WEN YA A0077001

This concept is extracted from the below link: http://en.wikipedia.org/wiki/Q_factor

In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency. 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 bandwidth.

Definition of the quality factor

In the context of resonators, Q is defined in terms of the ratio of the energy stored in the resonator to the energy supplied by a generator, per cycle, to keep signal amplitude constant, at a frequency (the resonant frequency), fr, where the stored energy is constant with time:

The factor 2π makes Q expressible in simpler terms, involving only the coefficients of the second-order differential equation describing most resonant systems, electrical or mechanical. In electrical systems, the stored energy is the sum of energies stored in lossless inductors and capacitors; the lost energy is the sum of the energies dissipated in resistors per cycle. In mechanical systems, the stored energy is the sum of the potential and kinetic energies; the lost energy is the work done by an external conservative force, per cycle, to maintain amplitude.

For high values of Q, the following definition is also mathematically accurate:

Where fr is the resonant frequency, Δf is the bandwidth, ωr = 2πfr is the angular resonant frequency, and Δω is the angular bandwidth.