Thanks very much for that additional information about the consequences
of the magnitude of the reflection coefficient exceeding one. I couldn't
find it in any of the electromagnetics or transmission line books on my
shelf, which at last count include about 13 texts. Chipman, alas, isn't
among them. It confirms what I suspected, and provides further evidence
that the posted equation is universally correct.

While I'm mentioning books, I picked up a couple at Powell's Technical
Bookstore yesterday evening that look like real winners. They're
_Engineering Electromagnetics_ by Nathan Ida (2000), and
_Electromagnetic Fields, Energy, and Waves_ by Leonard M. Magid (1972).

The thing that attracted me to Ida was that he explains things in very
clear terms, then follows each section with a number of examples showing
how the principles are applied to real problems. And answers to all the
exercises (separate from the examples) are at the back of the book. This
is a pretty recent book and fairly expensive. I was lucky to have found
a used copy at a reduced price.

Magid has the most rigorous derivation of power and energy flow on
transmission lines I've seen, as well as other extensive transmission
line information. One conclusion that pricked my ears was that on a line
with a pure standing wave (e.g., a lossless line terminated with an open
or short circuit), ". . . power (and therefore, energy) is completely
trapped within each [lambda]/4 section of this lossless line, never able
to cross the zero-power points and thus constrained forever to rattle to
and fro within each quarter-wave section of this line." I had reached
this same conclusion some time ago, but realized I hadn't properly
evaluated the constant term when integrating power to find the energy.
But I didn't want to get into the endless shouting match going on in the
newsgroup, and dropped it before going back and fixing my derivation.
Hopefully some of the participants in power and energy discussions will
read Magid's analysis before resuming. I found this book used at a very
modest price.

Roy Lewallen, W7EL

George, W5YR wrote:
Roy, Chipman on page 138 of "Theory and Problems of Transmission Lines"
makes the statement

" The conclusion is somewhat surprising, though inescapable, that a
transmission line can be terminated with a reflection coefficient whose
magnitude is as great as 2.41 without there being any implication that the
power level of the reflected wave is greater than that of the incident wave.
Such a reflection coefficient can exist only on a line whose attention per
wavelength is high, so that even if the reflected wave is in some sense
large at the point of reflection, it remains so for only a small fraction of
a wavelength along the line away from that point . . . The large reflection
coefficients are obtained only when the reactance of the terminal load
impedance is of opposite sign to the reactance component of the
characteristic impedance."

Chipman makes these remarks after his derivation of the operation of lines
with complex characteristic impedance.


--
73/72, George
Amateur Radio W5YR - the Yellow Rose of Texas
Fairview, TX 30 mi NE of Dallas in Collin county EM13QE
"In the 57th year and it just keeps getting better!"