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

Thread Starter

sp2821

Joined Jan 8, 2014
21
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?
 

Jony130

Joined Feb 17, 2009
4,969
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.
 

WBahn

Joined Mar 31, 2012
24,684
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?
What, pray tell, are even and odd impedances?

It might be nice if you provided an example.
 

BR-549

Joined Sep 22, 2013
4,936
google even/odd mode analysis.

Microwave ports. I am not familiar with such things.
 

BillB3857

Joined Feb 28, 2009
2,497
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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