a low pass filter analysis (an infinite chain of LCs)

Discussion in 'Homework Help' started by wannalearn, May 31, 2014.

  1. wannalearn

    Thread Starter New Member

    May 31, 2014
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    The question ultimately asks me to calculate the cutoff frqeuency but at this point, Im just trying to figure out how to calculate the total impedance of the LC network.

    The solution says Znet = Zl + (Zc * Znet)/(Zc + Znet) = Znet

    Based on the diagram, i would have thought it is (Zl + Znet) and Zc that are in series. So, I wouldve thought the solution must be the following: Znet = (1/(Znet+Zl) + 1/Zc) ^(-1)

    Im trying to analyze the given circuit (LC network) the same way I would analyze the following circuit : http://i.stack.imgur.com/n1eIX.jpg

    Rnet = r + (1/r + 1/Rnet) ^(-1) and solve for Rnet.
     
  2. shteii01

    AAC Fanatic!

    Feb 19, 2010
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    I can figure out what Zl and Zc represent.
    What does Znet represent?
     
  3. WBahn

    Moderator

    Mar 31, 2012
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    Znet is the impedance of the whole network.

    The key to analyzing this circuit is to note that, because it is an infinite chain, you can cut it off before any capacitor and the impedance looking into the rest of it will be unchanged. Hence, you can reduce it to a single cap and a single inductor that is connected to a network have an impedance of Znet.
     
  4. wannalearn

    Thread Starter New Member

    May 31, 2014
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    Thank you for the replies.
    I do understand the point of this being that you can cut it off and say the rest of the system still has the same net impedance.
    The trouble i have is what elements are in series and parallel
    Could you help me figure out what are in series and parallel?
     
  5. wannalearn

    Thread Starter New Member

    May 31, 2014
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    I hope this clarifies what I have misunderstood.
     
  6. WBahn

    Moderator

    Mar 31, 2012
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    You are correct. The given solution makes no sense.

    Note that you have a typo in your original post that made it appear that you were doing it wrong to since you said that (Zl+Znet) and Zc are in series. I think you meant to say parallel.
     
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