What is the difference between Butterworth and Chebyshev filters?

Butterworth filters have a maximally flat passband with no ripple but a slower roll-off. Chebyshev Type I filters allow a specified ripple in the passband, which gives a steeper transition from passband to stopband for the same order. Use Butterworth for flat response and Chebyshev when you need sharper attenuation and can tolerate ripple.

Which filter order should I choose?

Higher order filters have steeper roll-off and better stopband attenuation but require more components and are more sensitive to tolerances. Orders 3–5 are common for many audio and RF applications. Start with a lower order and increase only if your attenuation requirements are not met.

Can I use this calculator for active filters?

Yes. The normalized Butterworth and Chebyshev prototypes are the same starting point for many active filter topologies (such as Sallen–Key or multiple feedback). You can use the normalized g-values and frequency scaling to derive resistor and capacitor values for active implementations.

How accurate are the component values?

The calculator uses standard closed-form equations for normalized Butterworth and Chebyshev prototypes and ideal frequency and impedance scaling. Real-world performance will depend on component tolerances, parasitics, and layout. Always simulate and, if possible, prototype and measure your design.

Filter Design Calculator (Butterworth & Chebyshev)

Q: What does this filter design calculator do?

The calculator designs analog LC filters using Butterworth or Chebyshev prototypes. You enter the filter type, order, cutoff or center frequency, passband ripple, and source/load impedance. It returns normalized prototype g-values, scaled inductor and capacitor values, and an approximate magnitude response plot.

Design analog LC low‑pass, high‑pass, band‑pass, and band‑stop filters from specs. Get normalized prototype values, scaled L/C components, and an approximate magnitude response.

Butterworth Chebyshev Type I LC prototype

Filter design tool

Filter type

Approximation

Filter order (N)

Higher order → steeper roll‑off, more components. Supported: 1–10.

Cutoff / corner frequency

For low‑pass / high‑pass: 3 dB cutoff frequency \( f_c \).

Passband ripple (Chebyshev only)

Set to 0.5–1 dB for typical Chebyshev filters. Ignored for Butterworth.

Source impedance \( R_S \)

Load impedance \( R_L \)

Topology

All topologies are derived from the same normalized prototype.

Summary

Order: –
Cutoff / center: –
Approximation: –
Impedance: –

Component values

First, the normalized low‑pass prototype is computed, then scaled to your target frequency and impedance. For band‑pass / band‑stop, each element becomes a resonant L–C branch.

Normalized prototype (low‑pass) Cutoff \( \omega_c = 1 \), \( R_0 = 1 \,\Omega \)

Element	Type	g_k

Scaled components Ideal L / C values

Element	Connection	Component	Value

Approximate magnitude response

Log‑magnitude response \(|H(j\omega)|\) of the normalized prototype, plotted vs. normalized frequency \( \Omega = \omega / \omega_c \). This helps visualize passband ripple and roll‑off.

For band‑pass / band‑stop filters, the plot is still for the underlying low‑pass prototype.

How this filter design calculator works

This tool designs classical analog LC filters using normalized low‑pass prototypes. It supports Butterworth (maximally flat) and Chebyshev Type I (equiripple) responses and generates component values for low‑pass, high‑pass, band‑pass, and band‑stop filters.

1. Normalized low‑pass prototype

The starting point is a normalized low‑pass ladder network with cutoff angular frequency \( \omega_c = 1 \,\text{rad/s} \) and reference impedance \( R_0 = 1\,\Omega \). It is described by a sequence of prototype values \( g_0, g_1, \dots, g_{N+1} \).

For a Butterworth filter of order \( N \), the prototype values are:

\[ g_k = 2 \sin\left(\frac{(2k - 1)\pi}{2N}\right), \quad k = 1, 2, \dots, N \]

\[ g_0 = 1, \quad g_{N+1} = 1 \]

For a Chebyshev Type I filter with passband ripple \( \epsilon \) (related to ripple in dB), the prototype values are computed from the standard recursive formulas involving hyperbolic functions. The calculator derives \( \epsilon \) from your ripple setting:

\[ A_\text{ripple} = \text{ripple\_dB}, \quad \epsilon = \sqrt{10^{A_\text{ripple}/10} - 1} \]

2. Frequency and impedance scaling

Once the normalized prototype is known, it is scaled to your desired cutoff (or band edges) and impedance level. For a low‑pass filter with cutoff frequency \( f_c \) and reference impedance \( R_0 \), the angular cutoff is \( \omega_c = 2\pi f_c \).

For a low‑pass ladder with alternating series inductors and shunt capacitors:

Series inductors:

\[ L_k = \frac{R_0 \, g_k}{\omega_c} \]

Shunt capacitors:

\[ C_k = \frac{g_k}{R_0 \, \omega_c} \]

High‑pass, band‑pass, and band‑stop filters are obtained by standard low‑pass transformations (frequency inversion or band‑pass mapping). This calculator focuses on giving you the equivalent L/C values for each element.

3. Magnitude response

The magnitude response of a normalized Butterworth low‑pass filter of order \( N \) is:

\[ |H(j\Omega)| = \frac{1}{\sqrt{1 + \Omega^{2N}}} \]

For a Chebyshev Type I filter:

\[ |H(j\Omega)| = \frac{1}{\sqrt{1 + \epsilon^2 C_N^2(\Omega)}} \]

where \( C_N(\Omega) \) is the Chebyshev polynomial of the first kind of order \( N \).

The plot in this tool shows the log‑magnitude in dB vs. normalized frequency \( \Omega = \omega / \omega_c \) for the prototype, which you can map to your actual frequency axis using your chosen cutoff.

Design tips

Choose Butterworth when you need a flat passband (e.g., audio).
Choose Chebyshev when you need sharper roll‑off and can tolerate ripple.
Match source and load (e.g., 50 Ω) for best performance and minimal reflections.
Simulate your design (e.g., SPICE) to verify performance with real‑world component tolerances and parasitics.

FAQ

What does this filter design calculator do?

It computes normalized Butterworth or Chebyshev Type I low‑pass prototypes from your chosen order and ripple, then scales them to your desired cutoff frequency and impedance. It outputs the prototype g‑values, ideal inductor and capacitor values, and an approximate magnitude response plot.

Can I export the results to use in SPICE?

Yes. Copy the component table and translate each element into your simulator’s syntax (e.g., L1, C1, etc.). The ladder order in the table follows the signal path from source to load.

Does this account for parasitics or component tolerances?

No. The calculator assumes ideal components. In practice, parasitic inductance, stray capacitance, ESR, and tolerance will slightly detune the filter. Always simulate and, if possible, measure a prototype.

Can I use this for active filters?

Yes. Many active filter topologies start from the same normalized Butterworth or Chebyshev prototypes. Use the normalized g‑values and frequency scaling to derive resistor and capacitor values for Sallen–Key, multiple‑feedback, or state‑variable filters.