Standing-Wave Current vs Traveling-Wave Current
 

On Wed, 2 Jan 2008 06:14:58 -0500, "David J Windisch"
wrote:

What's the status on that DC long-line 'tween somewhere in your neck of the
woods south toward Baja, pls? Kind regards on behalf of all the lurkers
from Dave N3HE

?????

Hi Dave,

That is pretty obscure, which means you know more than I do.

On the other hand, the long-line to DC for me a few days ago was
American Airlines SEA to BWI; then back from National; both through
DFW.

73's
Richard Clark, KB7QHC

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
So far I haven't seen any analysis using alternative theories, ideas of
how sources work, or using power waves, which also correctly predict the
voltage at all times and in steady state.

This is hardly different from the other example. Total destructive
interference is still occurring in the source resistor resulting
in total constructive interference toward the load. The forward
and reflected powers are equal to 0.04 watts. All of the voltages
and currents are easy to calculate after that. What else do you
need to know?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

On Wed, 2 Jan 2008 05:04:17 -0800 (PST), Keith Dysart
wrote:

Given your previous writings, I suspect that you have
a solid understanding of the behaviour of an open-circuited
transmission line excited with a step function.

Hi Keith,

I do, but I haven't dwelled on the matter too much since my days in
RADAR where a Pulse Forming Network could provide a kick from a very
big bottled Thyratron. I can also in those early days recall an
inadvertent opening of a circuit to a constant current device -
another kick.

As for naming the multitude of combined stepped wave shapes, front
porch and back porch regularly make their appearances a Trillion times
an hour.

I simply couldn't wade through the myriad issues that you were trying
to pull together. I prefer to drill down on one thing at a time and
then bring them together. For instance, your last example of dueling
sources was clearly blighted and allowed for easy dismissal. However,
its inclusion was distinctly at odds with the other discussion which
reveals the hazard of the shotgun style of answering all of Cecil's
objections in one breath.

Cecil's crafted problems immediately fail with one detail, there is no
reason to pursue them all. One need only review the "purpose" of this
thread being
On Tue, 18 Dec 2007 09:33:23 -0600, Cecil Moore wrote:

There seems to be mass confusion even among the gurus on
this newsgroup as to the difference between standing-wave
current, as exists on a 1/2WL dipole, vs traveling-wave
current, as exists on a terminated antenna like a rhombic.
Clearly, Cecil was the most dazed and confused guru when I drilled
down on this "purpose" of his own choice, on his own terms. The
subsequent 450 postings have merely roiled in the seascape on sloshing
waves when this anchor of "purpose" was cast off.

Perhaps you could make an attempt at writing a clear
description of the behaviour of such a system in terms
of charge flow and storage. Since "wave" is a word
overloaded with meanings, it would be good not to use
it in the description.

I can appreciate your attempt to confine it to charge flow, but for me
that leading edge merely introduces a wide spectrum of RF rather than
restricting the topic. If I were to give any thought to the minutia
of current flow along infinitesimal sections, it has long since been
focused in the realm of coulomb blockades at the nano scale of quantum
dots, and where sound waves comfortably migrate in the 100s of THz. I
think few (make that zero) here are terribly interested in that
side-bar.

Once a clear description exists, I can extend it
using the same clear terminology to illustrate
the points of interest.

Methinks you are going to suffer it being ignored by the target of
your intentions (Cecil?). His affliction of Netzheimers only allows
any topic to be discussed to its logical confusion.

If, for the sake of lurkers, any topic merits an indepth study, it is
best left to publishing at a page. I committed several hundred pages
to fractals in the past, and Chip never manage to summon up more than
half a dozen; and certainly never any coherent theory. Drilling down
on the supporter's stated interest, on his own terms, almost always
rents open the seams of failure. Again, the points of interest I
elaborated on were consumed by the very few (maybe two, and mostly to
their astonishment of so much effort going to so much "so what?"). We
can all agree that the march of time has ravaged any millennium
aspirations of the dawn of the fractal age.

73's
Richard Clark, KB7QHC

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
I've completely accounted for the power and energy leaving the voltage
source, being dissipated in the resistor, and entering the line, at all
times from startup to steady state, and done it quantitatively with
numerical results. And I did this without any mention of propagating
waves of power or energy.

Yes, you did deliberately avoid mentioning the energy in
the forward and reflected waves in the stub. So what? The
energy supplied to the stub is in the form of EM wave
energy. As long as it is not transformed into a different
type of energy, it will remain EM energy whether you choose
to ignore it or not. Your failure to mention ExH energy/sec
doesn't mean it ceases to exist. The EM wave energy is still
there moving at the speed of light in the medium. It is exactly
equal to the energy necessary to support the forward and
reflected power.

Roy, if you think that your failure to mention reality changes
reality, I feel really sorry for you but it is not unusual for
gurus to suffer from delusions of grandeur.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 2, 1:50*pm, Cecil Moore wrote:
Roy Lewallen wrote:
I've completely accounted for the power and energy leaving the voltage
source, being dissipated in the resistor, and entering the line, at all
times from startup to steady state, and done it quantitatively with
numerical results. And I did this without any mention of propagating
waves of power or energy.

Yes, you did deliberately avoid mentioning the energy in
the forward and reflected waves in the stub. So what? The
energy supplied to the stub is in the form of EM wave
energy. As long as it is not transformed into a different
type of energy, it will remain EM energy whether you choose
to ignore it or not.

In a stub driven with a step function, where is the
energy stored?

...Keith

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
But do not expect the power dissipated in the resistor
to increase by the same amount as the "reflected power".
In general, it will not. This is what calls into question
whether the reflected wave actually contains energy.

Virtually every EM wave you see with your own eyes is
a reflection. For you to argue that there is no energy
in those reflected EM waves is ridiculous in the extreme.
Exactly how do your optic nerves detect photons that
contain no energy? Hey, maybe that's why you are
hallucinating. :-)

This again calls into question the concept of power
in a reflected wave, since there is no accounting
for where that "power" goes.

