What is the formula for Sallen-Key Low-Pass Filter Designer?

Core formula: f_c = 1/(2πR√(C1·C2)) ｜ Q = ½·√(C1/C2) with R1 = R2 = R. The tool returns results instantly using this formula and the selected parameters.

Sallen-Key Low-Pass Filter Designer

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Single op-amp second-order Sallen-Key low-pass: given cutoff and Q, get standard R/C values, the real fc/Q, peaking and a Bode plot.

Key points

Sallen-Key Low-Pass Filter Designer: Single op-amp second-order Sallen-Key low-pass: given cutoff and Q, get standard R/C values, the real fc/Q, peaking and a Bode plot. Formula: f_c = 1/(2πR√(C1·C2)) ｜ Q = ½·√(C1/C2) with R1 = R2 = R. Enter parameters on the DD-CAT IDE online tool page to get results instantly, with a calculation-model diagram that updates with the inputs. In unity-gain Sallen-Key, Q depends only on the C1/C2 ratio, and R1 = R2 keeps offset and common-mode behaviour predictable. Use C0G or film for C1 — X7R voltage coefficient makes the cut-off drift with signal amplitude.

Inputs

f_c = 1/(2πR√(C1·C2)) ｜ Q = ½·√(C1/C2) with R1 = R2 = R

Calculation model (updates with parameters)

Bode plot (magnitude / phase, updates with parameters)

R1 = R2	10.7 kΩ
C1 (op-amp + input to ground)	22 nF
C2 (input to + input)	10 nF
Actual cut-off f_c	1.003 kHz	target 1 kHz，偏差 0.28%
Actual Q	0.742	target 0.707
Peaking	+0.04 dB	Q > 0.707 lifts the response near f_c
Minimum op-amp GBW	74.37 kHz	Rule of thumb ≥100×f_c·Q, otherwise the roll-off slackens

Engineering notes

In unity-gain Sallen-Key, Q depends only on the C1/C2 ratio, and R1 = R2 keeps offset and common-mode behaviour predictable.
Use C0G or film for C1 — X7R voltage coefficient makes the cut-off drift with signal amplitude.

FAQ

What is Sallen-Key Low-Pass Filter Designer for?: Single op-amp second-order Sallen-Key low-pass: given cutoff and Q, get standard R/C values, the real fc/Q, peaking and a Bode plot.
What is the formula for Sallen-Key Low-Pass Filter Designer?: Core formula: f_c = 1/(2πR√(C1·C2)) ｜ Q = ½·√(C1/C2) with R1 = R2 = R. The tool returns results instantly using this formula and the selected parameters.
What engineering notes should I keep in mind when using Sallen-Key Low-Pass Filter Designer?: In unity-gain Sallen-Key, Q depends only on the C1/C2 ratio, and R1 = R2 keeps offset and common-mode behaviour predictable. Use C0G or film for C1 — X7R voltage coefficient makes the cut-off drift with signal amplitude.