Editing Q factor (section)

=== Relationship between {{mvar|Q}} and bandwidth ===

The 2-sided bandwidth relative to a resonant frequency of {{math|''F''<sub>0</sub>}} (Hz) is <math>\frac{F_0}{Q}</math>.

For example, an antenna tuned to have a {{mvar|Q}} value of 10 and a centre frequency of 100&nbsp;kHz would have a 3&nbsp;dB bandwidth of 10&nbsp;kHz.

In audio, bandwidth is often expressed in terms of [[octave]]s.  Then the relationship between {{mvar|Q}} and bandwidth is

<math display="block">Q = \frac{2^\frac{BW}{2}}{2^{BW} - 1} = \frac{1}{2 \sinh\left(\frac{1}{2}\ln(2) BW \right)},</math>
where {{mvar|BW}} is the bandwidth in octaves.<ref>{{Cite web|url=http://www.rane.com/note170.html|title=Bandwidth in Octaves Versus Q in Bandpass Filters|last=Dennis Bohn, Rane|date=January 2008|website=www.rane.com|access-date=2019-11-20}}</ref>