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
5,183
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
26,156
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.
 
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