quality factor (Q): one construct, many systems

The quality factor, Q, measures how lightly damped a resonant system is: it is defined as 2π times the energy stored in the resonator divided by the energy it loses per cycle, and equivalently as the resonant frequency divided by the width of the resonance peak (f₀/Δf). A high Q means little energy is lost each cycle, so the resonance is sharp and the oscillation rings for many cycles. The idea originated in electrical engineering and applies identically to RLC circuits, mechanical resonators and cavities, as French's Vibrations and waves sets out. It is one construct that recurs wherever something resonates.[1]

Unit

Dimensionless ratio of energy stored to energy lost per radian

Recovery means

Not applicable

Measured by

From the resonance bandwidth (f₀/Δf) or the decay of free oscillation

In precision timekeeping the same quality factor describes a clock's oscillator (a pendulum, balance wheel, quartz crystal or atomic transition) as the number of cycles it swings through before its energy decays appreciably. A higher-Q oscillator is less perturbed by outside forces and holds its natural frequency more steadily, so it keeps better time; Q rises roughly from a pendulum (order 10³) through quartz (10⁴–10⁶) to atomic standards (10⁸ and beyond). Matthys's Accurate clock pendulums applies the measure to pendulum design. It is the identical energy-stored-over-energy-lost construct as in physics, here read as timekeeping stability.[2]

Unit

Dimensionless Q of a clock oscillator

Recovery means

Not applicable

Measured by

From the oscillator's ring-down time or resonance width, and tied to its frequency stability