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Q factor and bandwidth

  1. Dec 20, 2014 #1
    Could some please explain to me how the equation BW=fr/Q is derived?
    Where BW=bandwidth, fr=resonance freq and Q is Quality factor.
    I understand this relationship suppose to hold, I just don't understand why.
    I basically am looking for a proof.

    thank you all a priori.
  2. jcsd
  3. Dec 21, 2014 #2


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  4. Dec 21, 2014 #3
    Thank you so much for your reply.
    Unfortunately I already read that Wiki page.
    I'm really looking for a proof and I can't seem to find one ANYWHERE.
    I understand intuitively how the relationship could work (or does work) but I really would like to see the math.
  5. Dec 21, 2014 #4


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    Start with the general 2nd order transfer function for a bandpass filter,
    remember Q = 1/(2ζ )
    replace s by jω
    calculate ω where the magnitude of the real part equals that of the imaginary part,
    you should be close to getting your answer
    http://thumbnails112.imagebam.com/37333/0363e9373324851.jpg [Broken]
    Last edited by a moderator: May 7, 2017
  6. Dec 24, 2014 #5


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    Googled q factor proof:
    This may answer your question.

    Your problem will be dealing with this:
    "By combining Equations (1.9), (1.10), 1.11) and (1.18) we obtain the relationship between the bandwidth and the Q factor"

    which, of course, he does not do in the paper.

    This paper has some proofs, but I didn't go through it rigorously to see if it actually answered your question. It takes a different approach.
    http://www.lightandmatter.com/html_books/lm/ch18/ch18.html [Broken]
    Last edited by a moderator: May 7, 2017
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