LC Filter Design Calculator (Bode Plot)
Design Low-pass, High-pass, and Band-pass LC filters. Calculates L and C values for Butterworth/Chebyshev topologies and generates an instant frequency response graph.
About
In RF and audio circuit design, separating desired signals from noise requires precise filtering. A simple RC filter often lacks the steep attenuation ("rolloff") needed for tight spectrum management. LC filters, using inductors and capacitors, provide superior performance with minimal resistive loss. This tool aids in synthesizing 2nd-order passive filters, critical for power supplies (ripple rejection) and radio transmitters (harmonic suppression).
The calculator not only outputs the theoretical component values based on the cutoff frequency (fc) and system impedance (Z0), but also visualizes the magnitude response. Seeing the curve is vital to understand the trade-offs: the flat passband of a Butterworth filter versus the steeper descent but rippled passband of a Chebyshev filter. It assumes ideal components, so real-world implementation should account for inductor DC resistance (DCR).
Formulas
For a standard 2nd-order Butterworth Low Pass filter, the component values for a given impedance Z0 and cutoff frequency fc are:
The resonant frequency is defined as f0 = 1 / (2π√LC).
Reference Data
| Filter Type | Optimized For | Phase Response | Transient Response |
|---|---|---|---|
| Butterworth | Max Flatness (Passband) | Moderate Non-linearity | Moderate Overshoot |
| Chebyshev | Steep Rolloff | Non-linear | High Ringing |
| Bessel | Linear Phase (Time Delay) | Linear (Constant Delay) | Min Overshoot |
| Elliptic | Max Steepness | Highly Non-linear | Severe Ringing |
| Order (n=2) | -12 dB/octave | -180° Shift | Standard LC Section |
| Order (n=3) | -18 dB/octave | -270° Shift | T or Pi Section |
| Low Pass | Passes f < fc | Lagging | Integrator-like |
| High Pass | Passes f > fc | Leading | Differentiator-like |