Walter Maxwell wrote:
Cecil, I found the two Vfwd's we're looking for. They are derived from V1y and
V2y. 70.7 v and 10.94 v. The interesting part is that 10.94 v is the exact
increase in voltage resulting from adding 33.333 w to 100 w.

Yes, that's superposition of voltages in action. All it takes to exist is
some constructive interference energy without which, superposition would
not occur. Without the constructive interference, the two waves are not
coherent and add like two incoherent waves.

This is because the
re-reflected forward voltage there, 40.82 v added to the source voltage 70.71 v
does not equal the real total forward voltage of 81.65 v.

Let me say it again. Your re-reflected voltage and Steve's re-reflected
voltage are not the same quantities because they have completely
different definitions.

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?

Therefore, my final comment on Eq 9 is that it works in specific cases but it
certainly is not valid in general.

It is valid for Steve's definition of re-reflected voltage. It is not valid
for your definition of re-reflected voltage. You guys are NOT using the
same analysis model. I don't know how to say it any clearer than that.
Steve's analysis model works for him. Your completely different analysis
model works for you. You both get the same answers but you are using
different models to get there.

Jim Kelley, as a physicist, defines energy transfer different than I, as
an engineer, do. Therefore, his values of energy transferred and mine will
NEVER agree. You and Dr. Best are in the same position. Your re-reflected
voltages and powers will NEVER agree because you define them differently.
If you accept his definitions, you will get the same results that he does.
If he accepts your definitions, he will get the same results that you do.
But neither one of you is willing to budge an inch.
--
73, Cecil http://www.qsl.net/w5dxp



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Let me say it again. Your re-reflected voltage and Steve's re-reflected
voltage are not the same quantities because they have completely
different definitions.

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?

Therefore, my final comment on Eq 9 is that it works in specific cases but it
certainly is not valid in general.

It is valid for Steve's definition of re-reflected voltage. It is not valid
for your definition of re-reflected voltage. You guys are NOT using the
same analysis model. I don't know how to say it any clearer than that.
Steve's analysis model works for him. Your completely different analysis
model works for you. You both get the same answers but you are using
different models to get there.

Cecil, I don't recall defining re-reflection, nor do I recall seeing any
definition of it by Steve. A re-reflection is a re-reflection. It's simply a
reflection of a wave established when an EM wave encounters a discontinuity in
its otherwise smooth path. How else can it be defined?

A forward traveling EM wave that is a result of re-reflection has no different
characteristics than any other EM wave, and therefore cannot be distinguished
from any othe EM wave.

Now let's take another look at Steve's Eqs 7 and 8. There is no question here
that there is anything different from being general. In fact, they're
straightforward, valid, and viable. They are general, and are understood in
exactly the same manner by any engineer speaking transmssion line language.

Now let's look at Eq 9. It too, is straigtforward, and it is entirely general if
the user knows that V1 and V2 are each delivered by two different sources of
energy. However, in general, V1 and V2 cannot be added, or superposed if the
energy involved comes from only one source. Note the operative word is 'in
general'. If there is a specific case, as in the 1/4 wl transformer where there
are two reflections that are re-reflected into the forward direction, the Eq
works, but it doesn't work in the configuration that was replaced by the 1/4 wl
transformer. Consequently, Eq 9 must be invalid in general.

I simply can't accept that there can be more than one definition of
re-reflection. Furthermore, anyone reading Steve's paper and encounters Eq 9
believing it valid in general, and applies it to a general case, he has no
assurance he's going to get the correct answer. The chances are he won't, the
same as I and others did. If Eq 9 is Steve's piece of cake he can't have it and
eat it too.

And as I said in a much earlier postI 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. This statement would be true in general
if you replace 'forward-traveling waves' with 'voltage', and specified that the
statement is following simple circuit theory. This is because only in special
cases will it be true where the voltages are forward-traveling waves. You know
very well there are cases involving transmission lines where circuit theory
fails and transmission-line theory must be involved to obtain the correct
solution to a problem.

This is what makes Eq 9 clearly invalid in general.

Walt

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, 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.

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.

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.

And as I said in a much earlier postI 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.
--
73, Cecil http://www.qsl.net/w5dxp



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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

snip
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.

Cecil, I'll give you an example below, taken from your own 1/4 wl transformer
analysis, that proves a virtual reflection coefficient can equal 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.

