Quality Factor (Bandwidth)

Formula

Description

The quality factor Q is a dimensionless measure of how selective or sharp a resonant circuit's frequency response is. It is defined as the ratio of the center (resonant) frequency to the -3dB bandwidth. A high Q circuit has a narrow passband and rejects frequencies outside its resonant peak very effectively, while a low Q circuit has a broad response. Q also represents the ratio of energy stored to energy dissipated per cycle, multiplied by 2π. In practical terms, a Q of 10 means the bandwidth is one-tenth of the center frequency.

Variables

• Q — Quality factor (dimensionless)
• f₀ — Resonant (center) frequency in hertz (Hz)
• BW — Bandwidth at -3dB points in hertz (Hz)

Practical Notes

Typical Q values: simple LC circuits 10-100, crystal oscillators 10,000-100,000, optical cavities over 10^9. Higher Q means better frequency selectivity but also slower transient response and tighter component tolerances required.