In an inverting unity-gain amplifier, which statements are true when R3 = R1?

In an inverting unity-gain amplifier, which statements are true when R3 = R1?

• A. Gain equals +1 and there is no inversion
• B. Gain equals -1, and the input impedance equals R1
• C. Gain equals -1, but the input impedance equals Rf
• D. Gain equals +1, and the input impedance is infinite

Answer: (B)

In an inverting amplifier, the closed-loop gain is set by -Rf/Rin. If the feedback resistor equals the input resistor, the gain becomes -1, so the output is inverted with the same magnitude as the input. Here the feedback resistor is R3 and the input resistor is R1, so with R3 = R1 the gain is -R3/R1 = -1. The input impedance seen by the source is essentially Rin, because the inverting input sits at a virtual ground and the source current flows through the input resistor into the summing node. Therefore, Zin = R1. Since R3 = R1, Zin also equals Rf numerically, but the standard relation is Zin = Rin. So the gain is -1 and the input impedance is R1, which matches the statement that is correct. The other options conflict with the negative sign of the gain for this configuration and with the fact that the input impedance is determined by Rin, not infinite.

In an inverting amplifier, the closed-loop gain is set by -Rf/Rin. If the feedback resistor equals the input resistor, the gain becomes -1, so the output is inverted with the same magnitude as the input. Here the feedback resistor is R3 and the input resistor is R1, so with R3 = R1 the gain is -R3/R1 = -1.

The input impedance seen by the source is essentially Rin, because the inverting input sits at a virtual ground and the source current flows through the input resistor into the summing node. Therefore, Zin = R1. Since R3 = R1, Zin also equals Rf numerically, but the standard relation is Zin = Rin.

So the gain is -1 and the input impedance is R1, which matches the statement that is correct. The other options conflict with the negative sign of the gain for this configuration and with the fact that the input impedance is determined by Rin, not infinite.