Inverting Amplifier

Vout = −Vin × Rf/Ri

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Result
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Formula

Vout = −Vin × Rf / Ri

Description

The inverting amplifier feeds the input signal through Ri to the inverting terminal of the op-amp, while the non-inverting input is grounded. The output is inverted (180 degrees out of phase) with a gain magnitude set by the Rf/Ri ratio. The input impedance equals Ri because the inverting input is at virtual ground. This configuration is preferred for summing amplifiers, integrators, and differentiators. The gain can be less than, equal to, or greater than unity depending on the resistor ratio.

Variables

  • Vout — Output voltage (V)
  • Vin — Input voltage (V)
  • Rf — Feedback resistor (Ω)
  • Ri — Input resistor (Ω)

Practical Notes

The inverting input is a virtual ground, meaning it sits at approximately 0V during operation. Input impedance is set by Ri, which is lower than the non-inverting configuration. For best DC accuracy, place a resistor equal to Rf||Ri on the non-inverting input to cancel bias current offset.

Related Formulas

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

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