Gene Fuller wrote:
I don't have to "prove" anything. Just set up the standard wave
equations with the standard boundary conditions and the problem
practically solves itself. The non-zero remaining waves are all moving
in the same direction. I forgot to ask them if they realize that Cecil
doesn't approve of such behavior.

You should have warned us that you were talking about NET waves and
NET energy transfer. I'm not discussing that at all. I am talking about
component waves and component energy transfer without which standing
waves cannot exist. Or maybe you can offer an example of standing waves
in the absence of at least two waves traveling in opposite directions.
If you can do that, I will admit defeat.

I suppose this is an prime example of being seduced by "math models",
but I believe that is a lesser fault than being seduced by Cecil's
imaginary models.

It is indeed an example of being seduced by the NET math model. Please
transfer over to the component math model and rejoin the discussion.
Lots of interesting things are happening below the threshold of the
NET math model. The NET math model doesn't explain anything except
the NET results. If your bank account balance doesn't change from one
month to another, do you also assume that you have written no checks
and have no income for that month? Literally speaking, please get real!
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil,

Who said anything about distinguishing net waves or component waves? I
was talking about a complete solution.

If you read what I wrote you will note that I said any purported waves
traveling in the reverse direction have zero amplitude. In other words
they do not exist.

If you choose to create any number of fictitious components that all
cancel, go right ahead. No professional does it that way.

You appear to misunderstand that it is essentially impossible to do
anything with all of your interfering component waves except wave your
hands and flap your gums about them. If you really want to get
quantitative answers then it is conventional to use ordinary
electromagnetic theory starting with Maxwell's equations. No fictitious
canceling component waves are needed as input, nor do they arise as
output from a correct analytical treatment.

Really, this is standard textbook stuff. If you would like exact
references by title and page I will be happy to provide them.


73,
Gene
W4SZ

Cecil Moore wrote:
Gene Fuller wrote:

I don't have to "prove" anything. Just set up the standard wave
equations with the standard boundary conditions and the problem
practically solves itself. The non-zero remaining waves are all moving
in the same direction. I forgot to ask them if they realize that Cecil
doesn't approve of such behavior.


You should have warned us that you were talking about NET waves and
NET energy transfer. I'm not discussing that at all. I am talking about
component waves and component energy transfer without which standing
waves cannot exist. Or maybe you can offer an example of standing waves
in the absence of at least two waves traveling in opposite directions.
If you can do that, I will admit defeat.

I suppose this is an prime example of being seduced by "math models",
but I believe that is a lesser fault than being seduced by Cecil's
imaginary models.


It is indeed an example of being seduced by the NET math model. Please
transfer over to the component math model and rejoin the discussion.
Lots of interesting things are happening below the threshold of the
NET math model. The NET math model doesn't explain anything except
the NET results. If your bank account balance doesn't change from one
month to another, do you also assume that you have written no checks
and have no income for that month? Literally speaking, please get real!

Gene Fuller wrote:
If you read what I wrote you will note that I said any purported waves
traveling in the reverse direction have zero amplitude. In other words
they do not exist.

So you disagree with "Wave Mechanics of Transmission Lines, Part 3:"
by S. R. Best, QEX Nov/Dec 2001?

Your statement denies reality. In the following system, 178 joules/sec
are rejected by the load and thus flow back toward the source. You can
measure it with a wattmeter. The very first thing you need to prove is
that standing waves can exist without two waves flowing in opposite
directions. Anything short of that proof is just handwaving and gum
flapping on your part.

278W forward--
100W XMTR---50 ohm feedline---x---1/2WL 450 ohm feedline---50 ohm load
--178W reflected

You appear to misunderstand that it is essentially impossible to do
anything with all of your interfering component waves except wave your
hands and flap your gums about them.

If that is beyond your comprehension, just say so but, in reality, those
interfering component waves obey the laws of physics as explained in _Optics_,
by Hecht and on the Melles-Groit web page:

http://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.