That you fail to understand where the EM reflected wave
energy goes is simply ignorance. Please alleviate your
ignorance on the subject and the problem will go away.
Optical physicists have been tracking that energy for
centuries. Where have you been for the past three
centuries? :-)

I suggest you start with Eugene Hecht's chapter on
interference in "Optics". You will learn about
destructive interference, constructive interference,
and why those two must balance. All of the ExH energy
in an EM wave is conserved. You are simply ignorant
of how that energy is conserved.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
Perhaps you could make an attempt at writing a clear
description of the behaviour of such a system in terms
of charge flow and storage.

Since you are unable to understand the more simple example
using only one sine wave, what makes you think you are
capable of understanding the more complex step function?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
I am not sure you have the methodology quite correct.
The source is not turned off; its output is set to 0.

That's exactly the same thing - turning a source off
and setting it to zero. I suggest you go back and
study the rules for superposition and get back to us.
Exactly the same concepts apply for an s-parameter
analysis. Please learn how s11 and s22 are measured
and get back to us.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
But this same information has been repeatedly provided
and ignored. Will this time be different?

I'm not the one who is ignoring that information.
Where are your calculations involving destructive
and constructive interference? Until you provide
that information, you are just blowing smoke.

When are you going to realize that the effective
reflection coefficient for a source supplying zero
power is |1.0|?

You can certainly use the reflection coefficient
that you posted but that is only a small part of
the total reflection story.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
Cecil Moore wrote:
There can be a large difference in the output
impedance of an amplifier designed to drive a 50 ohm
load and a 50 ohm Thevenin equivalent circuit.

Then your Thevenin circuit is not an equivalent
for the amplifier, is it?

No it isn't! So why are you trying to stuff it down
my throat?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Roger wrote:

In the last 24 hours, Roy posted a revised analysis that contains
results useful here. He presented a voltage example that resulted in a
steady state with steady state voltages 4 time initial value. Under
superposition, this would equate to 4 times the initial power residing
on the transmission line under the conditions presented. This concurs
with other authors who predict power on the transmission line may exceed
the delivered power due to reflected waves.

Your equation "Ptot = Ps + Pr + 2*SQRT(Ps*Pr)cos(A)" is taken from
illumination and radiation theory to describe power existing at a point
in space near a reflecting surface. If we consider space to be a
transmission media, and the reflecting surface to be a discontinuity in
the transmission media, then we have a situation very similar to an
electrical transmission line near a line discontinuity.

It is entirely reasonable to consider that the reflection ratio between
the space transmission media and the reflective surface would result in
an storage factor equaling 4 times the peak power of the initial forward
wave. By storage factor, I simply mean the ratio of forward power to
total power on the transmission media under standing wave conditions.

Under open circuit conditions, a half wavelength transmission line will
have a storage factor of 2. Roy presented an example where the storage
factor was 4. Perhaps the space transmission media also has a storage
factor of 4 under some conditions, as described by "Ptot = Ps + Pr +
2*SQRT(Ps*Pr)cos(A)".

Power is neither stored nor conserved, so a power "storage factor" is
meaningless. Consider a very simple example. Let's charge a capacitor
with a constant current DC source. We'll apply 1 amp to a 1 farad
capacitor for 1 second. During that time, the power begins at zero,
since the capacitor voltage is zero, then it rises linearly to one watt
as the capacitor voltage rises to one volt at the end of the one second
period. So the average power over that period was 1/2 watt, and we put
1/2 joule of energy into the capacitor. (To confirm, the energy in a
capacitor is 1/2 * C * V^2 = 1/2 joule.) Was power "put into" or stored
in the capacitor?

Now we'll connect a 0.1 amp constant current load to the capacitor, in a
direction that discharges it. We can use an ideal current source for
this. The power measured at the capacitor or source terminals begins at
0.1 watt and drops linearly to zero as the capacitor discharges. The
average is 0.05 watt. Why are we getting less power out than we put in?

"Where did the power go?" is heard over and over, and let me assure you,
anyone taking care with his mathematics and logic is going to spend a
long time looking for it. So in this capacitor problem, where did the
power go?

It takes 10 seconds to discharge the capacitor, during which the load
receives the 1/2 joule of energy stored in the capacitor. Energy was
stored. Energy was conserved. Power was neither stored nor conserved.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
You should really spend some time looking for a
reference to support your assertion that "It will
not be the impedance needed to calculate the
reflection coefficient seen by the reflected
waves."

You will not find one.

You have got to be kidding, Keith. Even some of the
people on your side will admit that the effective
reflection coefficient for a source supplying zero
power is |1.0| nowhere near the value you calculated.
I believe that is what Roy said.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
I assume that you have not provided a reference to support
this assertion because you have not been able to find one.

I provided the reference a number of times and you
chose to ignore it. The reference is the chapter on
interference in "Optics", by Hecht.

Unfortunately optics do not do well at explaining
transmission lines since they do not extend down
to DC.

On the contrary, most physics books on "Light" do
indeed extend down to DC. I'm surprised you don't
know that. "Light" and "visible light" are two
entirely different subjects. "Light" covers all
EM waves all the way down to DC.

I have yet to find anything about transmission lines
that needs constructive and destructive interference
for explanation.

Well, there's your entire problem in a nutshell. If
you don't ever look for something because you don't
"feel the need", you will never find it. Please don't
blame anyone else for your feelings. And you are not
alone. My mother never "felt the need" to understand
anything except God.

I am unsure why some are content to constrain
themselves to solution techniques and explanations
that only work on the special case of sinusoids.

Sinusoids are a test of your comprehension level.
Because we know if you cannot even comprehend the
most simple case, you have no hope of comprehending
anything more complicated. Don't feel bad. My
girlfriend cannot comprehend sinusoids either.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

On Wed, 02 Jan 2008 13:22:42 -0600, Cecil Moore
wrote:

Keith Dysart wrote:
Perhaps you could make an attempt at writing a clear
description of the behaviour of such a system in terms
of charge flow and storage.

Since you are unable to understand the more simple example
using only one sine wave, what makes you think you are
capable of understanding the more complex step function?

For extra credit, try explaining why a traveling wave antenna has
standing waves on it! :-0

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:

On Dec 27, 10:53 am, Cecil Moore wrote:

But I don't
comprehend the utility of the following:

The instantaneous value of voltage is 10 volts.
The instantaneous value of current is 1 amp.
The voltage and current are in phase.

The instantaneous power is 10 joules per 0 sec?


There is definitely a problem with that.

