All-Pass Filter Calculator

The all-pass filter concept dates to Hendrik Bode\'s 1945 monograph on feedback-amplifier design. Bode showed that any linear filter\'s magnitude and phase responses are related (Hilbert transform), and that "all-pass" networks — which shift phase while leaving magnitude flat — serve as building blocks for phase compensation and group-delay equalization.

Audio phaser effects (Mu-Tron Bi-Phase, Electro-Harmonix Small Stone) became cultural icons of 1970s funk and prog rock — fundamentally just 4-6 first-order all-passes with LFO-modulated R values creating a sweeping phase-shift signature. The same topology later appeared in digital form in every guitar pedal since the 1990s.

Modern DSP implements all-pass filters as z-domain biquads with specific coefficient symmetry. They remain central to spatial audio processing (reverb, Haas-effect stereo widening), SDR IQ generation, and FIR filter group-delay compensation.

Enter the center frequency f₀ where the phase crosses ±90° (1st order) or ±180° (2nd order). For 2nd-order, enter Q to set the transition sharpness. The tool solves for R (given C) and reports the group delay at f₀.

Topology: 1st-order = op-amp non-inverting input with RC network on non-inv, resistor to inv, feedback R to inv. 2nd-order = similar but with two RC stages. Gain is always exactly 1 across all frequencies — only phase changes. Everything runs client-side.