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Homework help: Transfer Function and Half Power Frequency

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data

    I made a quick drawing of the circuit, and I apologize because I am not good at using the computer to draw circuits! Anyway, in this particular circuit R=200Ω , and L=5mH.

    For part a I am supposed to find the Transfer Function H(jw) = (Vout/Vin) in terms of ω.

    For part b I am supposed to find the 1/2 power frequency for this filter in hertz.

    2. Relevant equations
    None given

    3. The attempt at a solution
    For part a, I believe I am correct in my thinking here. I used (Vout/Vin) = Zr/(Zr+Zl) which would give me:

    H(jw)= R/(R+jωL), and this would be my transfer function. I believe this is correct.

    On part B I am a little confused. I am setting the magnitude of my transfer function equal to 1/√2. Therefore I would have:

    [ R / √(R^2 + (ωL)^2)] = 1/√2.

    After multiplying things out and simplifying my equation here, I came up with that ω=R/L. This would give me ω=(200/.005), which means ω=40000.

    Considering I am supposed to find this in Hertz, I used ω=2∏f, therefore f= ω/2∏.

    This would give me f = 6366Hz. Am I doing this correctly? I have one of those feelings where I am not going about this in the right way.

    Thanks for your help.


    http://i47.tinypic.com/o5apt0.gif
     
  2. jcsd
  3. Oct 12, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    Your method and results look fine.
     
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