In the absence of absorption or scatter, the principle of CONSERVATION OF
ENERGY indicates all "lost" reflected intensity will appear as ENHANCED
INTENSITY [constructive interference] in the transmitted beam."

That's pretty clear - 100% destructive interference between the two rearward-
traveling reflected wave components - 100% of the energy involved in the destructive
interference is not lost and joins the forward-traveling wave since it has no
other possible direction.

FYI, the equations governing the irradiance involving a perfect non-glare
thin film a Ir1+Ir2-2*SQRT(Ir1*Ir2) = reflected irradiance = 0 and
If1+If2+2*SQRT(If1*If2) = total forward irradiance Page 388 of _Optics_.
--
73, Cecil http://www.qsl.net/w5dxp



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On Wed, 10 Mar 2004 22:43:11 -0600, Cecil Moore
wrote:

So you disagree with "Wave Mechanics of Transmission Lines, Part 3:"
by S. R. Best, QEX Nov/Dec 2001?

Cecil, are you saying you believe the total nonsense in Steve's Part 3? The
fiction he wrote there is totally incorrect and misleading. He introduced nine
new misconceptions that need dispelling, misconceptions that totally dispute my
explanations of the role of wave mechanics in impedance matching, including my
references from MIT and Harvard EE professors.

I can't disclose what's about to happen in the immediate future on this issue,
but when it does happen you'll see mathematical proof of where herr Best went
wrong. And it also totally supports your argument with Gene, who apparently
doesn't get it either, because I heard him claim that Steve's article is one of
the most illuminating and definitive he's read. Unfortunately, Steve's QEX
article is total BS.

Walt, kW2DU

Walter Maxwell wrote:

Cecil Moore wrote:
So you disagree with "Wave Mechanics of Transmission Lines, Part 3:"
by S. R. Best, QEX Nov/Dec 2001?

Cecil, are you saying you believe the total nonsense in Steve's Part 3?

No, Steve assumes the existence of forward and reflected energy waves.
I also assume the existence of forward and reflected energy waves and
think their existence can be proven. I assume that you agree with Steve
that forward and reflected energy waves exist. If I understand Gene
correctly, he believes that reflected energy waves do not exist in
a matched system even though there is a mismatch at the load.

I probably should have said: "So you disagree with the very existence
of reflected energy waves which is assumed by S. R. Best in his QEX
Nov/Dec 2001 article.

Since Steve's article asserts the existence of forward and reflected
energy waves, it cannot be "total nonsense". In fact, Steve's equation
for total forward power yields the correct answer. In a matched system,

Ptotal = P1 + P2 + 2*SQRT(P1*P2)

indeed yields the correct result given that:

P1 = Psource(1-rho)^2 = Psource times the power transmission coefficient

P2 = Pref(rho)^2 = Preflected times the power reflection coefficient

Steve's problem was that he did not recognize (actually denied) the role
of interference, destructive and constructive, and therefore left out half
of the explanation. In optics, 2*SQRT(P1*P2) is known as the "interference term"
and equal magnitudes of interference happen on both sides of the match point. In
a perfectly matched system, at the match point, there exists total destructive
interference toward the source, i.e. zero reflections, and total constructive
interference toward the load, i.e. all the energy winds up flowing toward the load.

The following two problems are virtually identical. 'n' is the index of
refraction.

air | glass
Laser-------------|---------
n=1.0 | n=1.5

XMTR---50 ohm coax---75 ohm load

The magnitudes of the reflection coefficients are identical at |0.2|

The solutions to those problems are virtually identical.

air | 1/4WL thin-film | glass
Laser-------------|------------------|-----------
n=1.0 | n=1.225 | n=1.5

XMTR---50 ohm coax--x--1/4WL 61.2 ohm coax--75 ohm load

Optical physicists fully understand what happens with the Laser. It is explained
on the Melles-Griot web page and in _Optics_, by Hecht. From the Melles-Griot web
page: http://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. 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."

