Sallen–Key high-pass calculator

Calculate a second-order active high-pass response, natural frequency and Q.

Schematic

Try in CircuitSim

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Results

Natural frequency1.59 kHz

Frequency response

Gain

Frequency: 1 kHz

Gain at selected frequency	0.59 V/V
Gain	-4.66 dB
Phase	124.34 °

Advanced results

Q	0.71
Pass-band gain	1.59 V/V

How sallen–key high-pass works

C1 and C2 form the series signal path. R1 connects their junction to the output; R2 returns the non-inverting input to ground. R3/R4 set gain. Natural frequency and −3 dB cutoff are different unless Q is 1/√2.

f_0=\frac{1}{2\pi\sqrt{R_1R_2C_1C_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
R1	10 kΩ
R2	10 kΩ
C1	10 nF
C2	10 nF
R3	10 kΩ
R4	5.9 kΩ
V1	1 kHz

Op-amp gain: $K=1+R_4/R_3$
$1+\frac{5.9\,\mathrm{k\Omega}}{10\,\mathrm{k\Omega}}$
≈ 1.59 V/V
Natural frequency: $f_0=\frac{1}{2\pi\sqrt{R_1R_2C_1C_2}}$
$\frac{1}{2\pi\times100\,\mathrm{\mu s}}$
≈ 1.59 kHz
Damping coefficient: $a_1=R_1(C_1+C_2)+R_2C_2(1-K)$
$141\,\mathrm{\mu s}$
≈ 141 µs
Quality factor: $Q=\frac{\sqrt{R_1R_2C_1C_2}}{a_1}$
$\frac{100\,\mathrm{\mu s}}{141\,\mathrm{\mu s}}$
≈ 0.71
Gain at selected frequency: $|H(j2\pi f)|$
$f=1\,\mathrm{kHz}$
≈ 0.59 V/V

Sallen–Key high-pass calculator

Configure

Schematic

Results

How sallen–key high-pass works

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