A CMRR Calculator, also known as a Common-Mode Rejection Ratio Calculator, helps audio engineers, electronics enthusiasts, circuit designers, and students understand how effectively a differential amplifier rejects unwanted signals that appear on both inputs.

Common-mode rejection is especially important in balanced audio equipment, microphone preamplifiers, operational amplifiers, instrumentation amplifiers, and sensitive measurement circuits.

When interference affects both input conductors in a similar way, a differential amplifier can reduce its influence on the output. The amplifier's Common-Mode Rejection Ratio, or CMRR, describes how strongly it responds to differential signals compared with common-mode signals.

This interactive calculator allows you to calculate CMRR in decibels, convert CMRR into a linear ratio, determine common-mode gain, calculate differential and common-mode input voltages, and estimate common-mode output error.

It also includes a rejection visualization and a reference table.

How to Use the CMRR Calculator

Start by selecting the calculation mode that matches the information you have.

Differential Gain + Common-Mode Gain: Enter both amplifier gains to calculate CMRR in decibels and as a linear ratio.

CMRR in dB to Linear Ratio: Enter a CMRR value to determine the corresponding linear rejection ratio.

Differential Gain + CMRR: Enter differential gain and CMRR to calculate the magnitude of common-mode gain.

Input Voltages: Enter the non-inverting and inverting input voltages to calculate differential voltage and common-mode voltage.

Common-Mode Voltage + CMRR: Enter common-mode voltage, differential gain, and CMRR to estimate the magnitude of the resulting common-mode output error.

Click Calculate CMRR to view the results.

What Is CMRR?

CMRR stands for Common-Mode Rejection Ratio.

It describes how effectively a differential amplifier rejects a signal that is present on both inputs.

A differential amplifier is designed to respond primarily to the voltage difference between its inputs.

If the same unwanted signal appears on both inputs, an ideal differential amplifier would reject it completely.

Real amplifiers are not perfect, so some common-mode signal may appear at the output.

CMRR measures the relationship between the amplifier's differential gain and common-mode gain.

CMRR Formula

The linear Common-Mode Rejection Ratio is:

CMRR = |Ad / Acm|

Where:

• Ad is the differential voltage gain.

• Acm is the common-mode voltage gain.

• The absolute value indicates that gain magnitudes are compared.

For example, suppose an amplifier has a differential gain of 1,000 and a common-mode gain of 0.01.

CMRR = 1,000 / 0.01 = 100,000

The linear CMRR is 100,000:1.

This means the amplifier has much greater sensitivity to differential signals than to common-mode signals.

How to Calculate CMRR in dB

CMRR is commonly expressed in decibels.

The formula is:

CMRR (dB) = 20 × log₁₀(|Ad / Acm|)

For example, a linear CMRR of 100,000 corresponds to:

CMRR = 20 × log₁₀(100,000) = 100 dB

A higher CMRR generally indicates stronger common-mode rejection relative to differential gain.

How to Convert CMRR From dB to a Linear Ratio

Use:

Linear CMRR = 10^(CMRR / 20)

For example:

• 20 dB = 10:1.

• 40 dB = 100:1.

• 60 dB = 1,000:1.

• 80 dB = 10,000:1.

• 100 dB = 100,000:1.

• 120 dB = 1,000,000:1.

These ratios compare differential and common-mode voltage gains.

They do not directly represent a guaranteed percentage reduction in all environmental noise.

What Is a Differential Signal?

A differential signal is the voltage difference between two inputs.

The formula is:

Vd = V+ − V−

For example, suppose the non-inverting input is 2.01 V and the inverting input is 2.00 V.

The differential voltage is:

Vd = 0.01 V

This equals 10 millivolts.

A differential amplifier responds to this difference according to its differential gain.

What Is a Common-Mode Signal?

A common-mode signal is the voltage component shared by both inputs.

It is calculated as the average of the input voltages:

Vcm = (V+ + V−) / 2

For example, if one input is 2.01 V and the other is 2.00 V:

Vcm = 2.005 V

The amplifier ideally responds to the differential component while rejecting the common-mode component.

Differential Gain vs. Common-Mode Gain

Differential gain describes how strongly an amplifier responds to the voltage difference between its inputs.

Common-mode gain describes how strongly the amplifier responds to the average voltage shared by both inputs.

For a linear differential amplifier, the output can be modeled as:

Vout = Ad × Vd + Acm × Vcm

An amplifier with high differential gain and very low common-mode gain has a high CMRR.

Why Is CMRR Important in Audio?

Audio equipment often handles relatively small electrical signals.

Microphone signals, in particular, may require substantial amplification before they reach a useful operating level.

Unwanted interference can enter cables and equipment through electromagnetic coupling and other mechanisms.

Differential inputs can help reject interference that appears similarly on both signal conductors.

This is one reason common-mode rejection is important in professional audio equipment.

CMRR in Balanced Audio Connections

Balanced audio connections use two signal conductors and a differential receiving circuit.

Interference that couples similarly onto both conductors can appear as a common-mode signal.

The differential receiver responds primarily to the voltage difference between the conductors.

As a result, it can reject some unwanted interference.

However, balanced wiring does not guarantee perfect noise rejection.

Cable construction, shielding, source impedance balance, and receiver design all affect real-world performance.

CMRR in Microphone Preamplifiers

Microphone preamplifiers amplify relatively low-level audio signals.

Because these signals can be small, unwanted interference may become more noticeable after amplification.

A microphone preamplifier with effective common-mode rejection can help reduce interference coupled onto both signal conductors.

CMRR is therefore one useful specification when evaluating microphone preamplifiers.

However, preamp noise, gain range, input impedance, distortion, and frequency response also matter.

CMRR in Operational Amplifiers

Operational amplifiers have differential inputs.

