LC Resonance Frequency Calculator

LC resonant frequency: formula and tuning

An LC oscillator — an inductor (L) connected to a capacitor (C) — resonates at f = 1 / (2π · √(L · C)), with L in henries (H), C in farads (F) and f in hertz (Hz). At resonance the capacitive reactance equals the inductive reactance (X_C = X_L): in a series LC the current peaks, in a parallel LC the current drops to a minimum. The quality factor Q describes how sharp the resonance is — higher Q means a narrower passband. Heinrich Hertz used a resonant LC circuit in 1887 to confirm Maxwell's electromagnetic waves, opening the door to radio. Example: L = 1 mH, C = 100 nF → f = 1 / (2π · √(10^-3 · 10^-7)) ≈ 15.9 kHz (audio range). For tuning AM radio at 1 MHz, the LC product must be around 25 µH·nF.

Applications: radio, filters and beyond

LC resonance powers AM/FM radio tuning, RF filters (band-pass, band-stop), clock generation in oscillators, and antenna design (quarter-wave antennas have length λ/4 = c / (4f)). It also appears in MRI (proton precession frequency in a magnetic field) and in acoustic instruments by analogy — strings and tubes resonate at frequencies determined by length and tension, much like LC circuits do with L and C.

FAQ

What is the difference between series and parallel LC? In series, impedance is minimum at resonance (maximum current). In parallel, impedance is maximum (minimum current) — a parallel LC is called a tank circuit.

Why is resistance not in the formula? The ideal LC formula assumes no losses. Real circuits have resistance that lowers Q and slightly shifts the peak, but resonance frequency is dominated by L and C.

How do I tune to a specific frequency? Pick L, then solve C = 1 / ((2πf)² · L). For variable tuning, use a trimmer capacitor or a varicap diode.

What units should I use? SI: henries and farads give hertz. For practical values, 1 µH = 10^-6 H, 1 nF = 10^-9 F. With L in µH and C in nF, frequency in MHz: fMHz ≈ 159.2 / √(LµH · CnF).