In the classic three-op-amp instrumentation amplifier topology used for precision differential measurements, which stage primarily provides the adjustable differential voltage gain (set by the gain resistor Rg), while the final op-amp mainly performs subtraction and common-mode rejection?

Introduction / Context:
Instrumentation amplifiers (in-amps) are widely used to extract small differential signals in the presence of large common-mode voltages. The most common topology is the three-op-amp in-amp, valued for its high input impedance, excellent common-mode rejection ratio (CMRR), and easily programmable gain. Knowing which stage sets the gain is essential for proper design and troubleshooting.

Given Data / Assumptions:

• Classic three-op-amp instrumentation amplifier.
• Two input buffer amplifiers (first stage) with a gain-setting resistor Rg between them.
• A third op-amp (second stage) configured as a differential amplifier with precision resistor ratios.

Concept / Approach:
In the classic in-amp, the first stage consists of two op-amps configured as noninverting amplifiers. Their gains are simultaneously set by Rg, which bridges their feedback networks. This stage establishes the bulk of the differential voltage gain while maintaining very high input impedance. The final (third) op-amp subtracts the two buffered signals using a resistor network to remove common-mode content and refine CMRR.

Step-by-Step Solution:
Identify stages: first stage = dual noninverting buffers with Rg; second stage = subtractor.Relate Rg to gain: decreasing Rg increases first-stage gain.Note function of last op-amp: implements subtraction with precise resistor ratios to maximize CMRR.Therefore, the differential voltage gain is primarily produced by the first stage.

Verification / Alternative check:
Manufacturers’ datasheets show gain equations like G ≈ 1 + (2R/Rg) for the first stage, confirming that Rg controls overall gain. The output stage gain is typically fixed by resistor ratios to enforce accurate subtraction.

Why Other Options Are Wrong:
Second stage/output op-amp: mainly subtracts; it is not the usual adjustable gain element.

“Mismatched resistors” reduce accuracy and CMRR; they do not set correct gain.

“Both stages equally” is incorrect; the programmable gain resides predominantly in the first stage.

Common Pitfalls:
Assuming the differential amplifier stage sets gain; in reality, its resistor matching is optimized for CMRR, not user-programmable gain.

Final Answer:
first stage