How to use the LC Filter Calculator
An LC filter uses the frequency-dependent reactance of an inductor (X_L = ωL, which grows with frequency) and a capacitor (X_C = 1/(ωC), which shrinks with frequency) to shape a circuit's frequency response. Enter the inductance, capacitance, and the resistive load the filter drives to find the cutoff frequency, characteristic impedance, and the quality factor that describes how the response behaves near that cutoff.
Deriving the cutoff frequency
The corner (cutoff) frequency of an LC filter is the point where the inductive and capacitive reactances are equal in magnitude: ωL = 1/(ωC). Solving for ω gives the angular cutoff frequency ω_c = 1/√(LC), and dividing by 2π converts it to the more familiar cutoff frequency in hertz: f_c = 1/(2π√(LC)). For a series-L, shunt-C low-pass section — the most common LC filter topology, used at the output of switching power supplies and Class-D amplifiers — signals below f_c pass with little attenuation while signals above f_c roll off at roughly -40 dB per decade, twice the rate of a single-pole RC or RL filter.
Characteristic impedance and the quality factor
The filter's characteristic impedance, Z₀ = √(L/C), describes how the inductor and capacitor trade energy independent of any load. How the filter actually behaves near f_c depends on the load resistance R relative to Z₀, expressed as the quality factor Q = R/Z₀ (equivalently Q = R√(C/L)). A load near Q ≈ 0.5 gives a critically damped response with no overshoot; Q well below 0.5 rolls off smoothly but sluggishly (overdamped); and Q above about 0.71 produces a resonant peak in the response right at f_c, which is usually undesirable in a filter meant to simply pass or block frequencies cleanly.