Sallen–Key low-pass calculator

Calculate a second-order active low-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	1.48 V/V
Gain	3.42 dB
Phase	-55.66 °

Advanced results

Q	0.71
Pass-band gain	1.59 V/V

How sallen–key low-pass works

R1 and R2 feed the non-inverting input. C1 feeds the output back to the resistor junction, while C2 connects the input node to ground. R3/R4 set the non-inverting gain. Natural frequency is not generally the −3 dB cutoff; they coincide for a Butterworth Q of 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: $a_1=C_2(R_1+R_2)+C_1R_1(1-K)$
$141\,\mathrm{\mu s}$
≈ 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: $|H(j2\pi f)|$
$f=1\,\mathrm{kHz}$
≈ 1.48 V/V

Sallen–Key low-pass calculator

Configure

Schematic

Results

How sallen–key low-pass works

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