Ideally, an op-amp responds only to the difference between its input voltages.

In practice, a common-mode signal may produce a small unwanted output contribution.

Op-amp datasheets often specify CMRR under particular test conditions.

The specification may vary with common-mode input voltage, temperature, supply voltage, and frequency.

CMRR in Instrumentation Amplifiers

Instrumentation amplifiers are designed for accurately amplifying small differential signals.

They are commonly used in measurement equipment and sensor systems.

High common-mode rejection is especially useful when the desired differential signal is small compared with the common-mode voltage.

However, the amplifier must also operate within its specified input common-mode voltage range.

What Is Common-Mode Output Error?

Common-mode output error is the output contribution caused by an unwanted common-mode input signal.

For a linear amplifier:

Vout,cm = Acm × Vcm

For example, suppose the common-mode input voltage is 1 V and the common-mode gain magnitude is 0.01.

The output error magnitude is:

0.01 V, or 10 millivolts.

This estimate assumes the amplifier operates within its linear range.

How to Calculate Common-Mode Gain From CMRR

If you know differential gain and CMRR, you can estimate common-mode gain magnitude.

Use:

|Acm| = |Ad| / 10^(CMRR / 20)

For example, suppose:

• Differential gain = 1,000.

• CMRR = 100 dB.

The linear CMRR is 100,000.

Therefore:

|Acm| = 1,000 / 100,000 = 0.01

This means the common-mode gain magnitude is 0.01 V/V.

Is Higher CMRR Always Better?

A higher CMRR generally indicates stronger rejection of common-mode signals relative to differential signals.

However, it does not guarantee that a particular audio system will be completely free of interference.

Other factors can limit practical rejection.

For example, unequal source impedances may convert common-mode interference into a differential signal before it reaches the amplifier.

Once interference becomes differential, it cannot be removed simply through common-mode rejection.

What Is a Good CMRR Value?

The CMRR required for an application depends on the signal level, interference environment, circuit design, and measurement conditions.

A value of 60 dB represents a differential-to-common-mode gain ratio of 1,000:1.

A value of 80 dB represents 10,000:1.

A value of 100 dB represents 100,000:1.

Higher values can be useful in sensitive measurement applications, but specifications should be compared at similar frequencies and operating conditions.

Does CMRR Change With Frequency?

Yes.

CMRR can vary with frequency.

An amplifier may provide excellent common-mode rejection at low frequencies while offering less rejection at higher frequencies.

This matters because interference can occur across a wide frequency range.

For example, power-line interference may occur at 50 or 60 Hz, while radio-frequency interference occurs at much higher frequencies.

A single CMRR specification does not describe the complete frequency-dependent response.

CMRR and 50/60 Hz Hum

Electrical power systems commonly operate at 50 Hz or 60 Hz, depending on the region.

Interference related to power wiring may couple into audio cables and equipment.

If that interference appears similarly on both balanced signal conductors, a differential input can help reject it.

However, ground loops, magnetic coupling, unbalanced wiring, and impedance mismatch can create interference that is not purely common-mode.

CMRR is one part of managing hum, not a complete solution.

CMRR vs. Signal-to-Noise Ratio

CMRR and signal-to-noise ratio describe different properties.

CMRR compares differential gain with common-mode gain.

Signal-to-noise ratio (SNR) compares the level of a desired signal with unwanted noise.

An amplifier can have excellent CMRR while still generating significant internal noise.

Likewise, an amplifier may have a low internal noise floor but insufficient common-mode rejection for a particular application.

CMRR vs. PSRR

CMRR stands for Common-Mode Rejection Ratio.

PSRR stands for Power Supply Rejection Ratio.

CMRR describes how an amplifier responds to signals common to both inputs.

PSRR describes how changes or disturbances in the power supply affect amplifier behavior.

Both specifications can matter when designing low-noise audio and measurement circuits.

How Do Resistor Tolerances Affect CMRR?

Some differential amplifier circuits rely on precisely matched resistor ratios.

When these ratios are mismatched, common-mode rejection can decrease.

This is especially important in differential amplifier designs built using external resistors.

Using appropriately matched resistor networks can help improve rejection.

However, actual CMRR also depends on the amplifier and circuit implementation.

How Does Cable Impedance Balance Affect CMRR?

In balanced audio systems, the impedances seen by the two signal conductors can influence interference rejection.

If the impedances differ, external interference may couple unequally into the conductors.

This can convert some common-mode interference into a differential voltage.

The receiving amplifier may then amplify that unwanted differential component.

Good impedance balance is therefore important for effective real-world noise rejection.

What Does the CMRR Visualization Show?

The calculator includes a visual comparison of differential and common-mode gain.

The differential gain is treated as the reference.

The common-mode gain is displayed relative to that reference on a logarithmic scale.

As CMRR increases, the common-mode gain becomes smaller relative to differential gain.

The visualization helps demonstrate the mathematical meaning of common-mode rejection.

It does not simulate an actual audio waveform or measure real-world interference.

Important Limitations of CMRR Calculations

This calculator uses idealized linear amplifier relationships.

It does not measure a physical amplifier or predict its full frequency-dependent performance.

The common-mode output error estimate assumes that the amplifier operates within its specified input and output ranges.

CMRR values can vary with frequency, temperature, gain setting, input voltage, and circuit construction.

The calculator also cannot determine gain polarity or phase from CMRR magnitude alone.

For actual circuit design, consult component datasheets and evaluate the complete system.

Tip: Start with a differential gain of 1,000 and a common-mode gain of 0.01. The calculator produces a CMRR of 100 dB. Next, increase the common-mode gain to 0.1 while keeping differential gain unchanged. The CMRR drops to 80 dB. This demonstrates how increasing unwanted common-mode amplification reduces an amplifier's rejection performance.

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