LC Butterworth Filter Calculator

This calculator calculates the capacitor and inductor values for an LC Butterworth filter for a given order up to 10.

Here are the prototype Butterworth filter elements for various orders \(N\):

Prototype filters with cut off at \(1 \text{rad/sec}\) and resistor of \(1 \text{ohm}\):

Order \(N\)Elements
12.0000
21.4142, 1.4142
31.0000, 2.0000, 1.0000
40.7654, 1.8478, 1.8478, 0.7654
50.6180, 1.6180, 2.0000, 1.6180, 0.6180
60.5176, 1.4142, 1.9319, 1.9319, 1.4142, 0.5176
70.4450, 1.2470, 1.8019, 2.0000, 1.8019, 1.2470, 0.4450
80.3902, 1.1111, 1.6629, 1.9616, 1.9616, 1.6629, 1.1111, 0.3902
90.3473, 1.0000, 1.5321, 1.8794, 2.0000, 1.8794, 1.5321, 1.0000, 0.3473
100.3129, 0.9080, 1.4142, 1.7820, 1.9754, 1.9754, 1.7820, 1.4142, 0.9080, 0.3129

Filter scaling equations:

\( C' = \left(\frac{R}{R'}\right)\left(\frac{w}{w'}\right)C \)

\( L' = \left(\frac{R'}{R}\right)\left(\frac{w}{w'}\right)L \)