Unity gain in an inverting configuration requires

Unity gain in an inverting configuration requires

• A. Rin equals zero.
• B. Rf equals infinity.
• C. Rin and Rf are equal.
• D. Rf is twice Rin.

Answer: (C)

In an inverting amplifier, the closed-loop gain is Av = -Rf / Rin. Unity gain means the output magnitude equals the input and the output is inverted, so Av should be -1. That happens precisely when Rf equals Rin. The negative sign comes from the inverting configuration, so the output is the input with a 180-degree phase shift. To see it briefly, the input current is Vin/Rin and the feedback current is -Vout/Rf (since the inverting node sits near ground due to negative feedback). Setting currents equal gives Vin/Rin = Vout/Rf, but with the sign from the node, Vout = - (Rf/Rin) Vin. For |Av| = 1, Rf/Rin must be 1, i.e., Rf = Rin. Why the other options don’t fit: zero Rin isn’t practical and would push the gain toward infinity; an infinite Rf removes the feedback path, giving an open-loop amplifier with a very large gain, not a controlled unity gain; and having Rf twice Rin yields a gain of -2, not -1.

In an inverting amplifier, the closed-loop gain is Av = -Rf / Rin. Unity gain means the output magnitude equals the input and the output is inverted, so Av should be -1. That happens precisely when Rf equals Rin. The negative sign comes from the inverting configuration, so the output is the input with a 180-degree phase shift.

To see it briefly, the input current is Vin/Rin and the feedback current is -Vout/Rf (since the inverting node sits near ground due to negative feedback). Setting currents equal gives Vin/Rin = Vout/Rf, but with the sign from the node, Vout = - (Rf/Rin) Vin. For |Av| = 1, Rf/Rin must be 1, i.e., Rf = Rin.

Why the other options don’t fit: zero Rin isn’t practical and would push the gain toward infinity; an infinite Rf removes the feedback path, giving an open-loop amplifier with a very large gain, not a controlled unity gain; and having Rf twice Rin yields a gain of -2, not -1.