Common-Mode Rejection Ratio (CMRR) Explained: Formula, Importance & Applications

When studying operational amplifiers (op-amps), one of the most important parameters you’ll encounter in datasheets and interviews is the Common-Mode Rejection Ratio (CMRR). It directly relates to how well an op-amp rejects unwanted noise and interference. In this blog, we’ll break down its meaning, formula, practical significance, and interview questions.

1. What is Common-Mode Signal?

A common-mode signal is a signal that appears identically on both input terminals of an op-amp. For example, external noise picked up equally on both + and – inputs is a common-mode signal.

2. CMRR Definition

The Common-Mode Rejection Ratio (CMRR) is a measure of how effectively an op-amp rejects common-mode signals while amplifying differential signals.

Formula:

CMRR = A_d / A_cm

Where:
A_d = Differential Gain (gain for difference of inputs)
A_cm = Common-Mode Gain (gain for signals common to both inputs)

Since it’s usually expressed in decibels (dB):

CMRR (dB) = 20 log (A_d / A_cm)

3. Importance of CMRR

• High CMRR = Better Noise Rejection: External interference (like 50/60 Hz mains hum) affects both inputs equally. A high CMRR means the op-amp cancels it out.
• Essential in Differential Amplifiers: In measurement systems (like ECG, audio), CMRR ensures the actual signal is amplified while rejecting noise.
• Precision Circuits: Low CMRR leads to error in sensitive analog circuits (instrumentation amplifiers).

4. Example Calculation

If an op-amp has:

• Differential Gain (A_d) = 100,000
• Common-Mode Gain (A_cm) = 0.5

CMRR = 100,000 / 0.5 = 200,000

CMRR (dB) = 20 log (200,000) ≈ 106 dB

5. Applications Where CMRR Matters

• Instrumentation Amplifiers: For medical devices like ECG/EEG where signal is tiny and noise is large.
• Audio Amplifiers: To reject power line interference.
• Sensor Interfaces: Strain gauges, temperature sensors — ensure accurate readings by rejecting common-mode noise.

6. Factors Affecting CMRR

• Mismatch in input transistors of the op-amp.
• Temperature variations.
• Frequency: CMRR usually decreases at higher frequencies.

7. Interview Questions on CMRR

• Define CMRR and explain its importance in op-amps.
• Why is a high CMRR desirable in instrumentation amplifiers?
• What factors cause degradation of CMRR in practical circuits?
• How does CMRR vary with frequency?

Conclusion

Common-Mode Rejection Ratio (CMRR) is a critical op-amp specification that ensures accurate amplification by rejecting unwanted common-mode signals. High CMRR is essential in precision and noise-sensitive applications. Mastering this concept is important for both circuit design and analog interview preparation.