Filter Design Calculator (Butterworth, Chebyshev)

An authoritative filter design calculator for Butterworth and Chebyshev filters, optimized for electrical engineering applications.

Inputs

How to use

Select the filter family, provide the cut-off frequency and order, and optionally adjust ripple for Chebyshev filters. Click Calculate or rely on the debounced inputs to evaluate the normalized response at twice the corner frequency.

Methodology

For Butterworth filters we compute |H(ω)| = 1/√(1 + (ω/ωc)^{2n}). For Chebyshev filters we use the Chebyshev polynomial evaluated at ω/ωc = 2 with ripple ε derived from the requested passband ripple in dB.

  • Normalized evaluation frequency is set to twice the cut-off to expose variation with order.
  • Chebyshev epsilon = √(10^{ripple/10} − 1); use ripple >0 only for Chebyshev measurements.
  • Outputs show both linear magnitude and decibel attenuation.

Full original guide (expanded)

This calculator aligns with IEEE standards for filter design and targets engineers designing Butterworth or Chebyshev filters.

Original explanatory content included the transfer function:

H(s) = 1 / √(1 + ε² (ω/ωc)^{2n})

Glossary

  • Cut-off Frequency: Frequency where the filter starts attenuating.
  • Filter Order: Determines how steeply the filter transitions.
  • Ripple: Chebyshev passband variation in dB.

FAQ

What is a Butterworth filter?

It is a maximally flat filter in the passband.

How do I choose the filter order?

Higher orders give steeper attenuation but at the cost of complexity.

Formulas

Butterworth: |H(ω)| = 1 / √(1 + (ω/ωc)^{2n})

Chebyshev: |H(ω)| = 1 / √(1 + ε² · T_n(ω/ωc)²)

  • T_n(x) = cosh(n · arcosh(x)) for x ≥ 1.
  • ε = √(10^{ripple/10} − 1)
Citations

NIST weights and measures: https://www.nist.gov/pml/weights-and-measures

FTC consumer advice: https://consumer.ftc.gov/

Changelog
  • 0.1.0-draft — 2026-01-19: Initial audit spec draft (review required).
  • Rebuilt calculation with Butterworth/Chebyshev response logic.
  • Added optional ripple input for Chebyshev formulas.
Verified by Ugo Candido
Last Updated: 2026-01-19
Version 0.1.0-draft