How this is calculated. Resonance is where the inductive and capacitive
reactances are equal and cancel, at
f₀ = 1 / (2π√(LC)). At that point a series LC
looks like a short and a parallel LC looks like an open — same frequency, opposite behaviour,
which is why the same formula serves a filter and a trap. The characteristic impedance
Z₀ = √(L/C) is what both reactances equal at resonance, and
Q = Z₀/R
sets how sharp the peak is: bandwidth is
f₀/Q.
Q is set by the losses, not by L
and C — the same resonant frequency built from a large L and small C has a much higher Z₀
and so a much higher Q for the same series resistance. In a real circuit that resistance
includes the inductor's winding resistance and core loss, which usually dominate.
Q below 0.5 means the circuit is overdamped — it will not ring or show a useful peak, and the resonance calculation describes something that barely resonates.