The Rest of the Story
 

On Mar 26, 1:37*pm, Cecil Moore wrote:
Keith Dysart wrote:
Now if the 200 W from the wave from source 1 and the
50 W from the wave from source 2 represent actual
energy flows, then the "interference energy" must
also be an actual energy flow to satisfy conservation
of energy.

One other observation: Although the interference model
will work for a lumped circuit example, there is no
reason to use it as it complicates the computations
and adds nothing to the solution. The wave reflection
model also works for circuits but there is simply no
good reason to use it for lumped circuit analysis.

Except when it can be called into service to disprove
some aspects of *your* "wave reflection model".

Where interference becomes a useful tool is when it
happens away from any compensating source. An analysis
of the interference of two EM light waves in free space
far removed from any source leaves us with two constant
sources of energy, the total energy of which has to go
somewhere. The following two web pages tell us exactly
where the energy goes.

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

http://micro.magnet.fsu.edu/primer/j...interference/w...

It is unfortunate that they did not expect someone to use
their website to try to understand the behavior of transmission
lines, or they might have taken more care to explain what is
happening at the sub-wavelength level.

Your theory seems to require that the EM waves must
know beforehand whether to carry energy or not from
a star light years away. You apparently have invented
a rather curious "smart wave theory".

That would be nice, but no, not required. Though it is
easy to see how one might be misguided into thinking so.

The question is, can you set aside the mis-guiding
influences long enough to learn about the alternative
explanations?

The question is: How did those two interfering waves
from Alpha Centauri know whether to arrive at the
planet Earth ten years later carrying ExH energy
or not carrying ExH energy?

It is a question, but only seems relevent if *your* model
is incorrect.

...Keith

The Rest of the Story
 

On Mar 26, 2:53*pm, Cecil Moore wrote:
Keith Dysart wrote:
Let us build a slightly better example that complies with
your "NOT =" expression above.

Your constant voltage sources are NOT a better example
and not even a good example. To confront the subject
being discussed, you should use constant power sources.

Well, if that is all it takes to stop you, here is a
variation that should satisfy. It aligns well with your
example of Fig 1-1......

Let us build a slightly better example that complies with
your "NOT =" expression above.

50 ohms 50 ohms
+------/\/\/\----------------+---/\/\/\---+
| | |
| \ |
Vs1(t) = 282.8cos(wt) Rload / Vs2(t) = 141.4cos(wt)
| = 200 Vrms 50 ohms \ | = 100 Vrms
| / |
| | |
+----------------------------+------------+

Using superposition the contribution from source 1 is
Vload.s1 = 100 Vrms
Iload.s1 = 2 Arms
and from source 2 is
Vload.s2 = 50 Vrms
Iload.s2 = 1 Arms
combining
Vload = 150 Vrms
Iload = 3 Arms

From
Pload = Vload * Iload
= 150 * 3
= 450 Waverage

As can be seen, this example satisfies your requirement
for interference:
[V1(t)^2 + V2(t)^2] NOT= [V1(t) + V2(t)]^2

Computing the imputed powers for the waves from each source
we have
Pload.s1 = 100 * 2
= 200 Waverage
Pload.s2 = 50 * 1
= 50 Waverage
To obtain the power in the load from these imputed powers
we need to use
Pload = Pload.s1 + Pload.s2 + Pload.correction
450 = 200 + 50 + Pload.correction
200 = Pload.correction

From previous analysis
Pcorrection = 2 * sqrt(P1 * P2)cos(theta)
(the cos(theta) term is appropriate here because these
are average powers being used)
Pcorrection = 2 * sqrt(10000) * 1
= 200
as required from above.

So according to your energy analsysis, the power in
the load comes from
the wave from source 1 = 200 W
the wave from source 2 = 50 W
"interference energy" = 200 W
for a total of
450 W as required.

Now if the 200 W from the wave from source 1 and the
50 W from the wave from source 2 represent actual
energy flows, then the "interference energy" must
also be an actual energy flow to satisfy conservation
of energy.

What element provides the energy for this "interference
energy" flow?

In other posts, you have suggested that this would be
a constructive interference energy and that there would
be an equal destructive interference energy to provide
it. If you still claim this, where is this destructive
interference happening?

...Keith

The Rest of the Story
 

Keith Dysart wrote:
Or perhaps the element you have identified does not have
the appropriate energy flow function? (It doesn't.)

Please prove your assertion.

This requires that the sum of the flows out of the
elements providing energy equals the sum of the flows
into the elements receiving the energy.

True for energy. Not true for power.

And we are still waiting for the energy flow function
for the element that you claim is doing the storing
of the energy.

If you cannot understand the reference I gave you,
I don't know what to tell you.

Does it detect energy? Are you sure?
Or is it voltage that it detects? Or current?

Please provide proof that voltage or current can
exist without energy.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
The question is, can you set aside the mis-guiding
influences long enough to learn about the alternative
explanations?

Sorry, I'm not interested in those religious
concepts.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
In other posts, you have suggested that this would be
a constructive interference energy and that there would
be an equal destructive interference energy to provide
it. If you still claim this, where is this destructive
interference happening?

I have said a source can match any destructive interference
by supplying less power and match any constructive interference
by supplying more power. If you have to falsify what I have
said to try to win the argument, you have already lost.
Since you have ample sources available in your example, my
assertion about interference far removed from any source
doesn't apply - but you know that.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
Cecil Moore wrote:
In fact, the thing you need to do is forget the transmission
line and deal with light waves encountering boundaries with
different indexes of refraction. The problem is identical,
but dealing with light out in the open prohibits you from
pushing your mashed-potatoes energy religion.

No. Light, in a 3 dimensional space and at such high frequency
makes the math and measurements so complicated that it is
extremely difficult to follow the energy.

Now how did I know that you would refuse to expose your
strange concepts to the light of day?
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Sun, 09 Mar 2008 21:33:41 -0400, Chuck
wrote:

On Sun, 9 Mar 2008 15:07:26 -0700 (PDT), K7ITM wrote:

snip


Note that, as far as I've been able to determine, Michelson did not
have a coherent light source to shine into his interferometer, but
still he saw interference patterns. Perhaps he had invented lasers

snip


It is said he used sodium vapor gas light (~589 nm). Coherent enough.

Monochromatic is not the same as coherent or in phase such as a
laser.


Chuck

----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==----
http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups
----= East and West-Coast Server Farms - Total Privacy via Encryption =----
Roger Halstead (K8RI & ARRL life member)
(N833R, S# CD-2 Worlds oldest Debonair)
www.rogerhalstead.com

The Rest of the Story
 

Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.

Roger, in a nutshell, what is the bottom line?

The bottom line in a nutshell? I'll try.

First, I added a note to both spreadsheets indicating that zero degrees
is CURRENT zero degrees. This because the source turns out to be
reactive, with current peak 45 degrees from voltage peak.

http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf

The spreadsheet addresses the following issues:

Does the traveling wave carry power? Yes. The spreadsheet was built
assuming that power is carried by traveling waves. Because the
resulting wave form and powers seem correct, the underlaying assumption
seems correct.

Is power conserved on the transmission line, meaning, can the energy
contained in power be conserved and located over time on the
transmission line? Yes, the spreadsheet was built assuming that power
could be conserved and traced over time so the underlaying assumption
seems correct.

Does interference occur in this example? The spreadsheet was built
assuming that voltage and currents from superpose in a manner consistent
with constructive and destructive interference, so the underlaying
assumption seems correct.

Is power stored in the reactive component for release in later in the
cycle or during the next half cycle? Yes, power is stored on the
transmission line during the time it takes for power to enter the line,
travel to the end and return. The time of wave travel on the
transmission line is related to the value of the reactive component.

