Explain the concept of operational amplifier (op-amp) common-mode rejection ratio (CMRR).

Common-mode signals are those that appear simultaneously and with the same magnitude on both the inverting and non-inverting inputs of an op-amp. Ideally, an op-amp should amplify only the difference between the voltages applied to its inputs (differential input), completely ignoring any common-mode voltage. However, due to imperfections and non-idealities in real-world op-amp circuits, some amount of common-mode voltage might get inadvertently amplified.

CMRR is a measure of how effectively an op-amp can reject or attenuate these common-mode signals and focus only on the desired differential input. It is defined as the ratio of the gain for the differential input to the gain for the common-mode input, both expressed in decibels (dB). Mathematically, CMRR can be expressed as:

CMRR

=

20

log

10

(

Differential Gain

Common-Mode Gain

)

CMRR=20log

10

(

Common-Mode Gain

Differential Gain

)

In this equation, the "Differential Gain" refers to the amplification an op-amp provides to the actual difference in voltage between its inverting and non-inverting inputs, while the "Common-Mode Gain" represents the amplification of any voltage that is present in equal magnitude on both inputs.

A higher CMRR value indicates better rejection of common-mode signals, and therefore, a higher degree of accuracy in amplifying only the intended differential input. CMRR is typically expressed in decibels (dB), a logarithmic unit that allows for easy comparison of signal levels.

It's important to note that achieving a high CMRR is crucial in applications where the desired signal is much smaller than any common-mode interference or noise. Engineers and designers often select op-amps with higher CMRR values for precision applications to minimize the impact of unwanted signals and improve the overall accuracy of the circuit.