Explain the basic topology of a three-op-amp instrumentation amplifier and give the gain expression in terms of R1, Rg, and the differential stage resistors.

Explain the basic topology of a three-op-amp instrumentation amplifier and give the gain expression in terms of R1, Rg, and the differential stage resistors.

• A. Vout ≈ (R4/R3) (V2 − V1) × (1 + 2R1/Rg)
• B. Vout ≈ (R2/R1) (V2 − V1) × (1 + 2R1/Rg)
• C. Vout ≈ (R4/R3) (V2 + V1) × (1 + 2R1/Rg)
• D. Vout ≈ (R4/R3) (V2 − V1) × (1 − 2R1/Rg)

Answer: (A)

The key idea is the two-stage structure: a front-end that converts the input difference into a amplified difference with gain set by the resistor that bridges the two inverting inputs, and a second stage that subtracts the two front-end outputs with a gain set by the differential stage resistor network. In the front-end, each input drives an op-amp with a feedback resistor R1 and the two inverting inputs tied together by Rg. This arrangement makes the front-end gain (for the differential signal) equal to 1 + 2R1/Rg. The outputs of these two op-amps then feed a differential amplifier in the second stage, whose gain is determined by the resistor ratio R4/R3. Multiplying the front-end differential gain by the differential-stage gain gives the overall output: Vout ≈ (R4/R3) × (V2 − V1) × (1 + 2R1/Rg). This captures why the signal is the difference between V2 and V1, scaled first by the front-end and then by the final differential stage. The other forms would misrepresent the subtraction, use the wrong resistor ratio, or place the gain factors incorrectly, which does not reflect how the three-op-amp instrumentation amplifier actually behaves.

The key idea is the two-stage structure: a front-end that converts the input difference into a amplified difference with gain set by the resistor that bridges the two inverting inputs, and a second stage that subtracts the two front-end outputs with a gain set by the differential stage resistor network. In the front-end, each input drives an op-amp with a feedback resistor R1 and the two inverting inputs tied together by Rg. This arrangement makes the front-end gain (for the differential signal) equal to 1 + 2R1/Rg. The outputs of these two op-amps then feed a differential amplifier in the second stage, whose gain is determined by the resistor ratio R4/R3. Multiplying the front-end differential gain by the differential-stage gain gives the overall output: Vout ≈ (R4/R3) × (V2 − V1) × (1 + 2R1/Rg). This captures why the signal is the difference between V2 and V1, scaled first by the front-end and then by the final differential stage. The other forms would misrepresent the subtraction, use the wrong resistor ratio, or place the gain factors incorrectly, which does not reflect how the three-op-amp instrumentation amplifier actually behaves.