Editing Q factor (section)

=== RLC circuits ===

In an ideal series [[RLC circuit]], and in a [[tuned radio frequency receiver]] (TRF) the {{mvar|Q}} factor is:<ref name=":1">{{Cite book|url=https://books.google.com/books?id=iRQa6dfeaKIC&q=quality+factor|title=Electric Circuits|last1=U.A.Bakshi|last2=A.V.Bakshi|date=2008|publisher=Technical Publications|isbn=9788184314526|pages=2–79|language=en}}{{Dead link|date=November 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>

<math display="block">Q = \frac{1}{R} \sqrt{\frac{L}{C}} = \frac{\omega_0 L}{R} = \frac {1} {\omega_0 R C}</math>

where {{mvar|R}}, {{mvar|L}}, and {{mvar|C}} are the [[electrical resistance|resistance]], [[inductance]] and [[capacitance]] of the tuned circuit, respectively. Larger series resistances correspond to lower circuit {{mvar|Q}} values.

For a parallel RLC circuit, the {{mvar|Q}} factor is the inverse of the series case:<ref>{{cite web|url=http://fourier.eng.hmc.edu/e84/lectures/ch3/node8.html|title=Complete Response I - Constant Input|website=fourier.eng.hmc.edu|url-status=live|archive-url=https://web.archive.org/web/20120110062257/http://fourier.eng.hmc.edu/e84/lectures/ch3/node8.html|archive-date=2012-01-10}}</ref><ref name=":1" />

<math display="block">Q = R \sqrt{\frac{C}{L}} = \frac{R}{\omega_0 L} = \omega_0 R C</math><ref>[http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/lecture-notes/resonance_qfactr.pdf Frequency Response: Resonance, Bandwidth, ''Q'' Factor] {{webarchive|url=https://web.archive.org/web/20141206172316/http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/lecture-notes/resonance_qfactr.pdf|date=2014-12-06|title=}} ([[PDF]])</ref>

Consider a circuit where {{mvar|R}}, {{mvar|L}}, and {{mvar|C}} are all in parallel. The lower the parallel resistance is, the more effect it will have in damping the circuit and thus result in lower {{mvar|Q}}. This is useful in filter design to determine the bandwidth.

In a parallel LC circuit where the main loss is the resistance of the inductor, {{mvar|R}}, in series with the inductance, {{mvar|L}}, {{mvar|Q}} is as in the series circuit. This is a common circumstance for resonators, where limiting the resistance of the inductor to improve {{mvar|Q}} and narrow the bandwidth is the desired result.