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Common Mode Rejection Ratio

Common mode rejection ratio (CMRR) measures how well an amplifier rejects signals that appear on both inputs at the same time (common mode) while amplifying the difference between them. A high CMRR means the amplifier ignores noise that is common to both inputs, such as power line hum. It is often expressed in decibels, and it is a key specification for instrumentation amplifiers and differential circuits.

Written by the Vorzep Team

Instrumentation Amplifiers

Common Mode Rejection Ratio Calculator

How well a differential amplifier ignores noise shared by both inputs.

CMRR = Ad / Acm

Inputs

Drag the handle (or use arrow keys on it) to reorder
Application and frequency
Calculating CMRR…

Results

CMRR at operating point
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Formula breakdown

CMRR versus frequency

Roll-off uses a single-pole model: CMRR(f) = CMRR0 / √(1 + (f/fc)²). Enable the switch to apply it; otherwise the curve is flat.

Differential amplifier model

Conversion table

V/V
dB
CMRR (dB)Ratio (V/V)RejectionInput error per 1 V CM

Key formulas and references

CMRR = Ad / Acm
CMRR(dB) = 20·log10(Ad/Acm) = Ad(dB) − Acm(dB)
Vout = Ad·Vd + Acm·Vcm
Verr,in = Vcm / CMRR
CMRR ≈ (1 + Rf/R1) / (4t)  (worst-case tolerance t)
  1. Sedra & Smith, Microelectronic Circuits, Oxford University Press: differential amplifiers and common-mode rejection.
  2. Horowitz & Hill, The Art of Electronics, Cambridge University Press: op-amp and instrumentation amplifier chapters.
  3. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, McGraw-Hill.
  4. Analog Devices, Op Amp Applications Handbook (W. Jung, ed.): instrumentation amplifier and CMRR sections.
  5. Texas Instruments, Precision Labs series on op-amp CMRR and PSRR.

Variables

Symbol Quantity Unit
CMRR Common mode rejection ratio dimensionless
A_d Differential gain dimensionless
A_cm Common-mode gain dimensionless

What it means

The common‑mode rejection ratio (CMRR) is the ratio of differential gain A_d to common‑mode gain A_cm, expressed as CMRR = A_d / A_cm. It indicates how well the amplifier rejects signals that appear simultaneously on both inputs (common‑mode signals, such as noise). CMRR is often specified in decibels: CMRR_dB = 20·log₁₀(A_d/A_cm). A high CMRR is essential for instrumentation amplifiers and precision measurement circuits. Example: If A_d = 100,000 and A_cm = 1, then CMRR = 100,000 (or 100 dB). This means that a 1V common‑mode signal is suppressed by a factor of 100,000, equivalent to 10 µV at the output. This is crucial for accurate measurement of small differential signals in the presence of common‑mode interference.

Worked example

Common Mode Rejection Ratio – Practical Example

Real‑World
Scenario: An op‑amp has differential gain Ad = 1000 and common‑mode gain Acm = 0.1. Find the CMRR.
ParameterValue
Ad1000
Acm0.1
FormulaCMRR = Ad / Acm
1CMRR = 1000 / 0.1 = 10,000
2CMRRdB = 20·log₁₀(10000) = 80 dB
Final Design CMRR = 80 dB ✓ Excellent rejection
Why: High CMRR means the amplifier rejects common‑mode signals (noise) effectively.

Common mistakes

Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.

Applications

Common‑mode rejection ratio CMRR = A_d/A_cm measures how well an amplifier rejects common‑mode signals. Higher CMRR means better rejection of noise that appears on both inputs. Engineers use it to evaluate instrumentation amplifiers, to design sensors with high immunity to interference, and to ensure accurate measurements in noisy environments. This is a key specification for precision analog circuits.

  • Instrumentation and sensor signal conditioning
  • Medical and biomedical signal amplification
  • Data acquisition systems with high noise immunity
  • Bridge circuit and differential amplifier design
  • Educational understanding of CMRR

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  • Published July 10, 2026
  • Last updated August 6, 2026