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The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
The Q factor is a widespread measure used to characterise resonators. It is defined as the peak energy stored in the circuit divided by the average energy dissipated in it per radian at resonance. Low-Q circuits are therefore damped and lossy and high-Q circuits are underdamped and prone to amplitude extremes if driven at the resonant frequency.
The quality of the resonance (how long it will ring when excited) is determined by its Q factor, which is a function of resistance: =. An idealized, lossless LC circuit has infinite Q , but all actual circuits have some resistance and finite Q , and are usually approximated more realistically by an RLC circuit .
The higher the Q factor, the greater the amplitude at the resonant frequency, and the smaller the bandwidth, or range of frequencies around resonance occurs. In electrical resonance, a high- Q circuit in a radio receiver is more difficult to tune, but has greater selectivity , and so would be better at filtering out signals from other stations.
A major reason for the wide use of crystal oscillators is their high Q factor. A typical Q value for a quartz oscillator ranges from 10 4 to 10 6, compared to perhaps 10 2 for an LC oscillator. The maximum Q for a high stability quartz oscillator can be estimated as Q = 1.6 × 10 7 /f, where f is the resonant frequency in megahertz. [21] [22]
The “dissipation factor”, D, is the inverse of the Q-factor: D = Q −1 = w/f r. The half-band-half-width, Γ, is Γ = w/2. The use of Γ is motivated by a complex formulation of the equations governing the motion of the crystal. A complex resonance frequency is defined as f r * = f r + iΓ, where the imaginary part, Γ, is half the ...
The quality factor is useful in determining the spectral range of the resonance condition for any given ring resonator. The quality factor is also useful for quantifying the amount of losses in the resonator as a low Q {\displaystyle Q} factor is usually due to large losses.
The Q factor of a particular mode in a resonant cavity can be calculated. For a cavity with high degrees of symmetry, using analytical expressions of the electric and magnetic field, surface currents in the conducting walls and electric field in dielectric lossy material. [14]