Multi-Feedback (MFB) Bandpass Filter Calculator

The Multi-Feedback (MFB) topology was developed in the 1960s at Motorola\'s analog-IC design group as a refinement of earlier single-feedback active filters. Unlike Sallen-Key (positive feedback), MFB uses two feedback paths — one via R2 and C2 to the op-amp\'s inverting input, another via C1. This dual-feedback structure produces an inverting output with well-behaved phase response and much higher stable Q than Sallen-Key bandpass.

MFB dominated DTMF decoder chips in the 1970s-80s — the M-957, MT8870, and TCM1520 all used cascaded MFB BP filters tuned to the 7 DTMF tones (697, 770, 852, 941, 1209, 1336, 1477 Hz). Each filter had Q ≈ 10 with tight center-frequency tolerance — achievable with MFB\'s low component-value sensitivity.

Modern CODECs use digital filtering instead, but MFB remains the textbook choice for any medium-Q bandpass between 10 Hz and 100 kHz, and the first-pass topology for analog spectrum-analyzer filter banks and audio-grade parametric EQ.

Enter center frequency f₀, Q (10-20 typical for narrow band, 1-3 for wider), midband gain magnitude |G| (typically 1-10; output is inverted so actual sign is negative), and capacitor value C. The tool solves R1, R2, R3 such that the three design equations hold simultaneously. Round to standard E24/E96 values.

Important constraint: G < 2Q². If you violate this, R3 would need to be negative (not realizable) — either reduce gain or increase Q. For high-Q filters, use TempCo-matched metal-film resistors and COG/NP0 capacitors; electrolytic and X7R caps drift too much. Everything runs client-side.