William E. Sabin wrote:
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
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
Mason's Rule is then applied to the collection of
circuit elements to get the system response.
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.