Resonant circuits and filters

Pair an inductor L with a capacitor C: at one particular frequency, their opposite reactances become equal and the circuit resonates. That's the resonant frequency:

f₀ = 1 / (2π·√(L·C))

Worth memorising: to raise the tuned frequency, decrease L or C; to lower it, increase them. That's exactly how a set "tunes in" to a station.

Quality factor Q: it measures the "sharpness" of the resonance. High Q = a narrow, selective peak (you isolate one frequency well); low Q = a broad response. Q also describes losses: the lower the losses, the higher the Q.

Filters — combine R, L, C to pass some frequencies and block others:

Low-pass: passes low frequencies, cuts high ones.
High-pass: the opposite.
Band-pass: passes only a range (a resonant circuit is one).
Band-stop / notch: removes a specific range (useful against a jammer).

In radio, filters are everywhere: selecting a band, removing harmonics on transmit, cleaning a signal on receive. A receiver's selectivity depends directly on its filters — see Émetteur et récepteur.