There is indeed a problem. The problem is that one amp does not equal
one coulomb per 0 sec.

73, ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

People who are having trouble with the concept of a -1 voltage
reflection coefficient for a perfect voltage source might benefit from
the following exercise:

Look at my first analysis, where the perfect source was connected
directly to the transmission line. Make no assumptions about the
impedance or reflection coefficient it presents. Then, when the
reflection of the initial forward wave returns, calculate the value the
re-reflected wave must have in order to make the sum of the waves
present, which is the line input voltage, equal to the perfect source
voltage. The voltage of the perfect source can't change, by definition.
The ratio of the re-reflected wave to the returning wave is the voltage
reflection coefficient (since we're dealing with voltage waves).

I'll do it for you:

The forward wave was vf(t, x) = sin(wt - x)
The returning wave was vr(t, x) = sin(wt + x)

The returning wave will strike the input end of the line and create a
new forward wave with value vf2(t, 0) = Gs * vr(t, 0) at the input,
where Gs is the source voltage reflection coefficient.

Before the first forward wave returns, we have only vf(t, 0) = sin(wt)
at the input end of the line. This is of course the source voltage.

After the wave arrives and re-reflects, we have at the input end

vtot(t, 0) = vf(t, 0) + vr(t, 0) + vf2(t, 0)
= vf(t, 0) + vr(t, 0) * (1 + Gs)

This must equal the source voltage, which is the line input voltage, and
cannot change. So plugging in values:

sin(wt) = sin(wt) + sin(wt) * (1 + Gs)

Solving for Gs = Gs = -1

I have made no statement about the "impedance" of the perfect source.
The only thing I've required is that the voltage remains constant, which
is the very definition of a perfect source. You can do a similar
exercise to show that the voltage reflection coefficient of a perfect
current source is +1.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
Cecil Moore rote:
But why don't you just say so clearly.

I explained why it only applies to coherent
waves. Every model has its limitations, even
yours unless you are presenting a theory of
everything.

Given that optical EM waves are only capable of
solving a subset of the uses of transmission lines,
it is not obvious why I should study them when
I can invest in learning approaches that will do
the whole job.

That's not a given and is in fact a falsehood.
RF waves are a subset of light waves. Perhaps
you are erroneously confusing "light waves" with
"visible light waves".

When a light wave is red-shifted to 10^12 times
its original wavelength, does it cease to be a
light wave? Feel free to answer yes or no.

Well, others more knowledgeable than I in optics
have disputed whether *your* approach accurately
represents those described in the textbooks.

The last resort is an argumentium ad verecundiam,
an appeal to reverence/authority. Who, in particular,
do you consider to be the High Priest of r.r.a.a?

The technical truth will win out in the long run.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:

Keith Dysart wrote:

Cecil Moore wrote:

The instantaneous power is 10 joules per 0 sec?


There is definitely a problem with that.

But an instantaneous value of 10 joules/sec; that
is useful.


But that instantaneous instant is NOT one second
long.

A rate of 10 joules/sec is valid at any time in which there is a 10
volt differential and a current flowing at a rate of one coulomb per
second (and a half coulomb in a half second, and a thousandth of
coulomb in a millisecond, and like that).

Exactly how long is that instantaneous
instant? 1 ms? 1 us? 1 ns? more? less?

That is a question more typically asked by someone who has never taken
a calculus class.

73, ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Roger wrote:
Perhaps the space transmission media also has a storage
factor of 4 under some conditions, as described by "Ptot = Ps + Pr +
2*SQRT(Ps*Pr)cos(A)".

Visualize visible interference rings between two equal
waves each of P magnitude, where the darkest of the rings
is completely black. If it is not obvious, the power in
the brightest of the rings would have to be 4P for the
energy to average out to the 2P in the source waves. That's
all there is to "black" destructive interference vs "bright"
constructive interference. (4P+0P)/2 = 2P = average power
It's a no-brainer for most folks.

On the source side of a Z0-match, the reflections are "black".
On the load side of a Z0-match with reflections, the forward
wave is "bright". What could be simpler?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Richard Clark wrote:
I committed several hundred pages to fractals in the past, ...

Richard, why didn't you commit several hundred pages
to your premise that reflections from non-reflective
glass are brighter than the surface of the sun?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
In a stub driven with a step function, where is the
energy stored?

Depends upon which valid model one is using.

1. Reflection Model - the energy is stored in the
forward and reflected traveling waves.

2. The LCLCLC transmission line model - the energy
is alternately stored in the L's and C's.

3. The Sloshing Model - I'll let Roy handle that one.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

On Wed, 02 Jan 2008 14:42:01 -0600, Cecil Moore
wrote:

Richard Clark wrote:
I committed several hundred pages to fractals in the past, ...

Richard, why didn't you commit several hundred pages
to your premise that reflections from non-reflective
glass are brighter than the surface of the sun?

Can't get past the trauma of your sunburn, can you? :-)

What do you see when you look in a conjugate mirror? (have to provide
two questions in the hope you can score 50% - MENSA standards).

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
"Where did the power go?"

Or more correctly, where did the energy go?
Was it destroyed or created? (Rhetorical)
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Richard Clark wrote:
For extra credit, try explaining why a traveling wave antenna has
standing waves on it! :-0

Ideal traveling-wave antennas have no standing waves.
You are simply pointing out the obvious difference
between the ideal and the real world. So what new?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
That is a question more typically asked by someone who has never taken a
calculus class.

The answer is typically asserted by someone who doesn't
know the difference between joules and joules per second.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Gene Fuller wrote:
For future reference, however, just remember: Fields first, then power
or energy. That's the way superposition really works.

Way back before optical physicists could measure light
wave fields, they were dealing with reflectance,
transmittance, and irradiance - all involving power
or energy. They are still using those concepts today
proven valid over the past centuries. Optical physicists
calculate the fields *AFTER* measuring the power density
and they get correct consistent answers.

"Way back" is irrelevant. One only needs to open a serious text book on
Optics, such as Born and Wolf, to see how optical physicists perform
analysis today.


Quoting HP AN 95-1: "The previous four equations show that
s-parameters are simply related to power gain and mismatch
loss, quantities which are often of more interest than the
corresponding voltage functions."

