All-Pass Filter Calculator
Design 1st- or 2nd-order all-pass filters for phase shaping. Output magnitude is flat; phase varies with frequency. Used for audio time-delay, PLLs, and group-delay equalization.
How to Use
- Enter center frequency f₀ (where phase = ±90° for 1st-order, ±180° for 2nd-order).
- Pick 1st or 2nd order; enter Q for 2nd-order.
- Result: R and C values; phase delay at f₀.
Show Work
Formulas
History
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.
About This Calculator
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.
About the All-Pass Filter Calculator
Working on electronics and circuit design? The All-Pass Filter Calculator is a free browser tool that gives you the answer in seconds. Design 1st- or 2nd-order all-pass filters for phase shaping. Output magnitude is flat; phase varies with frequency. Used for audio time-delay, PLLs, and group-delay equalization.
How it works
Put each value in its box and read the answer as you go. Because it recalculates live, you can play with the inputs to see how each one moves the result — handy for checking your own working or planning ahead. Everything happens on your device, so it is fast and private.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
What does all-pass do?
Passes all frequencies with the same magnitude (|H| = 1) but shifts their phase in a frequency-dependent way. Used to equalize group delay, implement audio time-delay, and shape phase in PLLs.
1st vs 2nd order?
1st order: phase goes 0° → -180° (lag) or 0° → +180° (lead). 2nd order: phase wraps 0° → -360°, with a center-frequency transition sharpness controlled by Q.
Why use?
Stereo phasers in audio, FM modulators, group-delay equalization in filter cascades. Also as a pair of 90°-offset all-passes for Hilbert-transform IQ signal generation.
How do I use the All-Pass Filter Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Audio Phaser Effect
4-stage 1st-order all-pass cascade with modulated R creates classic phaser sweep.
Hilbert Transform
Pair of wide-band all-passes 90° apart generates in-phase / quadrature channels.
Group Delay Equalizer
Compensate for Bessel filter's non-linear phase to recover flat group delay.
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