Practical differentiator calculator

Explore an op-amp differentiator with input and feedback bandwidth limits.

Schematic

Try in CircuitSim

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Results

Center frequency50.33 kHz

Frequency response

Gain

Frequency: 1 kHz

Gain at selected frequency	0.63 V/V
Gain	-4.05 dB
Phase	-93.96 °

Advanced results

Peak gain	9.09 V/V
Lower −3 dB frequency	13.44 kHz
Upper −3 dB frequency	188.51 kHz
−3 dB bandwidth	175.07 kHz

How practical differentiator works

C1 differentiates at low frequencies. R1 limits the input current and high-frequency gain. C2 in parallel with feedback resistor R2 adds a second roll-off, so the circuit does not amplify unlimited high-frequency noise.

H(s)=\frac{-sR_2C_1}{(1+sR_1C_1)(1+sR_2C_2)}

Ideal op-amp equations with ±15 V supplies. The simulated generic op amp has finite bandwidth and output limits. Keep signal levels within its linear range.

Change the form inputs or click a component value on the schematic. Choose Try in CircuitSim to simulate the configured circuit.

Do the math

Selected input values
C1	10 nF
R2	10 kΩ
R1	1 kΩ
C2	100 pF
V1	1 kHz

First RC corner: $f_1=1/(2\pi R_1C_1)$
$\frac{1}{2\pi\times10\,\mathrm{\mu s}}$
≈ 15.92 kHz
Second RC corner: $f_2=1/(2\pi R_2C_2)$
$\frac{1}{2\pi\times1\,\mathrm{\mu s}}$
≈ 159.15 kHz
Center frequency: $f_0=\sqrt{f_1f_2}$
$\sqrt{15.92\,\mathrm{kHz}\times159.15\,\mathrm{kHz}}$
≈ 50.33 kHz
Peak gain magnitude: $|H(f_0)|=|b_1|/a_1$
$\frac{100\,\mathrm{\mu s}}{11\,\mathrm{\mu s}}$
≈ 9.09 V/V
Gain at selected frequency: $|H(j2\pi f)|$
$f=1\,\mathrm{kHz}$
≈ 0.63 V/V

Practical differentiator calculator

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Schematic

Results

How practical differentiator works

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