I agree with this statement completely (surprised??). S-parameter
analysis is very useful. However, the "corresponding voltage functions"
are equally valid, even if not as "interesting". What you might also
notice in AN 95-1 is that there is no mention of incident and reflected
waves on a transmission line, each carrying energy (or power or whatever
you prefer), and passing like ships in the night.

You like to talk about conservation of energy, implying that your
"powerful" reflected wave model is essential to meeting the conservation
of energy requirement. In fact, your model is a poster child for the
violation of energy conservation. Electromagnetic energy, like any
energy, is a scalar quantity, and it is only positive. It is not
possible to "net" the non-zero energy contributed from your
counter-traveling waves to zero. The direction of the wave propagation
does not change the sign of the energy. Be careful here; energy is *not*
the same as the energy flux or Poynting vector. Don't mix terms that
have totally different units. What *can* be assigned negative values are
the fields. (Voltage and current are not exactly "fields", but they will
work for these transmission line examples.) A "net" of zero volts or
current is exactly what happens at the standing wave nodes resulting
from the counter-traveling waves. After you have done the superposition
correctly, using fields, not energy or power, then you can easily
determine the energy and power state as needed. Conservation of energy
will be automatically satisfied, assuming no mathematical blunders. The
Maxwell equations would be pretty useless if they did not provide
conservation of energy.

For future reference, just remember: Fields first, then power
or energy. That's the way superposition really works.

73,
Gene
W4SZ

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:

On Dec 29, 2:31 pm, Cecil Moore wrote:

Roger wrote:

Are there reflections at point "+"? Traveling waves going in opposite
directions must pass here, therefore they must either pass through one
another, or reflect off one another.

In the absence of a real physical impedance discontinuity,
they cannot "reflect off one another". In a constant Z0 transmission
line, reflections can only occur at the ends of the line and only
then at an impedance discontinuity.


Roger: an astute observation. And Cecil thinks he has
the ONLY answer. Allow me to provide an alternative.

Many years ago, when I first encountered this news group
and started really learning about transmission lines, I
found it useful to consider not only sinusoidallly
excited transmission lines, but also pulse excitation.
It sometimes helps remove some of the confusion and
clarify the thinking. So for this example, I will use
pulses.

Consider a 50 ohm transmission line that is 4 seconds
long with a pulse generator at one end and a 50 ohm
resistor at the other.

The pulse generator generates a single 1 second pulse
of 50 volts into the line. Before and after the pulse
its output voltage is 0. While generating the pulse,
1 amp (1 coulomb/s) is being put into the line, so
the generator is providing 50 watts to the line.

After one second the pulse is completely in the line.
The pulse is one second long, contains 1 coulomb of
charge and 50 joules of energy. It is 50 volts with
1 amp: 50 watts.

Let's examine the midpoint (2 second) on the line.
At two seconds the leading edge of the pulse arrives
at the midpoint. The voltage rises to 50 volts and
the current becomes 1 amp. One second later, the
voltage drops back to 0, as does the current. The
charge and the energy have completely passed the
midpoint.

When the pulse reaches the end of the line, 50
joules are dissipated in the terminating resistor.

Notice a key point about this description. It is
completely in terms of charge. There is not a single
mention of EM waves, travelling or otherwise.

Now we expand the experiment by placing a pulse
generator at each end of the line and triggering
them to each generate a 50V one second pulse at
the same time. So after one second a pulse has
completely entered each end of the line and these
pulse are racing towards each other at the speed
of light (in the line). In another second these
pulses will collide at the middle of the line.

What will happen? Recall one of the basics about
charge: like charge repel. So it is no surprise
that these two pulses of charge bounce off each
and head back from where they came. At the center
of the line, for one second the voltage is 100 V
(50 V from each pulse), while the current is
always zero. No charge crossed the mid-point. No
energy crossed the mid-point (how could it if
the current is always zero (i.e. no charge
moves) at the mid-point.

It is a minor extension to have this model deal
with sinusoidal excitation.

What happens when these pulses arrive back at the
generator? This depends on generator output
impedance. If it is 50 ohms (i.e. equal to Z0),
then there is no reflection and 1 joule is
dissipated in each generator. Other values
of impedance result in more complicated
behaviour.

So do the travelling waves "reflect" off each
other? Save the term "reflect" for those cases
where there is an impedance discontinuity and
use "bounce" for those cases where no energy
is crossing a point and even Cecil may be
happy. But bounce it does.

...Keith

It's fairly safe to make this argument when both pulses are identical.
I challenge you to obtain this result when they are not. :-)

73, Jim AC6XG

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
. . .
But do not expect the power dissipated in the resistor
to increase by the same amount as the "reflected power".
In general, it will not. This is what calls into question
whether the reflected wave actually contains energy.

Do some simple examples with step functions. The math
is simpler than with sinusoids and the results do not
depend on the phase of the returning wave, but simply
on when the reflected step arrives bach at the source.

Examine the system with the following terminations on
the line: open, shorted, impedance greater than Z0,
and impedance less than Z0.

Because excitation with a step function settles to
the DC values, the final steady state condition is
easy to compute. Just ignore the transmission line
and assume the termination is connected directly
to the Thevenin generator. When the line is present,
it takes longer to settle, but the final state will
be the same with the line having a constant voltage
equal to the voltage output of the generator which
will be the same as the voltage applied to the load.

Then do the same again, but use a Norton source. You
will find that conditions which increase the dissipation
in the resistor of the Thevenin equivalent circuit
reduce the dissipation in the resistor of the Norton
equivalent circuit and vice versa.

This again calls into question the concept of power
in a reflected wave, since there is no accounting
for where that "power" goes.

I heartily second Keith's recommendations.

For some simple illustrations of one problem with chasing "power waves"
around, see http://eznec.com/misc/Food_for_thought.pdf, particularly the
"Forward and Reverse Power" section beginning on p. 6 and the table on
p. 8. This was originally written and posted more than five years ago
and, to my knowledge, the problems it raises with the concept of "power
waves" still haven't been addressed in the thousands of postings on the
topic in the intervening time.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
On Jan 2, 9:59 am, Cecil Moore wrote:


Please reference a good book on optical EM waves
for a complete answer.



It is a body of physics knowledge that has existed
since long before you were born. It should have
been covered in your Physics 201 class. That you
are apparently unaware of such is a display of
basic ignorance of the science of EM waves.



