What resistor relationships are required in a differential amplifier circuit to achieve Vout = (R2/R1)(V2 − V1)?

What resistor relationships are required in a differential amplifier circuit to achieve Vout = (R2/R1)(V2 − V1)?

• A. R1 = R3 and R2 = R4; ratio sets gain; common-mode rejection is improved with matching.
• B. R1 = R2 and R3 = R4; no effect on CMRR.
• C. All four resistors equal; maximum gain.
• D. Only R2 matters for gain.

Answer: (A)

In a four-resistor differential amplifier, the output tracks the difference between the two inputs with a gain set by a simple ratio. To get Vout = (R2/R1)(V2 − V1), the two signal paths must be treated symmetrically. That symmetry is achieved by making the input resistor on the inverting side equal to the input resistor on the non-inverting side (R1 = R3) and by making the feedback resistor on the inverting path equal to the resistor from the non-inverting input to ground (R2 = R4). When these equalities hold, the differential gain is cleanly set by the ratio R2/R1, and any signal common to both inputs tends to cancel at the output, improving common-mode rejection. If the resistor pairs aren’t matched this way, the gains on the two sides won’t be identical and the circuit won’t subtract the inputs in the desired, proportional way, and common-mode signals will leak through, degrading CMRR. The gain is determined by the ratio R2/R1, not by a single resistor alone, and all four resistors must be paired as described for the target expression to hold.

In a four-resistor differential amplifier, the output tracks the difference between the two inputs with a gain set by a simple ratio. To get Vout = (R2/R1)(V2 − V1), the two signal paths must be treated symmetrically. That symmetry is achieved by making the input resistor on the inverting side equal to the input resistor on the non-inverting side (R1 = R3) and by making the feedback resistor on the inverting path equal to the resistor from the non-inverting input to ground (R2 = R4). When these equalities hold, the differential gain is cleanly set by the ratio R2/R1, and any signal common to both inputs tends to cancel at the output, improving common-mode rejection.

If the resistor pairs aren’t matched this way, the gains on the two sides won’t be identical and the circuit won’t subtract the inputs in the desired, proportional way, and common-mode signals will leak through, degrading CMRR. The gain is determined by the ratio R2/R1, not by a single resistor alone, and all four resistors must be paired as described for the target expression to hold.