Op-amp characteristics: How does common-mode voltage gain (Ac) typically compare with differential voltage gain (Ad) in a high-quality differential amplifier stage?

Introduction:
Differential amplifiers and op-amps are designed to amplify differences between inputs while rejecting signals common to both inputs (common-mode). This question checks understanding of the relative magnitudes of differential gain (Ad) and common-mode gain (Ac) and their relationship to common-mode rejection ratio (CMRR).

Given Data / Assumptions:

• Balanced differential input pair with proper biasing.
• Common-mode signals are ideally rejected.
• High-performance integrated op-amp topology.

Concept / Approach:
Ideal differential amplifiers have Ac = 0, meaning perfect rejection of common-mode input. Real amplifiers have small but nonzero Ac. Since Ad is intentionally large, the ratio CMRR = Ad / Ac is also large (often specified in dB). Thus, Ac is far smaller than Ad in a good design.

Step-by-Step Solution:

Verification / Alternative check:
Data sheets typically show CMRR values of 80–120 dB, implying Ac is orders of magnitude lower than Ad. Bench tests injecting identical signals into both inputs yield minimal output variation compared to differential stimulation.

Why Other Options Are Wrong:

• Equal/greater than differential gain: Would yield poor common-mode rejection and is contrary to op-amp purpose.
• None of the above: Unnecessary; the correct qualitative relationship is clear.

Common Pitfalls:
Assuming infinite CMRR; forgetting that resistor mismatch and finite transistor Early effects raise Ac; ignoring frequency dependence—CMRR typically degrades at higher frequency.

Final Answer:
Smaller than differential voltage gain.