The basic theory applies specifically to coherent
waves (which are the only EM waves capable of truly
interfering). CW RF waves are close enough to ideal
coherency that the theory works well. It would no
doubt work for a coherent Fourier series as well
but I don't want to spend the time necessary
to prove that assertion.



Again, it is not *my* approach and is described in any
textbook on "Optics" including Hecht and Born & Wolf.

Well, others more knowledgeable than I in optics
have disputed whether *your* approach accurately
represents those described in the textbooks.

In any case, being applicable only to sinusoids
limits the general applicability to transmission
lines which happily work at DC.

...Keith


It is sadly amusing that Cecil takes so much comfort in optics. The
electromagnetic theory for optics (e.g. somewhere in the vicinity of
visible light) is of course identical to the electromagnetic theory for
HF. The preferred applications and shortcuts are sometimes a bit
different, but that is simply a matter of convenience and of no
importance here.

I have a couple of editions of Born and Wolf, which is a high level
reference and often considered the standard for optics. I have been
unable to find even one mention of "constructive" or "destructive"
interference in their writing. Of course they delve into the topic of
interference in excruciating detail. They don't, however, ascribe any
particular mysticism or magic to interference. It is simply what happens
when the wave fields are superposed.

The more popular accounts, such as the FSU Java applet on interference,
the Melles-Griot web site, and apparently the text by Hecht, stay a bit
further from rigorous analysis. Therefore they resort to handwaving
requirements such as destructive must be balanced by constructive, blah,
blah, blah.

Adding the voltages in the manner you and Roy have done is precisely the
same operation as Cecil's interference method, without the emotional
baggage.

73,
Gene
W4SZ

Standing-Wave Current vs Traveling-Wave Current
 

On Wed, 02 Jan 2008 21:19:53 GMT, Cecil Moore
wrote:
For extra credit, try explaining why a traveling wave antenna has
standing waves on it! :-0

Ideal traveling-wave antennas have no standing waves.

Ideal? You mean your dream of desires. Schoolgirl stuff for diaries
under pillows, not technical discussion (not that I'm surprised, I
actually enjoy your tendency toward heart-throb writing).

You are simply pointing out the obvious difference
between the ideal and the real world. So what new?

What new? What new shows us you don't get any extra credit, that what
new! You can try again, if you wish. That is, if you can resuscitate
the corpse you strangled when your "purpose" went off the rails.

+ +
|
___

Standing-Wave Current vs Traveling-Wave Current
 

Gene Fuller wrote:
"Way back" is irrelevant. One only needs to open a serious text book on
Optics, such as Born and Wolf, to see how optical physicists perform
analysis today.

The readers may be interested in how it is done today.
Please tell us how the phase of light is measured today.

What you might also notice in AN 95-1 is that there
is no mention of incident and reflected ...

Sorry Gene, I'm tired of wasting my time proving that you
are lying. Anyone who wants to prove how unethical you are
can do so by accessing:

http://www.ecs.umass.edu/ece/labs/an...parameters.pdf

and searching for "incident" and "reflected".
Lots of unethical BS deleted after that.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
I heartily second Keith's recommendations.

Of course you two want to deny that reflected waves
contain any energy at all. If there is any energy
in reflected waves, your house-of-cards collapses.

So Roy, please explain how all those reflected
waves that are incident upon your optic nerves
don't contain any energy. (I'm not going to hold
my breath for your answer.)
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Gene Fuller wrote:
The
electromagnetic theory for optics (e.g. somewhere in the vicinity of
visible light) is of course identical to the electromagnetic theory for
HF.

Thanks Gene, I never thought you would ever admit that
fact of physics. Now that you have, your entire argument
collapses. If interference can happen in free space, it
certainly can happen in a transmission line.

I have a couple of editions of Born and Wolf, which is a high level
reference and often considered the standard for optics. I have been
unable to find even one mention of "constructive" or "destructive"
interference in their writing.

Try "Optics" by Hecht. He devotes an entire chapter
to interference. Hecht mentions destructive and constructive
interference dozens of times. I can quote page after page
of such if you want me to. Feel free to dispute Hecht if
you want, but that is your problem, not mine.

Of course they delve into the topic of
interference in excruciating detail. They don't, however, ascribe any
particular mysticism or magic to interference. It is simply what happens
when the wave fields are superposed.

Neither do I. It is just what happens when the wave fields
are superposed. The destructive interference must balance
the constructive interference to avoid violation of the
conservation of energy principle.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

I'm top posting this so readers won't have to scroll down to see it, but
so I can include the original posting completely as a reference.


Keith, you've presented a very good and well thought out argument. But
I'm not willing to embrace it without a lot of further critical thought.
Some of the things I find disturbing a

1. There are no mathematics to quantitatively describe the phenomenon.
2. I don't understand the mechanism which causes waves to bounce.
3. No test has been proposed which gives measurable results that will
be different if this phenomenon exists than if it doesn't. (I
acknowledge your proposed test but don't believe it fits in this category.)
4. I'm skeptical that this mechanism wouldn't cause visible
distortion when dissimilar waves collide. But without any describing
mathematics or physical basis for the phenomenon, there's no way to
predict what should or shouldn't occur.
5. Although the argument about no energy crossing the zero-current
node is compelling, I don't feel that an adequate argument has been
given to justify the wave "bouncing" theory over all other possible
explanations.

None of these make an argument with your logical development, although I
think I might be able to do that too. But I'm very reluctant to accept a
view of wave interaction that's apparently contrary to established and
completely successful theory and one, if true, might have profound
effects on our understanding of how things work. So frankly I'm looking
hard for a flaw in your argument. And I may have found one.

A large part of the argument seems to revolve around a single point in a
perfect transmission line, where the current is exactly zero. This is an
infinitesimal point on a perfect line, so some anomalous things might be
expected to happen there.

Let's consider a transmission line as a huge number of series inductors
and shunt capacitors, each an ideal lumped device. In the ideal case, of
course, there would be an infinite number of each, and each would have
an infinitesimal value. However, the LC product and ratio must remain
correct even in the limiting case. Each L and C is an ideal device, so
the current into one terminal of an inductor has to equal the current
out of the other. A consequence of this is that either we have a whole
inductor with zero current, or the zero current point occurs between
inductors, at a node to which a capacitor is connected. I think we'll
get the same result using either scenario, but let's consider the second.

