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

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

For a reciprocal lossless N -port junction,

1) Why is Pavg = 0.5*[V] t [ I ] * instead of Pavg = 0.5*[V] * [ I ] t or Pavg = 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

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2. ## Re: Why Z and Y matrices must be pure imaginary for reciprocal lossless N-port juncti

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

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3. ## Re: Why Z and Y matrices must be pure imaginary for reciprocal lossless N-port juncti

There is no help, since it is too easy.
This is true for all your posts.