Difference Amplifier

Vout = (Rf/Ri) × (V2 − V1)

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Result
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Formula

Vout = (Rf / Ri) × (V2 − V1)

Description

The difference amplifier amplifies the voltage difference between two inputs while rejecting any signal common to both (common-mode rejection). It uses matched resistor pairs on each input to achieve balanced operation. The gain is set by the Rf/Ri ratio. Ideal CMRR requires perfect resistor matching; even 0.1% mismatch significantly degrades common-mode rejection. For high CMRR applications, instrumentation amplifiers with laser-trimmed internal resistors are preferred over discrete difference amplifier circuits.

Variables

  • Vout — Output voltage (V)
  • V1 — Inverting input voltage (V)
  • V2 — Non-inverting input voltage (V)
  • Rf — Feedback resistor (Ω)
  • Ri — Input resistor (Ω)

Practical Notes

CMRR of a discrete difference amplifier is limited by resistor matching: 0.1% resistors give about 60 dB CMRR, 0.01% about 80 dB. Dedicated difference amplifier ICs like the INA143 achieve 80-100 dB CMRR. Use this topology for current sensing across shunt resistors and measuring small differential signals in the presence of large common-mode voltages.

Related Formulas

Non-Inverting Amplifier Inverting Amplifier Summing Amplifier Gain-Bandwidth Product Common-Mode Rejection Ratio Op-Amp Integrator Gain

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