1 Answer
CMRR stands for Common-Mode Rejection Ratio, and it's an important parameter of an operational amplifier (op-amp). It measures how well the op-amp can reject common-mode signals, or unwanted noise that appears on both input terminals, relative to the difference between the two inputs (which is the signal the op-amp is supposed to amplify).
In simpler terms, the CMRR tells us how effectively the op-amp can differentiate between the real input signal and any noise or interference that appears equally on both input pins.
Formula for CMRR:
\[
\text{CMRR} = \frac{A_{\text{differential}}}{A_{\text{common}}}
\]
Where:
CMRR in dB:
CMRR is often expressed in decibels (dB), and the formula is:
\[
\text{CMRR(dB)} = 20 \log_{10} \left( \frac{A_{\text{differential}}}{A_{\text{common}}} \right)
\]
Why CMRR matters:
For practical purposes, op-amps usually have a high CMRR, often in the range of 80 dB to 120 dB or more, especially in precision applications.
In simpler terms, the CMRR tells us how effectively the op-amp can differentiate between the real input signal and any noise or interference that appears equally on both input pins.
Formula for CMRR:
\[\text{CMRR} = \frac{A_{\text{differential}}}{A_{\text{common}}}
\]
Where:
- \(A_{\text{differential}}\) is the differential gain (the gain when the op-amp amplifies the difference between the two inputs).
- \(A_{\text{common}}\) is the common-mode gain (the gain when the same signal appears on both inputs).
CMRR in dB:
CMRR is often expressed in decibels (dB), and the formula is:\[
\text{CMRR(dB)} = 20 \log_{10} \left( \frac{A_{\text{differential}}}{A_{\text{common}}} \right)
\]
Why CMRR matters:
- A high CMRR means the op-amp is good at rejecting common-mode signals, and it's ideal for applications where you need to amplify small signals while rejecting noise, like in audio equipment, instrumentation, or sensor circuits.
- A low CMRR means the op-amp will amplify not only the desired signal but also any noise that is present equally on both inputs, leading to poor performance in noisy environments.
For practical purposes, op-amps usually have a high CMRR, often in the range of 80 dB to 120 dB or more, especially in precision applications.