Electronics · Free Calculator
Op Amp Differential Amplifier Calculator
Find the output of a single op amp difference amplifier from its two inputs and four resistors.
Vout = (R2/R1)(V2 − V1)Four resistorsCommon modeShunt amplifier
V
V
V
Output voltage0.5 V
Differential gain R2/R110
Difference V2 − V10.05 V
Ratio mismatch0.000 %
How this result was calculated
- Vout = V2 × R4/(R3 + R4) × (1 + R2/R1) − V1 × R2/R1 = 0.5 V
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Difference Amplifier Formula
Vout = V2 × [R4 ÷ (R3 + R4)] × (1 + R2 ÷ R1) − V1 × (R2 ÷ R1)
When R1 = R3 and R2 = R4: Vout = (R2 ÷ R1) × (V2 − V1)
When R1 = R3 and R2 = R4: Vout = (R2 ÷ R1) × (V2 − V1)
Worked example
R1 = R3 = 10 kΩ, R2 = R4 = 100 kΩ, V2 = 1.25 V, V1 = 1.20 V: Vout = 10 × 0.05 = 0.5 V.
Key insight: a 0.1 % mismatch between the two resistor ratios limits common mode rejection to about 66 dB at unity gain, which is why precision difference amplifiers use laser trimmed resistor networks.
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Frequently Asked Questions
What does a differential amplifier do?
It amplifies the difference between two inputs and rejects any voltage common to both.
Why must the resistor ratios match?
Any mismatch converts common mode voltage into output error, reducing CMRR.
When should I use an instrumentation amplifier instead?
When the source impedance is high or unequal, such as a bridge sensor, because the simple difference amplifier loads the inputs.
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