Does the direction of wave travel affect the measurement of voltage and
the application of power to a device? Yes. A wave loses energy (and
therefore voltage) as it travels through a resistance. As a result,
power from the prime source is ALWAYS applied across the sum of the
resistance from the resistor AND transmission line. The spreadsheet was
built using this assumption and seems correct. (At times during the
cycle, the forward and reflected waves oppose, resulting in very little
current through the resistor. During those times, the power applied to
the transmission line is much HIGHER because the reflected wave reflects
from the load and source, and merges/adds to the forward wave from the
source.)

Is the power interference equation Ptot = P1 + P2 +
2*SQRT(P1*P2)cos(theta) valid? The equation was not reviewed on this
spreadsheet.

The bottom line, but maybe not in a nutshell.

73, Roger, W7WKB

The Rest of the Story
 

Roger wrote:

Note that, as far as I've been able to determine, Michelson did not
have a coherent light source to shine into his interferometer, but
still he saw interference patterns. Perhaps he had invented lasers

It is said he used sodium vapor gas light (~589 nm). Coherent enough.

Monochromatic is not the same as coherent or in phase such as a
laser.

Just a slight addition here. Before lasers, the way to get a
coherent light source was to bottle-up a high-intensity,
monochromatic source, such as the aforementioned sodium-
vapor light, in a reflective cavity with a very small pinhole in
its side. As the photons dribble out through the pinhole, they
are forced into a somewhat phase-coherent wave train. This
source was used in optical processors for synthetic-aperture
radar imagery back in the 50's....

Jim, K7JEB

The Rest of the Story
 

Roger Sparks wrote:
The bottom line in a nutshell? I'll try.

Thanks Roger, good stuff and much appreciated.
My digesting of your spread sheets is about to
be interrupted by surgery.

During those times, the power applied to
the transmission line is much HIGHER because the reflected wave reflects
from the load and source, and merges/adds to the forward wave from the
source.)

May I suggest that you use the word "redistributed"
instead of "reflected" as does the FSU web page at:

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

For the purposes of this discussion, I would suggest
that the word "reflection" be reserved for something
that happens to a single wave. When two waves are
superposed, energy can be redistributed but technically
it is not an ordinary reflection. I once used the
word "reflection" to describe both phenomena and it
confused people. Now I am careful to call the
reversal of energy flow due to superposition a
"redistribution" instead of a "reflection".

For instance, the multi-colored patterns seen when
a thin film of oil is on top of a puddle of water
is not an ordinary reflection but a combination
of multiple reflections and interference.

In addition, the reflection coefficient seen by the
reflected wave in our examples is 0.0 since the source
impedance equals the characteristic impedance of the
transmission line. There are no ordinary reflections
when the reflection coefficient is zero.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Mar 26, 9:35*pm, Cecil Moore wrote:
Keith Dysart wrote:
Or perhaps the element you have identified does not have
the appropriate energy flow function? (It doesn't.)

Please prove your assertion.

So you are having difficulty doing the math to justify
your hypothesis.

This requires that the sum of the flows out of the
elements providing energy equals the sum of the flows
into the elements receiving the energy.

True for energy. Not true for power.

Ummmmm. Conservation of energy requires that the total
quantity of energy in the system not change. This requires
that the sum of the changes of the quantity of energy in
each element be zero. A change in energy quantity is a
flow. The energy flows must sum to zero. Energy flow is
power. The powers must sum to 0 to satisfy conservation
of energy.

And we are still waiting for the energy flow function
for the element that you claim is doing the storing
of the energy.

If you cannot understand the reference I gave you,
I don't know what to tell you.

You could simply do the derivation for an example that
demonstrates your hypothesis.

Does it detect energy? Are you sure?
Or is it voltage that it detects? Or current?

Please provide proof that voltage or current can
exist without energy.

I realize now that you were probably thinking of a TDR
that sent a pulse (I was thinking of one that sent a
step). My assertion is that when
Ptotal = Pfor - Pref
the idea that Pfor and Pref describe actual energy
flows is very dubious. Ptotal always describes an
energy flow.

When Pfor is 0, then Pref is equal to Ptotal and since
Ptotal is always describing an energy flow, Pref does
in this case as well. Similarly when Pref is 0.

-------

And now, since you are having trouble computing the
energy flows into the various elements here they are
again, for the circuit in the example of Fig 1-1, 100 Vrms
sinusoidal source, 50 ohm source resistor, 45 degrees of
50 ohm line, 12.5 ohm load, after the reflection returns...

The power flow into the line is
Pg(t) = 32 + 68cos(2wt)
and along with
Ps(t) = 100 + 116.6190379cos(2wt-30.96375653)
Prs(t) = 68 + 68cos(2wt-61.92751306)
energy is nicely conserved because
Ps(t) = Prs(t) + Pg(t)

The load presented by the line has a resistive and a
reactive component, so we can separate the power into
two parts
Pg.resis(t) = 32 + 32cos(2wt-61.92751306)
Pg.react(t) = 0 + 60cos(2wt+28.07248694)
which, for confirmation, nicely sums to Pg(t) above.

Now as I recall, your claim was that the total power
dissipated in the source resistor would be the power
dissipated before the reflection returned plus the
power imputed to be in the reflected wave plus the
power stored in and returned from some other element
in the circuit.
Prs(t) = 50 + 50cos(2wt)
+ Pr.g(t)
+ Pstorage
= 50 + 50cos(2wt)
+ 18 - 18cos(2wt)
+ Pstorage
Pstorage = 68 + 68cos(2wt-61.92751306)
- 50 - 50cos(2wt)
- 18 + 18cos(2wt)
= 0 + 36cos(2wt-90)
which is not the power function of the reactive
component of the line input impedance, Pg.reac(t),
computed above. So the energy is not being stored
in the reactive component of the line input
impedance.

...Keith

The Rest of the Story
 

On Mar 26, 9:51*pm, Cecil Moore wrote:
Keith Dysart wrote:
In other posts, you have suggested that this would be
a constructive interference energy and that there would
be an equal destructive interference energy to provide
it. If you still claim this, where is this destructive
interference happening?

I have said a source can match any destructive interference
by supplying less power and match any constructive interference
by supplying more power. If you have to falsify what I have
said to try to win the argument, you have already lost.
Since you have ample sources available in your example, my
assertion about interference far removed from any source
doesn't apply - but you know that.

I had not realized that you had these alternate sources for
the interference energies, not having seen that in your papers.

But it is one way to sidestep the issue; different rules for
the expectations of superposition and interference in different
scenarios.

I am surprised then, for the example of Fig 1-1 with 12.5 ohms,
that you don't just say "There is a source nearby, that *must*
be where the unaccounted energy comes from", and leave it at
that.

...Keith

The Rest of the Story
 

On Thu, 27 Mar 2008 11:49:03 GMT
Cecil Moore wrote:

Roger Sparks wrote:
The bottom line in a nutshell? I'll try.

Thanks Roger, good stuff and much appreciated.
My digesting of your spread sheets is about to
be interrupted by surgery.

Thanks for the kind words. Sorry to hear about your surgery. I hope it goes well and you have a quick recovery.

During those times, the power applied to
the transmission line is much HIGHER because the reflected wave reflects
from the load and source, and merges/adds to the forward wave from the
source.)

May I suggest that you use the word "redistributed"
instead of "reflected" as does the FSU web page at:

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

Clip

I think "redistributed" would be the word if the discontinuity included a resistance. "Reflection" is the historical word for wave reversal and implies a "mirror image", which is not the same as the forward image.

I hope the surgery does not take you away from the discussion for long.

--
73, Roger, W7WKB

The Rest of the Story
 

Keith Dysart wrote:
So you are having difficulty doing the math to justify
your hypothesis.

Actually no, the math is not difficult. I'm pre-
occupied with something else and think it's just
time to agree with Hecht that instantaneous power
is "of limited utility".

Have you taken a look at Roger's spreadsheets?

Conservation of energy requires that the total
quantity of energy in the system not change.

:-) Isn't the whole purpose of a transmitting
antenna to radiate energy away from the antenna
system? And that radiation continues to be "lost"
from the system space for some time after the
source power is removed?

