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The Q factor or quality factor is a measure of the "quality" of a resonant system. Resonant systems respond to frequencies close to the natural frequency much more strongly than they respond to other frequencies. On a graph of response versus frequency, the bandwidth is defined as the 3 dB change in voltage level besides the center frequency.
The definition of the bandwidth as the "full width at half maximum" or FWHM is wrong.
The Q factor is defined as the resonant frequency (center frequency) f0 divided by the bandwidth Δf or BW:
- <math>
Q = \frac{f_0}{f_2 - f_1} = \frac{f_0}{\Delta f}
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Bandwidth BW or Δf = f2 - f1, where f2 is the upper and f1 the lower cutoff frequency.
In a tuned radio frequency receiver (TRF) the Q factor is:
- <math>
Q = \frac{1}{R} \sqrt{\frac{L}{C}}
<math>
where R, L and C are the resistance, inductance and capacitance of the tuned circuit, respectively.
From the expression for the resonant frequency of a tuned circuit,
- <math>
\omega = \sqrt{\frac{1}{LC}}
<math>
the alternative formulation:
- <math>
Q = \frac{\omega{}L}{R}
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can be derived.
In optics, the optical Q factor of a resonant cavity is the ratio of energy stored to energy dissipated in the cavity. If the Q factor of a laser's cavity is abruptly changed, the laser can be induced to emit a pulse of light; this technique is known as Q-switching.
Other uses
In marketing and pop culture commentary, Q factor is sometimes used as a casual synonym for Q Score.
External link
Conversion: Quality factor Q to 'bandwidth per octaves' and 'bandwidth per octaves' N to quality factor Q (http://www.sengpielaudio.com/calculator-bandwidth.htm)
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