In your 1/4 wl transfomer analysis we have Pfwd total = 133.33 w. 33.333 w of
this incident power was reflected, even though in originally separate, but
eventually integrated waves to sum to 33.333 w. The originally separate, but
eventually integrated voltages were totally re-reflected at the match point. I
know that you agree that all reflected waves are totally re-reflected at the
match point. How do you suppose those waves became totally re-reflected? It can
be accomplished only if the aggregate reflection coefficient is 1.0.
Consequently, in the steady state the input of the 1/4 wl transformer presents a
reflection coefficient of 1.0 to the integrated sum of individual reflected
waves. The separate forward and reflected waves that appear in your analysis
occur separately only during the transition period from the initial state to the
steady state condition. Can't be any other way, Cecil. Believe it!

Walter Maxwell wrote:
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.

I agree the results are identical - It matters within the analysis but it
doesn't matter to the outcome. You and Steve get the same outcome. The
things you are arguing over is what happens inside the model each of you
is using.

Now I see your problem, Cecil, and that is because you still don't understand
why a reflection coefficient of 1.0 IS established when two waves equal in
magnitude but of equal and opposite phase occur at the match point.

Walt, please listen to this again. I understand why a reflection coefficient
of 1.0 is established in your model. I understand why it is impossible for a
reflection coefficient of 1.0 to exist in Dr. Best's model. It is now up to you
to understand why it is impossible for a reflection coefficient of 1.0 to exist
in Dr. Best's model. A reflection coefficient of 1.0 also does not and cannot
exist in an S-parameter analysis of the following example.

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.

It is IMPOSSIBLE to establish a reflection coefficient of 1.0 in an S-parameter
analysis of the following:

100W XMTR---50 ohm line---x---1/2WL 150 ohm line---50 ohm load

The reflection coefficient at point 'x' in Dr. Best analysis is ABSOLUTELY
CONSTANT at 0.5. It NEVER changes from 0.5. It is always (150-50)/(150+50)
equals 0.5. It NEVER becomes 1.0 as it does in your analysis. A reflection
coefficient of 1.0 is ABSOLUTELY IMPOSSIBLE using an S-parameter analysis of
the above configuration.

Using an S-parameter analysis, a reflection coefficient of 1.0 DOES NOT exist
anywhere and CANNOT exist anywhere. Until you accept that fact, you will continue
to be confused.

Let me say it once again: THE "REFLECTION COEFFICIENT" THAT YOU ARE USING HAS
A DIFFERENT DEFINITION THAN THE "REFLECTION COEFFICIENT" THAT DR. BEST IS USING.
IT IS IMPOSSIBLE FOR DR. BEST'S REFLECTION EVER TO EQUAL 1.0. Dr. Best's rho is
NOT equal to and is NEVER equal to SQRT(Pr/Pf). Why is that so hard to understand?
--
73, Cecil http://www.qsl.net/w5dxp



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Walter Maxwell wrote:
Cecil, I'll give you an example below, taken from your own 1/4 wl transformer
analysis, that proves a virtual reflection coefficient can equal 1.0.

Save your energy, Walt. An S-parameter analysis does NOT allow for virtual
reflection coefficients. Virtual reflection coefficients DO NOT EXIST and
CANNOT EXIST in an S-parameter analysis. I don't know how to convey that
fact to you any stronger than I already have. Virtual reflection coefficients
are completely irrelevant to an S-parameter analysis. Virtual reflection
coefficients simply do NOT exist within the S-parameter math model.

Consequently, in the steady state the input of the 1/4 wl transformer presents a
reflection coefficient of 1.0 to the integrated sum of individual reflected
waves.

Walt, virtual reflection coefficients simply don't exist in an S-parameter
analysis. Therefore, in all the examples discussed, reflection coefficients
of 1.0 are COMPLETELY IRRELEVANT to any discussion involving S-parameters.
Reflection coefficients of 1.0 DO NOT EXIST in an S-parameter analysis of a
matched system involving 50 ohms and 150 ohms. s11 is the reflection coefficient
looking into port 1. It is fixed constant at 0.5 and doesn't chance no matter
what the conditions. Your assertions are simply irrelevant to an S-parameter
analysis.
--
73, Cecil http://www.qsl.net/w5dxp



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On Thu, 10 Jun 2004 13:16:34 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
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.

