CMRR vs Common Mode Gain: Why a High Number Still Moves

Apply the same signal to both inputs of an amplifier, which is a purely common mode stimulus in theory, and the output still moves a little. The immediate conclusion is that the amplifier is not delivering the CMRR printed on its datasheet. The more common explanation is that two different quantities are being compared.

The ratio of output change to common mode input describes the common mode gain. CMRR is a different ratio, because it also contains the differential gain. Confusing the two produces a measurement that cannot be compared with the datasheet figure, and an investigation that starts from the wrong number rarely reaches the right cause.

Split the Input Into Two Components

Any pair of input voltages can be decomposed into a differential component, which is the difference between them and carries the signal you want to measure, and a common mode component, which is their average and represents what both inputs do together. A real amplifier has substantial gain for the differential part and a small but non zero response to the common mode part.

The output is therefore the superposition of the amplified differential signal and a common mode error term. Keeping those two separate in the analysis is what makes the rest of the measurement meaningful.

CMRR Is Not the Common Mode Gain

The common mode gain describes how much output change a common mode input produces. The differential gain describes how much the wanted signal is amplified. CMRR is defined as the ratio of the differential gain to the common mode gain, usually expressed in decibels. Dividing the output change by the common mode input change gives the common mode gain alone, and reporting that as CMRR overstates the error by exactly the differential gain.

The distinction also explains a common source of confusion during testing. If the gain configuration is changed, the CMRR figure changes while the common mode gain may not. A comparison between two measurements taken at different gains is therefore not a comparison of the same quantity.

Why a High CMRR Does Not Give a Zero Output

First, the common mode gain is small rather than zero, so a large common mode swing multiplied by a small gain can still produce a measurable output change. Second, external mismatch matters: unequal input resistances, unequal filtering or asymmetric routing convert part of the common mode stimulus into a differential signal before it ever reaches the amplifier.

Third, error sources add. Offset, drift, noise, input bias current and the behaviour of the following converter all appear in the same measurement, and attributing the whole result to common mode rejection assumes those contributions are negligible, which is rarely true in a real system.

CMRR Is a Function of Frequency

The rejection capability falls as frequency rises. Datasheets usually provide curves at more than one gain, precisely because the figure is not a single constant. Fast edges and wideband interference therefore see less rejection than a low frequency measurement suggests, and an externally asymmetric filter can reduce it further.

This matters most in an EMC context, where the disturbance is rarely a slow DC quantity. A common mode disturbance contains a broad spectrum, and quoting a single low frequency or DC figure cannot describe how the system behaves against a fast transient. The relevant number is the rejection at the frequencies the disturbance occupies, in the gain configuration actually used.

Four Things to Check Before Measuring

Confirm that the common mode input stays inside the range the device allows and that the output still has room to swing. Record the differential gain configuration, so that the common mode gain and the CMRR are not confused. State the test frequency and the bandwidth, and do not use a DC specification to explain a high frequency observation. Finally, keep the source, the input network, the shielding, the grounding and the measurement channels symmetric, because an asymmetric fixture will itself convert common mode into differential and produce an error that belongs to the test bench rather than to the device.

After the device has been characterised, the board still has to be examined. Two input paths with unequal impedances convert common mode interference into a differential voltage before the amplifier sees it, and from that point on the internal CMRR of the device cannot remove the error, because the error is no longer common mode. Input RC networks, protection devices, connectors, trace lengths, parasitic capacitance and shielding all need to be matched as closely as the layout permits.

Common Mode to Differential Conversion on the Board

This conversion is the mechanism that turns an EMC disturbance into a measurement error, and it is a layout property rather than a component property. Replacing the amplifier with a better one cannot recover a signal that has already been corrupted by asymmetric routing, which is why the review should compare the two input paths as a pair rather than approving each one in isolation.

Practical measures include routing the two inputs side by side for their whole length, keeping the parasitic capacitance to ground equal, avoiding a test point on one side only, and placing the filter components symmetrically. Where one input must pass near a switching node and the other cannot, the asymmetry is a known quantity that has to be budgeted rather than ignored.

Where This Leaves the Board Level Design

The practical conclusion is that common mode rejection is a property of a channel rather than of a component. Component selection sets the ceiling, and the layout determines how much of that ceiling is actually available in the finished product. A device with an excellent CMRR placed behind two asymmetric input networks will underperform a more modest device in a symmetric one.

That makes the two input paths a paired object during the layout review, and it also makes the interface protection part of the same decision, since a clamp device on one input and not the other is an intentional asymmetry with a measurable consequence. Where the sensor cable arrives from outside the enclosure, the cable and enclosure design decides how much common mode disturbance reaches the board in the first place, which is often a cheaper place to reduce the problem than the input network itself.

Finally, decide how the result will be verified. A measurement made with an asymmetric fixture proves nothing, so the test setup deserves the same symmetry requirement as the board, and the acceptance criteria should state the frequency range over which the rejection is required.

FAQ

Can CMRR be measured directly? It is usually derived from measured common mode gain and a known differential gain, which is why the gain configuration has to be recorded.

Why does the output move more at high frequency? Because rejection falls with frequency and because asymmetric parasitics convert more of the disturbance into a differential signal.

Does a differential ADC solve the problem? It helps, but the same requirement for input symmetry applies to the path in front of it.

Is a DC CMRR figure useful? It is useful as a starting point and misleading as a description of behaviour under fast interference.

Summary

When the output follows a common mode signal, separate the three candidates: the common mode gain of the device, the CMRR figure derived from it together with the differential gain, and the common mode to differential conversion created by the board. Define the gain, the frequency and the input range before quoting a number, and treat the symmetry of the two input paths as part of the design rather than a detail of the test setup.