Why is total impedance equal to geometric mean of even and odd impedances?

Discussion in 'General Electronics Chat' started by sp2821, Nov 20, 2015.

  1. sp2821

    Thread Starter New Member

    Jan 8, 2014
    12
    0
    I am trying to find an input impedance of a symmetric circuit by using an even/odd mode analysis.
    I was able to find correct values for Zin,even and Zin,odd
    But why is total input impedance equal to geometric mean of even and odd mode impedances, sqrt(Zin,even * Zin,odd)?
    Why is it not average, (Zin,even+Zin,odd)/2?
     
  2. Jony130

    AAC Fanatic!

    Feb 17, 2009
    3,957
    1,097
    I do not know the answer to your question, but hey notice that mother nature love geometric mean in all AC circuit in all forms and shapes.
     
  3. WBahn

    Moderator

    Mar 31, 2012
    17,736
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    What, pray tell, are even and odd impedances?

    It might be nice if you provided an example.
     
  4. BillB3857

    Senior Member

    Feb 28, 2009
    2,400
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    Are Odd and Even equated to Leading and Lagging?
     
  5. hsazerty2

    New Member

    Sep 25, 2015
    22
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    I think he is talking about transmission lines; not clear though.
     
  6. BR-549

    Well-Known Member

    Sep 22, 2013
    1,982
    388
    google even/odd mode analysis.

    Microwave ports. I am not familiar with such things.
     
  7. BillB3857

    Senior Member

    Feb 28, 2009
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    This is all I could find on the subject. The diagram is for a OPEN transmission line, but can be applied to an SHORTED transmission line by simply reversing the Voltage/Current tags.
     
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