If we analyze this situation carefully, we'll find that the inductor on
each side of the zero-current point does have a finite current, equal in
amplitude and flowing in opposite directions. So for half of the cycle,
both are putting positive charge in the capacitor, and for the other
half of the cycle, both are removing charge. The capacitor voltage goes
up and down as a result, as we can also see by looking at the voltage at
this zero-current point. So current from both sides is contributing to
the capacitor charge, and turning off either one would change the line
conditions. Any change in the current from the inductor on one side
would change the capacitor voltage, and hence the current on the other
side. So there is an interchange of information from one side to the
other. Each inductor is conveying energy to the capacitor, which is
storing and returning it.

Ok, so let's break the capacitor into two, each being half the original
value, and constrain each inductor to deliver charge only to "its"
capacitor. The wire between the capacitors carries no current because
the capacitors always have equal voltages, and can be cut with no effect.

When there was one capacitor, it shared energy from both sides. When we
broke it into two, there was no mixing of energy from either side. Why
might one be a better description of reality than the other? It looks to
me like the argument devolves into speculation about how small the
"point" is at which the current drops to zero.

It would be instructive to see what happens as, for example, the load
resistance is increased toward infinity or decreased toward zero
arbitrarily closely, but not at the point at which it's actually there.
If the "bouncing" phenomenon is necessary only to explain the limiting
case of infinite SWR on a perfect line but no others, then an argument
can be made that it's not necessary at all. I suspect this is the case.

I agree with your argument about two sources energized in turn, and have
used that argument a number of times myself to refute the notion of
superposing powers. Once two voltage or current waves occupy the same
space, the only reality is the sum. We're free to split them up into
traveling waves or any other combination we might dream up, with the
sole requirement being that the sum of all our creations equals the
correct total. (And the behavior of waves you're describing seemingly go
beyond this.) The advantage to the non-interacting traveling wave model
is that it so neatly predicts transient phenomena such as TDR and run-up
to steady state. I spent a number of years designing TDR circuitry,
interfacing with customers, and on several occasions developing and
teaching classes on TDR techniques, without ever encountering any
phenomena requiring explanations beyond classical traveling wave theory.
So you can understand my reluctance to embrace it based on a problem
with energy transfer across a single infinitesimal point in an ideal line.

Roy Lewallen, W7EL

Keith Dysart wrote:
On Dec 30 2007, 6:18 pm, Roy Lewallen wrote:
Keith Dysart wrote:

I predict that the pulse arriving at the left end will
have the same voltage, current and energy profile as
the pulse launched at the right end and the pulse
arriving at the right end will be similar to the
one launched at the left.
They will appear exactly AS IF they had passed
through each other.
The difficulty with saying THE pulses passed
through each other arises with the energy. The
energy profile of the pulse arriving at the left
will look exactly like that of the one launched
from the right so it will seem that the energy
travelled all the way down the line for delivery
at the far end. And yet, from the experiment above,
when the pulses arriving from each end have the
same shape, no energy crosses the middle of the
line.
So it would seem that the energy that actually
crosses the middle during the collision is
exacly the amount of energy that is needed to
reconstruct the pulses on each side after the
collision.
If all the energy that is launched at one end
does not travel to the other end, then I am
not comfortable saying that THE pulse travelled
from one end to the other.
But I have no problem saying that the system
behaves AS IF the pulses travelled from one
end to the other.
You said that:

What will happen? Recall one of the basics about
charge: like charge repel. So it is no surprise
that these two pulses of charge bounce off each
and head back from where they came.

Yet it sounds like you are saying that despite this charge repulsion and
bouncing of waves off each other, each wave appears to be completely
unaltered by the other? It seems to me that surely we would detect some
trace of this profound effect.

. . .
Is there any test you can conceive of which would produce different
measurable results if the pulses were repelling and bouncing off each
other or just passing by without noticing the other?

There are equations describing system behavior on the assumption of no
wave interaction, and these equations accurately predict all measurable
aspects of line behavior without exception. Have you developed equations
based on this charge interaction which predict line behavior with
equal accuracy and universal applicability?

No equations. I expect that such equations would be more complex
than those describing the behaviour using superposition. Since
the existing equations and techniques for analysis are tractable
and produce accurate results, I am not motivated to develop an
alternate set with lower utility.

And yet the "no interaction" model, while accurately predicting
the behaviour has some weaknesses with explaining what is
happening. It is, I suggest, these weaknesses that help lead
some so far astray.

To illustrate some of these weaknesses, consider an example
where a step function from a Z0 matched generator is applied
to a transmission line open at the far end. Charge begins to
flow into the line. The ratio of the current to voltage on
the line is defined by the distributed inductance and
capacitance. The inductance is resisting the change in current
which causes a voltage to charge the capacitance. A voltage
step (call this V for later use) propagates down the line
at the speed of light. In front of this step, the voltage,
current and charge in the line is zero. After the step, the
capacitance is charged to the voltage and charge is flowing
in the inductance.

The step function eventually reaches the open end where
the current can no longer flow. The inductance insists
that the current continue until the capacitance at the
end of the line is charged to the voltage which will stop
the flow. This voltage is double the voltage of the step
function applied to the line (i.e 2*V). Once the
infinitesimal capacitance at the end of the line is
charged, the current now has to stop just a bit earlier
and this charges the inifinitesimal capacitance a bit
further from the end. So a step in the voltage propagates
back along the line towards the source. In front of this
step, current is still flowing. Behind the step, the
current is zero and voltage is 2*V. The charge that
is continuing to flow from the source is being used
to charge the distributed capacitance of the line.

The voltage that is propagating backwards along the
line has the value 2*V, but this can also be viewed as
a step of voltage V added to the already present voltage
V. The latter view is the one that aligns with the "no
interaction" model; the total voltage on the line is
the sum of the forward voltage V and the reverse
voltage V or 2*V.

In this model, the step function has propagated to the
end, been reflected and is now propagating backwards.
Implicit in this description is that the step continues
to flow to the end of the line and be reflected as
the leading edge travels back to the source.

