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# How to get from Q=X/R to Q=f0/&#916;f - Q is the quality

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#### CVT

##### Newbie level 4
The following is quoted from (**broken link removed**) Section titled : Q and bandwidth of a resonant circuit

"
The Q, quality factor, of a resonant circuit is a measure of the “goodness” or quality of a resonant circuit. A higher value for this figure of merit correspondes to a more narrow bandwith, which is desirable in many applications. More formally, Q is the ration of power stored to power dissipated in the circuit reactance and resistance, respectively:

Q = Pstored/Pdissipated = I2X/I2R
Q = X/R
where: X = Capacitive or Inductive reactance at resonance
R = Series resistance.

"

This definition of Q makes perfect sense to me.
Notice that in the above quote he already related Q to the bandwidth.

Other sources like wikipedia (https://en.wikipedia.org/wiki/Q_factor) states that Q = resonant frequency/ 3dB Bandwidth (Q=f0/Δf) which is not intuitive, specially in the light of the previous definition for Q in terms of Power stored and dissipated.

So how do I rewrite Q=X/R in terms of f,L,C etc to get to Q=f0/Δf.

This well help me to form an intuitive understanding of Q=f0/Δf.

Thanks
Chris

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