This fits perfectly with Reflections II, chapter 23: "Therefore, while reflection
angles for waves reflected at the input mismatch (point x above) are 180 deg for voltage,
and 0 deg for current, the corresponding angles at the input for the waves reflected
from the output mismatch (75 ohm load above) are reversed, 0 deg for voltage and 180
deg for current. Consequently, all corresponding voltage and current phasors are 180
deg out of phase at the matching point. ... With equal magnitudes and opposite phase
at the same point (point x, the matching point) the sum of the two waves is zero."

That is a perfect description of total destructive interference. I have your reference,
J. C. Slater's book, _Microwave_Transmission_, on order.
--
73, Cecil http://www.qsl.net/w5dxp



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On Thu, 11 Mar 2004 09:52:28 -0600, Cecil Moore
wrote:

Walter Maxwell wrote:

Cecil Moore wrote:
So you disagree with "Wave Mechanics of Transmission Lines, Part 3:"
by S. R. Best, QEX Nov/Dec 2001?

Cecil, are you saying you believe the total nonsense in Steve's Part 3?

No, Steve assumes the existence of forward and reflected energy waves.
I also assume the existence of forward and reflected energy waves and
think their existence can be proven. I assume that you agree with Steve
that forward and reflected energy waves exist. If I understand Gene
correctly, he believes that reflected energy waves do not exist in
a matched system even though there is a mismatch at the load.

I probably should have said: "So you disagree with the very existence
of reflected energy waves which is assumed by S. R. Best in his QEX
Nov/Dec 2001 article.

Cecil, it's not whether reflected waves exist that's wrong with Steve's paper,
it's his misuse them that's wrong, and it's the misuse that is 'total nonsense'.

Since Steve's article asserts the existence of forward and reflected
energy waves, it cannot be "total nonsense". In fact, Steve's equation
for total forward power yields the correct answer. In a matched system,

Ptotal = P1 + P2 + 2*SQRT(P1*P2)

indeed yields the correct result given that:

P1 = Psource(1-rho)^2 = Psource times the power transmission coefficient

P2 = Pref(rho)^2 = Preflected times the power reflection coefficient

Cecil, your equations for P1 and P2 yield absurd answers if you plug the numbers
into them. The value for P1 should read "Psource (1 - rho^2) = ..., and the
value for P2 should read "P2 = Pref (rho^2). Beega difference! Then the value
for Ptotal will be correct.

Steve's problem was that he did not recognize (actually denied) the role
of interference, destructive and constructive, and therefore left out half
of the explanation.

Exactly!!! And it's the correct interference relationship I present in QEX and
Reflections that he insists is incorrect. In much earlier emails with Steve he
told me that using my statements appearing there he could prove me technically
incompetent. He simply would not accept any of my pleadings with him to see the
correct application of the interference between reflected waves that achieves
the impedance match.

In optics, 2*SQRT(P1*P2) is known as the "interference term"
and equal magnitudes of interference happen on both sides of the match point. In
a perfectly matched system, at the match point, there exists total destructive
interference toward the source, i.e. zero reflections, and total constructive
interference toward the load, i.e. all the energy winds up flowing toward the load.

The following two problems are virtually identical. 'n' is the index of
refraction.

air | glass
Laser-------------|---------
n=1.0 | n=1.5

XMTR---50 ohm coax---75 ohm load

The magnitudes of the reflection coefficients are identical at |0.2|

The solutions to those problems are virtually identical.

air | 1/4WL thin-film | glass
Laser-------------|------------------|-----------
n=1.0 | n=1.225 | n=1.5

XMTR---50 ohm coax--x--1/4WL 61.2 ohm coax--75 ohm load

Optical physicists fully understand what happens with the Laser. It is explained
on the Melles-Griot web page and in _Optics_, by Hecht. From the Melles-Griot web
page: http://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. 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."

No one in his right mind can successfully argue against this. Anyone who would
argue against this is either of closed mind or an ignorant moron.

