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

Common-Mode Rejection (CMR) refers to a system’s ability to suppress signals that appear identically on both input lines of a differential circuit. This is critical in high-noise environments — especially in RF and audio systems — where external interference (e.g. from power lines, switching supplies, Ethernet, etc.) can be coupled equally into both conductors.

In practice, CMR is not perfect. A small portion of the common-mode signal still leaks into the output. That leakage is what CMRR, the Common-Mode Rejection Ratio, quantifies.

What Is CMRR?

CMRR is the ratio of differential gain to common-mode gain. It tells you how well a system rejects unwanted common-mode signals compared to the wanted differential signal.

CMRR = Ad / Ac

Where:

• Ad = differential-mode gain
• Ac = common-mode gain

In decibels:

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

A higher CMRR means better suppression of noise that is common to both inputs.

Real-World Example: RF Amplifier or Active Antenna

Let’s say you have an active loop antenna using a push-pull design. Atmospheric signals (the wanted ones) induce a differential signal in the loop, while local power line hum or Ethernet hash may appear equally on both loop ends — that’s common-mode noise.

If your front-end amplifier has CMRR = 60 dB, then a 1 V common-mode disturbance at the input would be suppressed down to 1 mV at the output — a rejection factor of 1000.

Why CMRR Degrades in Practice

CMRR is never infinite due to:

• Component mismatches (resistors, transistor β, op-amp input impedance)
• Layout asymmetry (PCB traces or antenna feedline routing)
• Imbalanced source impedance (like unequal coax shields or poor ground references)

Even a perfectly matched differential amplifier can lose CMRR performance if the cables or antenna are not symmetrical with respect to noise sources.

CMRR vs Frequency

It’s important to understand that CMRR is frequency-dependent.

• Most op-amps or MMICs have good CMRR at low frequencies (DC–1 kHz), but performance often degrades rapidly above 10–100 kHz.
• In RF design, active antennas and differential preamps should have balanced layout, short leads, and matched impedances to maintain decent CMRR in the MHz range.

Why Symmetry Matters: Push-Pull and Balanced Inputs

Balanced systems using push-pull amplifiers inherently achieve higher CMRR, because they maintain electrical symmetry between the signal paths. In such configurations:

• The gain and impedance seen by each leg of the input are tightly matched.
• Any noise that appears equally on both legs is effectively canceled at the differential output.

This symmetry is difficult to maintain with single-ended systems or poorly matched inputs. Even small mismatches in trace length, parasitic capacitance, or transformer balance can degrade CMRR significantly.

In contrast, push-pull stages driven by truly balanced sources (like a shielded twisted pair or symmetric loop) tend to reject common-mode noise more effectively across a wide frequency range.

Measuring CMRR

A common lab method:

1. Drive both inputs of the differential circuit with the same signal (common-mode).
2. Measure the output.
3. Then drive with differential signal.
4. Compute:

CMRR(dB) = 20 * log10(V_diff_out / V_cm_out)

Summary

• CMR is the mechanism; CMRR is the metric.
• High CMRR is essential in environments with high interference or long cable runs.
• For differential receivers, active antennas, ADC front-ends, or even balanced audio gear, good CMRR is the difference between a clean signal and a mess of local RFI.
• Always check how CMRR changes over frequency — not just the datasheet value at DC.
• Push-pull balanced circuits with symmetric inputs are key to maximizing CMRR, especially in RF and low-noise applications.

CMRR quantifies how immune your circuit is to symmetrical garbage riding on both input wires — and it gets worse at high frequencies if you're not careful.

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