Inverting Op-Amp Gain
Enter feedback resistor Rf and input resistor Rin in ohms to get the closed-loop voltage gain Av = −Rf / Rin, negative because the output inverts phase.
Av (V/V)
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Inverting op-amp gain
An inverting amplifier feeds the input through Rin into the op-amp's inverting (−) pin, while feedback resistor Rf runs from the output back to that same node. If you take the ideal assumptions at face value (infinite open-loop gain, virtual short, no input current), the closed-loop gain comes out to Av = −Rf / Rin, with Vout = −Vin · Rf / Rin. That minus sign is the output sitting 180° out of phase with the input. The non-inverting (+) pin gets tied to ground, or to mid-rail on a single supply. Example: Rf = 10 kΩ and Rin = 1 kΩ give a gain of −10, so feeding in +0.5 V drops the output to −5 V. Add more inputs, each through its own Ri into the (−) node, and the circuit turns into a summing amplifier: Vsum = −Σ(Vi · Rf / Ri).
Applications: audio pre-amps, sensors, active filters
The inverting topology shows up everywhere. It's behind audio pre-amplifiers (microphone, phono RIAA) and sensor amplification (photodiode transimpedance, thermocouples). It handles analog summing in audio mixers and the current-to-voltage stage after a DAC, and it forms the backbone of active filters such as Sallen-Key, multiple-feedback Butterworth, integrators and differentiators. The virtual ground sitting at the (−) input makes node analysis easy and pins the input impedance to Rin.
FAQ
Why is the gain negative? The feedback lands on the inverting pin, so whenever the input rises the output is pushed down to hold the (−) pin at virtual ground.
What is the input impedance? It equals Rin. That's a good deal lower than the non-inverting topology, so it can load down high-impedance sources.
Can gain be less than 1? Yes. Just make Rf < Rin, so Rf = 1 kΩ with Rin = 10 kΩ gives −0.1, attenuating the signal while still flipping its sign.
Why add a resistor to the (+) pin? A bias resistor sized to Rf‖Rin balances the input bias current on both pins and trims down the DC offset.
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