I agree the results are identical - It matters within the analysis but it
doesn't matter to the outcome. You and Steve get the same outcome. The
things you are arguing over is what happens inside the model each of you
is using.

Cecil, you keep saying Steve and I get the same outcome. Where do you see that
result ? The fact that Steve's outcome is incorrect in general, and nowhere
agrees with mine, how can you say we get the same outcome?

Now I see your problem, Cecil, and that is because you still don't understand
why a reflection coefficient of 1.0 IS established when two waves equal in
magnitude but of equal and opposite phase occur at the match point.

Walt, please listen to this again. I understand why a reflection coefficient
of 1.0 is established in your model. I understand why it is impossible for a
reflection coefficient of 1.0 to exist in Dr. Best's model. It is now up to you
to understand why it is impossible for a reflection coefficient of 1.0 to exist
in Dr. Best's model. A reflection coefficient of 1.0 also does not and cannot
exist in an S-parameter analysis of the following example.

Why do you keep insisting on an S-parameter analysis? What good are you
accomplishing with it ? And speaking of Steve's model--he shows it in his Fig 5
as a simple T-network as used in most antenna tuners. The effect at the input
of the network is no different than in a stub model or a 1/4 wl transformer
model. You can't rely on 'different models' to explain away the problem. When
properly adjusted to match the output to the input in his T-network the
reflected power reaching the input is totally re-reflected. This results only
from a reflection coefficient of 1.0. Saying that it is impossible for a 1.0 to
exist in Steve's model is simply not true. Steve simply doesn't understand the
wave mechanics involved here.

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.

It is IMPOSSIBLE to establish a reflection coefficient of 1.0 in an S-parameter
analysis of the following:

100W XMTR---50 ohm line---x---1/2WL 150 ohm line---50 ohm load

It's true that the physical reflection coefficient is 0.5. How then do you
account for ALL the reflected energy being re-reflected to the load? The fact
is that a reflection coefficient of 1.0 is also established there by wave
interference. You really must come to the grips with the fact that a reflection
coefficient of 1.0 can be established by wave interference. You are now the one
who won't budge.

The reflection coefficient at point 'x' in Dr. Best analysis is ABSOLUTELY
CONSTANT at 0.5. It NEVER changes from 0.5. It is always (150-50)/(150+50)
equals 0.5. It NEVER becomes 1.0 as it does in your analysis. A reflection
coefficient of 1.0 is ABSOLUTELY IMPOSSIBLE using an S-parameter analysis of
the above configuration.

Using an S-parameter analysis, a reflection coefficient of 1.0 DOES NOT exist
anywhere and CANNOT exist anywhere. Until you accept that fact, you will continue
to be confused.

Let me say it once again: THE "REFLECTION COEFFICIENT" THAT YOU ARE USING HAS
A DIFFERENT DEFINITION THAN THE "REFLECTION COEFFICIENT" THAT DR. BEST IS USING.
IT IS IMPOSSIBLE FOR DR. BEST'S REFLECTION EVER TO EQUAL 1.0. Dr. Best's rho is
NOT equal to and is NEVER equal to SQRT(Pr/Pf). Why is that so hard to understand?

I haven't seen anything in Steve's paper that shows he's using an S-Parameter,
can you show me where? Not that it would make any difference in the outcome.

In addition, referring to your paragraph immediately above, where did you get
the idea that I said Steve's rho = SQRT(Pr/Pf)? Cecil, that's simply SWR, not
rho.

At this point, Cecil, if you are still unable to accept the concept of
establishing a reflection coefficient of 1.0 through wave interference then
there is no use of continuing this discussion. It will never go forward until
you do. I know there are others on this rraa who agree with you, but there are
many more who understand the concept and agree that it's true.

Walt

Walter Maxwell wrote:
Cecil, you keep saying Steve and I get the same outcome. Where do you see that
result ?

You both get the same measurable forward and reflected powers,
forward and reflected voltages, and forward and reflected currents.

Why do you keep insisting on an S-parameter analysis?

Because that is essentially what Steve used and it works. It has
worked for decades. Please download the HP AN 95-1 and see for yourself.

When
properly adjusted to match the output to the input in his T-network the
reflected power reaching the input is totally re-reflected. This results only
from a reflection coefficient of 1.0.

Only in your model, Walt, not in Steve's. Reflection coefficients of 1.0
are INVALID in Steve's quasi-S-parameter model.

