The Common-Mode Rejection Ratio (CMRR) is a measure of how well a differential amplifier rejects common-mode signals (noise that appears on both inputs) while amplifying differential-mode signals (the desired signal).
The exact formulas for CMRR are:
- CMRR = Adiff / Acom
- CMRR [dB] = Adiff [dB] - Acom [dB]
Understanding the CMRR Formula
The CMRR is expressed as a ratio or in decibels (dB). Both forms relate the amplifier's gain for the desired signal to its gain for unwanted noise.
- Adiff: This is the differential-mode gain. It represents how much the amplifier amplifies the difference between the two input signals. This is the desired amplification.
- Acom: This is the common-mode gain. It represents how much the amplifier amplifies the portion of the signal that is common to both inputs (e.g., noise picked up equally on both wires). This is the unwanted amplification.
A high CMRR indicates that the amplifier is very good at rejecting common-mode noise. Ideally, Acom would be zero, resulting in infinite CMRR.
CMRR in Decibels (dB)
The CMRR is often specified in decibels because gain values are commonly expressed this way. The formula for CMRR in dB is derived from the ratio formula:
CMRR [dB] = 20 * log10 (Adiff / Acom)
Using the property of logarithms (log(a/b) = log(a) - log(b)), this becomes:
CMRR [dB] = 20 * log10 (Adiff) - 20 * log10 (Acom)
Since Adiff [dB] = 20 * log10 (Adiff) and Acom [dB] = 20 * log10 (Acom), the formula simplifies to:
CMRR [dB] = Adiff [dB] - Acom [dB]
Practical Example
The reference provides a clear example of how high CMRR benefits performance:
- For instance, the NF differential amplifier 5307 has a CMRR of 120 dB (minimum) at utility frequency.
- This high CMRR means that even if a significant noise component (Vn) of 1 V is present as a common-mode signal at the input, only a tiny fraction of it appears at the output.
- Specifically, with 120 dB CMRR, the common-mode gain is extremely low. A 1 V common-mode input results in only 1 µV (1 microvolt) appearing at the output due to common-mode amplification.
This demonstrates the effectiveness of high CMRR in suppressing noise and interference, which is crucial in applications like instrumentation, medical devices, and data acquisition systems where weak differential signals need to be amplified in the presence of significant common-mode noise.
Summary Table
| Measurement | Formula | Description |
|---|---|---|
| CMRR (Ratio) | CMRR = Adiff / Acom | Ratio of differential gain to common-mode gain. |
| CMRR (Decibels) | CMRR [dB] = Adiff [dB] - Acom [dB] | Difference between differential and common-mode gain in dB. |
