Why Z and Y matrices must be pure imaginary for reciprocal lossless N-port junction ?

[promach]

For a reciprocal lossless N -port junction,

1) Why is P_avg = 0.5*[V] ^t [ I ] ^* instead of P_avg = 0.5*[V] ^* [ I ] ^t or P_avg = 0.5*[ I ] ^t [V] ^* ?

2) Why [V] = [Z][ I ] instead of [V] = [ I ][Z] ?

3) If we set all port currents equal to zero except for the nth current , which port will the nth current flow to ? This seems to be related to ports decoupling theorem ?

Note: The following screenshot is from Microwave engineering 4th edition by David Pozar

 

[KlausST]

Hi,

Maybe I don't understand the question.
My answer is: for "lossless" you need "imaginary", because "real" means "loss".

Imaginary: pure lossless capacitors and lossless inductors. No dissipated power, no heat, no loss.
Real: resistors. Every voltage and/or current causes dissipated power = heat = loss.

Klaus

 

[pancho_hideboo]

There is no help, since it is too easy.
This is true for all your posts.
https://www.edaboard.com/showthread.php?385763#5