Wouldn't you have to define the "system" as the
entire universe for your statement to be true?

The powers must sum to 0 to satisfy conservation
of energy.

That may be true, but there's still no conservation
of instantaneous power principle. A hot resistor
continues to radiate heat long after any power
source is removed.

You could simply do the derivation for an example that
demonstrates your hypothesis.

Already done on my web page. My only actual hypothesis
concerns average power. I've wasted too much time
bantering about something that Hecht says is "of
limited utility".

the idea that Pfor and Pref describe actual energy
flows is very dubious.

Again, look yourself in the mirror and tell yourself
that what you are seeing contains no energy. The
theory that some EM waves contain energy and some
do not is not new to you. Dr. Best was the first to
theorize that canceled waves continue to propagate
forever devoid of energy. Someone else asserted that
canceled waves never contained any energy to start
with. I strongly suspect that what you are seeing
in the mirror are the waves that didn't cancel and
that do contain energy. :-)

So the energy is not being stored
in the reactive component of the line input
impedance.

Assuming you have not made an error, so what? Energy
stored in the reactance is only one of the possibilities
that I listed earlier. As I said in an earlier posting
which you declared a non-sequitor (sic), one or more of
the following is true:

1. The source adjusts to the energy requirements.

2. The reactance stores and delivers energy.

3. Wave energy is redistributed during superposition.

4. Something I haven't thought of.

The ExH reflected wave energy exists and cannot
be destroyed. It goes somewhere and its average
value is dissipated in the source resistor in
my special case example. You are attempting to
destroy the reflected wave energy using words
and math presumably knowing all along that
reflected wave energy cannot be destroyed.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
I had not realized that you had these alternate sources for
the interference energies, not having seen that in your papers.

I only posted it three times here and you chose to
ignore all of those postings. I have published only
one paper with three more to go. The special case
Part 1 contains zero average interference so there
is no alternate source for average interference and
indeed, none is needed for Part 1.

But it is one way to sidestep the issue; different rules for
the expectations of superposition and interference in different
scenarios.

That's why I have four parts only one of which has
been published. The rules are not different but the
conditions within the examples are different. Part 2
will be an example with the condition of average
destructive interference existing at the source
resistor. Although there are no ordinary reflections
because the reflection coefficient is 0.0, there will
exist something that looks a lot like a reflection
caused by superposition/interference. The FSU web page
calls it a "redistribution", not a "reflection".
I am satisfied with FSU's word "redistribution" for
the results of coherent wave interaction.

I am surprised then, for the example of Fig 1-1 with 12.5 ohms,
that you don't just say "There is a source nearby, that *must*
be where the unaccounted energy comes from", and leave it at
that.

Since my special case example contains zero average
interference, the average power output of the source
is constant and unaffected by zero interference.
There is zero average energy unaccounted for.

Part 2 will illustrate the source adjusting its power
output to compensate for destructive interference.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Roger Sparks wrote:
I think "redistributed" would be the word if the discontinuity
included a resistance. "Reflection" is the historical word for
wave reversal and implies a "mirror image", which is not the same
as the forward image.

What I am suggesting is that "redistribution" be used
instead of "reflection" for cases where there exists
no discontinuity. If the source resistor matches the
Z0 of the feedline, there is no discontinuity and
therefore no conventional reflection, yet there are
cases where reflected energy is redistributed back
toward the load. That reversal appears to be a reflection
but is actually the result of superposition along
with destructive interference between *two* waves.
That is what causes the disparity between the physical
reflection coefficient, (Z1-Z2)/(Z1+Z2), and the virtual
reflection coefficient, SQRT(Pref/Pfor).

I hope the surgery does not take you away from the discussion
for long.

At the least, I should still have one good eye left. ;-)
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Cecil Moore wrote:


What I am suggesting is that "redistribution" be used
instead of "reflection" for cases where there exists
no discontinuity.

This is sad.

But I suppose that if you are going to invent new science you might as
well invent new terminology as well. 8-)

Yes, I know that the now-famous FSU web page uses "redistribution". Did
you happen to notice that the page was created by a lab tech and a Java
programmer? Do you suppose Hecht, Born and Wolf, and all of the other
acknowledged experts would support dumping "reflection"?

73,
Gene
W4SZ

The Rest of the Story
 

Gene Fuller wrote:
Yes, I know that the now-famous FSU web page uses "redistribution".
Do you suppose Hecht, Born and Wolf, and all of the other
acknowledged experts would support dumping "reflection"?

I would guess the answer is "yes" when the physical
reflection coefficient is zero - in order to avoid
a logical contradiction.

How does a "reflection" occur when the physical reflection
coefficient is zero, in violation of the wave reflection
model? Why is there often a difference between the
physical reflection coefficient and the virtual
reflection coefficient? Which one is wrong?

The convention that I have adopted is that the word
"reflection" is reserved for single wave events.

For multiple wave events where interference exists,
something besides a simple "reflection" takes place.
The intricate color patterns on the surface of a thin
film of oil floating on a puddle of water are not
simple reflections but instead an interaction of
multiple reflected waves. The resulting image bears
absolutely no resemblance to the incident image.

Following the FSU web page usage, the word "redistribution"
is used for multiple wave interaction events like wave
cancellation. (The words we choose to use to describe the
phenomena have zero effect on the phenomena.)

"A rose by any other name would smell as sweet."
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Gene Fuller wrote:
Did you happen to notice that the page was
created by a lab tech and a Java programmer?

Gene, if a tech asserts a fact and an expert
asserts a falsehood, who are you going to
choose to believe?
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Mar 27, 6:44*pm, Cecil Moore wrote:
Gene Fuller wrote:
Did you happen to notice that the page was
created by a lab tech and a Java programmer?

Gene, if a tech asserts a fact and an expert
asserts a falsehood, who are you going to
choose to believe?

The simulator at that web site does seem to have
its issues. Ask it to simulate 700 nm + 680 nm
at the same amplitude and see if the result
represents reality.

...Keith

PS. The result should look like a 689.8 nm sine
wave of continuously varying amplitude.

The Rest of the Story
 

Keith Dysart wrote:
The simulator at that web site does seem to have
its issues. Ask it to simulate 700 nm + 680 nm
at the same amplitude and see if the result
represents reality.

The duration of each calculation appears to be
about one second and then a reboot.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Mar 27, 2:06 am, Roger Sparks wrote:
Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.

Roger, in a nutshell, what is the bottom line?

The bottom line in a nutshell? I'll try.

First, I added a note to both spreadsheets indicating that zero degrees
is CURRENT zero degrees. This because the source turns out to be
reactive, with current peak 45 degrees from voltage peak.

http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf

I was not able to discern the derivation of the various equations
though the data in the columns looked somewhat reasonable. Were
the equation really based on the opening paragraph statement of
100 Vrms, or is it scaled to a different source voltage. The sin
functions have an amplituted of 100, which suggests a source of
200 volts or Vrms of 141.4 volts.

The spreadsheet addresses the following issues:

Does the traveling wave carry power? Yes. The spreadsheet was built
assuming that power is carried by traveling waves. Because the
resulting wave form and powers seem correct, the underlaying assumption
seems correct.

It was not obvious which columns were used to draw this correlation.

However, even if this experiment is consistent with the hypothesis
it only takes one experiment which is not to disprove the hypothesis.

Is power conserved on the transmission line, meaning, can the energy
contained in power be conserved and located over time on the
transmission line? Yes, the spreadsheet was built assuming that power
could be conserved and traced over time so the underlaying assumption
seems correct.

Does interference occur in this example? The spreadsheet was built
assuming that voltage and currents from superpose in a manner consistent
with constructive and destructive interference, so the underlaying
assumption seems correct.

Is power stored in the reactive component for release in later in the
cycle or during the next half cycle? Yes, power is stored on the
transmission line during the time it takes for power to enter the line,
travel to the end and return. The time of wave travel on the
transmission line is related to the value of the reactive component.