And this is the major weakness in the model. It claims
the step function is still flowing in the portion of
the line that has a voltage of 2*V and *zero* current.

Now without a doubt, when the voltages and currents
of the forward and reverse step function are summed,
the resulting totals are correct. But it seems to
me that this is just applying the techniques of
superposition. And when we do superposition on a
basic circuit, we get the correct totals for the
voltages and currents of the elements but we do
not assign any particular meaning to the partial
results.

A trivial example is connecting to 10 volt batteries
in parallel through a .001 ohm resistor. The partial
results show 10000 amps flowing in each direction
in the resistor with a total of 0. But I do not
think that anyone assigns significance to the 10000
amp intermediate result. Everyone does agree that
the actual current in the resistor is zero.

The "no interaction" model, while just being
superposition, seems to lend itself to having
great significance applied to the intermediate
results.

Partially this may be due to poor definitions. If the
wave is defined as just being a voltage wave, then
all is well.

But, for example, when looking at a solitary pulse,
it is easy (and accurate) to view the wave as having
more than just voltage. One can compute the charge,
the current, the power, and the energy. But when
two waves are simultaneously present, it is only
legal to superpose the voltage and the current.
But it is obvious that a solitary wave has voltage,
current, power, etc. But when two waves are present
it is not legal to.... etc., etc.
The "no interaction" model does not seem to resolve
this conflict well, and some are lead astray.

And it was this conflict that lead me to look for
other ways of thinking about the system.

Earlier you asked for an experiment. How about this
one....

Take two step function generators, one at each end
of a transmission line. Start a step from each end
at the same time. When the steps collide in the
middle, the steps can be viewed as passing each
other without interaction, or reversing and
propagating back to their respective sources. We
can measure the current at the middle of the line
and observe that it is always 0. Therefore the
charge that is filling the capacitance and causing
the voltage step which is propagating back towards
each generator must be coming from the generator
to which the step is propagatig because no charge
is crossing the middle of the line.

Do you like it?

...Keith

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:

It's fairly safe to make this argument when both pulses are identical.
I challenge you to obtain this result when they are not. :-)

73, Jim AC6XG

I proposed this some time ago, and got the response that dissimilar
pulses would still bounce off each other, yet appear exactly as though
they were passing through without interaction. I haven't been able to
understand why this would be, but there are no mathematics to explain it.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Jim Kelley wrote:

That is a question more typically asked by someone who has never taken
a calculus class.


The answer is typically asserted by someone who doesn't
know the difference between joules and joules per second.

Or so it might seem to someone who had neglected to consider that the
'per second' in Joules per second in this case derives from the rate
at which charge is moving.

73, ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

On Wed, 02 Jan 2008 16:38:36 -0800, Roy Lewallen
wrote:

2. I don't understand the mechanism which causes waves to bounce.

If I might amplify a similar concern.

Bounce is a phenomenon in everbody's experience, hence the term easily
clouds the conversation as it also not a very rigorous term in RF.

In the day to day world of, say, rubber balls, bounce implies:
1. an inelastic deformation upon collision;
2. the conversion of kinematic energy into potential energy;
3. a period or interval of holding that potential energy (or further
accumulation of potential energy);
4. the cessation of the inelastic deformation and the rebound
unwinding 1-3 above as potential energy is converted back into
kinematic energy.

So, for this "bounce" in a wave, can I observe the inelastic
deformation? (Not just the superposition of waves, but the actual
inelastic crush against resistance.) Inelastic often has loss
attending it, do you care to characterize it as elastic? If so, then
the usage of "bounce" is running against the grain of popular usage.

In this "bounce" in a wave, can I observe the time interval during
which kinematic energy is converted to potential energy and then back
to kinematic energy? (Is there a retardation in the wave migration? I
would suspect a phase change might reveal this, and not just a phase
inversion, nor a phase reversal.)

73's
Richard Clark, KB7QHC

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Gene Fuller wrote:

What you might also notice in AN 95-1 is that there is no mention of
incident and reflected ...

Sorry Gene, I'm tired of wasting my time proving that you
are lying. Anyone who wants to prove how unethical you are
can do so by accessing:

http://www.ecs.umass.edu/ece/labs/an...parameters.pdf

and searching for "incident" and "reflected".
Lots of unethical BS deleted after that.

I guess I must be hitting close to target. You always get nasty when I
create problems for your pet theories.

Thanks for the reference to AN 95-1, even though I have several copies
already. Your directed search terms prove my point exactly. I suppose
puncturing your balloon is "unethical", but that is your problem, not mine.

I challenged you to find any case in AN 95-1 that supports your claim of
counter-traveling waves in a transmission line, with each wave carrying
its own energy that somehow nets out to zero. You came up with exactly
nothing, which is not surprising.

Ranting and raving does not have any impact on the correct physical
reality.

Oh, by the way, my full comment was, ". . . there is no mention of
incident and reflected waves on a transmission line, each carrying
energy (or power or whatever you prefer), and passing like ships in the
night."

Your careful trimming is noted.

73,
Gene
W4SZ

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Gene Fuller wrote:
The electromagnetic theory for optics (e.g. somewhere in the vicinity
of visible light) is of course identical to the electromagnetic theory
for HF.

Thanks Gene, I never thought you would ever admit that
fact of physics. Now that you have, your entire argument
collapses. If interference can happen in free space, it
certainly can happen in a transmission line.


Cecil,

No one has ever said anything different. No one has ever denied
interference.

You are really grasping at straws now.

73,
Gene
W4SZ

Standing-Wave Current vs Traveling-Wave Current
 

On 2 Jan, 16:38, Roy Lewallen wrote:
I'm top posting this so readers won't have to scroll down to see it, but
so I can include the original posting completely as a reference.

Keith, you've presented a very good and well thought out argument. But
I'm not willing to embrace it without a lot of further critical thought.
Some of the things I find disturbing a

* *1. There are no mathematics to quantitatively describe the phenomenon.
* *2. I don't understand the mechanism which causes waves to bounce.
* *3. No test has been proposed which gives measurable results that will
be different if this phenomenon exists than if it doesn't. (I
acknowledge your proposed test but don't believe it fits in this category.)
* *4. I'm skeptical that this mechanism wouldn't cause visible
distortion when dissimilar waves collide. But without any describing
mathematics or physical basis for the phenomenon, there's no way to
predict what should or shouldn't occur.
* *5. Although the argument about no energy crossing the zero-current
node is compelling, I don't feel that an adequate argument has been
given to justify the wave "bouncing" theory over all other possible
explanations.

