This is interesting. But how did it lead you to the equation you
determined must be correct? That is, what definition of reflection
coefficient did you start with, where did you get it, and how did you
get from there to the reflection coefficient equation you presented?

I assume that, consistent with the admonition in the last paragraph of
your posting, you were "careful to follow through and be consistent with
your definitions, measurements, algebra, and arithmetic". It would be
very instructive for us to be able to follow the process you did in
coming to what you feel is the "right answer".

Roy Lewallen, W7EL

Peter O. Brackett wrote:

Easy now boy! You'r almost as bad as me!

It is entirely possible, in fact I know this to be true, that there can be
more than one *definition* of "the reflection coefficient". And so... one
cannot say definitively that one particular defintion is WRONG.

If the definition of the reflection coefficient is given as rho = (Z - R)/(Z
+ R) then that's what it is. This particular definition corresponds to the
situation which results in rho being null when the unknown Z is equal to the
reference impedance R, i.e. an "image match". If the definition is given as
rho = (Z - conj(R))/(Z + conj(R)) then rho will be null when the unknown Z
is equal to the conjugate of the reference impedance conj(R), i.e. a
"conjugate match".

Nothing is WRONG if the definition is first set up to correspond to what the
definer is trying to accomplish. And so one has got to take care when
making statements about RIGHT ways and WRONG ways to define things.
Everyone is entitled to go to hell their own way if they are the onesmaking
the definitions. Just as long as no incorrect conclusions are drawn from
the definitions. That may occur when folks don't accept or agree on a
definition.

OTOH....

Definitions and semantics aside, what we should really be interested in is
what is the physical meaning of any particular definition and what are its'
practical uses.
. . .

Every one is entitled to go to hell their own way when defining the
wave to
electrical variable transformations required to make their
measurements and
solve their problems and this will result in a variety of definitions for
the scattering [reflection] parameters. Nothing more nothing less.
Others
may not agree with your tools, methodologies and definitions, but just be
careful to follow through and be consistent with your definitions,
measurements, algebra, and arithmetic and you will always get the right
answers.