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Old April 27th 07, 01:20 PM posted to rec.radio.amateur.antenna
Cecil Moore[_2_] Cecil Moore[_2_] is offline
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First recorded activity by RadioBanter: Mar 2007
Posts: 3,521
Default Analyzing Stub Matching with Reflection Coefficients

Keith Dysart wrote:
Hmmm. Having a complete inability to articulate any issues
with the model, you are, none-the-less, convinced that it does
not work in 'reality'. Hmmm.


I have been articulating issues with the model for weeks
now and I am just about articulated out. We are repeating
the same things over and over and unless you take time
out to comprehend interference, there's no reason to
continue.

The fact that zero energy is dissipated in a source
is prima facie evidence of destructive interference
and a "redistribution of energy in a direction that
allows constructive interference".


But then what is the fact that 4 times the energy is
dissipated in the source prime facie evidence of?


Of *total constructive interference* in the source, of
course. I already answered that question days ago. It
is futile to try to communicate with someone who refuses
to listen. Here are the power intensity equations
governing the power dissipated in the two sources in
the previous two examples.

Thevenin equivalent if P1 = P2:
Pdis = P1 + P2 - 2*SQRT(P1*P2) = 0
*Total Destructive Interference* as defined by Hecht in
"Optics", 4th edition, page 388.

Norton equivalent if P1 = P2:
Pdis = P1 + P2 + 2*SQRT(P1*P2) = 4*P1
*Total Constructive Interference* as defined by Hecht in
"Optics", 4th edition, page 388.

Until you learn to recognize interference when it is staring
you in the face, you are going to continue to make the same
mistakes over and over. Forward and reflected energy is alive
and well and obeys the conservation of energy principle. That
you cannot figure out where the photonic energy goes during
a wave interference event is not my problem. Hints about
destructive interference:

www.mellesgriot.com/products/optics/oc_2_1.htm

"Clearly, if the wavelength of the incident light and the thickness
of the film are such that a phase difference exists between reflections
of p, then reflected wavefronts interfere destructively, and overall
reflected intensity is a minimum. If the two reflections are of equal
amplitude, then this amplitude (and hence intensity) minimum will be
zero."

Note that "intensity" is *power density* in watts/unit-area.

"In the absence of absorption or scatter, the principle of conservation
of energy indicates all 'lost' reflected intensity will appear as
enhanced intensity in the transmitted beam. The sum of the reflected and
transmitted beam intensities is always equal to the incident intensity.
This important fact has been confirmed experimentally."

http://micro.magnet.fsu.edu/primer/j...ons/index.html

"... when two waves of equal amplitude and wavelength that are 180-
degrees out of phase with each other meet, they are not actually
annihilated. All of the photon energy present in these waves must
somehow be recovered or *redistributed in a new direction*, according to
the *law of energy conservation* ... Instead, upon meeting, the photons
are *redistributed to regions that permit constructive interference*, so
the effect should be considered as a *redistribution* of light waves and
photon energy rather than the spontaneous construction or destruction
of light."

emphasis mine
--
73, Cecil http://www.w5dxp.com