What it does
Op-amps are the building block of analog electronics. Pick one of six classic circuits, type the parts, and the calculator gives:
- Gain: −Rf/R1 (inverting), 1 + Rf/R1 (non-inverting), (Rf/R1)(V2 − V1) (difference), −Rf × ΣVi/Ri (summing), and the frequency-dependent gain of the integrator and differentiator.
- Bandwidth from the op-amp’s gain-bandwidth product (GBW): the closed-loop −3 dB frequency is about GBW divided by the noise gain 1/β, worked out exactly with a single-pole op-amp model.
- Output swing and clipping: the DC and sine output against the supply rails, the largest input that does not clip, and whether the slew rate can keep up.
- For the difference amplifier, the common-mode rejection caused by mismatched resistors.
The Bode plot compares the ideal circuit with your op-amp, and the waveform shows two periods of the input and the (clipped) output.
How to use it
- Choose the circuit; the help line under it says how it is wired.
- Type resistor values as 10k, 4k7 or 1M, and capacitors as 10n or 100p.
- Give the op-amp’s GBW and slew rate from its data sheet, the supply voltages, and how close the output gets to each rail.
- Give a DC input and a sine (peak and frequency) to see the output and check for clipping. For the summing amplifier type one DC value per input, comma separated.
Worked example
The page opens with an inverting amplifier, R1 = 10 kΩ and Rf = 100 kΩ: gain −10 (20 dB). The noise gain is 11, so with a 1 MHz op-amp the bandwidth is about 1 MHz ÷ 11 = 90.9 kHz. A 1 V peak sine at 1 kHz gives 10 V peak at the output (9.998 V with the real op-amp). On ±15 V supplies with a 1.5 V swing limit the output can reach ±13.5 V, so there is about 3.5 V to spare and the largest input before clipping is 1.35 V peak. The sine needs 0.0628 V/µs of slew rate against the 0.5 V/µs available; the full-power bandwidth at 10 V peak is 7.96 kHz.
Tips
- An inverting amplifier with gain −1 has a noise gain of 2, so it has half the bandwidth of a unity-gain buffer.
- A difference amplifier made from 1 % resistors may reject common-mode signals by only about 48 dB at gain 10. Use 0.1 % resistors or a matched network, or an instrumentation amplifier.
- A pure integrator has unlimited DC gain: any offset drives it to a rail. A large resistor across the capacitor fixes that.
FAQ
What does the model leave out? Input offset voltage, bias currents, noise, output current limits and the op-amp’s second pole. Check those on the data sheet. For study and planning, not a substitute for professional judgement.
Why does my differentiator ring? Its gain rises with frequency until it meets the op-amp’s falling gain, where the phase margin is small. A resistor in series with the capacitor limits the high-frequency gain.
Where the numbers come from
- Ideal op-amp circuit gains and the feedback-factor model of a single-pole op-amp, closed-loop gain G × Aβ/(1 + Aβ), as in electronics textbooks (for example Horowitz and Hill, The Art of Electronics; Franco, Design with Operational Amplifiers and Analog Integrated Circuits; equations only).
- Full-power bandwidth SR/(2πVpeak) and the difference-amplifier common-mode rejection formulas (standard results).
- Checked against python-control and an independent NumPy node-equation solve. The op-amp figures in the example (1 MHz, 0.5 V/µs) are made up, not from any data sheet.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.