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Inverting Op-Amp Gain

G=−RfRinG = -\frac{R_{f}}{R_{in}}

Worked example: 100 kΩ over 10 kΩ → gain −10 — press Try an example to run it live, then adjust anything.

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Inverting Op-Amp Gain explained

RinRfG

Negative feedback drives the inverting input to the same potential as the grounded non-inverting input — the "virtual earth". The source current Vin/Rin therefore has nowhere to go but through Rf, and the output must sit at −(Rf/Rin)Vin. A 100 kΩ feedback resistor with a 10 kΩ input resistor gives a gain of −10: ten times bigger, upside down. The op-amp's own gain, a million or more, barely enters the result — which is the whole point of feedback.

Note that the input impedance of this stage is just Rin, so it loads the source; where that matters, the non-inverting configuration is the better choice. Two more practicalities: gain-bandwidth product is fixed, so a ×100 stage on a 1 MHz op-amp runs out of steam at 10 kHz, and the virtual earth makes this the natural summing point for mixers — several inputs, each with its own resistor, add at that node.

Inverting Op-Amp Gain formula

G=−RfRinG = -\frac{R_{f}}{R_{in}}
Where
  • GG= Voltage gain
  • RfR_{f}= Feedback resistance (Ω)
  • RinR_{in}= Input resistance (Ω)

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