Roger Sparks wrote:
To me, this shows that my traveling wave analysis on an instant basis
is not correct because the energy can not be located precisely on a
degree-by-degree scale. Yes, it is correct on the average over 360
degrees, but not instantaneously. We are missing something.

What you are missing is the localized interference patterns
within the individual cycles. The interference changes from
destructive to constructive every 90 degrees. For every
negative (destructive) interference term, there is an equal
magnitude positive (constructive) interference term 90 degrees
later. These, of course, average out to zero. Exactly the
same thing happens when a coil or capacitor is present in
a circuit. When the instantaneous voltage of a source is
zero and thus delivering zero instantaneous power, a
circuit capacitor is delivering energy back into the
circuit that can be dissipated by a resistor.

Central to traveling waves is the assumption that the wave is not
compressable. The energy is assumed to flow in a consistantly
predictable mannor that is linear and described by a sine wave.
That assumption is violated when energy is delayed for reasons
other than distance of travel, which is demonstrated in this example.

Power is certainly compressible. One can stuff 100 amphere-
hours into a battery in 2 hours and take 20 hours to remove it.
Why can't 60 watts of instantaneous power be stuffed into
a reactance and be removed 90 degrees later?

I am not ready to suggest a cure for my traveling wave analysis. I
only see that it does not work to my expectations.

Your expectations seem to be based on a conservation of
power principle which doesn't exist. There is no violation
of linearity if the energy dissipation is delayed by 90
degrees or by ten billion years.

I don't recall any published material where anyone tried
to explain where the instantaneous energy goes while at
the same time denying the possibility of interference.
--
73, Cecil http://www.w5dxp.com

On Mon, 24 Mar 2008 16:15:21 GMT
Cecil Moore wrote:

Roger Sparks wrote:
To me, this shows that my traveling wave analysis on an instant basis
is not correct because the energy can not be located precisely on a
degree-by-degree scale. Yes, it is correct on the average over 360
degrees, but not instantaneously. We are missing something.

What you are missing is the localized interference patterns
within the individual cycles. The interference changes from
destructive to constructive every 90 degrees. For every
negative (destructive) interference term, there is an equal
magnitude positive (constructive) interference term 90 degrees
later. These, of course, average out to zero. Exactly the
same thing happens when a coil or capacitor is present in
a circuit. When the instantaneous voltage of a source is
zero and thus delivering zero instantaneous power, a
circuit capacitor is delivering energy back into the
circuit that can be dissipated by a resistor.

Central to traveling waves is the assumption that the wave is not
compressable. The energy is assumed to flow in a consistantly
predictable mannor that is linear and described by a sine wave.
That assumption is violated when energy is delayed for reasons
other than distance of travel, which is demonstrated in this example.

Power is certainly compressible. One can stuff 100 amphere-
hours into a battery in 2 hours and take 20 hours to remove it.
Why can't 60 watts of instantaneous power be stuffed into
a reactance and be removed 90 degrees later?

I am not ready to suggest a cure for my traveling wave analysis. I
only see that it does not work to my expectations.

Your expectations seem to be based on a conservation of
power principle which doesn't exist. There is no violation
of linearity if the energy dissipation is delayed by 90
degrees or by ten billion years.

I don't recall any published material where anyone tried
to explain where the instantaneous energy goes while at
the same time denying the possibility of interference.
--
73, Cecil http://www.w5dxp.com

Hi Cecil,

I feel better today. I think I have connected the dots and now have the spreadsheet showing that we really can use the traveling waves to solve the shorted transmission line problem on a instantaneous basis without the delay of energy into the next half cycle.

Here is a link to the new spreadsheet.

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

I used the logic and formula presented in my post "Subject: The Rest of the Story
Date: Thu, 20 Mar 2008 10:07:44 -0700"

You called it interference. Keith used your power equation and called the interference term a mathematical correction. It looks to me like the correction can be avoided by choosing the correct sin wave offset.

Ultimately, the waves can be resolved into one more powerful wave carrying the power described by Keith's "false power" equation. This is demonstrated in a spreadsheet found at

http://www.fairpoint.net/~rsparks/Re...em%20Power.pdf

You need to take a look at the spreadsheets. I think they support the theory that we can track the power on an instant basis using traveling waves.
--
73, Roger, W7WKB

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

Roger, in a nutshell, what is the bottom line?
--
73, Cecil http://www.w5dxp.com

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

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

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

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

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

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

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