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What is Q factor (quality factor)?

A dimensionless quantity expressing the sharpness of resonance. It is the resonant frequency divided by the bandwidth, Q = f0/BW, and also corresponds to the ratio of the energy stored to the energy lost per cycle. For a series RLC circuit Q = (1/R)√(L/C), and for a parallel RLC circuit Q = R√(C/L); the smaller the losses, the larger Q. Crystal resonators and MEMS resonators reach tens of thousands or more.

Japanese name: Q値(クオリティファクタ)

Q factor (quality factor) appears in 4 practice questions across 3 topics, including Circuit Analysis: AC, Linear Circuits and Transients, Analog and electronic circuits, Circuit and electromagnetism basics.

Field: Circuit Analysis: AC, Linear Circuits and Transients

Try it: questions about Q factor (quality factor)

What does a high Q (quality factor) of a resonant circuit mean?

  1. AA high resonant frequency
  2. BLow loss and a sharp resonant peak (narrow bandwidth)
  3. CHigh loss and wide bandwidth
Show answer and explanation

Answer: B. Low loss and a sharp resonant peak (narrow bandwidth)

Q expresses the sharpness of resonance: Q = f0/Δf (resonant frequency ÷ bandwidth). Higher Q means lower loss, a sharper peak and a narrower bandwidth; f0 = 1 MHz with Q = 100 gives 10 kHz of bandwidth. For a series RLC circuit, Q = (1/R)√(L/C), so lower resistance (loss) raises it. Highly selective filters and low-phase-noise oscillators require high Q.

Q factor (quality factor) in the explanations

Questions that mention Q factor (quality factor) (4)

  1. What does a high Q (quality factor) of a resonant circuit mean?
  2. Which is closest to the bandwidth (the difference between the two frequencies at which the current falls to 1/√2 of its resonant value) of a series RLC resonant circuit with R = 10 Ω, L = 1 mH and C = 10 nF?
  3. In the series RLC circuit in the figure, R = 10 Ω, L = 10 mH and C = 1 µF, and the frequency of a 1 V RMS sinusoidal voltage is set to the resonant frequency. Which of the following is the RMS voltage VC across the capacitor?
  4. In the parallel RLC circuit in the figure, R = 20 kΩ, L = 1 mH and C = 10 nF. Near the resonant frequency, which of the following is closest to the difference between the two frequencies at which the magnitude of the circuit impedance falls to 1/√2 of its value at resonance (the bandwidth)?

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Related terms

Resonant circuit Reactance Impedance Admittance Mesh analysis Nodal analysis Norton's theorem Partial fraction decomposition Phasor Reactive power

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