None of these make an argument with your logical development, although I
think I might be able to do that too. But I'm very reluctant to accept a
view of wave interaction that's apparently contrary to established and
completely successful theory and one, if true, might have profound
effects on our understanding of how things work. So frankly I'm looking
hard for a flaw in your argument. And I may have found one.

A large part of the argument seems to revolve around a single point in a
perfect transmission line, where the current is exactly zero. This is an
infinitesimal point on a perfect line, so some anomalous things might be
expected to happen there.

Let's consider a transmission line as a huge number of series inductors
and shunt capacitors, each an ideal lumped device. In the ideal case, of
course, there would be an infinite number of each, and each would have
an infinitesimal value. However, the LC product and ratio must remain
correct even in the limiting case. Each L and C is an ideal device, so
the current into one terminal of an inductor has to equal the current
out of the other.

That is not correct. If both the capacitor and the inductance are
ideal
they cannot return the same amount of energy. This can only happen
when the
summation of all vectors are parallel to the axis of the conductor.
One only has to look at the vectors involved with out assigning length
to the vectors to see that the vectorial summation cannot be parallel
to the radiator axis. This is exactly why for maximum horizontal gain
the radiator is tipped away from the earth's surface. This response
is clearly shown when a time varient is added to Gaussian law.




A consequence of this is that either we have a whole
inductor with zero current, or the zero current point occurs between
inductors, at a node to which a capacitor is connected. I think we'll
get the same result using either scenario, but let's consider the second.

If we analyze this situation carefully, we'll find that the inductor on
each side of the zero-current point does have a finite current, equal in
amplitude and flowing in opposite directions. So for half of the cycle,
both are putting positive charge in the capacitor, and for the other
half of the cycle, both are removing charge.

That can only be true for a full wave radiator which emulates
a tank circuit. A half wave radiator is a series circuit,
a whole different ball game !





The capacitor voltage goes
up and down as a result, as we can also see by looking at the voltage at
this zero-current point. So current from both sides is contributing to
the capacitor charge, and turning off either one would change the line
conditions.

Not at the change over point where voltages are equal since a
capacitor
has a slight delay before discharging because of initial inductance
delay.



Any change in the current from the inductor on one side
would change the capacitor voltage, and hence the current on the other
side. So there is an interchange of information from one side to the
other. Each inductor is conveying energy to the capacitor, which is
storing and returning it.

It takes energy to propagate does it not?
Why would you ignore that?

Ok, so let's break the capacitor into two, each being half the original
value, and constrain each inductor to deliver charge only to "its"
capacitor. The wire between the capacitors carries no current because
the capacitors always have equal voltages, and can be cut with no effect.
Again that cannot be. The filling of all the capacitors fill up in a
series format.
snip
Art



Roy Lewallen, W7EL



Keith Dysart wrote:
On Dec 30 2007, 6:18 pm, Roy Lewallen wrote:
Keith Dysart wrote:

I predict that the pulse arriving at the left end will
have the same voltage, current and energy profile as
the pulse launched at the right end and the pulse
arriving at the right end will be similar to the
one launched at the left.
They will appear exactly AS IF they had passed
through each other.
The difficulty with saying THE pulses passed
through each other arises with the energy. The
energy profile of the pulse arriving at the left
will look exactly like that of the one launched
from the right so it will seem that the energy
travelled all the way down the line for delivery
at the far end. And yet, from the experiment above,
when the pulses arriving from each end have the
same shape, no energy crosses the middle of the
line.
So it would seem that the energy that actually
crosses the middle during the collision is
exacly the amount of energy that is needed to
reconstruct the pulses on each side after the
collision.
If all the energy that is launched at one end
does not travel to the other end, then I am
not comfortable saying that THE pulse travelled
from one end to the other.
But I have no problem saying that the system
behaves AS IF the pulses travelled from one
end to the other.
You said that:

* What will happen? Recall one of the basics about
* charge: like charge repel. So it is no surprise
* that these two pulses of charge bounce off each
* and head back from where they came.

Yet it sounds like you are saying that despite this charge repulsion and
bouncing of waves off each other, each wave appears to be completely
unaltered by the other? It seems to me that surely we would detect some
trace of this profound effect.

. . .
Is there any test you can conceive of which would produce different
measurable results if the pulses were repelling and bouncing off each
other or just passing by without noticing the other?

There are equations describing system behavior on the assumption of no
wave interaction, and these equations accurately predict all measurable
aspects of line behavior without exception. Have you developed equations
* based on this charge interaction which predict line behavior with
equal accuracy and universal applicability?

No equations. I expect that such equations would be more complex
than those describing the behaviour using superposition. Since
the existing equations and techniques for analysis are tractable
and produce accurate results, I am not motivated to develop an
alternate set with lower utility.

And yet the "no interaction" model, while accurately predicting
the behaviour has some weaknesses with explaining what is
happening. It is, I suggest, these weaknesses that help lead
some so far astray.

To illustrate some of these weaknesses, consider an example
where a step function from a Z0 matched generator is applied
to a transmission line open at the far end. Charge begins to
flow into the line. The ratio of the current to voltage on
the line is defined by the distributed inductance and
capacitance. The inductance is resisting the change in current
which causes a voltage to charge the capacitance. A voltage
step (call this V for later use) propagates down the line
at the speed of light. In front of this step, the voltage,
current and charge in the line is zero. After the step, the
capacitance is charged to the voltage and charge is flowing
in the inductance.

The step function eventually reaches the open end where
the current can no longer flow. The inductance insists
that the current continue until the capacitance at the
end of the line is charged to the voltage which will stop
the flow. This voltage is double the voltage of the step
function applied to the line (i.e 2*V). Once the
infinitesimal capacitance at the end of the line is
charged, the current now has to stop just a bit earlier
and this charges the inifinitesimal capacitance a bit
further from the end. So a step in the voltage propagates
back along the line towards the source. In front of this
step, current is still flowing. Behind the step, the
current is zero and voltage is 2*V. The charge- Hide quoted text -

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