Sallen-Key Low-Pass Filter Calculator

R.P. Sallen and E.L. Key at MIT Lincoln Laboratory published their active-filter topology in 1955 in a paper titled "A Practical Method of Designing RC Active Filters." The topology was designed for early analog computer simulations of missile-control systems — an application needing stable 2nd-order LP/HP/BP sections built from vacuum-tube op-amps.

The circuit proved ideal for the op-amp era. Its "unity gain" variant needs just two resistors, two capacitors, and one op-amp to make a clean 2nd-order filter with low sensitivity to component tolerance. Cascaded Sallen-Key stages implement Butterworth, Bessel, and Chebyshev filters of any order with predictable pole placement.

Modern switched-capacitor filter ICs (MAX7400, LTC1069) and digital biquads have displaced Sallen-Key for many applications, but the topology remains the textbook first example and the simplest on-the-breadboard active filter — built into every analog electronics course worldwide.

Enter cutoff frequency and either pick a filter-type preset (Butterworth, Bessel, Chebyshev) or enter custom Q. Enter a capacitor value C2; the tool computes required R (equal-R topology: R1=R2) and C1 = (2Q)²·C2. Round to standard E24 or E96 for build.

For filter orders > 2, cascade 2nd-order Sallen-Key sections with the Q values from standard filter tables. For 6th-order Butterworth: three sections with Q = 0.518, 0.707, 1.932. Use the Active Filter Order tool to compute required order for your stopband spec. Everything runs client-side.