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

#### sp2821

Joined Jan 8, 2014
23
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
5,230
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
26,398
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.

#### BillB3857

Joined Feb 28, 2009
2,543
Are Odd and Even equated to Leading and Lagging?

#### hsazerty2

Joined Sep 25, 2015
28
I think he is talking about transmission lines; not clear though.

#### BR-549

Joined Sep 22, 2013
4,938
google even/odd mode analysis.

Microwave ports. I am not familiar with such things.

#### BillB3857

Joined Feb 28, 2009
2,543
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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