What it does
A filter lets some frequencies through and cuts others. This designer works out the parts for the classic analog filters:
- Butterworth: the flattest possible passband, −3 dB at the corner.
- Chebyshev (type I): a steeper cut for the same order, in return for a small ripple in the passband. The corner is where the ripple band ends.
- Low-pass or high-pass, of order 1 to 12. Each order adds 20 dB per decade of cut far from the corner.
You can build it as Sallen-Key active stages (one op-amp per two orders, unity gain), a passive LC ladder between equal source and load resistances, or a single RC or RL for a simple first-order filter. Every part is listed exactly and rounded to standard E-series values, and the Bode plot shows both, so you can see whether rounding matters.
How to use it
- Choose low-pass or high-pass and how to build it.
- Pick the shape, the order and the corner frequency (use k for kilohertz: 1k, 4.7k).
- For Sallen-Key, choose a capacitor value you have (10n is a good start for audio); the resistors follow. For an LC ladder, give the source and load resistance (50 Ω for RF, 8 Ω for a speaker).
- Not sure of the order? Open What order do I need?, type the cut you want at some frequency, and press Use this order.
- For passive designs, copy the netlist into the circuit simulator to check it with your own source and load.
Worked example
The page opens on a fourth-order Butterworth low-pass at 1 kHz built from Sallen-Key stages with C = 10 nF. The two stages both have f0 = 1 kHz, with Q = 0.541 and Q = 1.307. For the first stage, C2 = 10 nF, C1 = 4Q²C = 11.72 nF and both resistors are 1/(2Q × 2π × 1 kHz × 10 nF) = 14.7 kΩ. The response is −3 dB at 1 kHz, −24.1 dB at 2 kHz and −80 dB at 10 kHz. Asking for 40 dB at 3 kHz says order 5 is needed.
Tips
- High-Q stages are sensitive to part tolerance; a Chebyshev with large ripple and high order has very high Q stages.
- Even-order Chebyshev Sallen-Key designs start at 0 dB and ripple up to the ripple value; even-order Chebyshev LC ladders need a load resistance different from the source, which the tool works out.
- For an op-amp stage, pick one whose gain-bandwidth is at least 100 × f0 × Q.
FAQ
Why is the LC ladder’s gain −6 dB? The source and load resistances form a 2 : 1 divider. The plot shows the response relative to that.
Can I make a band-pass? Put a high-pass and a low-pass in series when the band is wide. Narrow band-pass designs need a different method.
Are the formulas exact? For ideal parts, yes. Real op-amps, inductor resistance and capacitor tolerance change the response. For study and planning, not a substitute for professional judgement.
Where the numbers come from
- Butterworth and Chebyshev type I pole formulas, the minimum-order formulas, and doubly terminated ladder g-values (Matthaei, Young and Jones, Microwave Filters, Impedance-Matching Networks and Coupling Structures, 1964; equations only, the values are computed).
- Unity-gain Sallen-Key low-pass and high-pass transfer functions derived from nodal analysis (Sallen and Key, 1955), with the common equal-resistor and equal-capacitor choices.
- Checked against SciPy signal.butter, signal.cheby1 (analog), signal.freqs, buttord and cheb1ord; the LC ladders were simulated with the fibub circuit simulator. Example values are made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.