Frequência ressonante LC

LC resonant frequency: f = 1 / (2π · √(LC))

In an LC tank, energy keeps sloshing back and forth between the capacitor's electric field and the inductor's magnetic field. The circuit settles into oscillation at its resonant frequency f = 1 / (2π · √(L · C)). When Heinrich Hertz demonstrated electromagnetic waves for the first time in 1887, he did it with a resonant LC circuit. As an example, tuning to an AM broadcast at 1 MHz needs roughly L · C ≈ 25 µH · nF. How wide the passband is comes down to the quality factor Q: raise Q and the band gets narrower, which is what lets a receiver pick out one station from its neighbors.

Applications: radio, oscillators, MRI

You'll find LC resonance underneath AM/FM/SDR receivers and RF transmitters, in antenna matching (a quarter-wave antenna has λ/4 = c / 4f), in clock oscillators, and in the RF coils of an MRI scanner, which are tuned to the Larmor frequency of hydrogen protons.

FAQ

Why does the circuit oscillate? The energy bounces between the capacitor (electric field) and the inductor (magnetic field). If there were no losses, that hand-off would never stop.

What sets the Q factor? For a series tank, Q = (1/R) · √(L/C). Drop the series resistance or push up the L/C ratio and Q climbs, which tightens the bandwidth.

Why isn't Q infinite in practice? Real inductors carry wire resistance, capacitors leak through dielectric losses, and the load draws off energy of its own. Every one of those damps the oscillation.