RLC Resonance Frequency Calculator

RLC resonance frequency

For an ideal LC pair the resonance frequency works out to f₀ = 1 / (2π sqrt(L · C)), which comes out in Hertz as long as L is in Henries and C in Farads. At that point the inductive reactance matches the capacitive reactance (Xl = Xc), and energy just sloshes back and forth between L and C while R barely gets a say. Plug in L = 10 mH and C = 1 µF and the calculator gives f₀ ≈ 1.59 kHz, the kind of value you run into in audio crossovers and intermediate-frequency stages.

In a series RLC circuit, f₀ is where current peaks and impedance bottoms out. Flip to a parallel RLC and it's the other way around: impedance peaks, line current drops to a minimum. How wide a band you get around f₀ depends on the quality factor Q = (1/R)·sqrt(L/C) in the series case, and that's what sets how selective the filter ends up being.

Applications

You'll find resonance-frequency design behind radio tuners (AM, FM, RF front-ends), LC oscillators like the Colpitts, Hartley and Clapp, EMC filters built to IEC 61000-4 and CISPR 11, the intermediate-frequency stages of superheterodyne receivers, wireless charging coils, and snubbers in switching converters. If you want to dig deeper, Sedra/Smith - Microelectronics and Boylestad - Circuit Analysis both cover it, as do the IEEE standards for filter and antenna design.

FAQ

Does R change the resonance frequency? Not in the ideal model. In real circuits, though, heavy losses nudge the damped frequency down to ωd = sqrt(ω0² - (R/2L)²).

How do I tune a filter to a given frequency? Start with an L you can actually buy off the shelf and solve for C = 1 / ((2πf₀)² · L). Or do it the other way around if C is the fixed one.

What is the practical limit of f₀? Once you push past a few hundred MHz, stray capacitance and lead inductance start to take over. Above that, engineers switch to distributed elements like microstrip and cavities.