On Wed, 09 Jun 2004 23:07:03 -0500, Cecil Moore wrote:

Walter Maxwell wrote:

W5DXP wrote:
Think about that. Why would you expect your re-reflected voltage and Steve's
re-reflected voltage to be the same value when they have completely different
definitions?

Where are the completely different definitions?

Steve defines re-reflected voltage as voltage reflected from the load
multiplied by the rearward-looking physical reflection coefficient,
(Z1-Z2)/(Z1+Z2). That's certainly not the definition of your reflection
coefficient for reflected voltage. Why are you surprised that you two
guys get different values of re-reflected voltage when you are using
entirely different voltage reflection coefficients?

Cecil, the only difference that can obtain between reflection coefficents is in
magnitude and phase. It matters not whether a reflection is established by a
physical discontinuity or wave interference, the result is identical.

Cecil, I don't recall defining re-reflection, nor do I recall seeing any
definition of it by Steve.

And that, in a nutshell, is the entire problem. You implied your definition
of re-reflection in _Reflections_. Steve implied his definition of re-reflection
in his QEX article. They are NOT the same definitions. Your definition of re-
reflected voltage involves a reflection coefficient of 1.0 at your virtual short.
Steve's reflection coefficient is the *physical reflection coefficient*, not the
virtual reflection coefficient and is NEVER equal to 1.0.

Now I see your problem, Cecil, and that is because you still don't understand
why a reflect ion coefficient of 1.0 IS established when two waves equal in
magnitude but of equal and opposite phase occur at the match point. If the two
waves are of unequal magnitude the coefficient is simply less than 1.0. So I
repeat for emphasis, it matters not whether the reflection is established by
physical or virtual means. This is another error in Steve's article. He disputes
this established fact, saying incorrectly that a physical short is required to
establish reflections--totally wrong.

However, in general, V1 and V2 cannot be added, or superposed if the
energy involved comes from only one source.

True for your model - not true for Steve's model. You guys are NOT
using the same model. You are as far apart as the wave/particle
controversy.

True in general, period.

I simply can't accept that there can be more than one definition of
re-reflection.

But there is, Walt. The S-parameter analysis defines re-reflection differently
than you do. In the equation, b2 = s21(a1) + s22(a2), the s22(a2) term is
the re-reflected voltage. It is defined as the voltage reflected from the
load multiplied by the physical reflection coefficient looking into port 2
when the source is replaced by Z0. That is NOT the way you define re-reflected
voltage.

Cecil, to perform an S-parameter test on an antenna tuner one would first
adjust it to match the input impedance of the line connecting it to the antenna
then disconnect it from the line and replace the line with a pure resistance =
to Zo. Now the input impedance is measured. Then the setup is reversed, placing
the Zo termination at the input and measuring the impedance looking rearward
into the output. These measurements yield the transfer impedance of the tuner,
but they don't yield the input and output impedances established during
operation. The reflections are not defined differently in either case.

And as I said in a much earlier post I must remind you that Steve made a vital
error when he said:

"When two forward-traveling waves add, general superposition theory and
Kirchhoff's voltage law require that the vector sum of the individual
forward-traveling voltages such that VFtotal = V1 + V2."

This statement is not true in general.

That statement is true in general for an S-parameter analysis. You and
Dr. Best are not using the same analysis model.

This is what makes Eq 9 clearly invalid in general.

Eq 9 is valid for an S-parameter analysis. I doubt that you are going
to be able to discredit the entire field of S-parameter analysis so
you might as well accept the fact that you are calling a shrub a "tree"
and Steve is calling a shrub a "plant". Either both of your are right
or both or you are wrong.

Cecil, we don't need to argue the conditions concerning S-parameter analysis,
because I've put my finger on the problem you're having with this entire
discussion, that is you're (and Steve's) unwillingness to understand that wave
interference can establish a reflection coefficient of 1.0 without any physical
means.

This vital error in Steve's belief that physical means is required to establish
reflections is why he wrote his article for the express purpose of trying to
prove my writings in Reflection incorrect. The material in his article hasn't
proven them wrong because they aren't wrong, he has merely shown the world that
he doesn't understand the wave mechanics involved in impedance matching.

Walt