Does the direction of wave travel affect the measurement of voltage and
the application of power to a device? Yes. A wave loses energy (and
therefore voltage) as it travels through a resistance. As a result,
power from the prime source is ALWAYS applied across the sum of the
resistance from the resistor AND transmission line.

I am not sure that I would describe this as the wave losing energy,
but rather as the voltage dividing between the two impedances.
If the source resistance was replaced by another transmission,
which could easily be set to provide a 50 ohm impedance, would
you still describe it as the wave losing energy?

The spreadsheet was
built using this assumption and seems correct. (At times during the
cycle, the forward and reflected waves oppose, resulting in very little
current through the resistor. During those times, the power applied to
the transmission line is much HIGHER because the reflected wave reflects
from the load and source, and merges/adds to the forward wave from the
source.)

I am not convinced. When there is very little current through the
resistor,
there is also very little current into the transmission line. This
suggests to me that the power applied to the transmission line is low.

....Keith

The Rest of the Story
 

On Mar 27, 11:10 am, Cecil Moore wrote:
Keith Dysart wrote:
So you are having difficulty doing the math to justify
your hypothesis.

Actually no, the math is not difficult. I'm pre-
occupied with something else and think it's just
time to agree with Hecht that instantaneous power
is "of limited utility".

Have you taken a look at Roger's spreadsheets?

Yes.

Conservation of energy requires that the total
quantity of energy in the system not change.

:-) Isn't the whole purpose of a transmitting
antenna to radiate energy away from the antenna
system? And that radiation continues to be "lost"
from the system space for some time after the
source power is removed?

Wouldn't you have to define the "system" as the
entire universe for your statement to be true?

Sort of, but there is an easy work-around. Since we
are not particularly interested in what happens to
the energy going to the source resistor, for
example, we define the boundary of the system to
pass through the resistor and simply account for
the energy as a flow out of the system. And we
do the same for the source since we are not
particularly interested in where the energy for
the source comes from; we just account for it as
a flow into the system. And lastly, we don't
really care where the energy on the line goes to
or comes from, so we just account for it as a flow
out of the system. You may have noticed that we
have removed all the components from the system,
it is a null system, and all we are doing is
accounting for the flows into and out of the
system. Hence
Ps(t) = Prs(t) + Pg(t)

The powers must sum to 0 to satisfy conservation
of energy.

That may be true, but there's still no conservation
of instantaneous power principle.

To conserve energy however, i.e. to have no energy
accumulate in the null system described above, the
flows must balance at all times, that is,
instantaneously.

A hot resistor
continues to radiate heat long after any power
source is removed.

If you want to be that complicated you can; energy
is delivered instantaneously to the resistor according
to Vr*Ir (or equivalently, V**2/R), stored in the
resistor as heat and dissipated to the environment
later.

But for our purposes, we can stop that analysis at
the point where the energy enters the resistor and
use Vr(t) * Ir(t) to compute the instantaneous flow
into the resistor.

You could simply do the derivation for an example that
demonstrates your hypothesis.

Already done on my web page. My only actual hypothesis
concerns average power. I've wasted too much time
bantering about something that Hecht says is "of
limited utility".

Unfortunately for your hypothesis, average power is
insufficient to account for energy which might be in
the reflected wave. An average power analysis agrees
with your hypothesis, while a more detailed instaneous
analysis disproves it.

the idea that Pfor and Pref describe actual energy
flows is very dubious.

Again, look yourself in the mirror and tell yourself
that what you are seeing contains no energy. The
theory that some EM waves contain energy and some
do not is not new to you. Dr. Best was the first to
theorize that canceled waves continue to propagate
forever devoid of energy. Someone else asserted that
canceled waves never contained any energy to start
with. I strongly suspect that what you are seeing
in the mirror are the waves that didn't cancel and
that do contain energy. :-)

If it was just a 'suspicion' you could probably let
go of the idea long enough to learn what is really
happening and why it is not inconsistent with the
idea that reflected wave energy is a dubious concept.

So the energy is not being stored
in the reactive component of the line input
impedance.

Assuming you have not made an error,

You *have* found it hard to the do the math; otherwise,
you could detect an error, if there was one.

so what? Energy
stored in the reactance is only one of the possibilities
that I listed earlier. As I said in an earlier posting
which you declared a non-sequitor (sic), one or more of
the following is true:

1. The source adjusts to the energy requirements.

2. The reactance stores and delivers energy.

3. Wave energy is redistributed during superposition.

4. Something I haven't thought of.

Your explanation is not complete until you can identify
the element that stores and returns the energy and its
energy transfer function.

The ExH reflected wave energy exists and cannot
be destroyed. It goes somewhere and its average
value is dissipated in the source resistor in
my special case example.

Or not, as has been shown with the detailed analysis.

You are attempting to
destroy the reflected wave energy using words
and math presumably knowing all along that
reflected wave energy cannot be destroyed.

Energy can not be destroyed. This leads inexorably
to the conclusion that the reflected wave does not
necessarily contain energy.

....Keith

The Rest of the Story
 

On Mar 27, 11:37 am, Cecil Moore wrote:
Keith Dysart wrote:
I had not realized that you had these alternate sources for
the interference energies, not having seen that in your papers.

I only posted it three times here and you chose to
ignore all of those postings. I have published only
one paper with three more to go. The special case
Part 1 contains zero average interference so there
is no alternate source for average interference and
indeed, none is needed for Part 1.

But it is one way to sidestep the issue; different rules for
the expectations of superposition and interference in different
scenarios.

That's why I have four parts only one of which has
been published. The rules are not different but the
conditions within the examples are different. Part 2
will be an example with the condition of average
destructive interference existing at the source
resistor. Although there are no ordinary reflections
because the reflection coefficient is 0.0, there will
exist something that looks a lot like a reflection
caused by superposition/interference. The FSU web page
calls it a "redistribution", not a "reflection".
I am satisfied with FSU's word "redistribution" for
the results of coherent wave interaction.

I am surprised then, for the example of Fig 1-1 with 12.5 ohms,
that you don't just say "There is a source nearby, that *must*
be where the unaccounted energy comes from", and leave it at
that.

Since my special case example contains zero average
interference, the average power output of the source
is constant and unaffected by zero interference.
There is zero average energy unaccounted for.

Part 2 will illustrate the source adjusting its power
output to compensate for destructive interference.

Perhaps you should complete part one so that it fully
accounts for the energy flows before progressing to
writing part two. Average is not a full accounting.

....Keith

The Rest of the Story
 

On Sat, 29 Mar 2008 12:45:48 -0700 (PDT)
Keith Dysart wrote:

On Mar 27, 2:06 am, Roger Sparks wrote:
Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.

Roger, in a nutshell, what is the bottom line?

The bottom line in a nutshell? I'll try.

First, I added a note to both spreadsheets indicating that zero degrees
is CURRENT zero degrees. This because the source turns out to be
reactive, with current peak 45 degrees from voltage peak.

http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf

I was not able to discern the derivation of the various equations
though the data in the columns looked somewhat reasonable. Were
the equation really based on the opening paragraph statement of
100 Vrms, or is it scaled to a different source voltage. The sin
functions have an amplituted of 100, which suggests a source of
200 volts or Vrms of 141.4 volts.

I simplified and changed the phase for the equation in column C from '100sin(wt-90) + 100sin(wt-180)' to '100sin(wt+90) + 100sin(-wt)' so that the total voltage in column D better matches with the voltages from my formula in column G.

The equation for column B is just the sine wave for the base wave, showing the voltage resulting to the source resistor from the peak current. The equation in column C is the same (from current) but recognizes that current from the reflected wave will cancel the current from the forward wave coming through Rs. The two waves are traveling in opposite directions so one angle must be labeled with a negative sign so that it will rotate in the opposite direction. In column C, the first term is the reflected wave and the second term is the base wave.

