the quality factor (Q)
When a resonant circuit rings, how long does the ringing last and how sharp is its tuning? The quality factor Q answers both: it measures how pure or low-loss the resonance is. A high-Q circuit is a finely tuned bell that rings a long clear note; a low-Q one is a dull thud that dies fast.
Q is the ratio of energy stored to energy lost per cycle. For a resonant peak it also equals the resonant frequency divided by the bandwidth: Q = f0 / bandwidth. So a filter centred at 5 kHz that passes a 250 Hz-wide band has Q = 5000/250 = 20. High Q means a narrow, selective peak; low Q means a broad, gentle one. Resistance is the enemy of Q; it is the loss that damps the ringing.
Q sets how selective a radio tuner is, how stable an oscillator's frequency is, and how much a filter peaks or rings near its edge. Honest caveat: more Q is not always better. A very high-Q filter rings and overshoots on fast signals and is touchy about exact component values, while too low a Q is mushy and unselective. Good design picks a Q on purpose, it does not just maximise it.
A radio front-end tuned to 100 MHz with Q = 100 has a bandwidth of 100 MHz/100 = 1 MHz, wide enough for the station yet narrow enough to reject its neighbours.
Q sets how narrow the tuning is.
Higher Q is not automatically better. It brings ringing, overshoot, and sensitivity to component tolerances; design chooses a Q on purpose.