Op-Amp Differentiator
Ideal differentiator
Enter input amplitude, frequency, C and R; output amplitude and phase appear live with a waveform.
Differentiator output
How to use this calculator
An ideal op-amp differentiator has a capacitor at the input and a resistor in the feedback path. For a sinusoidal input Vs·sin(2πft), the output is Vout = 2πf·R·C·Vs·sin(2πft) — the amplitude grows with frequency and the output is in phase with the input. Enter the input amplitude, frequency, C and R, and the calculator shows the output amplitude, phase, and a live plot of both waveforms.
What it means in a real circuit
For Vs = 1 V, f = 1 kHz, C = 100 nF, R = 10 kΩ, the output amplitude is 2π×1000×1e-7×10000 ≈ 6.28 V and is in phase with the input. The differentiator is used for edge detection, slope measurement, and as part of active filters. In practice, a real differentiator amplifies high-frequency noise aggressively, so a small resistor is placed in series with the input capacitor to limit the high-frequency gain — the ideal model shown here assumes that noise limiting is handled elsewhere. Use this to size C and R for a target output amplitude at a given frequency, or to check that the output won't clip at high frequencies.