On Jun 8, 5:57*am, Keith Dysart wrote:
As soon as one assigns tangible energy to the reflected wave, it
becomes reasonable to ask for an accounting of this energy and
the model is incapable of properly accounting for the energy.

Then one is using the wrong model which is typical of many RF
engineers. Optical physicists have been accounting for reflected
energy for decades. That one is ignorant of where reflected energy
goes is not a good reason to abandon the law of physics that says that
*ALL* EM waves contain ExH energy, including reflected EM waves. EM
waves cannot exist without ExH energy so you might as well say that
reflected waves do not exist at all because that is the logical
conclusion based on your false premises.

Optical physicists have been aware of the power-density/interference
equation for a long, long time. It is covered in any good reference
book on optics, e.g. by Hecht and by Born and Wolf. I have posted the
details - why do choose to remain ignorant? At least take time to
comprehend the technical information available from the field of
optics and report back to us why many decades of that EM wave
knowledge is wrong. Here is the equation that explains where the
reflected energy goes. All you have to to is track the energy back in
time.

Ptot = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

where A is the angle between the two voltages. The last term is known
as the "interference term".

When two coherent, collimated, signals interfere while traveling in
the same direction in a transmission line: If they are 90 degrees
apart, there is zero interference and the I and Q components are
easily recovered.

If they are less than 90 degrees apart, the interference is
constructive and the phasor superposition of the two waves results in
*more power in the total superposed wave* than in the arithmetic sum
of the two powers. The extra energy has to come from somewhere. In the
absence of a local source, the extra energy has to come from
destructive interference in the opposite direction, e.g. at a Z0-
match.

If they are between 90 degrees and 180 degrees apart, the interference
is destructive and the phasor superposition of the two waves results
in *less power in the total superposed wave* than in the arithmetic
sum of the two waves. The "left-over" energy has to go somewhere so it
has to be delivered in the opposite direction to the area that
supports constructive interference.

Here is what Hecht said: "Briefly then, optical (EM wave) interference
corresponds to the interaction of two or more (EM) lightwaves yielding
a resultant irradiance (power density) that deviates from the sum of
the component irradiances."

Hecht's statement hints to where the reflected energy goes. In the
case of wave cancellation at a Z0-match that eliminates ExH reflected
energy flowing toward the load, all of the ExH reflected energy is
recovered and redistributed back toward the load.

Following this weakness back through the model, the root cause
is the attempt to assign tangible energy to the reflected wave.
Think of it as a reflected voltage or current wave and all will
be well, but assign power to it and eventually incorrect
conclusions will be drawn.

Only if the model is inadequate. Optical physicists assign tangible
energy to reflected waves all the time. Many are probably reading
these postings and laughing at the collective ignorance about EM
waves.

Take a look at this web page:

http://www.teachspin.com/instruments...eriments.shtml

Scroll down to, "Using Dielectric Beamsplitters to find the "missing
energy" in destructive interference". There it is, all spelled out for
you - where the reflected energy goes. Reflected energy is never
actually missing - what are missing are a few of the brain cells that
need to be used to think about reflected energy. :-)

For those who understand this, and know that "where did the
reflected energy go?" is an invalid question, using the power
model within its limits will not cause difficulties. But for
those who are not careful, great difficulties arise and a lot
of fancy dancing is offered to work around the difficulties,
unsuccessfully.

Yes, throughout history, ignorant people have brought great
difficulties upon themselves because they refuse to alleviate their
ignorance. Those who refuse to learn from their mistakes are destined
to repeat those same mistakes. And you were making these exact same
mistakes years ago. You can lead a horse to water ...

In his Nov/Dec 2001 QEX article, Dr. Best attempted to explain where
the reflected energy goes. Shackled by ignorance, he got many things
wrong e.g. phantom EM waves that exist without energy. But the article
alludes to the conceptual path that needs to be taken to alleviate
that ignorance. In "Wave Mechanics of Transmission Lines, Part 3", Dr.
Best published the above power-density/interference equation although
he ignorantly asserted on this newsgroup that interference did not
exist.

Interference resulting from superposition at an impedance
discontinuity is the key missing link in explaining everything that
happens to the energy in a transmission line including Roy's food-for-
thought article. Why is there so much reluctance to adopt a proven law
of EM wave physics from the field of optics?
--
73, Cecil, w5dxp.com