Saying that it is impossible for a 1.0 to
exist in Steve's model is simply not true.

Yes, it is true, for the configurations discussed so far. The ONLY time a
reflection coefficient of 1.0 exists in Steve's model is for a *physical*
short, a *physical* open, or a *physical* pure reactance. In Steve's model,
virtual stuff is invalid.

It's true that the physical reflection coefficient is 0.5. How then do you
account for ALL the reflected energy being re-reflected to the load? The fact
is that a reflection coefficient of 1.0 is also established there by wave
interference. You really must come to the grips with the fact that a reflection
coefficient of 1.0 can be established by wave interference. You are now the one
who won't budge.

You are asking me to budge away from the rules of an S-parameter analysis?

Sorry, Walt, virtual reflection coefficients are INVALID in an S-parameter
analysis like Steve is using. The s11 reflection coefficient that Steve uses
is defined as the "input reflection coefficient looking into port 1 with
the output port terminated by a matched load." Since there is no such thing
as a Z0 = 0 or a Z0 = infinity, there is no such thing as a reflection
coefficient equal to 1.0. The reflection coefficient, s11, that Steve is
using can *NEVER* be zero or one - *NOT EVER*.

I haven't seen anything in Steve's paper that shows he's using an S-Parameter,
can you show me where? Not that it would make any difference in the outcome.

His reflection coefficient is (Z2-Z1)/(Z2+Z1). That is identical to the S-parameter
reflection coefficient, s11. It is a constant and never changes to 1.0, no matter
what happens to the reflected power. Dr. Best simply doesn't use virtual
reflection coefficients. Using virtual reflection coefficients in an S-parameter
analysis is *INVALID*, i.e. they simply do not exist.

In addition, referring to your paragraph immediately above, where did you get
the idea that I said Steve's rho = SQRT(Pr/Pf)? Cecil, that's simply SWR, not
rho.

Let's take the 133.33W forward and 33.33W reflected example. rho equals the square
root of (33.33/133.33) = 0.5. That's not SWR, Walt. SWR cannot be less than unity.
That is indeed the physical voltage reflection coefficient.

At this point, Cecil, if you are still unable to accept the concept of
establishing a reflection coefficient of 1.0 through wave interference then
there is no use of continuing this discussion.

I accept the concept of a reflection coefficient of 1.0 for your model, Walt.
But a reflection coefficient of 1.0 is simply NOT allowed in the quasi-S-parameter
analysis that Steve uses. The S-parameter analysis works and has been used for
decades but an s11 of 1.0 simply never happens (except at a short or an open).
The reflection coefficients in an S-parameter analysis and in Steve's analysis
are ***PHYSICAL***. They are ***NEVER*** virtual. I'm sorry if that upsets you.
I don't know what else to say.
--
73, Cecil http://www.qsl.net/w5dxp



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On Thu, 10 Jun 2004 21:17:58 -0500, Cecil Moore wrote:

Walter Maxwell wrote:

In addition, referring to your paragraph immediately above, where did you get
the idea that I said Steve's rho = SQRT(Pr/Pf)? Cecil, that's simply SWR, not
rho.

Let's take the 133.33W forward and 33.33W reflected example. rho equals the square
root of (33.33/133.33) = 0.5. That's not SWR, Walt. SWR cannot be less than unity.
That is indeed the physical voltage reflection coefficient.

You're right, Cecil, the print is so small on my screen I confused the r and f,
yes, it's rho.

At this point, Cecil, if you are still unable to accept the concept of
establishing a reflection coefficient of 1.0 through wave interference then
there is no use of continuing this discussion.

I accept the concept of a reflection coefficient of 1.0 for your model, Walt.
But a reflection coefficient of 1.0 is simply NOT allowed in the quasi-S-parameter
analysis that Steve uses. The S-parameter analysis works and has been used for
decades but an s11 of 1.0 simply never happens (except at a short or an open).
The reflection coefficients in an S-parameter analysis and in Steve's analysis
are ***PHYSICAL***. They are ***NEVER*** virtual. I'm sorry if that upsets you.
I don't know what else to say.

I'm sorry, Cecil, but you are missing the entire point of the discussion. I'm
not upset, I'm just dismayed that you don't see the light. So as I said above
there is no point in continuing the discussion. Some day you'll come to
understand the basis for the problem, and then I'm sure we'll agree.

C ya, Cecil, and take care!

Walt