Butterworth LC Low-Pass Filter Calculator (Coil and Capacitor Values)

What this tool does

A Butterworth filter is the flattest one possible in the pass band, and its element values come from a simple rule: g_k = 2 sin((2k − 1)π ÷ 2n). Each value is then scaled to the cut-off frequency and the impedance: C = g ÷ (2π f_c R) for capacitors and L = g R ÷ (2π f_c) for coils. The attenuation grows by about 6 dB per octave for each order, so a 5th-order filter at twice the cut-off frequency is already 30 dB down. Real parts have tolerances and the coils have resistance, so expect the corner to land a little off.

Formula

g_k = 2 sin((2k − 1)π ÷ 2n) · C = g ÷ (2π f_c R) · L = g R ÷ (2π f_c) · attenuation = 10 log₁₀(1 + (f ÷ f_c)^2n)

Variables

Worked example

Limitations

• Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.
• The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.