If Vo equals V2 minus V1, which resistor condition ensures this relationship?

If Vo equals V2 minus V1, which resistor condition ensures this relationship?

• A. All four resistors equal
• B. R1 equals R2 and R3 equals R4
• C. R1 equals R3 and R2 equals R4
• D. R1 equals R4 and R2 equals R3

Answer: (A)

This is about a differential amplifier using four resistors and how to get the output to be V2 minus V1 with unity gain. The op-amp will drive Vo so that its two inputs are at the same voltage. The non-inverting input is fed by a divider from V2 through the resistors in the top/bottom of that side, so with all four resistors equal, the non-inverting input sits at V2/2. On the inverting side, V1 is connected through one resistor and the output Vo through the feedback resistor. If those two resistors are equal, the currents at the inverting node satisfy (V1 − V−) + (Vo − V−) = 0, which leads to Vo = 2V− − V1. Since the op-amp forces V− to equal V+, and V+ was V2/2, you get Vo = 2*(V2/2) − V1 = V2 − V1. So having all four resistors equal ensures Vo = V2 − V1 with unity gain. (Equivalently, matching the pairs R1 = R2 and R3 = R4 would also work, but all-four-equal is the simplest, most robust condition.)

This is about a differential amplifier using four resistors and how to get the output to be V2 minus V1 with unity gain. The op-amp will drive Vo so that its two inputs are at the same voltage. The non-inverting input is fed by a divider from V2 through the resistors in the top/bottom of that side, so with all four resistors equal, the non-inverting input sits at V2/2.

On the inverting side, V1 is connected through one resistor and the output Vo through the feedback resistor. If those two resistors are equal, the currents at the inverting node satisfy (V1 − V−) + (Vo − V−) = 0, which leads to Vo = 2V− − V1. Since the op-amp forces V− to equal V+, and V+ was V2/2, you get Vo = 2*(V2/2) − V1 = V2 − V1.

So having all four resistors equal ensures Vo = V2 − V1 with unity gain. (Equivalently, matching the pairs R1 = R2 and R3 = R4 would also work, but all-four-equal is the simplest, most robust condition.)