CMRR: Common-Mode Rejection Ratio Explained

Common-Mode Rejection Ratio (CMRR) sounds complex.
In practice, it answers one simple question:

How well does a circuit ignore noise it should not care about?

In precision analog design, that question decides accuracy, safety, and trust. This guide explains CMRR from first principles to real-world decisions—clearly, deeply, and without fluff.

What Is CMRR?

Definition of Common-Mode vs Differential Signals

A differential signal is what you want.
It is the voltage difference between two inputs.

A common-mode signal is what you do not want.
It appears equally on both inputs—noise, hum, or ground shift.

Good amplifiers amplify the difference and reject the common part.

Mathematical Definition of CMRR

CMRR compares how much differential signal is amplified versus how much common-mode signal leaks through.

Term	Meaning
Ad	Differential gain
Acm	Common-mode gain
CMRR	Ad / Acm

CMRR Formula and dB Expression

CMRR is almost always stated in decibels:

[
\text{CMRR(dB)} = 20 \log_{10}\left(\frac{A_d}{A_{cm}}\right)
]

Higher is better. Always.

Intuitive Explanation

Imagine two people talking in a noisy room.
CMRR is the listener’s ability to hear the difference between voices while ignoring the crowd.

Simple Numerical Example

Differential gain = 1000
Common-mode gain = 0.1

CMRR = 10,000 → 80 dB

That means common-mode noise is reduced by 10,000×.

Why CMRR Matters in Analog Circuit Design

Signal Accuracy and Noise Immunity

Low-level signals drown easily.
A poor CMRR lets noise sneak in and distort results.

Power-Line Noise, EMI, and Ground Offset

The most common enemies:

50/60 Hz mains hum
EMI from motors and radios
Ground potential differences

All are common-mode problems.

Real-World Examples

Strain gauges near motors
Medical sensors on human bodies
Industrial ADC inputs across long cables

In each case, CMRR separates signal from chaos.

DC CMRR vs AC CMRR

What Is DC CMRR?

DC CMRR measures rejection at 0 Hz.
It reflects resistor matching and input stage symmetry.

What Is AC CMRR?

AC CMRR changes with frequency.
As frequency rises, rejection usually falls.

Why CMRR Degrades at High Frequency

Parasitic capacitance
Internal transistor imbalance
Limited loop gain

Physics always wins.

Which Applications Care Most?

Application	DC CMRR	AC CMRR
Load cells	Critical	Moderate
Audio	Moderate	Critical
High-speed ADCs	Low	Critical

CMRR vs Frequency: The Hidden Trade-Off

Internal Op-Amp Limits

CMRR is not flat.
Datasheets often show a steep drop beyond 1 kHz or 10 kHz.

Interpreting Datasheet Curves

Look for:

Test frequency
Common-mode voltage level
Gain setting

Never trust a single number.

Most Affected Applications

Switching power environments
Long cable sensors
High-resolution data acquisition

CMRR vs PSRR

Both reject noise—but from different places.

Spec	Rejects Noise From
CMRR	Inputs
PSRR	Power rails

Precision systems need both.

CMRR vs Gain

Higher closed-loop gain can hide poor CMRR.
But the error is still there—just scaled.

Gain Error vs Common-Mode Error

Gain errors scale the signal.
CMRR errors corrupt it.

That difference matters.

Input Common-Mode Range and Its Effect on CMRR

What Is Input Common-Mode Range?

It is the voltage window where the input stage works correctly.

CMRR Near the Rails

Near supply rails:

Input transistors saturate
Matching degrades
CMRR collapses

Rail-to-Rail Trade-Offs

Rail-to-rail inputs offer flexibility.
They often sacrifice peak CMRR.

Read datasheets carefully.

What Determines CMRR Performance?

Internal Resistor Matching

CMRR lives and dies by matching.

A 0.1% mismatch can ruin a 100 dB spec.

Why Instrumentation Amplifiers Win

They use:

Laser-trimmed resistors
Symmetrical architectures

Result: 110–130 dB CMRR is common.

External Resistor Matching

In discrete designs:

Use 0.01% resistors
Match temperature coefficients
Place resistors close together

External and PCB-Level Factors That Degrade CMRR

Source Impedance Imbalance

Even perfect amplifiers fail if sources differ.

Equalize source resistance whenever possible.

Wiring, Cables, and Connectors

Twisted pairs
Equal length traces
Shielding

Small asymmetries matter.

PCB Layout Strategy

Best practices:

Differential routing
Solid ground planes
No ground loops

Layout can destroy datasheet performance.

Typical CMRR Values and Benchmarks

Device Type	Typical CMRR
General op-amp	70–90 dB
Precision op-amp	100–120 dB
Instrumentation amp	110–130 dB
Medical-grade systems	≥120 dB

Higher standards demand higher rejection.

How to Evaluate CMRR When Choosing ICs

Typical vs Minimum Specs

Always design to minimum, not typical.

Temperature and Voltage Conditions

CMRR degrades:

At temperature extremes
Near supply limits

Check the fine print.

Datasheet Red Flags

Single-frequency specs
“Typical only” curves
Unrealistic test conditions

If it looks too good, it is.

Practical Design Tips and Final Takeaways

Proven Ways to Improve CMRR

Balance source impedances
Use instrumentation amplifiers
Match resistors tightly
Route symmetrically
Filter common-mode noise early

Common Mistakes

Ignoring AC CMRR
Trusting one-number specs
Poor grounding

Final Thought

CMRR is not just a number.
It is a system-level promise.

As a classic engineering proverb says:

“What you don’t measure—and reject—will measure you later.”

Design for CMRR early.
Your signals will thank you.