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 maximum possible stored energy, or the total energy, i.e. the sum of the potential and kinetic energies at some point in time; 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 half-power bandwidth i.e. the bandwidth over which the power of vibration is greater than half the power at the resonant frequency, ωr = 2πfr is the angular resonant frequency, and Δω is the angular half-power bandwidth.
More generally and in the context of reactive component specification (especially inductors), the frequency-dependent definition of Q is used:
where ω is the angular frequency at which the stored energy and power loss are measured. This definition is consistent with its usage in describing circuits with a single reactive element (capacitor or inductor), where it can be shown to be equal to the ratio of reactive power to real power. (See Individual reactive components.)
Read more about this topic: Q Factor
Famous quotes containing the words definition of, definition, quality and/or factor:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“The quality of mercy is not strained.
It droppeth as the gentle rain from heaven
Upon the place beneath. It is twice blest:
It blesseth him that gives, and him that takes.
‘Tis mightiest in the mightiest. It becomes
The thronèd monarch better than his crown.”
—William Shakespeare (1564–1616)
“Children of the middle years do not do their learning unaffected by attendant feelings of interest, boredom, success, failure, chagrin, joy, humiliation, pleasure, distress and delight. They are whole children responding in a total way, and what they feel is a constant factor that can be constructive or destructive in any learning situation.”
—Dorothy H. Cohen (20th century)