This fits perfectly with Reflections II, chapter 23: "Therefore, while reflection
angles for waves reflected at the input mismatch (point x above) are 180 deg for voltage,
and 0 deg for current, the corresponding angles at the input for the waves reflected
from the output mismatch (75 ohm load above) are reversed, 0 deg for voltage and 180
deg for current. Consequently, all corresponding voltage and current phasors are 180
deg out of phase at the matching point. ... With equal magnitudes and opposite phase
at the same point (point x, the matching point) the sum of the two waves is zero."

I'm glad you find that Chapter 23 fits, because I've known all along that it
fits perfectly with Melles-Griot. Steve (Best), on the other hand says Chapter
23 is totally wrong. You might also note that Chapter 23 is identical with my
paper in QEX in the Mar/Apr 1998 issue, which Steve also disputes in all three
parts of his QEX article.

That is a perfect description of total destructive interference. I have your reference,
J. C. Slater's book, _Microwave_Transmission_, on order.

You might find Slater (1943) difficult to obtain. I can email you a copy of the
pertinent part if you wish.

Walt, W2DU

In all these sort of discussions I have never heard any mention of
"Interaction Loss", ie., that which occurs directly between the reflection
coefficients of the source and load.

It seems something important has long been and is still being neglected. It
may be that some points of dispute could be resolved by taking Interaction
Loss into account.
----
Reg.

Walter Maxwell wrote:
Cecil, your equations for P1 and P2 yield absurd answers if you plug the numbers
into them. The value for P1 should read "Psource (1 - rho^2) = ..., and the
value for P2 should read "P2 = Pref (rho^2). Beega difference! Then the value
for Ptotal will be correct.

Yep, Walt, I made a typo. It should be (1-rho^2). When I think in words while
typing, "one minus rho squared", is ambiguous. Obviously (rho)^2 + (1-rho^2)
*must* equal unity, i.e. the total.

I'm glad you find that Chapter 23 fits, because I've known all along that it
fits perfectly with Melles-Griot. Steve (Best), on the other hand says Chapter
23 is totally wrong.

I don't know how he can say that. The Melles-Griot data for perfect non-glare
glass depends upon two 'I' irradiance equations.

Irradiance toward the source (reflected irradiance) equals:

Ir1 + Ir2 - 2*(Ir1*Ir2) = 0 = Ir1 + Ir2 - total_destructive_interference

Irradiance toward the load (total forward irradiance) equals:

If1 + If2 + 2*(If1*If2) = If1 + If2 + total_constructive_interference

It may not be apparent but (Ir1*Ir2) *must* equal (If1*If2).

Steve and I had an argument about this stuff years ago before he published his
QEX article. He denied that any interference exists even though his 2*SQRT(P1*P2)
term is know as the "interference term".

Irradiance, 'I', for a laser beam, is equivalent to power. Reflectance, 'R' in optics, is
the power reflection coefficient. Transmittance, 'T' in optics, is the power transmission
coefficient. Thus:

Ir1 = R*Isource Ir2 = T*Iref If1 = T*Isource If2 = R*Iref

You might find Slater (1943) difficult to obtain. I can email you a copy of the
pertinent part if you wish.

Thanks, but my used copy has already shipped through http://www.powellsbooks.com

Walt, as you know, QEX refused to publish my rebuttal of Steve's article. There's
some good stuff and some bad stuff in his article. This is not a black and white
argument. IMO, about a third of Steve's Part 3 article is valid. My objections
are with the other 2/3.
--
73, Cecil http://www.qsl.net/w5dxp



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Hi Walt,

I am quite surprised and disappointed that you commented on my review of
Steve Best's QEX articles in the manner quoted he

On Thu, 11 Mar 2004 09:17 Walter Maxwell wrote:

And it also totally supports your argument with Gene, who apparently
doesn't get it either, because I heard him claim that Steve's article is one of
the most illuminating and definitive he's read. Unfortunately, Steve's QEX
article is total BS.

Walt, kW2DU

************************************************** *

Here is an exact quote from my email to you dated January 31, 2003.

