Figure 1: An LC filter combines inductor and capacitor for a second-order response with −40 dB/decade roll-off — twice as sharp as RC or RL. No resistor means no power loss (ideal), but real components have parasitic resistance.
Table of Contents
What Is an LC Filter?
An LC filter combines an inductor and capacitor for a second-order frequency response with −40 dB/decade roll-off — twice as sharp as first-order RC or RL filters. The cutoff frequency is fc = 1/(2π√LC). Because there is no resistor in the ideal circuit, LC filters have theoretically zero power loss in the passband.
LC filters are the workhorses of RF circuits, power supply output stages, speaker crossovers, and any application requiring sharp frequency selectivity. The Filter Cutoff Frequency Calculator compares RC, RL and LC side by side.
The Formula
Second-order response: −40 dB/decade roll-off
At resonance: XL = XC, impedance is minimum (series) or maximum (parallel)
Worked Example — Power Supply Output
fc = 1/(2π√(0.01 × 1×10−6)) = 1592 Hz
Switching power supplies typically switch at 50–500 kHz, well above this fc, so the LC filter heavily attenuates the switching noise. The Butterworth Filter Calculator can optimise the response flatness.
Worked Example — RF Bandpass
fc = 1/(2π√(250×10−6 × 100×10−12)) = 1.007 MHz
This is in the AM broadcast band — a tuned LC circuit can select a single station. The Band Pass Filter Calculator analyses the bandwidth and Q factor of such circuits.
Worked Example — Speaker Crossover
fc = 1/(2π√(0.001 × 10×10−6)) = 1592 Hz
Damping and Ringing
Without damping resistance, an LC filter rings at its resonant frequency. The Q factor determines how much ringing occurs. Adding a small series resistance lowers Q and reduces ringing at the cost of passband loss. The High Pass Filter Calculator shows how component arrangement changes the response from low-pass to high-pass.
Practical Considerations
Real inductors have parasitic resistance (DCR) and capacitance (SRF). Real capacitors have equivalent series resistance (ESR) and inductance (ESL). These parasitics limit filter performance at extreme frequencies. For critical applications, use the Active Filter Calculator to design op-amp-based filters that avoid inductor limitations entirely.
Resonant Frequency Calculator: The Resonant Frequency Calculator analyses the resonance point of LC circuits, which determines cutoff frequency and Q factor.
Frequently Asked Questions
What does first-order vs second-order mean?
Can I use this for audio applications?
What is the phase shift at cutoff?
How do I make a bandpass filter?
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