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:
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“A quality is something capable of being completely embodied. A law never can be embodied in its character as a law except by determining a habit. A quality is how something may or might have been. A law is how an endless future must continue to be.”
—Charles Sanders Peirce (1839–1914)
“In his very rejection of art Walt Whitman is an artist. He tried to produce a certain effect by certain means and he succeeded.... He stands apart, and the chief value of his work is in its prophecy, not in its performance. He has begun a prelude to larger themes. He is the herald to a new era. As a man he is the precursor of a fresh type. He is a factor in the heroic and spiritual evolution of the human being. If Poetry has passed him by, Philosophy will take note of him.”
—Oscar Wilde (1854–1900)