# 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
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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
3,990
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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
18,085
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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
2,402
348
Are Odd and Even equated to Leading and Lagging?

5. ### hsazerty2 New Member

Sep 25, 2015
22
1
I think he is talking about transmission lines; not clear though.

6. ### BR-549 Well-Known Member

Sep 22, 2013
2,177
418

Microwave ports. I am not familiar with such things.

7. ### BillB3857 Senior Member

Feb 28, 2009
2,402
348
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.

• ###### Odd-Even-Nodes.pdf
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2.3 MB
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7
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