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Resonate Frequency of Bandpass Filter

  1. May 2, 2012 #1
    1. The problem statement, all variables and given/known data

    See attached.

    Can somebody explain how the resonant frequency w0=1/RC. I worked it out by setting imaginary Z(s)=0. The answer I get is j√2 which is obviously wrong. Is it wrong to calculate the resonant frequency in this manner in this case?


    2. Relevant equations



    3. The attempt at a solution

    See Attached
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. May 2, 2012 #2

    NascentOxygen

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    Staff: Mentor

    For a bandpass function, as with any filter, we are interested in Vout/Vin. So they derived this transfer function as H(s) near the bottom of the solution. Are you able to examine that denominator and by relating it to the general second order system describe Ѡn and Q here? (Or the damping ratio, ζ zeta)?

    As for your approach, I'm cautious about endorsing shortcuts. But I think it might be valid, thereby allowing you to determine Ѡn at least. But you haven't indicated how you changed Z(s) to something with imaginary terms, so that needs to be checked.
     
  4. May 2, 2012 #3
    Are you able to examine that denominator and by relating it to the general second order system describe Ѡn and Q here? (Or the damping ratio, ζ zeta)?

    No. Are you aware of a good internet resource which explains it?
    Thanks for your help
     
  5. May 2, 2012 #4

    NascentOxygen

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    Staff: Mentor

    Towards the end of this article: http://www.swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/Filters.html

    they state that the second-order filter denominator takes the form:

    https://www.physicsforums.com/images/icons/icon2.gif [Broken] s² + (Ѡn/Q)s + Ѡ²n

    where (Ѡn/Q) is the bandwidth, with Q being the "Q-factor" of the system.

    It's well worth memorizing this expression, and what the co-efficients mean.

    If you prefer the corresponding one from control theory, it's: s² + 2ζѠns + Ѡ²n
    where zeta is the co-efficient of damping and you can see ζ=1/(2Q)
     
    Last edited by a moderator: May 6, 2017
  6. May 3, 2012 #5
    Thanks for that. Makes things somewhat easier than how I was doing it.
     
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