My formula, displayed in column G, uses the applied voltage of 141.4 volts. I thought it would be easier to see how the spreadsheet was built using current to find the voltages. You can see how the results of column D match well with those from column G.


The spreadsheet addresses the following issues:

Does the traveling wave carry power? Yes. The spreadsheet was built
assuming that power is carried by traveling waves. Because the
resulting wave form and powers seem correct, the underlaying assumption
seems correct.

It was not obvious which columns were used to draw this correlation.


Column E and column F display power. Column F recognizes that if 100 watts is applied continueously (on the average) over an entire 360 degree cycle, the final power applied over time would be 360 * 100 = 36000 watt-degrees. Part of the power comes from the reflection, part comes directly. Obviously, interference is very much at work in this example.

However, even if this experiment is consistent with the hypothesis
it only takes one experiment which is not to disprove the hypothesis.


True!

Is power conserved on the transmission line, meaning, can the energy
contained in power be conserved and located over time on the
transmission line? Yes, the spreadsheet was built assuming that power
could be conserved and traced over time so the underlaying assumption
seems correct.

Does interference occur in this example? The spreadsheet was built
assuming that voltage and currents from superpose in a manner consistent
with constructive and destructive interference, so the underlaying
assumption seems correct.

Is power stored in the reactive component for release in later in the
cycle or during the next half cycle? Yes, power is stored on the
transmission line during the time it takes for power to enter the line,
travel to the end and return. The time of wave travel on the
transmission line is related to the value of the reactive component.

Does the direction of wave travel affect the measurement of voltage and
the application of power to a device? Yes. A wave loses energy (and
therefore voltage) as it travels through a resistance. As a result,
power from the prime source is ALWAYS applied across the sum of the
resistance from the resistor AND transmission line.

I am not sure that I would describe this as the wave losing energy,
but rather as the voltage dividing between the two impedances.
If the source resistance was replaced by another transmission,
which could easily be set to provide a 50 ohm impedance, would
you still describe it as the wave losing energy?


It should be OK to think of the voltage dividing between two impedances. The important thing is to consider how the reflected voltage sums with the forward voltage where it is measured. Because the two waves are traveling in opposite directions, the measured voltage is not the voltage applied to either Rs or the transmission line. This is why columns B and C must be added to find the total voltage across Rs.

The spreadsheet was
built using this assumption and seems correct. (At times during the
cycle, the forward and reflected waves oppose, resulting in very little
current through the resistor. During those times, the power applied to
the transmission line is much HIGHER because the reflected wave reflects
from the load and source, and merges/adds to the forward wave from the
source.)

I am not convinced. When there is very little current through the
resistor,
there is also very little current into the transmission line. This
suggests to me that the power applied to the transmission line is low.

I don't follow you here. Right, power into the transmission line is low when the current in is low, and it is high when the current is high. It is clear that peak current and peak voltage do not occur at the same time except when measured across the resistor in column D.


...Keith


This is just one example, but it seems like the power is accounted for here. We need another example where power can NOT be accounted for.

--
73, Roger, W7WKB

The Rest of the Story
 

On Mar 29, 7:18 pm, Roger Sparks wrote:
On Sat, 29 Mar 2008 12:45:48 -0700 (PDT)

Keith Dysart wrote:
On Mar 27, 2:06 am, Roger Sparks wrote:
Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.

Roger, in a nutshell, what is the bottom line?

The bottom line in a nutshell? I'll try.

First, I added a note to both spreadsheets indicating that zero degrees
is CURRENT zero degrees. This because the source turns out to be
reactive, with current peak 45 degrees from voltage peak.

http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf

I was not able to discern the derivation of the various equations
though the data in the columns looked somewhat reasonable. Were
the equation really based on the opening paragraph statement of
100 Vrms, or is it scaled to a different source voltage. The sin
functions have an amplituted of 100, which suggests a source of
200 volts or Vrms of 141.4 volts.

I simplified and changed the phase for the equation in column C from '100sin(wt-90) + 100sin(wt-180)' to '100sin(wt+90) + 100sin(-wt)' so that the total voltage in column D better matches with the voltages from my formula in column G.

The equation for column B is just the sine wave for the base wave, showing the voltage resulting to the source resistor from the peak current. The equation in column C is the same (from current) but recognizes that current from the reflected wave will cancel the current from the forward wave coming through Rs. The two waves are traveling in opposite directions so one angle must be labeled with a negative sign so that it will rotate in the opposite direction. In column C, the first term is the reflected wave and the second term is the base wave.

My formula, displayed in column G, uses the applied voltage of 141.4 volts. I thought it would be easier to see how the spreadsheet was built using current to find the voltages. You can see how the results of column D match well with those from column G.

I am still having difficulty matching these equations with mine. Just
to make sure we are discussing the same problem....

The circuit is a voltage source
Vs(t) = 141.4 sin(wt-45)
driving a source resistor of 50 ohms and 45 degress of 50 ohm
transmission line that is shorted at the end.

My calculations suggest that
Vrs.total(t) = 100 sin(wt-90)
Irs.total(t) = 2 sin(wt-90)

which agrees with you column D but not the introduction which
says that the zero current is at 0 degrees. With -100 volts
across the source resistor at 0 degrees, the current should
be -2 amps through the source resistor at 0 degrees; in other
words, a current maximum.

Using superposition, I compute the the contribution of the
source to be
Vrs.source(t) = 70.7 sin(wt-45)
and the contribution from the reflected wave to be
Vrs.reflected(t) = -70.7 sin(wt+45)
which sum to
Vrs.total(t) = 100 sin(wt-90)
as expected.

So while I can construct an expression for Column D, the
contributing values do not agree with those you have
provided in Columns B and C.

Column E follows from Column D and my calculations agree.
And also with Column F.

The spreadsheet addresses the following issues:

Does the traveling wave carry power? Yes. The spreadsheet was built
assuming that power is carried by traveling waves. Because the
resulting wave form and powers seem correct, the underlaying assumption
seems correct.

It was not obvious which columns were used to draw this correlation.

Column E and column F display power. Column F recognizes that if 100 watts is applied continueously (on the average) over an entire 360 degree cycle, the final power applied over time would be 360 * 100 = 36000 watt-degrees. Part of the power comes from the reflection, part comes directly. Obviously, interference is very much at work in this example.

Column E is the power dissipated in the resistor, and Column F
is the integral of Column and represents the total energy which
has flowed in to the resistor over the cycle. It is also the
average energy per cycle.

If you were to extend your analysis to compute the energy
in each degree of the reflected wave and add it to the energy
in each degree of Vrs.source(t) and sum these, you would
find that the instantaneous energy from Vrs.source and
Vrs.reflected does not agree with the instantaneous energy
dissipated in the source resistor. It is this disagreement
that is the root of my argument that the power in the
reflected wave is a dubious concept.

Using averages, the computed powers support the hypothesis,
but when examined with finer granularity, they do not.

However, even if this experiment is consistent with the hypothesis
it only takes one experiment which is not to disprove the hypothesis.

True!

Is power conserved on the transmission line, meaning, can the energy
contained in power be conserved and located over time on the
transmission line? Yes, the spreadsheet was built assuming that power
could be conserved and traced over time so the underlaying assumption
seems correct.

Does interference occur in this example? The spreadsheet was built
assuming that voltage and currents from superpose in a manner consistent
with constructive and destructive interference, so the underlaying
assumption seems correct.

Is power stored in the reactive component for release in later in the
cycle or during the next half cycle? Yes, power is stored on the
transmission line during the time it takes for power to enter the line,
travel to the end and return. The time of wave travel on the
transmission line is related to the value of the reactive component.

Does the direction of wave travel affect the measurement of voltage and
the application of power to a device? Yes. A wave loses energy (and
therefore voltage) as it travels through a resistance. As a result,
power from the prime source is ALWAYS applied across the sum of the
resistance from the resistor AND transmission line.

