LC Filter Cutoff Frequency

fc = 1 / (2π × √(L × C))

Quick answer

This calculator solves fc = 1 / (2π × √(L × C)) for Cutoff Frequency. With Inductance 100 µH, Capacitance 100 µF, the result is 1.592 kHz. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Cutoff Frequency (kHz)
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Formula

fc = 1 / (2π × √(L × C))

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.

Symbols and units

Symbol Meaning Default unit Accepted units
fc Cutoff Frequency kHz Hz, kHz, MHz, GHz
L Inductance µH nH, µH, mH, H
C Capacitance µF pF, nF, µF, mF, F

Step by step

  1. 1. What you know: Inductance 100 µH, Capacitance 100 µF
  2. 2. The relation: fc = 1 / (2π × √(L × C))
  3. 3. Substitute: L = 100 µH, C = 100 µF
  4. 4. Result: Cutoff Frequency = 1.592 kHz

Worked examples

Minimum range

Given: Inductance 100 nH, Capacitance 100 nF

Result: Cutoff Frequency = 1.592 MHz

Low range

Given: Inductance 1 µH, Capacitance 1 µF

Result: Cutoff Frequency = 0.1592 MHz

Typical

Given: Inductance 100 µH, Capacitance 100 µF

Result: Cutoff Frequency = 1.592 kHz

High range

Given: Inductance 0.47 mH, Capacitance 1 mF

Result: Cutoff Frequency = 0.2322 kHz

Maximum range

Given: Inductance 4.7 mH, Capacitance 10 mF

Result: Cutoff Frequency = 23.22 Hz

Solving for each variable

Solve for Cutoff Frequency

Inductance 100 nH, Capacitance 100 nF → 1.592 MHz

Solve for Inductance

Cutoff Frequency 100 Hz, Capacitance 100 nF → 25.33 H

Solve for Capacitance

Cutoff Frequency 100 Hz, Inductance 100 nH → 25.33 F

How Cutoff Frequency changes with Inductance

Inductance (input) Cutoff Frequency (result)
10 µH 5.033 kHz
25 µH 3.183 kHz
50 µH 2.251 kHz
75 µH 1.838 kHz
100 µH 1.592 kHz
150 µH 1.299 kHz
0.2 mH 1.125 kHz
0.4 mH 0.7958 kHz
0.7 mH 0.6015 kHz
1 mH 0.5033 kHz

The same result in other units

Unit Value
Hz 1592
kHz 1.592
MHz 0.001592

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Frequently asked questions

How do you calculate LC Filter Cutoff Frequency?

Use fc = 1 / (2π × √(L × C)). With Inductance 100 µH, Capacitance 100 µF, Cutoff Frequency works out to 1.592 kHz.

What is the formula for LC Filter Cutoff Frequency?

The formula is fc = 1 / (2π × √(L × C)). The LC filter is a second-order filter with a cutoff frequency determined by the inductance and capacitance values.

How do you find Inductance when you know the other values?

Rearrange for Inductance: with Cutoff Frequency 100 Hz, Capacitance 100 nF, Inductance is 25.33 H.

How do you find Capacitance when you know the other values?

Rearrange for Capacitance: with Cutoff Frequency 100 Hz, Inductance 100 nH, Capacitance is 25.33 F.

What units does LC Filter Cutoff Frequency use?

Cutoff Frequency is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Filters formulas →
RC Low-Pass Filter RC High-Pass Filter Bandpass Bandwidth Filter Rolloff Rate Notch Frequency Butterworth Q Factor Sallen-Key Cutoff Frequency Chebyshev Filter Order

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