Common-Mode Rejection
Understanding Common-Mode Rejection
Any pair of signals on two conductors can be decomposed into two independent components: a differential-mode component, which is the difference between the two voltages, and a common-mode component, which is the average voltage present equally on both. In a balanced link the wanted information travels as the differential mode, while most coupled interference arrives as the common mode because external fields and ground shifts tend to affect both closely spaced conductors the same way. Common-mode rejection is the property that lets a receiver respond to the first component while ignoring the second, and it is the foundation of noise immunity in differential signaling.
Mathematically, if the two input voltages are V1 and V2, the differential voltage is Vd = V1 minus V2 and the common-mode voltage is Vcm = (V1 plus V2) / 2. A real amplifier produces an output that is the sum of a wanted term, Ad times Vd, and an unwanted term, Acm times Vcm. The whole goal of differential design is to make Ad large and Acm as close to zero as possible. The ratio of these two gains, expressed in decibels, is the common-mode rejection ratio.
The CMRR Formula and Its Meaning
CMRR is the single number that captures rejection performance. A device with 100 dB of CMRR attenuates a common-mode signal by a factor of 100,000 relative to a differential signal of the same amplitude. This is why a sensor cable running beside a noisy motor drive can still deliver a clean millivolt-level reading: the interference is largely common mode and is rejected, while the small wanted difference passes through.
CMRR (dB) = 20 · log10( Ad / Acm )
Output of a real differential stage:
Vout = Ad · Vd + Acm · Vcm
Mode decomposition:
Vd = V1 − V2, Vcm = ( V1 + V2 ) / 2
Where Ad = differential gain, Acm = common-mode gain, V1 and V2 = the two input voltages. Example: Ad = 100, Acm = 0.001 gives CMRR = 20 log10(100,000) = 100 dB.
What Sets the Limit
In low-frequency circuits CMRR is set largely by the matching of the active device and its feedback resistors; a 0.1 percent resistor mismatch in a simple difference amplifier can cap CMRR near 66 dB no matter how good the op-amp is. At RF and microwave frequencies the dominant limit shifts to physical balance. Unequal trace lengths, asymmetric parasitic capacitance to ground, and amplitude or phase error in baluns all convert a portion of the common-mode signal into a differential error that the receiver cannot distinguish from the wanted signal. As a rule of thumb, about 1 degree of phase imbalance or 0.1 dB of amplitude imbalance limits achievable rejection to roughly 40 dB, which is why symmetric layout and well-balanced transformers matter more than the device datasheet at high frequency.
Why It Matters in RF Systems
Common-mode rejection appears throughout RF and mixed-signal hardware. Balanced antenna feeds, mixer and amplifier differential ports, high-speed serial links, and instrumentation front ends all rely on it to stay immune to ground noise and external coupling. A balun translates between an unbalanced coaxial line and a balanced load while ideally rejecting common-mode current; a common-mode choke adds series impedance only to the common-mode path, knocking down conducted EMI on cables. Designers also use CMRR figures to budget noise: if interference of a known common-mode level is present, the CMRR tells how much of it leaks into the signal chain as differential error.
- Symbol and unit: CMRR, expressed in dB (higher is better).
- Dominant low-frequency limit: resistor and device matching.
- Dominant RF limit: path imbalance, balun amplitude and phase error.
- Frequency behavior: CMRR typically falls 20 dB per decade as frequency rises.
- Typical applications: instrumentation front ends, balanced RF links, EMI suppression on cables.
Typical CMRR by Component Type
| Component / Context | Typical CMRR (dB) | Primary Limiting Factor | Notes |
|---|---|---|---|
| Instrumentation amplifier (DC) | 90 to 120 | Internal trimming, device matching | Falls with frequency above ~1 kHz |
| Difference amp, 0.1% resistors | ~66 | Resistor mismatch | 0.01% resistors raise it to ~86 dB |
| Audio / instrumentation cable | 60 to 90 | Twist quality, source impedance balance | Twisted pair improves coupling symmetry |
| RF balun (transformer) | 30 to 50 | Amplitude and phase imbalance | Degrades toward band edges |
| Common-mode choke (cable) | 20 to 50 | Choke impedance vs. circuit impedance | Frequency-dependent insertion of CM impedance |
| High-speed differential pair | 20 to 40 | Length and skew mismatch | Tight skew control is essential |
Frequently Asked Questions
What is common-mode rejection?
Common-mode rejection is the ability of a differential circuit or balanced transmission path to suppress a signal that appears equally on both of its inputs or conductors while still passing the wanted differential signal. The common-mode component is typically interference picked up identically on both lines, such as power-supply hum, ground-potential differences, or radiated EMI. Because an ideal differential receiver responds only to the difference between its two inputs, anything common to both is canceled. The effectiveness is measured by the common-mode rejection ratio (CMRR), in decibels, as the ratio of the differential gain to the common-mode gain.
How is the common-mode rejection ratio (CMRR) calculated?
CMRR is the differential gain divided by the common-mode gain, expressed in decibels: CMRR(dB) = 20 log10(Ad / Acm). For example, an instrumentation amplifier with a differential gain of 100 and a common-mode gain of 0.001 has a CMRR of 20 log10(100/0.001) = 100 dB. Equivalently, CMRR can be measured by driving both inputs together with a known common-mode voltage and recording the resulting differential output; a 1 V common-mode input that produces a 10 microvolt output referred to the input corresponds to 100 dB. CMRR generally degrades with frequency because parasitic capacitance and gain-bandwidth limits raise the common-mode gain.
What limits common-mode rejection at RF frequencies?
At RF, common-mode rejection is limited mainly by physical imbalance between the two paths rather than by the active device alone. Mismatched trace lengths, unequal parasitic capacitance to ground, asymmetric coupling, and amplitude or phase error in baluns all convert part of the common-mode signal into a differential error. A phase imbalance of just a few degrees or a small amplitude mismatch caps achievable rejection: roughly 1 degree of phase error or 0.1 dB of amplitude error limits CMRR to about 40 dB. This is why high-frequency designs emphasize tightly matched differential routing, symmetric layout, and well-balanced baluns or common-mode chokes rather than relying on the amplifier specification.