Hi Walt,

I'm back.

I have re-read the Best QEX article, I have read your rebuttal
carefully, and I have re-read parts of Reflections II.

I have to say that I believe the QEX article in question is fair and
correct. I cannot find a single flaw in it.

I have documented my response by adding comments to the rebuttal draft
you sent me the other day. My comments are in red.

In summary, I think the QEX article is completely correct in items 1, 2,
and 3. I am less comfortable about making any sort of definitive
statement on item 4.

I have been aware of the controversy for some time, and I am somewhat
dumbfounded by the entire matter.

I tacitly believed that all of this stuff had been fully defined,
understood, and non-controversial for many decades. Certainly there is
no new science in classical transmission line theory in 2003.

To the best of my understanding this entire matter has somewhat the
character of a tempest in a teapot. I have not found the slightest
evidence that your model and Steve Best's model disagree in any
measurable way. Clearly the insides of the models are different, but the
visible, measurable parts are not.

Is there a single case in which Best's model gives the wrong answer by
any measurement technique?

Is there a single case in which your model gives the wrong answer by any
measurement technique?

From a visualization and conceptualization point the models are quite
different. You note that many engineers appreciate your model as it
provides them a good understanding of the reflection behavior. To be
brutally honest, I prefer the approach taken by Best. I like the
equations to balance explicitly, and I am less comfortable with relying
on concepts like virtual opens and shorts.

Again, I do not see any physically measurable difference in the output
from the models. The rest is philosophy.

snip of irrelevant pleasantries

************************************************** *

Soooo, Walt, what did I write that elicited your unkind comment?


73,
Gene
W4SZ

Cecil,

OK, I will 'see' your references and 'raise' my bid to Born and Wolf
"Principles of Optics", 7th edition.

I recommend section 1.6, "Wave propagation in a stratified medium.
Theory of dielectric films". This section runs from page 54 to page 74,
and it describes in full detail everything you would want to know about
propagation of waves in multilayered structures.

There is a disclaimer in the introduction to this section which says,
"For the treatment of problems involving only a small number of films it
is naturally not necessary to use the general theory, and accordingly we
shall later describe an alternative and older method based on the
concept of multiple reflections." The reference is to section 7.6
"Multiple-beam interference", which runs from page 359 to page 409.

Similar sections are included in the 6th edition of this book, on pages
51 to 70 and 323 to 367 respectively. I am sure you can find one or both
of these editions in the TAMU library. I prefer the 7th edition, as it
seems easier on the eyes.

If you choose not to actually read these references I will tell you that
the first section is a full-blown Maxwell's equations treatment, and the
second section employs an interfering wave treatment.

What I find interesting is that there is not one mention of bouncing
energy waves or waves that have disappeared but their energy lives on.
If you read your favorite Melles-Griot material carefully without adding
your own spin (how else could it be, etc.) you will see that they do not
discuss bouncing energy waves either. You will notice that M-G say the
energy "appears" in the transmitted wave. This is good, since we like to
believe conservation of energy is maintained. M-G do not discuss the
mechanism. All of the stuff about bouncing energy rejoining the forward
wave is purely in your imagination.

I think I have finally figured out the root of the disagreement. Your
approach is similar to a one-trick pony. You have latched onto the
concept of interference to the exclusion of any other valid approach. As
a consequence it becomes *necessary* to imagine such things as bouncing
energy waves. The Maxwell's equations approach does not require this
sort of crutch. Try it, you might like it.

I am quite familiar with both analytical methods, and I am comfortable
in using either one. The key is understanding when a given analytical
technique will be the most useful, most direct, most intuitive, and so
on. I have nothing against interference, but its misapplication is like
using a pipe wrench to drive a nail while a hammer is right at hand.

73,
Gene
W4SZ



Cecil Moore wrote:



If that is beyond your comprehension, just say so but, in reality, those
interfering component waves obey the laws of physics as explained in
_Optics_, by Hecht and on the Melles-Groit web page:

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