Common-mode rejection ratio (CMRR) for operational amplifiers: CMRR is defined as the ratio of which two quantities?

Introduction / Context:Operational amplifiers are designed to amplify the difference between their two inputs while rejecting any signal common to both. The figure of merit that quantifies this ability is the common-mode rejection ratio (CMRR), typically expressed in decibels for convenience.

Given Data / Assumptions:

• Linear operation of the op-amp around its operating point.
• Differential-mode gain Ad is much larger than common-mode gain Acm in good designs.
• Voltages used for gain definitions (not power).

Concept / Approach:By definition, CMRR = Ad / Acm, where Ad is the differential voltage gain and Acm is the common-mode voltage gain. In dB form, CMRR_dB = 20 * log10(Ad / Acm). High CMRR indicates excellent rejection of common-mode interference such as hum or coupled noise appearing equally on both inputs.

Step-by-Step Solution:

Verification / Alternative check:Datasheets provide typical and minimum CMRR values (e.g., 80 dB to 120 dB) measured over specified frequencies and supply conditions, confirming the voltage-gain-based definition.

Why Other Options Are Wrong:Differential/common power gains: power terminology is not used for CMRR definition. Ideal to actual gain: unrelated; that would describe bandwidth or open-loop vs closed-loop differences. Signal to noise: a different metric (signal-to-noise ratio), not CMRR.

Common Pitfalls:Confusing CMRR with PSRR (power-supply rejection ratio) or with input common-mode range; mixing voltage and power terms.

Final Answer:the differential voltage gain, the common-mode voltage gain