On Jan 30, 11:13 pm, "camelot" wrote:
Hi Tom,
well, after few researches on several books, I found that the formula
I provided by me works only for real Z0. The general formula valid in
case Z0 is complex is the follow:

S11=(Zin-Z0*)/(Zin+Z0)

Where Z0* is the conjugate of Z0. Obviously, if Z0 is real, the
conjugate coincide with the real one.
However, thank you for your interest ;-)

Camelot

But I'm curious. Why do you think that the formula you wrote above
doesn't work when Z0 is complex? In what way do you think it does not
work?

I'm also curious why you would pick a complex reference impedance for
S-parameter work, but that's really a different issue.

Cheers,
Tom


I'm not sure where you got it, but the formula with the complex
conjugate is NOT correct! The formula without complex conjugate is
correct, for complex Z and Z0, both.

That the formula using the complex conjugate is incorrect is trivial
to see: consider that a line terminated in a load equal to the line's
characteristic impedance (be it purely resistive, or complex) has no
reflection. That is, if load Z = Z0, there is no reflection. Then if
Z0 is complex and has a non-zero reactive component, your formula
yields S11 which is not zero, for a line which is terminated to have
no reflection. As far as I am concerned, that would be incorrect.
The original formula, without complex conjugate, yields the correct
answer for this case. Can you come up with a case where it is
incorrect?

Cheers,
Tom