In article .com,
"K7ITM" wrote:

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)


Hello, and I don't know where you obtained that formula but it's
incorrect. S11 in terms of a reflection coefficient is given by your
formula above but without the complex conjugate of Z0. I have seen
reflection coefficients in technical journals defined with a complex
conjugate Z0 as you have shown but that's not consistent with scattering
or transmission line theory (unless Z0 is real). I know it seems
counterintuitve but a source of complex Z0 would be matched (no
voltage/current reflections) to a transmission line having the same
characteristic impedance. This condition does not in general correspond
to the condition of maximum power transfer from source to line.
Conversely a line of complex Z0 impedance connected to a source of complex
Z0* impedance represents maximum power transfer from source to line but we
still have voltage and current "reflections" RELATIVE to Z0. What you
have to keep in mind is that incident (forward) and reflected
voltages/currents only have meaning when they are referenced to an
impedance, say Z0. And to monitor steady-state incident and reflected
waves you need to separate the steady-state voltage (or current) into
these components using a bridge or directional coupler (sampling devices
that are also designed to use Z0 (e.g. 50 + j0 ohms) as a reference).

In most applications what I've said is moot since line impedance is
usually real or very close to real and we are dealing with sources having
real or very close to real impedances. Under these conditions the matched
condition coincides with maximum power transfer.

If you want an in-depth treatment of what I've attempted to summarize I
recommend the chapter on circuit analysis in the "Electronic Designers'
Handbook", ed. E.J. Giacoletto, published by McGraw-Hill. Sincerely,

John Wood (Code 5550) e-mail:
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337