Sallen-Key filter cutoff calculator
fc = 1 ÷ (2π·√(R1·R2·C1·C2)). Design a unity-gain Sallen-Key 2nd-order low-pass or high-pass — Butterworth, Bessel or Chebyshev — in equal-R or equal-C form, or analyze an existing component set for its fc and Q.
Frequently asked questions
How is the cutoff frequency of a Sallen-Key filter calculated?
The calculator uses fc = 1 ÷ (2π·√(R1·R2·C1·C2)) for the unity-gain Sallen-Key. With its default design of R1 = R2 = 10 kΩ, C1 = 10 nF and the Butterworth Q of 0.7071 (which sets C2 = 20 nF), that gives fc = 1 ÷ (2π × 10⁴ × √(10⁻⁸ × 2×10⁻⁸)) ≈ 1125 Hz, and the section rolls off at −40 dB per decade beyond it.
What does Q mean in a Sallen-Key filter?
Q is the quality factor of the pole pair: it sets the peaking at the corner and the damping. For the default equal-R design the tool picks C2 = 4·Q²·C1, so Butterworth (Q = 0.7071) gives C2 = 2·C1 — a 10 nF C1 becomes 20 nF C2. Bessel uses Q = 0.5774 (C2 = 1.33·C1) for linear phase, and Chebyshev uses Q = 0.8638 or 0.9565 for a steeper transition with passband ripple. The damping ratio follows as ζ = 1 ÷ (2Q).
What is the difference between the equal-R and equal-C design modes?
Equal-R fixes R1 = R2 and computes C2 = 4·Q²·C1 from a C1 you pick — the fastest way to a Butterworth response. Equal-C fixes C1 = C2 and solves the two resistor roots from R1·R2 = 1 ÷ (2π·fc·C)² and R1 + R2 = √(R1·R2) ÷ Q, which is the mode to use when a target cutoff matters more than the component values. High-pass design swaps the R and C roles: with equal elements the high-pass Q is limited to 0.5, so use the equal-C mode for the Bessel or Chebyshev presets.
Worked example
Build a Butterworth low-pass with R1 = R2 = 10 kΩ and C1 = 10 nF: the response preset sets C2 = 4 × 0.7071² × 10 nF = 20 nF, and the cutoff lands at fc = 1 ÷ (2π × 10⁴ × √(10⁻⁸ × 2×10⁻⁸)) ≈ 1125 Hz. A 1 kHz signal passes with negligible loss while a 100 kHz signal is attenuated by roughly 40·log₁₀(100/1.125) ≈ 78 dB — two decades of −40 dB/decade roll-off. Swap the R/C roles to make the same filter high-pass.
Ideal-op-amp Sallen-Key model with an infinite-gain assumption; real op-amps add bandwidth and slew-rate limits. ICBOMS provides this tool for reference only.