Roy Lewallen wrote:


I have only two texts which deal with S
parameters in any depth. One, _Microwave Transistor Amplifiers: Analysis
and Design_ By Guillermo Gonzalez, consistently uses forward and reverse
voltage to mean exactly what they do in transmission line analysis.
Consequently, he consistently ends up with the same equation for voltage
reflection coefficient I've been using, and states several places that
the reflection is zero when the line or port is terminated in its
characteristic or source impedance (not conjugate). And this all without
an assumption that Z0 or source Z is purely real. The other book,
however, _Microwave Circuit Design Using Linear and Nonlinear
Techniques_ by Vendelin, Pavio, and Rohde, uses a different definition
of V+, V- than either of us does, and different a and b than you do. To
them, a = V+ * sqrt(Re(Zg)) / Zg* where Zg is the source impedance, and
b = V- * sqrt(Re(Zg))/Zg. They end up with three different reflection
coefficients, Gammav, Gammai, and one they just give as Gamma. Gammav is
V-/V+, Gammai is I-/I+, and plain old Gamma, which they say is equal to
b/a, turns out to be equal to Gammai. Incidentally, their equation for
Gammav, the voltage reflection coefficient, is:

Gammav = [Zg(Z - Zg*)]/[Zg*(Z + Zg)]

This formula is Gonzalez's definition of voltage
reflection coefficient, based on *power wave*
theory (not *transmission line* theory) on page 48
of his *second edition*. We need to keep in mind
that a power wave is a different kind of wave than
the ones that we are used to thinking about in
transmission lines (Gonzalez's words).

If you don't have his second edition, I suggest
get on-line and buy it. It has a lot of stuff not
found in the first edition. The discussion of
power waves is excellent and readable, with some
mental suffering.

The power wave concept is quite valid. We need to
come to grips with this and learn to accept it. It
is the actual basis for microwave simulation
programs. In these programs transmission lines are
treated as "circuit elements" with certain
properties and calculated scattering parameters.
But we must wear a different "hat" when dealing
with it. The idea of "power wave" requires some
meditation.

I discussed some of this in a previous post.

Bill W0IYH