Op amp gain calculator
Closed-loop gain and output voltage for the four basic op amp circuits, with a warning when the output would hit a supply rail.
Gain, V/V (inverting)
-10
- Gain in dB
- 20 dB
- Output for V1
- -5 V Ideal op amp. Real outputs stop short of the rails: check the output swing in the datasheet.
- Input resistance
- 10 kΩ R1, since the inverting input sits at virtual ground.
Method
How this is calculated
Inverting: G = −Rf / R1 Non-inverting: G = 1 + Rf / R1 Difference: Vout = (Rf / R1) · (V2 − V1) Summing: Vout = −Rf · ( V1/R1 + V2/R2 + V3/R3 ) Gain (dB) = 20 · lg |G|
- Ideal op amp
- Infinite open-loop gain and input impedance, zero output impedance. Real gain falls with frequency: check the closed-loop bandwidth against the gain-bandwidth product.
- Difference amplifier
- Assumes matched pairs: R1 on both inputs and Rf both as feedback and from the + input to ground. Mismatch between the pairs degrades common-mode rejection.
- Rails
- The warning fires when the ideal output is past a rail. Most op amps stop short of the rails, by an amount given in the datasheet as output swing.
Sources
- Texas Instruments SBOA092B, Handbook of Operational Amplifier Applications (Carter and Brown)Revision B, September 2016, pages 53, 54, 64 and 74
FAQ
Questions
−Rf/R1. With Rf = 100 kΩ and R1 = 10 kΩ the gain is −10 V/V, 20 dB, so 0.5 V in gives −5 V out. The input impedance is R1.
1 + Rf/R1. The same 100 kΩ and 10 kΩ give 11 V/V, 20.8 dB. A non-inverting stage cannot have a gain below 1.
With matched resistor pairs it outputs (Rf/R1)(V2 − V1). With 100 kΩ and 1 kΩ, a 50 mV difference becomes 5 V. Common-mode voltage is rejected as long as the pairs match.
The op amp cannot drive past its supply. A 12 V rail and a gain of 10 clip any input above 1.2 V, and most parts clip earlier than the rail itself.
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