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ECG Amplifier CMRR Calculation (Differential Gain vs Common-Mode Gain)

ECG Amplifier CMRR Calculation (Differential Gain vs Common-Mode Gain)

Verified Sources
Nov 4, 2026

CMRR (common-mode rejection ratio) quantifies how well an amplifier suppresses common-mode signals compared with differential signals. For a gain specified by a differential (desired) gain AdA_d and a common-mode (undesired) gain AcmA_{cm}, CMRR is commonly defined as a ratio and then expressed in decibels using a logarithmic conversion.2

In dB:

CMRRdB=20log⁡10(AdAcm)\text{CMRR}_{\text{dB}} = 20\log_{10}\left(\frac{A_d}{A_{cm}}\right)

Key terms:

  • CMRR
  • Differential gain
  • Common-mode gain
  • dB

Footnotes

  1. "CMRR common-mode rejection ratio definition and dB formula (20 log10 for gain ratios)" - Provides decibel relationships for ratios and common 20log1020\\log_{10} usage for amplitude/gain quantities. ↩

  2. "Common-mode rejection ratio (CMRR) concept and typical gain-ratio usage" - Defines CMRR as a ratio of differential to common-mode gain and discusses dB expression. ↩

Common Mode Rejection Ratio (CMRR) and dB Calculation

Compute CMRR in dB from given gains

  1. 1
    Step 1

    Given Ad=1000A_d = 1000 and Acm=0.1A_{cm} = 0.1.

  2. 2
    Step 2

    Compute 2˘00bAdAcm=10000.1=10000\u200b\frac{A_d}{A_{cm}} = \frac{1000}{0.1} = 10000.

  3. 3
    Step 3

    Use CMRRdB=20log⁡10(Ad/Acm)\text{CMRR}_{\text{dB}} = 20\log_{10}(A_d/A_{cm}) to get CMRRdB=20log⁡10(10000)\text{CMRR}_{\text{dB}} = 20\log_{10}(10000).

  4. 4
    Step 4

    Since log⁡10(10000)=4\log_{10}(10000)=4, then CMRRdB=20×4=80 dB\text{CMRR}_{\text{dB}} = 20\times4 = 80\text{ dB}.

  5. 5
    Step 5

    CMRR =80 dB= 80\text{ dB}.

Result:

CMRRdB=80 dB\text{CMRR}_{\text{dB}} = 80\text{ dB}

Interpretation: A higher CMRR means the amplifier suppresses common-mode interference more strongly relative to differential signal amplification. This is a core requirement for ECG instrumentation, where common-mode noise (e.g., from power-line coupling and patient coupling) must be rejected.2

Footnotes

  1. "CMRR common-mode rejection ratio definition and dB formula (20 log10 for gain ratios)" - Provides decibel relationships for ratios and common 20log1020\\log_{10} usage for amplitude/gain quantities. ↩

  2. "Common-mode rejection ratio (CMRR) concept and typical gain-ratio usage" - Defines CMRR as a ratio of differential to common-mode gain and discusses dB expression. ↩

dB conversion sanity check

If Ad/Acm=104A_d/A_{cm}=10^4, then 20log⁡10(104)=20⋅4=80 dB20\log_{10}(10^4)=20\cdot4=80\text{ dB}. A quick check like this helps avoid base-10 vs base-e or 10 vs 20 mistakes.2

Footnotes

  1. "CMRR common-mode rejection ratio definition and dB formula (20 log10 for gain ratios)" - Provides decibel relationships for ratios and common 20log1020\\log_{10} usage for amplitude/gain quantities. ↩

  2. "Common-mode rejection ratio (CMRR) concept and typical gain-ratio usage" - Defines CMRR as a ratio of differential to common-mode gain and discusses dB expression. ↩

Use 20·log10 for gain ratios (not 10·log10)

For CMRR expressed using gain terms AdA_d and AcmA_{cm} (voltage or amplitude gain), the standard decibel conversion is 20log⁡10(⋅)20\log_{10}(\cdot). Using 10log⁡10(⋅)10\log_{10}(\cdot) would produce a value that is too small by a factor of 2.2

Footnotes

  1. "CMRR common-mode rejection ratio definition and dB formula (20 log10 for gain ratios)" - Provides decibel relationships for ratios and common 20log1020\\log_{10} usage for amplitude/gain quantities. ↩

  2. "Common-mode rejection ratio (CMRR) concept and typical gain-ratio usage" - Defines CMRR as a ratio of differential to common-mode gain and discusses dB expression. ↩

Given Gains and Their Ratio

Differential gain vs common-mode gain, and the resulting CMRR ratio

CMRR definitions & common pitfalls

ECG Amplifier Performance Metric Flow

Model inputs

1) Define gains

Identify differential gain AdA_d and common-mode gain AcmA_{cm}."

CMRR ratio

2) Compute ratio

Form Ad/AcmA_d/A_{cm} as the rejection factor."

CMRR(dB)

3) Convert to dB

Compute 20log⁡10(Ad/Acm)20\log_{10}(A_d/A_{cm}) for a decibel measure."

Knowledge Check

Question 1 of 4
Q1Single choice

Given Ad=1000A_d = 1000 and Acm=0.1A_{cm} = 0.1, what is the CMRR in dB?

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