CMR vs CMRR vs Common-Mode Impedance

 Or why Ohms-to-dB Is Usually the Wrong Conversation

CMR, CMRR, and “common-mode impedance in dB” get mixed up constantly. One moment we’re talking about amplifier behavior, the next we’re discussing choke impedance, and suddenly someone converts ohms to dB and everything goes sideways.

This explainer untangles the terminology and shows when you can — and cannot — turn impedance into attenuation.

Differential-mode vs common-mode fundamentals

Any pair of signals v₁(t) and v₂(t) can be described as:

Differential-mode voltage:
v_diff = v₁ − v₂

Common-mode voltage:
v_cm = (v₁ + v₂) / 2

DM = what differs between the wires.
CM = what is the same on both wires relative to a reference (often chassis or earth).

Most differential receivers care about DM, and ideally ignore CM — that ability is “common-mode rejection”.

What CMR actually means

CMR (common-mode rejection) is a qualitative property:

• “This front end needs good common-mode rejection.”
• “Twisted pair gives better common-mode rejection.”

It is not a number. It is the behavior of suppressing CM signals.

To quantify it, we need a ratio — that’s CMRR.

CMRR: the ratio (and the one that belongs in dB)

For an amplifier or ADC input stage:

• A_d = differential gain
• A_c = common-mode gain

CMRR = A_d / A_c

In dB:

CMRR_dB = 20·log₁₀(A_d/A_c)

Characteristics:

• Dimensionless ratio (not ohms)
• dB is meaningful because it’s a ratio
• Frequency-dependent
• Applies to systems, not isolated passive parts

Common-mode impedance: a totally different quantity

Common-mode impedance Z_CM is measured in ohms. It is the impedance seen when both conductors move together with respect to reference.

For a common-mode choke:

• Z_DM is small — differential signals pass
• Z_CM is large — common-mode noise is impeded

It is not a ratio, so turning it directly into dB is meaningless unless you define a voltage divider.

Why “common-mode impedance in dB” is usually wrong

Example misunderstanding:

“My choke has Z_CM = 1 kΩ → 60 dB rejection.”

What actually happened is:

20·log₁₀(1000 Ω / 1 Ω) ≈ 60 dB

That is converting ohms relative to 1 Ω — not relating it to any circuit.

To get actual attenuation, you need a CM voltage divider:

V_out/V_in = Z_system / (Z_system + Z_CM)

For a 50 Ω system and Z_CM = 1000 Ω:

Att = 20·log₁₀(50 / 1050) ≈ −26.4 dB

So 1 kΩ → ~26 dB attenuation in a 50 Ω system — not 60 dB.

The correct dB depends entirely on the surrounding circuit.

CMRR vs ZCM — who describes what?

CMR / CMRR

• • Domain: amplifiers, receivers, ADC inputs
  • Units: ratio (dimensionless), usually dB
  • Meaning: how much CM leaks through compared to DM

Common-mode impedance

• • Domain: chokes, filters, cables, connectors
  • Units: ohms vs frequency
  • Meaning: how strongly CM current is impeded

Why they cannot be interchanged

CMRR is always meaningful in dB because it is a ratio.

ZCM in dB is meaningless without a reference and a circuit model.

Worked mini-examples

Amplifier CMRR

A_d = 100 (40 dB)
A_c = 0.01 (−40 dB)

CMRR = 100 / 0.01 = 10,000

CMRR_dB ≈ 80 dB

Common-mode choke

Z_CM = 2 kΩ
Z_system ≈ 100 Ω

Att = 20·log₁₀(100 / 2100) ≈ −26 dB

Again: impedance ≠ attenuation unless you specify the network.

How to talk about this clearly

• Use “CMR” as a behavior word.
• Use “CMRR” only for ratios in dB.
• Never call impedance “CMRR”.
• If quoting dB, specify what ratio it represents.
• When asked “what is ZCM in dB?”, reply: “relative to what source/load?”

Quick cheat-sheet

• CMR — qualitative ability to ignore CM
• CMRR — A_d/A_c, in dB
• ZCM — impedance in ohms vs frequency
• CM attenuation — dB ratio after solving the actual CM divider

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