I am not sure that I would describe this as the wave losing energy,
but rather as the voltage dividing between the two impedances.
If the source resistance was replaced by another transmission,
which could easily be set to provide a 50 ohm impedance, would
you still describe it as the wave losing energy?

It should be OK to think of the voltage dividing between two impedances. The important thing is to consider how the reflected voltage sums with the forward voltage where it is measured. Because the two waves are traveling in opposite directions, the measured voltage is not the voltage applied to either Rs or the transmission line. This is why columns B and C must be added to find the total voltage across Rs.

Whether one needs to add or subtract is more a matter of the
convention
being used for the signs of the values. When Vf and Vr are derived
using
Vtot = Vf + Vr; Itot = If + Ir
one would expect to have to add the negative of Vr to the contribution
from Vs to arrive at the total voltage across the source resistor.

The spreadsheet was
built using this assumption and seems correct. (At times during the
cycle, the forward and reflected waves oppose, resulting in very little
current through the resistor. During those times, the power applied to
the transmission line is much HIGHER because the reflected wave reflects
from the load and source, and merges/adds to the forward wave from the
source.)

I am not convinced. When there is very little current through the
resistor,
there is also very little current into the transmission line. This
suggests to me that the power applied to the transmission line is low.

I don't follow you here. Right, power into the transmission line is low when the current in is low, and it is high when the current is high. It is clear that peak current and peak voltage do not occur at the same time except when measured across the resistor in column D.

Power into the transmission line is low when either the voltage or
the current is low; when either is zero, the power is zero.

Since the highest voltage occurs with zero current and the highest
current occurs with zero voltage, maximum power into the transmission
line occurs when the voltage and current are both medium; more
precisely, when they are both at .707 of their maximum values.

This is just one example, but it seems like the power is accounted for here. We need another example where power can NOT be accounted for.

I suggest it is the same example, but the granularity of the
analysis needs to be increased.

....Keith

The Rest of the Story
 

Keith Dysart wrote:
Unfortunately for your hypothesis, average power is
insufficient to account for energy which might be in
the reflected wave. An average power analysis agrees
with your hypothesis, while a more detailed instaneous
analysis disproves it.

One more time: My hypothesis doesn't apply to instantaneous
powers at all so there is nothing to disprove. Please
leave me out of any discussion of instantaneous powers.

If it was just a 'suspicion' you could probably let
go of the idea long enough to learn what is really
happening and why it is not inconsistent with the
idea that reflected wave energy is a dubious concept.

One look in a mirror should convince you otherwise.

You *have* found it hard to the do the math;

Nope, I just think that instantaneous power math is a
waste of my time. Seems to also be a waste of your
time.

Your explanation is not complete until you can identify
the element that stores and returns the energy and its
energy transfer function.

I simply don't have anything at all to say about
instantaneous powers. In my opinion, such is
a waste of my time. You might as well be demanding
that I produce the math for how many angels can
dance on the head of a pin.

Energy can not be destroyed.

Yet, you are trying your best to destroy the energy
in the reflected wave. Since you cannot destroy
reflected energy at the average power level, you
are trying to destroy it at the instantaneous
level.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
Perhaps you should complete part one so that it fully
accounts for the energy flows before progressing to
writing part two. Average is not a full accounting.

Average is the only accounting that I consider to
be important and the only accounting that I am going
to do. I have added a disclaimer about instantaneous
power to my Part 1 article. I personally don't think
that anyone else cares about instantaneous powers.

If you need an instantaneous power article written,
please feel free to write it yourself. I wish you luck
but I personally consider it to be a waste of time.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
Using averages, the computed powers support the hypothesis,
but when examined with finer granularity, they do not.

Well Keith, yours also falls apart at finer granularity
where you are required to determine the position and
momentum of the individual charge carriers.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Mar 30, 8:28*pm, Cecil Moore wrote:
Keith Dysart wrote:
Unfortunately for your hypothesis, average power is
insufficient to account for energy which might be in
the reflected wave. An average power analysis agrees
with your hypothesis, while a more detailed instaneous
analysis disproves it.

One more time: My hypothesis doesn't apply to instantaneous
powers at all so there is nothing to disprove. Please
leave me out of any discussion of instantaneous powers.

You state that your hypothesis is that for this specific
circuit, "the energy in the reflected wave is dissipated in
the source resistor". This claim is amenable to analysis
using instantaneous energy flows. When so analyzed, the
hypothesis fails.

I can see why you want to limit the kinds of analysis
applied to your hypothesis, but that is not how science
works.

If you wish to narrow your hypothesis to "the average energy
in the reflected wave is simply numerically equal to the
increase in the average dissipation in the source
resistor" I will not object since that hypothesis would
be completely accurate and not misleading.

As long as you wish to claim that there is actual energy
in the reflected wave, and that this energy is dissipated
in the source resistor, you must be prepared to offer a
full accounting.

If it was just a 'suspicion' you could probably let
go of the idea long enough to learn what is really
happening and why it is not inconsistent with the
idea that reflected wave energy is a dubious concept.

One look in a mirror should convince you otherwise.

You *have* found it hard to the do the math;

Nope, I just think that instantaneous power math is a
waste of my time. Seems to also be a waste of your
time.

Not at all. I've learned a new (at least to me) technique
for analyzing where the energy goes. I've increased my skills
with complex numbers in Excel. I have a firmer grasp about
power computations. I've explored the tautology of
Ptotal = Pforward - Preflected. I've learned a bit about
macros in Excel. I've tried Calc and found it wanting.
I've looked at energy flows in circulators. I've explored
active and passive circulators. And I've proved your
hypothesis to be false.

Not a waste at all.

Your explanation is not complete until you can identify
the element that stores and returns the energy and its
energy transfer function.

I simply don't have anything at all to say about
instantaneous powers. In my opinion, such is
a waste of my time.

A higly convenient opinion since it allows you to continue
to believe your hypothesis.

You might as well be demanding
that I produce the math for how many angels can
dance on the head of a pin.

No. Instantaneous flows *can* be computed. Angels on a pin
are a little more problematic.

Energy can not be destroyed.

Yet, you are trying your best to destroy the energy
in the reflected wave.

Since you start with an unshakeable belief in the
existance of energy in the reflected wave, this would be
your natural conclusion.

Those of us whose beliefs are not so fixed, evaluate
the proofs and come to the conclusion that energy in
the reflected wave is a dubious concept.

Since you cannot destroy
reflected energy at the average power level, you
are trying to destroy it at the instantaneous
level.

"Average" is just a data reduction from "instantaneous".
An agreement of averages is not a proof of anything
except that the "averages are numerically equal".

...Keith

The Rest of the Story
 

On Mar 30, 8:43*pm, Cecil Moore wrote:
Keith Dysart wrote:
Perhaps you should complete part one so that it fully
accounts for the energy flows before progressing to
writing part two. Average is not a full accounting.

Average is the only accounting that I consider to
be important and the only accounting that I am going
to do. I have added a disclaimer about instantaneous
power to my Part 1 article.

But the meaning of the disclaimer is not clear to the
reader. You really need to restate your hypothesis to
remove the possibility of misleading the reader.

I would suggest something along the lines of "My
hypothesis is that the average energy in the reflected
wave is *numerically* equal to the increase in dissipation
of the source resistor. It should be noted that this
says nothing about whether the energy in the reflected
wave is actually dissipated in the source resistor."
That would be completely accurate and very unlikely to
be misconstrued by the reader.

I personally don't think
that anyone else cares about instantaneous powers.

I am sure some do not. But anyone interested in a full
understanding does.

If you need an instantaneous power article written,
please feel free to write it yourself. I wish you luck
but I personally consider it to be a waste of time.

It is convenient when you just ignore the analysis
that disproves your hypothesis. But it does not make
the hypothesis more correct.

