Question

Express closed loop voltage gain (AF) in terms of open loop gain (A) and feedback circuit gain (B)?

(a) AF = A/AB

(b) AF = 1+ (A/AB)

(c) AF = A/(1+AB)

(d) AF = AB/(1+A)

I had been asked this question by my college professor while I was bunking the class.

This intriguing question comes from Voltage Series Feedback Amplifier topic in section Operational Amplifier Characteristics of Linear Integrated Circuits

Answer 1

The correct expression for the closed-loop voltage gain (AFA_FAF​) in terms of the open-loop gain ($A$) and the feedback circuit gain ($B$) is:

(c) AF=A1+ABA_F = \frac{A}{1 + AB}AF​=1+ABA​

Explanation:

This is derived from the general formula for a feedback amplifier, where:

• $A$ is the open-loop voltage gain of the op-amp,
• $B$ is the feedback network gain (which is the feedback voltage divided by the output voltage),
• AFA_FAF​ is the closed-loop voltage gain.

The relationship between the open-loop gain, feedback, and the closed-loop gain for a feedback amplifier is given by:

AF=A1+ABA_F = \frac{A}{1 + AB}AF​=1+ABA​

This formula shows that with negative feedback, the closed-loop gain is reduced by a factor depending on both the open-loop gain $A$ and the feedback factor $B$. The closed-loop gain becomes more stable and less sensitive to variations in the open-loop gain $A$ when feedback is applied.