two input paths are imbalanced. Unequal electrode impedance, bridge lead resistance, protection resistor tolerance or filter mismatch can convert common-mode interference into a real differential signal before the amplifier has a chance to reject it.

A simple imbalance screen uses a fractional mismatch:

where Z_+ and Z_- are the effective source impedances seen by the two inputs. If:

then:

That does not directly equal CMRR loss, but it is a warning sign. A realistic CMRR test should include plausible source imbalance rather than only shorted inputs.

Biomedical Use

In bioinstrumentation, CMRR is often tied to patient coupling and mains pickup. ECG, EEG, EMG and other biopotential measurements need differential gain for physiological signals and strong rejection of environmental common-mode voltage. Driven-reference or driven-right-leg circuits can reduce common-mode voltage at the body, but they do not replace isolation, leakage-current control, electrode checks or validation under intended-use conditions.

Biomedical CMRR evidence should include electrode impedance cases, cable motion, lead-off or degraded contact behavior, power-line frequency and harmonics, filter settings, gain settings, saturation recovery, patient-safety controls and the displayed or stored signal requirement.

Bridge and Sensor Use

In bridge sensors, common-mode voltage often comes from the excitation. A Wheatstone bridge excited from 0 to V_{ex} can place both amplifier inputs near:

The differential bridge output may be only millivolts. The front end must therefore satisfy two separate checks: enough CMRR to reject common-mode interference and enough input common-mode range and output swing to avoid saturation. A CMRR number does not prove headroom.

Measurement Setup

A CMRR test usually applies a known common-mode signal to both inputs and measures the residual output or input-referred error. The test should state:

• common-mode amplitude and frequency;
• differential gain and input range;
• source impedance and imbalance;
• cable, shield, filter and protection configuration;
• supply voltage, temperature and bandwidth;
• measurement instrument noise and calibration;
• acceptance limit and uncertainty.

For biomedical devices, the fixture should represent accessories, electrodes and use conditions closely enough for the claim being made.

Limits and Common Mistakes

CMRR is frequency dependent. A front end can have excellent DC CMRR but much worse rejection at mains frequency, switching-regulator frequency, RF interference or during motion. Filtering can reduce residual noise, but it may also distort diagnostic signal content or hide short transients.

Common mistakes include quoting amplifier CMRR without source impedance, measuring only with shorted inputs, ignoring input common-mode range, assuming a driven-reference circuit fixes all interference, and using CMRR as a substitute for EMC or patient-safety evidence. A defensible CMRR review states differential gain, common-mode voltage, frequency, source imbalance, input range, residual error, bandwidth, uncertainty and the requirement affected by the result.