...Keith

The Rest of the Story
 

On Mar 30, 8:48*pm, Cecil Moore wrote:
Keith Dysart wrote:
Using averages, the computed powers support the hypothesis,
but when examined with finer granularity, they do not.

Well Keith, yours also falls apart at finer granularity
where you are required to determine the position and
momentum of the individual charge carriers.

Perhaps, but it is highly improbable that it falls apart
in a manner that ends up supporting the original failed
hypothesis.

...Keith

The Rest of the Story
 

Keith Dysart wrote:
You state that your hypothesis is that for this specific
circuit, "the energy in the reflected wave is dissipated in
the source resistor".

First, let's correct your out-of-context quotation.
Here is what you should have quoted: "When zero
interference exists at the source resistor, the
energy in the reflected wave is dissipated in the
source resistor."

This is actually a fact for both average powers
and instantaneous powers. Since all of your examples
are associated with a non-zero level of interference,
they are irrelevant to the stated conditions.

Here is a quote from that article:
"Please note that any power referred to in this paper is an AVERAGE
POWER. Instantaneous power is irrelevant to the following discussion."
The word "average" is implied in every statement I make.

This claim is amenable to analysis
using instantaneous energy flows. When so analyzed, the
hypothesis fails.

No, it doesn't fail. You have simply failed to satisfy
the zero interference precondition.

If you wish to narrow your hypothesis to "the average energy
in the reflected wave is simply numerically equal to the
increase in the average dissipation in the source
resistor" I will not object since that hypothesis would
be completely accurate and not misleading.

That is, in fact, the only hypothesis presented in
my Part 1 article. Since my hypothesis never applied
to instantaneous power, I don't have to narrow the
hypothesis. My article stands as written. Please
cease and desist with the unfair innuendo.

Not a waste at all.

Obviously, your opinion differs from mine. To the best
of my knowledge, you are the first person to spend any
mental effort on instantaneous power. If that's what
you want to do, be my guest. I consider it to be little
more than mental masturbation, "of limited utility" as
Hecht said.

In fact, I proved my assertion was true even at the
instantaneous power level when the "zero interference"
precondition is met.

Since you start with an unshakeable belief in the
existance of energy in the reflected wave, this would be
your natural conclusion.

Since you are incapable of producing an EM wave devoid
of energy (or an angel dancing on the head of a pin) both
concepts are unrelated to reality IMO.

Your challenge is the same as it has always been. Just
produce an EM wave containing zero energy and get it
over with.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
But the meaning of the disclaimer is not clear to the
reader. You really need to restate your hypothesis to
remove the possibility of misleading the reader.

What is it about "Please note that any power referred to
in this paper is an AVERAGE POWER. Instantaneous power
is irrelevant to the following discussion." that you
do not understand?

I would suggest ...

I would suggest that you write your own article.
Mine stands as written in the *stated context*
of zero interference and average powers. I am
not interested in attempting a unified theory
of everything.

I personally don't think
that anyone else cares about instantaneous powers.

I am sure some do not. But anyone interested in a full
understanding does.

Anyone interested in a *full* understanding would
take the discussion down to the quantum level which,
interestingly enough, you have chosen to ignore.

It is convenient when you just ignore the analysis
that disproves your hypothesis. But it does not make
the hypothesis more correct.

If you think your unethical innuendo, out-of-context
quotes, and straw man arguments disprove anything,
I feel sorry for you.

Once again, the context of my Part 1 assertions is
*ZERO INTERFERENCE* and *AVERAGE POWERS*. You have
disproved nothing so far. You were even taken aback
when it was true at the instantaneous level in the
context of zero instantaneous interference.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
Perhaps, but it is highly improbable that it falls apart
in a manner that ends up supporting the original failed
hypothesis.

Since the original hypothesis is in the context of
zero interference (and average powers) it has not
failed. So far, I have made no assertions about
conditions when interference is present as it is
in all of your examples. None of your observations
are relevant to my Part 1 article because they are
all outside the stated context of the article.

The challenge for you is to present a zero interference
example for which my hypothesis is false. So far, you
have failed to do so.

I have asserted, "If zero interference exists, then 'A'
is true". You have said 'A' is not true when interference
exists. I actually agree with you but it is irrelevant
to the stated 'if' portion of my premise. Where did
you study logic?

Maybe you don't realize that if the 'if' portion of
an 'if/then' statement is false, the entire statement
is true, by definition.

My assertions about conditions when interference is
present will appear in Parts 2 and 3 (which would have
been completed by now if I had ignored your diversions).
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Sun, 30 Mar 2008 07:43:59 -0700 (PDT)
Keith Dysart wrote:

On Mar 29, 7:18 pm, Roger Sparks wrote:
On Sat, 29 Mar 2008 12:45:48 -0700 (PDT)

Keith Dysart wrote:
On Mar 27, 2:06 am, Roger Sparks wrote:
Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.
clip
http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf
clip

I am still having difficulty matching these equations with mine. Just
to make sure we are discussing the same problem....

As I tried to understand your problem, I finally realized that it was really my problem. As a result, I redid the spreadsheet. I now label "my formula" as being erroneous, this because it does relate to the current, not the voltage, and must be displaced by 45 degrees.

My formula (labeled erroneous) was the result of the formulas of columns B and C added with trig identities. What I did not realize was that the adding, while correct, rotates the phase. The formula is wrong because it does not recognize the phase shift that had been assumed for line one.

The spreadsheet addresses the following issues:

Does the traveling wave carry power? Yes. The spreadsheet was built
assuming that power is carried by traveling waves. Because the
resulting wave form and powers seem correct, the underlaying assumption
seems correct.

It was not obvious which columns were used to draw this correlation.

Column E and column F display power. Column F recognizes that if 100 watts is applied continueously (on the average) over an entire 360 degree cycle, the final power applied over time would be 360 * 100 = 36000 watt-degrees. Part of the power comes from the reflection, part comes directly. Obviously, interference is very much at work in this example.

Column E is the power dissipated in the resistor, and Column F
is the integral of Column and represents the total energy which
has flowed in to the resistor over the cycle. It is also the
average energy per cycle.

If you were to extend your analysis to compute the energy
in each degree of the reflected wave and add it to the energy
in each degree of Vrs.source(t) and sum these, you would
find that the instantaneous energy from Vrs.source and
Vrs.reflected does not agree with the instantaneous energy
dissipated in the source resistor. It is this disagreement
that is the root of my argument that the power in the
reflected wave is a dubious concept.


I think the energy adds correctly now. Of course it depends upon how we measure the energy because energy is stored in the transmission line at all times, but the stored energy is only measured across either Rs or the transmission line. We do not measure the energy within the transmission line in this example, which is the sum of the applied power for 90 degrees.

Using averages, the computed powers support the hypothesis,
but when examined with finer granularity, they do not.

I think each degree has the correct power now. I apologize for the errors, and hope that I have them all removed.

However, even if this experiment is consistent with the hypothesis
it only takes one experiment which is not to disprove the hypothesis.

True!

Is power conserved on the transmission line, meaning, can the energy
contained in power be conserved and located over time on the
transmission line? Yes, the spreadsheet was built assuming that power
could be conserved and traced over time so the underlaying assumption
seems correct.

Does interference occur in this example? The spreadsheet was built
assuming that voltage and currents from superpose in a manner consistent
with constructive and destructive interference, so the underlaying
assumption seems correct.

Is power stored in the reactive component for release in later in the
cycle or during the next half cycle? Yes, power is stored on the
transmission line during the time it takes for power to enter the line,
travel to the end and return. The time of wave travel on the
transmission line is related to the value of the reactive component.

Does the direction of wave travel affect the measurement of voltage and
the application of power to a device? Yes. A wave loses energy (and
therefore voltage) as it travels through a resistance. As a result,
power from the prime source is ALWAYS applied across the sum of the
resistance from the resistor AND transmission line.

