Common-Mode Rejection (CMR) and CMRR: What They Really Mean

Common-Mode Rejection (CMR) is a differential system’s ability to ignore signals that appear (ideally) the same on both input conductors. This matters in noisy environments — including RF, audio, and sensor front-ends — where interference from mains wiring, switching supplies, Ethernet, etc. can couple into both conductors in a similar way.

In real hardware, rejection is finite. Some of that common-mode disturbance gets converted into a differential error and shows up at the output. CMRR (Common-Mode Rejection Ratio) is the standard metric that quantifies how well the circuit suppresses that common-mode-to-output leakage.

What Is CMRR?

CMRR is the ratio of differential gain to common-mode gain. In other words, it tells you how much larger the wanted differential response is compared to the unwanted common-mode response.

CMRR = |Ad| / |Ac|

Where:

• Ad = differential-mode gain (magnitude)
• Ac = common-mode gain (magnitude)

In decibels:

CMRR(dB) = 20 * log10(|Ad| / |Ac|)

A higher CMRR means better suppression of signals that are truly common to both inputs. (Datasheets typically specify CMRR at stated conditions — frequency, gain, and sometimes common-mode voltage — because those conditions matter.)

Real-World Example: Differential RF Front-End (Active Antenna, Loop, Preamplifier)

Consider an active loop antenna or a balanced RF preamp in a high-interference location. The wanted signal is differential (it appears as opposite polarity on the two input nodes), while local noise may couple in a way that’s largely common-mode.

If the front-end has CMRR = 60 dB, that corresponds to a 1000:1 ratio between differential gain and common-mode gain. So, assuming unity differential gain (Ad = 1), a 1 V common-mode input would produce about 1 mV at the output from the common-mode path.

Key point: CMRR does not magically remove noise that has already become differential at the inputs. Once interference is converted from common-mode into differential (because of imbalance), it will pass through like any other signal.

Why Common-Mode Rejection Degrades in Practice

CMRR is never infinite. Two practical “CMR killers” show up again and again:

• Internal mismatch in the differential stage (resistor ratio errors, unequal input impedances, device parameter mismatch, parasitic capacitance differences). These create a nonzero Ac.
• External imbalance that converts common-mode into differential before the amplifier ever sees it (unequal source impedances, asymmetrical wiring, different stray capacitance-to-ground on each leg, imperfect transformer/balun balance, or common-mode current on feedlines).

So while the amplifier may have excellent intrinsic CMRR on the bench, the effective system rejection can collapse if the antenna, cabling, and layout are not truly symmetrical with respect to the local noise environment.

CMRR vs Frequency

CMRR is frequency-dependent. As frequency rises, tiny parasitics (capacitance, inductance, trace geometry, connector symmetry, transformer balance, etc.) make the two input paths less identical — which increases common-mode-to-differential conversion and reduces effective rejection.

• Many op-amps/instrumentation amps show high CMRR at low frequency, then a steady drop as frequency increases. Always check the CMRR-vs-frequency curve, not just the “headline” number.
• In RF designs, maintaining symmetry (tight matching, short balanced runs, controlled return paths) and using appropriate baluns/common-mode chokes can help preserve useful rejection into the MHz range — but it should be verified in the real mechanical/layout environment.

Why Symmetry Matters: Push-Pull and Balanced Inputs

Balanced, push-pull signal chains can achieve excellent common-mode rejection — if the symmetry is maintained throughout the input network, layout, and source impedance.

• Each input “leg” should see the same impedance and the same parasitics.
• When that condition is met, common-mode pickup appears similarly on both legs and largely cancels in the differential stage.

But symmetry is not automatic: even small mismatches (trace length, pad capacitance, transformer imbalance, unequal coupling to ground) can significantly reduce rejection at higher frequencies.

Measuring CMRR

A practical lab approach is to measure the two gains and compute their ratio:

1. Differential test: drive the input differentially (equal magnitude, opposite polarity) with Vdiff_in and measure Vout_diff.
2. Common-mode test: tie the two inputs together, drive them with the same signal Vcm_in, and measure Vout_cm.
3. Compute the gains and then CMRR:

Ad = Vout_diff / Vdiff_in
Ac = Vout_cm   / Vcm_in
CMRR(dB) = 20 * log10(|Ad| / |Ac|)

If you use the same input magnitude for both tests (Vdiff_in and Vcm_in matched by definition), you’ll often see a simplified form written as:

CMRR(dB) ≈ 20 * log10(|Vout_diff| / |Vout_cm|)

Just be careful to keep the measurement conditions consistent (frequency, gain setting, load, and whether you’re measuring a single-ended or differential output).

Summary

• CMR is the concept (rejection of common-mode input); CMRR is the numeric metric (usually in dB).
• CMRR = differential gain / common-mode gain. Bigger is better.
• In real systems, imbalance often defeats CMR by converting common-mode pickup into differential signal before it reaches the amplifier.
• CMRR almost always drops with frequency, so symmetry, layout, and parasitic control matter — especially in RF.
• Push-pull + balanced inputs can deliver excellent rejection, but only if the entire path stays matched and symmetrical.

CMRR tells you how much “equal-on-both-wires” garbage sneaks through — and at higher frequencies, tiny asymmetries are enough to let it in.

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