Differential Op-Amp

Check differential gain, resistor matching, and ideal output swing.

Formulas

k = R2 / R1; b = R4 / (R3 + R4)

V+ = b × V2 + (1 − b) × Vref

Vout = (1 + k) × V+ − k × V1

Ad = [(1 + k) × b + k] / 2; Acm = (1 + k) × b − k

Ratio mismatch = [(R4 / R3) / (R2 / R1) − 1] × 100%

Model & assumptions

R1 connects V1 to −IN; R2 is feedback. R3 connects V2 to +IN; R4 connects +IN to Vref.

With matched ratios, Vout = (R2 / R1) × (V2 − V1) + Vref. With mismatch, differential gain is defined at fixed input common-mode.

Real input common-mode range and output limits depend on the selected op-amp. Supply rails are only ideal bounds.

Example with default inputs

Ideal output voltage

2 V

Differential gain

10 V/V

Resistor-ratio mismatch

0 %

Common-mode gain

0 V/V

Ideal input-node voltage

1.09091 V