Calculate CMRR, differential gain, or common mode gain from any two values, with V/V, ratio, and dB unit options for amplifier analysis.
CMRR Formula
CMRR, or common mode rejection ratio, compares an amplifier’s differential gain to its common mode gain. It uses gain magnitudes at the same frequency and operating point. Select the quantity to solve for and the result format; dB values use the voltage-gain convention.
- CMRR = common mode rejection ratio, expressed as a plain ratio
- CMRR_dB = common mode rejection ratio in decibels
- A_d = differential gain, usually in V/V or dB
- A_cm = common mode gain, usually in V/V or dB
- log10 = base-10 logarithm
Choose CMRR, differential gain, or common-mode gain in Solve for, then enter the two known quantities. Signed V/V gains are accepted; inverse gain results give magnitude, not polarity. CMRR ratios cannot be negative, while negative dB values are valid. Logarithms are combined directly for dB calculations to avoid overflowing intermediate ratios.
CMRR Ratio Examples
Higher CMRR means better rejection of signals that appear equally on both inputs, such as electrical noise or interference.
| CMRR Ratio | CMRR dB | General Interpretation |
|---|---|---|
| 100:1 | 40 dB | Common-mode gain is 1/100 of differential gain |
| 1,000:1 | 60 dB | Common-mode gain is 1/1,000 of differential gain |
| 10,000:1 | 80 dB | Common-mode gain is 1/10,000 of differential gain |
| 100,000:1 | 100 dB | Common-mode gain is 1/100,000 of differential gain |
| 1,000,000:1 | 120 dB | Common-mode gain is 1/1,000,000 of differential gain |
CMRR Examples
Example 1: Calculate CMRR from two gains
You have a differential gain of 10,000 V/V and a common mode gain of 1 V/V.
The CMRR is 10,000:1, or 80 dB.
Example 2: Calculate common mode gain
You have a differential gain of 2,000 V/V and a CMRR of 100 dB.
The common mode gain is 0.02 V/V.
CMRR FAQ
What does a higher CMRR mean?
A higher CMRR means the amplifier rejects more common mode signal compared with the differential signal it is meant to amplify. In practical terms, higher CMRR helps reduce noise that appears on both inputs at the same time.
Why does the dB formula use 20 instead of 10?
CMRR is based on voltage gain ratios, so the decibel conversion uses 20 * log10(ratio). The factor 10 is used for power ratios, not voltage or amplitude ratios.
Can CMRR be calculated if common mode gain is zero?
Nonzero differential gain with zero common-mode gain gives an idealized unbounded CMRR. If both gains are zero, CMRR is undefined. The calculator distinguishes these cases; a measured finite CMRR needs nonzero common-mode gain. Zero differential gain with nonzero common-mode gain gives a zero ratio, which has no finite dB value.
