LC Filter Cutoff Frequency

Formula

Description

The LC filter is a second-order filter with a cutoff frequency determined by the inductance and capacitance values. Unlike the first-order RC filter, the LC filter provides 40 dB/decade (12 dB/octave) rolloff and can have a resonant peak at the cutoff frequency if not properly damped. LC filters are widely used as output filters in switching power supplies, EMI filters, and audio crossover networks. The same formula applies to both low-pass and high-pass LC configurations — the topology (series or shunt element first) determines the filter type.

Variables

• fc — Cutoff frequency, −3 dB point (Hz)
• L — Inductance (H)
• C — Capacitance (F)

Practical Notes

An undamped LC filter has infinite Q at resonance, causing a sharp peak in the frequency response. Damping resistors, ESR, or load resistance provide the necessary damping. For a critically damped response (Q = 0.5), use R = 2×√(L/C). For a Butterworth response (Q = 0.707), use R = √(2L/C). In SMPS output filters, the load resistance typically provides sufficient damping, but light-load instability can occur if the Q is too high.