Common-Mode Rejection Ratio
CMRR = 20 × log10(Ad / Acm)
Quick answer
This calculator solves CMRR_dB = 20 × log10(Ad / Acm) for CMRR. With Differential Gain 0.5, Common-Mode Gain 1.1, the result is -6.848 dB. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Common-mode rejection ratio quantifies how well a differential amplifier or instrumentation amplifier rejects signals that appear equally on both inputs (common-mode signals) while amplifying the difference signal. Higher CMRR means better rejection of noise, power supply variations, and ground potential differences. Ideal op-amps have infinite CMRR, but real devices range from 60-120 dB. CMRR degrades with frequency due to asymmetric parasitic capacitances and finite gain-bandwidth product. External resistor matching in discrete difference amplifiers often limits CMRR more than the op-amp itself.
Variables
- CMRR — Common-mode rejection ratio (dB)
- Ad — Differential gain (V/V, linear)
- Acm — Common-mode gain (V/V, linear)
Practical Notes
Typical CMRR: general purpose op-amp 80-100 dB, precision op-amp 100-120 dB, instrumentation amplifier 80-120 dB. A CMRR of 80 dB means a 1V common-mode signal produces only 100 µV of error at the output. For Wheatstone bridge measurements with remote sensors, high CMRR is essential to reject noise picked up on the long cable connecting the bridge to the amplifier.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| CMRR | CMRR | dB | dB |
| Ad | Differential Gain | — | — |
| Acm | Common-Mode Gain | — | — |
Step by step
- 1. What you know: Differential Gain 0.5, Common-Mode Gain 1.1
- 2. The relation: CMRR_dB = 20 × log10(Ad / Acm)
- 3. Substitute: Ad = 0.5, Acm = 1.1
- 4. Result: CMRR = -6.848 dB
Worked examples
Minimum range
Given: Differential Gain 0.025, Common-Mode Gain 0.055
Result: CMRR = -6.848 dB
Low range
Given: Differential Gain 0.25, Common-Mode Gain 0.55
Result: CMRR = -6.848 dB
Typical
Given: Differential Gain 0.5, Common-Mode Gain 1.1
Result: CMRR = -6.848 dB
High range
Given: Differential Gain 0.8, Common-Mode Gain 1.76
Result: CMRR = -6.848 dB
Maximum range
Given: Differential Gain 8, Common-Mode Gain 17.6
Result: CMRR = -6.848 dB
Solving for each variable
Solve for CMRR
Differential Gain 0.025, Common-Mode Gain 0.055 → -6.848 dB
Solve for Differential Gain
CMRR 0.3 dB, Common-Mode Gain 0.055 → 0.05693
Solve for Common-Mode Gain
CMRR 0.3 dB, Differential Gain 0.025 → 0.02415
How CMRR changes with Differential Gain
| Differential Gain (input) | CMRR (result) |
|---|---|
| 0.05 | -26.85 dB |
| 0.125 | -18.89 dB |
| 0.25 | -12.87 dB |
| 0.375 | -9.347 dB |
| 0.5 | -6.848 dB |
| 0.75 | -3.327 dB |
| 1 | -0.8279 dB |
| 2 | 5.193 dB |
| 3.5 | 10.05 dB |
| 5 | 13.15 dB |
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<p><a href="https://vbatpower.com/formulas/cmrr/">Common-Mode Rejection Ratio</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Common-Mode Rejection Ratio?
Use CMRR_dB = 20 × log10(Ad / Acm). With Differential Gain 0.5, Common-Mode Gain 1.1, CMRR works out to -6.848 dB.
What is the formula for Common-Mode Rejection Ratio?
The formula is CMRR_dB = 20 × log10(Ad / Acm). Common-mode rejection ratio quantifies how well a differential amplifier or instrumentation amplifier rejects signals that appear equally on both inputs (common-mode signals) while amplifying the difference signal.
How do you find Differential Gain when you know the other values?
Rearrange for Differential Gain: with CMRR 0.3 dB, Common-Mode Gain 0.055, Differential Gain is 0.05693.
How do you find Common-Mode Gain when you know the other values?
Rearrange for Common-Mode Gain: with CMRR 0.3 dB, Differential Gain 0.025, Common-Mode Gain is 0.02415.
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