CMR vs CMRR vs Common-Mode Impedance

CMR, CMRR and “common-mode impedance in dB” get mixed up constantly. One moment we are discussing a differential receiver, the next a choke, and then someone divides an ohmic value by 1 Ω and calls the result rejection. That last step is dimensionally legal and electrically empty. My first question is always: which input, which output, which reference and which surrounding circuit?

Define Differential and Common Mode at a Port

For two terminal voltages measured to the same reference, one common convention is:

Differential mode is the voltage difference between the conductors. Common mode is their average voltage relative to a declared third reference: chassis, shield, ground plane, fixture or another return structure. Without that reference and a return path, “common-mode voltage” and “common-mode current” do not identify a complete circuit.

Current conventions also have to be stated. In this article, icm = i1 + i2. Some instruments and standards normalize the modal currents and reference impedances differently. Their S-parameters can be perfectly valid while a directly copied ohmic value differs by a scale factor. Use one convention throughout the model and measurement.

Keysight's balanced-measurement guidance uses the same difference-and-average voltage decomposition and makes the physical-to-logical port mapping explicit.

CMR Can Be a Description or a Number

Common-mode rejection, or CMR, names the ability of a device or signal path to prevent a common-mode stimulus from producing an unwanted response. Engineers also use CMR as a numeric abbreviation, often in dB. Analog Devices, for example, labels the dB curve in its MT-042 op-amp tutorial “CMR” while discussing the underlying common-mode rejection ratio.

That means CMR is not safely assumed to be qualitative. A statement such as “good CMR” is descriptive; a statement such as “CMR = 90 dB” is quantitative. In the second case, the document must define the stimulus, response, port terminations, frequency and ratio used.

Common-mode rejection can characterize active or passive paths. A differential amplifier may convert common input voltage into differential output error. A transformer, cable or balanced filter may pass common mode or convert it to differential mode through asymmetry. The measurement name does not replace the port definition.

CMRR Is a Declared Response Ratio

For a linear differential amplifier, let Ad be differential gain from a differential input to the declared output, and let Acm be gain from common-mode input to the same output quantity under the same reference conditions. One familiar definition is:

The ratio is dimensionless. It varies with frequency, common-mode level, differential gain setting, source balance, loading, supply, temperature and device operating point. For precision op amps, a DC specification may instead be obtained from change in input-referred offset versus change in common-mode voltage. Those definitions are related, but the test method and conditions must travel with the number.

At RF, mixed-mode S-parameters make the port directions explicit. Sdd21 is differential output caused by differential input. Sdc21 is differential output caused by common input; Scd21 is the reverse mode conversion. A test may define a rejection ratio from |Sdd21/Sdc21|, but only after declaring the mixed-mode reference impedances, logical-port mapping and terminations. The Keysight mixed-mode notation explicitly puts response mode first and stimulus mode second.

Worked CMRR Example

Suppose a linear differential stage is tested at one frequency, gain setting, common-mode bias and load. The differential input-to-output gain is Ad = 100 V/V, or 40 dB. The common-mode input produces the same output quantity with Acm = 0.01 V/V, or −40 dB.

The arithmetic is sound because numerator and denominator are compatible voltage gains to the same output definition. It is not a permanent property of every circuit using that device. Analog Devices' test note shows how external resistor mismatch can limit a measured differential-amplifier CMR even when the op amp itself is better, while TI AN-1447 demonstrates the same dependence on gain resistors and board layout in a fully differential amplifier.

Input Common-Mode Impedance Is Not Rejection

With the current convention declared above, the common-mode input impedance of a device is:

This is the impedance looking into the device's common-mode port relative to its reference and with all other ports terminated as specified. It may be resistive, inductive or capacitive and will usually vary with frequency and operating state.

A high Zin,cm can reduce current drawn from one source yet allow a large common-mode voltage. A low value can shunt current to chassis while changing the upstream network. Neither establishes how much of that common-mode stimulus becomes differential output. Two receivers can have similar input common-mode impedance and very different CMRR because their symmetry and internal conversion differ.