I am not sure that I would describe this as the wave losing energy,
but rather as the voltage dividing between the two impedances.
If the source resistance was replaced by another transmission,
which could easily be set to provide a 50 ohm impedance, would
you still describe it as the wave losing energy?

It should be OK to think of the voltage dividing between two impedances. The important thing is to consider how the reflected voltage sums with the forward voltage where it is measured. Because the two waves are traveling in opposite directions, the measured voltage is not the voltage applied to either Rs or the transmission line. This is why columns B and C must be added to find the total voltage across Rs.

Whether one needs to add or subtract is more a matter of the
convention
being used for the signs of the values. When Vf and Vr are derived
using
Vtot = Vf + Vr; Itot = If + Ir
one would expect to have to add the negative of Vr to the contribution
from Vs to arrive at the total voltage across the source resistor.

The spreadsheet was
built using this assumption and seems correct. (At times during the
cycle, the forward and reflected waves oppose, resulting in very little
current through the resistor. During those times, the power applied to
the transmission line is much HIGHER because the reflected wave reflects
from the load and source, and merges/adds to the forward wave from the
source.)

I am not convinced. When there is very little current through the
resistor,
there is also very little current into the transmission line. This
suggests to me that the power applied to the transmission line is low.

I don't follow you here. Right, power into the transmission line is low when the current in is low, and it is high when the current is high. It is clear that peak current and peak voltage do not occur at the same time except when measured across the resistor in column D.

Power into the transmission line is low when either the voltage or
the current is low; when either is zero, the power is zero.

Since the highest voltage occurs with zero current and the highest
current occurs with zero voltage, maximum power into the transmission
line occurs when the voltage and current are both medium; more
precisely, when they are both at .707 of their maximum values.

This is just one example, but it seems like the power is accounted for here. We need another example where power can NOT be accounted for.

I suggest it is the same example, but the granularity of the
analysis needs to be increased.

...Keith

I hope I have the spread sheet displaying correct values now. Thank you for your careful analysis.

I doubt that this will satisfy your power location concerns because the spread sheet shows more power being delivered to the resistor than is present in the voltage. This is because the impedance of the power equation has changed due to the contribution of the current component. Consider that for columns B and C, the same current flows whether the voltage in B is applied or the voltage in C is applied. This can only happen if the impedance seen by each respective voltage is different. This is interference at work
--
73, Roger, W7WKB

The Rest of the Story
 

On Mon, 31 Mar 2008 10:03:52 -0700
Roger Sparks wrote:

On Sun, 30 Mar 2008 07:43:59 -0700 (PDT)
Keith Dysart wrote:

On Mar 29, 7:18 pm, Roger Sparks wrote:
On Sat, 29 Mar 2008 12:45:48 -0700 (PDT)

Keith Dysart wrote:
On Mar 27, 2:06 am, Roger Sparks wrote:
Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.
clip
http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf
clip


I doubt that this will satisfy your power location concerns because the spread sheet shows more power being delivered to the resistor than is present in the voltage. This is because the impedance of the power equation has changed due to the contribution of the current component. Consider that for columns B and C, the same current flows whether the voltage in B is applied or the voltage in C is applied. This can only happen if the impedance seen by each respective voltage is different. This is interference at work
--
73, Roger, W7WKB

After posting previosly, I got to thinking that interference here is wrecking the analysis of Column D. The traveling wave analysis is correct (Column H). Only one current is flowing through Rs, and the current is not enough to supply the power suggested in column D. While it is logical to add the voltages from Column B and Column C, the two voltages are often in opposition so they are not "seen" by Rs. As a result, we must have a reflection from Rs that I am not taking into account.
--
73, Roger, W7WKB

The Rest of the Story
 

On Mar 31, 2:22*pm, Roger Sparks wrote:
On Mon, 31 Mar 2008 10:03:52 -0700

Roger Sparks wrote:
On Sun, 30 Mar 2008 07:43:59 -0700 (PDT)
Keith Dysart wrote:

On Mar 29, 7:18 pm, Roger Sparks wrote:
On Sat, 29 Mar 2008 12:45:48 -0700 (PDT)

Keith Dysart wrote:
On Mar 27, 2:06 am, Roger Sparks wrote:
Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.
clip
http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf
clip

I doubt that this will satisfy your power location concerns because the spread sheet shows more power being delivered to the resistor than is present in the voltage. *This is because the impedance of the power equation has changed due to the contribution of the current component. Consider that for columns B and C, the same current flows whether the voltage in B is applied or the voltage in C is applied. *This can only happen if the impedance seen by each respective voltage is different. *This is interference at work *
--
73, Roger, W7WKB

After posting previosly, I got to thinking that interference here is wrecking the analysis of Column D. *The traveling wave analysis is correct (Column H). *Only one current is flowing through Rs, and the current is not enough to supply the power suggested in column D. *While it is logical to add the voltages from Column B and Column C, the two voltages are often in opposition so they are not "seen" by Rs. *As a result, we must have a reflection from Rs that I am not taking into account. *

Column B is correct; this being the voltage produced by the source
divided by two.
It is also the forward voltage on the line.
Vrs.source(t) = Vf(t) = 70.7 sin(wt)

Column C is the reflected voltage (not the reflected voltage impressed
across the
source resistor). The reflection coefficient is -1, and the delay is
90 degrees
so the reflected voltage at the generator is
Vr(t) = -1 * Vf(t - 90 degrees)
= - 70.7 sin(wt-90)
= 70.7 sin(wt+90)

But Vr is impressed across the resistor in the opposite direction to
that of
Vrs.source, so the equation for total Vrs is
Vrs.total(t) = Vrs.source(t) - Vr(t)
thus column D should be B31-C31.

Alternatively,
Vrs.reflect(t) = -Vr(t)
and then
Vrs.total(t) = Vrs.source(t) + Vrs.reflect(t)

Column E is correctly computing the instantaneous power from Column D
since
P(t) = V(t) * I(t)
= V(t) * V(t) / R
= V(t) * V(t) / 50 (in this example)
but has the wrong data because of the error in Column D.

Column F is integrating the power to yield either the energy in a
cycle or
the average power per cycle (though presented in unusual units).

I agree G is erroneous and I am not sure what H is computing.

...Keith

The Rest of the Story
 

Roger Sparks wrote:
While it is logical to add the voltages from Column B and Column C,
the two voltages are often in opposition so they are not "seen" by Rs.
As a result, we must have a reflection from Rs that I am not taking
into account.

It's not a "reflection" of a single wave, Roger, it is
a "redistribution" of energy caused by superposition
of two waves accompanied by interference. Eugene Hecht
explains it all in Chapter 9: Interference in "Optics".

For anyone who thinks he is already omniscient
about EM waves, I would highly recommend reading
Hecht's chapter on interference.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Mon, 31 Mar 2008 19:11:56 -0500
Cecil Moore wrote:

Roger Sparks wrote:
While it is logical to add the voltages from Column B and Column C,
the two voltages are often in opposition so they are not "seen" by Rs.
As a result, we must have a reflection from Rs that I am not taking
into account.

It's not a "reflection" of a single wave, Roger, it is
a "redistribution" of energy caused by superposition
of two waves accompanied by interference. Eugene Hecht
explains it all in Chapter 9: Interference in "Optics".

For anyone who thinks he is already omniscient
about EM waves, I would highly recommend reading
Hecht's chapter on interference.
--
73, Cecil http://www.w5dxp.com

I had to chuckle when I read this Cecil. First I looked up the word "omniscient" to refresh my memory about meaning, but then I thought "anyone who thinks he is omniscient is not about to read the works of others and learn new tricks". Just human nature.

You can see from my postings that I am still trying to better understand the wave and reflections, still looking how to describe the energy distribution within the cycle. The storage of the redistributed energy must be close to the wires of the circuit so we should be able to describe it mathmatically, if I just knew how. We are probably close on the spreadsheet, but it is not yet crystal clear in my mind.

--
73, Roger, W7WKB