Engineering Reference
Common Op-Amp Configurations Formula Reference
Compact op-amp topology formulas for non-inverting, inverting, differential, summing, instrumentation, integrator and differentiator circuits with ideal-model boundaries.
Configuration Formula Table
| Configuration | Ideal relationship | Polarity | Input behavior | Boundary |
|---|---|---|---|---|
| Non-inverting amplifier | Vout/Vin = 1 + Rf/Rg | 0° | Very high ideal input impedance | Noise gain equals signal gain |
| Inverting amplifier | Vout/Vin = −Rf/Rin | 180° | Approximately Rin | Noise gain = 1 + Rf/Rin |
| Voltage follower | Vout = Vin | 0° | Very high ideal input impedance | Requires unity-gain stability |
| Difference amplifier | Vout = (R2/R1)(V2−V1), matched ratios | Difference polarity | Set by network | CMRR depends on ratio matching |
| Inverting summer | Vout = −Rf Σ(Vi/Ri) | Inverting | Each input sees Ri | Each weight is −Rf/Ri |
| Three-op-amp instrumentation amplifier | G = 1 + 2R/Rg (adopted model) | Difference polarity | High input impedance | Integrated-device equations vary |
| Ideal integrator | Vout/Vin = −1/(sRC) | Frequency dependent | Input ≈ R | Practical circuits limit DC and HF response |
| Ideal differentiator | Vout/Vin = −sRC | Frequency dependent | Frequency dependent | Practical circuits band-limit noise gain |
| Dominant-pole bandwidth | fCL ≈ GBW / noise gain | — | — | Approximation, not universal |
Bandwidth Check
10 MHz GBW with noise gain 10 gives approximately 1 MHz.
Slew-Rate Check
5 V peak at 100 kHz requires about 3.142 V/µs before margin.
Ideal-Model Boundary
Assumes negative feedback, valid common-mode range, unsaturated output, sufficient open-loop gain and stable loading. Verify tolerance, offset, noise, GBW, slew rate, phase margin, current and thermal limits.
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Calculate ideal non-inverting op-amp closed-loop gain from feedback and ground resistor values, including gain in V/V and dB.
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Calculate ideal inverting op-amp closed-loop gain from input and feedback resistor values, including gain magnitude, dB, and phase shift.
Differential Amplifier Calculator
Calculate ideal differential amplifier gain and output voltage from V1, V2, R1, and R2 for matched four-resistor op-amp circuits.
Summing Amplifier Calculator
Calculate ideal two-input inverting summing amplifier output voltage, input contributions, and weighted gains from resistor values.
Instrumentation Amplifier Calculator
Calculate ideal three-op-amp instrumentation amplifier gain, differential voltage, and output voltage from V+, V−, Rg, and internal resistor values.
Op-Amp Integrator & Differentiator Calculator
Calculate ideal op-amp integrator output, differentiator output, RC time constant, characteristic frequency, and transfer function summary.
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Calculate required op-amp gain-bandwidth product, maximum closed-loop bandwidth, maximum gain, and noise gain.
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Op-Amp Feedback, Gain, and Signal Conditioning Basics
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Design practical op-amp active filters, integrators, and differentiators while checking noise gain, gain-bandwidth product, slew rate, output swing, stability, and loading limits.
Related References
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FAQ
Why is non-inverting gain never below one?
Its ideal gain is 1 + Rf/Rg, with unity as the minimum.
Why is inverting gain negative?
Negative feedback drives the output in the opposite direction to hold the summing node near its reference.
What is noise gain?
It is the closed-loop gain seen by an equivalent input error source and governs first-order bandwidth and stability.
Why must difference-amplifier ratios match?
Mismatch converts common-mode voltage into output error.
Can a summing amplifier use different weights?
Yes. Each ideal contribution is weighted by −Rf/Ri.
Do all instrumentation amplifiers use the same gain formula?
No. The listed equation is for the adopted discrete model; integrated devices specify their own equation.
Why band-limit practical integrators and differentiators?
Added components control DC saturation, noise gain, stability and high-frequency response.
Does GBW/noise gain guarantee usable bandwidth?
No. Slew rate, phase margin, loading and output limits can be tighter.