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 |
| 1 | 2.0000 |
| 2 | 1.4142, 1.4142 |
| 3 | 1.0000, 2.0000, 1.0000 |
| 4 | 0.7654, 1.8478, 1.8478, 0.7654 |
| 5 | 0.6180, 1.6180, 2.0000, 1.6180, 0.6180 |
| 6 | 0.5176, 1.4142, 1.9319, 1.9319, 1.4142, 0.5176 |
| 7 | 0.4450, 1.2470, 1.8019, 2.0000, 1.8019, 1.2470, 0.4450 |
| 8 | 0.3902, 1.1111, 1.6629, 1.9616, 1.9616, 1.6629, 1.1111, 0.3902 |
| 9 | 0.3473, 1.0000, 1.5321, 1.8794, 2.0000, 1.8794, 1.5321, 1.0000, 0.3473 |
| 10 | 0.3129, 0.9080, 1.4142, 1.7820, 1.9754, 1.9754, 1.7820, 1.4142, 0.9080, 0.3129 |
Filter scaling equations:
\( C' = \left(\frac{R}{R'}\right)\left(\frac{w}{w'}\right)C \)
\( L' = \left(\frac{R'}{R}\right)\left(\frac{w}{w'}\right)L \)