Choke Common-Mode Impedance Is a Series Element

The common-mode impedance of a choke is the complex impedance it inserts into a specified common-mode current path:

That is not the same quantity as a receiver's input common-mode impedance. It is also not automatically “rejection.” Its resistive part dissipates common-mode energy; its reactive part stores and returns energy; parasitic capacitance can bypass it; and resonance can move both magnitude and phase. The exact winding connection and fixture determine whether the published value is per line, for the combined pair or for a single exterior-current path. TDK's common-mode choke measurement note shows separate connection fixtures for common- and differential-mode impedance.

Differential current ideally produces cancelling core flux in a coupled common-mode choke, but winding resistance, leakage inductance, capacitance and imbalance remain. So “large Zcm” and “small differential disturbance” are separate frequency-dependent checks.

Ohms Become Attenuation Only Inside a Network

Dividing |Zch,cm| by 1 Ω and applying 20 log10 merely expresses the impedance magnitude relative to 1 Ω. It does not predict a voltage, current or power ratio in an installation.

For a one-loop common-mode Thévenin model, declare:

• Vs,cm: open-circuit common-mode source voltage;
• Zs,cm: source and upstream return impedance;
• Zch,cm: series choke impedance, including its fixture boundary; and
• ZL,cm: downstream load and return-path impedance.

V_s,cm ── Z_s,cm ── Z_ch,cm ── Z_L,cm ── return

Compare the same network with and without the choke. If the source and load paths remain unchanged, the common-mode load-voltage ratio is:

All impedances are complex and frequency dependent. A parallel capacitive path around the choke, multiple chassis returns, cable radiation or a changed load requires a larger network. The differential characteristic impedance of a coax or pair is not automatically Zs,cm or ZL,cm.

Worked Common-Mode Network Example

Consider a synthetic one-frequency example—not a typical value for every station:

Without the choke, |Icm| = 2.48 mA and |VL,cm| = 0.668 V. With the choke, |Icm| = 0.552 mA and |VL,cm| = 0.149 V. The with/without voltage ratio is 0.2225, or −13.05 dB.

The choke magnitude is about 1.44 kΩ, which could be written as about 63.2 dBΩ relative to 1 Ω. That number is not the network's 13.05 dB change. If the source, load, phase or bypass path changes, the attenuation changes even though the choke impedance does not.

Use 20 log10 for a compatible voltage or current ratio. Use 10 log10 for a power ratio. Do not equate the two when the compared port impedances differ.

Fixture Attenuation Is Not Installed Rejection

Component datasheets often publish common-mode insertion loss in a standardized fixture. That is valuable, but its reference impedances and terminations define the result. Coilcraft explicitly states in its common-mode choke measurement notes that its impedance and attenuation curves are measured and that attenuation is referenced to 50 Ω. Such a curve predicts that fixture, not an unknown antenna, cable shield or chassis return.

For a balanced four-port, mixed-mode measurements can separately show:

• Scc21: common-mode transmission;
• Sdd21: differential-mode transmission;
• Sdc21: common input converted to differential output; and
• Scd21: differential input converted to common output.

Those four terms answer different questions. A choke can show strong common-mode insertion loss in a 50 Ω mixed-mode fixture while producing a different installed current reduction. It can also disturb the desired differential signal or create mode conversion through imbalance. Keep the complex data and the port map.

How to Specify a Rejection Result

A defensible CMR, CMRR or choke-attenuation statement includes:

• the physical terminals, logical ports and common-mode reference;
• the voltage/current normalization and reference impedances;
• the exact stimulus mode and measured response mode;
• frequency, amplitude, common-mode bias, gain, bandwidth and linear operating range;
• source and load impedances, terminations, fixture and calibration or de-embedding plane;
• magnitude and phase, or full complex data, when circuit interaction matters;
• with/without topology and every parallel return path for an insertion claim; and
• measurement uncertainty, noise floor and dynamic-range limit.

So when someone asks, “What is this common-mode impedance in dB?”, the useful reply is not a conversion. Ask: “Which source, return path, load, response and reference plane?” Once those exist, solve or measure the ratio that actually matters.

Questions, antenna-factor records or height trials to share? Contact RF.Guru.