Active filter designer — Butterworth, order 2–8
Higher-order low-pass and high-pass filters as cascaded Sallen-Key stages: pole Qs, standard-part values, and the response you'll actually get.
Achieved values (green) are recomputed from the snapped standard parts — what your filter will actually do. Cascade order matters in practice: lowest-Q stage first keeps internal signals from clipping before the output does.
The circuit this computes
Op-Amp Amplifier (non-inverting) — fully explained →How it works
An order-N Butterworth has pole pairs with Q_k = 1 / (2·sin((2k−1)π/2N)) — one Sallen-Key stage per pair, plus a plain RC for the real pole when N is odd. Each low-pass stage uses equal resistors: C1 = 4Q²·C2 and R = 1/(ω₀√(C1·C2)); high-pass mirrors it with equal capacitors and R2 = 4Q²·R1. Every stage shares the same ω₀ = 2πf_c — only Q differs. The calculator snaps each value to a standard E-series part, then recomputes the cutoff and Q those snapped parts actually deliver — the ideal you asked for and the filter you'll solder are rarely the same thing, and the gap is shown, not hidden.
Stages are listed lowest-Q first — build them in that order. High-Q stages peak near cutoff (up to Q× the input), so putting them last keeps intermediate op-amp outputs inside the rails.
Common questions
Because any filter polynomial factors into first- and second-order terms with real coefficients — an 8th-order response IS four biquads in a row, exactly. Nobody builds one giant 8th-order RC network: the cascade is mathematically identical, far less sensitive to component tolerances, and you can probe and debug it stage by stage.
Where the poles sit. Butterworth spaces them evenly on a semicircle, which makes the passband maximally flat — no ripple, moderate rolloff, well-behaved step response. Chebyshev trades passband ripple for a steeper edge; Bessel trades rolloff for flat group delay (clean pulses). Butterworth is the default for a reason: it's the no-surprises choice.
The unity-gain Sallen-Key realizes Q through a component RATIO: C1/C2 = 4Q² (low-pass) or R2/R1 = 4Q² (high-pass). Order 8's hottest stage has Q ≈ 2.56 — already a 26:1 capacitor spread — and the stage's actual Q rides on that ratio, so tolerance errors hit hardest exactly where the response peaks. If you need still-sharper filters, that's the cue for a different topology (MFB) or a gain-of-K stage, not bigger ratios.