Role of the feedback resistor — does it “add to” op-amp gain? In closed-loop op-amp amplifiers, does the feedback resistor simply add to the intrinsic gain of the op-amp, or does it set the closed-loop gain via a ratio with the input network?

Introduction / Context:
Students often conflate the op-amp’s huge open-loop gain with the closed-loop gain obtained using external resistors. The feedback resistor Rf does not “add to” the op-amp’s gain; instead, Rf, together with the input resistor(s), sets the closed-loop gain by determining how much output is fed back to the input node.

Given Data / Assumptions:

• Negative feedback topology (inverting or noninverting).
• Ideal op-amp model for intuition: Aol → ∞.
• Linear operation within output swing and bandwidth limits.

Concept / Approach:
Closed-loop gain is a function of the external network. For an inverting amplifier, Av = −Rf/Rin. For a noninverting amplifier, Av = 1 + Rf/Rg. In neither case is the open-loop gain “added” to by Rf. Rather, feedback forces the effective gain to the value implied by resistor ratios, largely independent of the enormous Aol so long as loop gain is high over the signal band.

Step-by-Step Solution:

Verification / Alternative check:
Circuit simulators and lab benches show that changing Rf while holding Rin (or Rg) fixed scales the closed-loop gain in the predicted ratio; the open-loop gain is not “added to.”

Why Other Options Are Wrong:

• Correct: Misstates the role of Rf.
• Only correct for open-loop comparator use: Open-loop comparators do not use Rf to set linear gain.
• Only correct when Rf = Rin: Even with Rf = Rin, gain is −1 (inverting) or 2 (noninverting with proper Rg), still ratio-defined.

Common Pitfalls:
Thinking of gain as additive; ignoring the feedback fraction and loop-gain concepts.

Final Answer:
Incorrect