1. Defining CMRR: Common Mode Rejection Ratio (CMRR) is a measure of an Op-Amp's ability to reject common-mode signals (like electrical noise or interference) that appear on both inputs simultaneously. It is defined as the ratio of the Differential Gain ($A_d$) to the Common-mode Gain ($A_{cm}$):
$$CMRR = \frac{A_d}{A_{cm}}$$
2. Ideal Characteristics:
• Ideal Differential Gain ($A_d$): In an ideal Op-Amp, the differential gain is considered infinite.
• Ideal Common-mode Gain ($A_{cm}$): An ideal Op-Amp should perfectly ignore any signal that is the same on both inputs, meaning the common-mode gain is zero ($A_{cm} = 0$).
3. Calculation for Ideal Case: Substituting these ideal values into the formula:
$$CMRR = \frac{\infty}{0} = \infty$$
In practical applications, CMRR is usually expressed in decibels (dB). While real Op-Amps have very high CMRR values (e.g., 90 dB or 100 dB), only a theoretical
ideal Op-Amp reaches infinity.