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Transfer function of third order filter

  1. May 5, 2014 #1

    Maylis

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    Hello, I am trying to do this example problem in my textbook
    ImageUploadedByPhysics Forums1399350470.018469.jpg


    I have my KVL and KCL equations written. I am trying to use substitutions to find V_c1 in terms of Vs and also in terms of Vout, so I can find Vout in terms of Vs. However, it seems like no matter what sequence of substitutions I do yield 0 = 0, and I am not making progress in finding the answer.

    ImageUploadedByPhysics Forums1399350485.593870.jpg
    ImageUploadedByPhysics Forums1399350498.917678.jpg
     
  2. jcsd
  3. May 5, 2014 #2

    Maylis

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    Here is my closest attempt so far

    ImageUploadedByPhysics Forums1399352222.306117.jpg

    Edit: I followed through with the algebra and it turns out to give the correct answer. My question though is this: I sort of chose to do this substitution from exhaustion. Meaning, I tried many other substitutions that yielded nothing. In a timed situation, how do I know which substitution I should make so I don't waste time trying other ones that are dead ends?
     
    Last edited: May 6, 2014
  4. May 6, 2014 #3

    Maylis

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    Well, since I got the part with the impedances correct, I am having a hell of a time trying to get it in the form they have with the H(ω). Any tips for this? I am trying to multiply by the complex conjugate but the algebra here is way too much and its too easy to make a mistake.
     
  5. May 6, 2014 #4

    The Electrician

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    You need to make use of this:

    attachment.php?attachmentid=69476&stc=1&d=1399364247.png

    Then you can proceed like this:

    attachment.php?attachmentid=69477&stc=1&d=1399364247.png
     

    Attached Files:

  6. May 6, 2014 #5

    Maylis

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    Thanks for that. I will look carefully over these steps.
     
  7. May 10, 2014 #6

    Maylis

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    I'm having trouble getting from

    ''After we make these substitutions....we get these results''
     
  8. May 10, 2014 #7

    Maylis

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    I finally got it. That is such an annoying problem. Sometimes I wonder if this is a circuits class or a complex algebra class......
     
  9. May 10, 2014 #8

    The Electrician

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    Count yourself lucky. If it hadn't been for Steinmetz:

    http://en.wikipedia.org/wiki/Charles_Proteus_Steinmetz

    you would be solving simultaneous differential equations instead of simple algebra with complex arithmetic! :smile:
     
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