The Rest of the Story
 

On Apr 11, 9:25*am, Cecil Moore wrote:
Keith Dysart wrote:
The computation using energy instead of power has
also been done (and published here) and found also
to demonstrate that the reflected is not dissipated
in the source resistor.

Well, that certainly violates the conservation of
energy principle. We know the reflected energy is
not dissipated in the load resistor, by definition.

The only other device in the entire system capable
of dissipation is the source resistor. Since the reflected
energy is not dissipated in the load resistor and you say
it is not dissipated in the source resistor, it would
necessarily have to magically escape the system or build
up to infinity (but it doesn't).

You seem to have forgotten that a voltage source can
absorb energy. This happens when the current flows
into it rather than out.

Recall the equation
Ps(t) = Prs(t) + Pg(t)

When the voltage source voltage is greatr than the
voltage at the terminals of the line (Vg(t)), energy
flows from the source into the resistor and the line.
When the voltage at the line terminals is greater
than the voltage source voltage, energy flows from
the line into the resistor and the voltage source.

At all times
Ps(t) = Prs(t) + Pg(t)
holds true.

Conservation of energy at work. No lost energy.

gartuitous comment snipped

How many joules are there in 100 watts of
instantaneous power?

Obviously. It depends on how long you let the
100 W of instantaneous power flow. Integrate and
the answer shall be yours.

I'm not the one making the assertions. How many joules
of energy exist in *YOUR* instantaneous power calculations?

We have been down that path; the spreadsheet has been
published. The flows of energy described by
Ps(t) = Prs(t) + Pg(t)
always balance.

The integration of these energy flows over any interval
also balance.

Energy is conserved. The world is as it should be.

...Keith

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On Apr 11, 9:32*am, Cecil Moore wrote:
Keith Dysart wrote:
If care is taken with the selection of modulation
frequencies with regards to the carrier, then nodes
can be created on the transmission line and neither
the carrier nor the modulation will cross such a
node.

Please prove your assertion on the bench. Until you
do, there is little left to discuss.

Speculating that this is your way of asking for an
explantion...
With a shorted line, nodes occur every 90 degrees. These
90 degree nodal points are at different places on
the line for different frequencies because the
wavelengths are different. With the nodes at
different physical locations for the different
frequencies, when you sum the responses for all of
the frequencies there are no longer well defined
nodes.

If the frequencies are rational numbers, then
nodes for the total response will exist at the lowest
common multiples of the wavelengths, but it will
typically take a very long line to find one.

...Keith

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On Apr 11, 3:30*pm, Cecil Moore wrote:
Roger Sparks wrote:
You write "The only other device in the entire system capable
of dissipation is the source resistor." which is a correct statement.

Therefore, all power dissipated in the circuit must be dissipated
in the load resistor and the source resistor because there is
nowhere else for it to go.

Please do not forget the source. It can absorb energy.

Since the reflected power is not
dissipated in the load, by definition, it has to be dissipated
in the source resistor but not at the exact time of its arrival.
There is nothing wrong with delaying power dissipation for 90
degrees of the cycle.

If you can't identify where the energy is stored for those 90
degrees you do not have a complete story. Or you are violating
conservation of energy and therefore have no story what-so-ever.

In Parts 2 and 3 of my articles, I will show
how the source decreases it power output to compensate for destructive
interference and increases it power output to compensate for
constructive interference.

Unfortunately, the circuit is intended to illustrate the absence of
[AVERAGE] interference under special circumstances but an instant analysis shows
that all the power can not be accounted for. *

Not surprising since there is no conservation of power principle.

Conservation of energy means that energy flows must be conserved.
Therefore, conservation of power.

We can only conclude that
[instantaneous] interference is present. Not good because the circuit was intended to
illustrate a case of NO [AVERAGE] interference.

I took the liberty of adding adjectives in brackets[*] to your
above statements. It doesn't matter about the instantaneous values
of power since not only do they not have to be conserved, but they
are also "of limited usefulness", according to Eugene Hecht, since
the actual energy content of instantaneous power is undefined even
when the instantaneous power is defined.

Are you sure that is why Hecht wrote what he did? He would, in all
likelihood, have an apoplexy if he knew how his words were being used.

The circuit is very useful to investigate interference more carefully because on the AVERAGE,

the interference IS zero. *Using spreadsheets, we can see how the
interference both adds and

subtracts from the instantaneous applied voltage, resulting in cycling
variations in the power

applied to the resistor and other circuit elements. *A very instructive
exercise.

Instructive as long as we remember that a conservation of power
principle doesn't exist and therefore, equations based on instantaneous
powers do not have to balance. The joules, not the watts, are what must
balance.

Since the total energies in your equations do not balance either,
there is still a problem with your hypothesis.

It would be helpful, however, if you could actually demonstrate a
system where the energies balance, but the flows do not. This would
settle the matter once and for all. (You won't find one, since
balanced flows are a consequence of conservation of energy).

...Keith

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Keith Dysart wrote:
It would be helpful, however, if you could actually demonstrate a
system where the energies balance, but the flows do not.

That's obviously easy to demonstrate in a distributed
network system. We can have energy flowing into both
ends of a loading coil at the same time and 180 degrees
later, energy flowing out of both ends at the same time.
The energies balance but the flows are completely
unbalanced and indeed defy the lumped circuit model.
--
73, Cecil http://www.w5dxp.com

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On Apr 12, 3:39*pm, Cecil Moore wrote:
Keith Dysart wrote:
It would be helpful, however, if you could actually demonstrate a
system where the energies balance, but the flows do not.

That's obviously easy to demonstrate in a distributed
network system. We can have energy flowing into both
ends of a loading coil at the same time and 180 degrees
later, energy flowing out of both ends at the same time.
The energies balance but the flows are completely
unbalanced and indeed defy the lumped circuit model.

You are not quite looking at the system correctly.

It is a system with two ports (bottom and top) where
energy can enter or leave, and one element (coil)
which can store energy.

The energy that flows in the bottom either flows out
the top or increases the energy stored in the coil.
The energy flowing into the bottom is equal to
the sum of the energy flowing out the top plus the
increase in the energy stored in the coil.
Expressed arithmetically
Pbottom(t) = Pcoil(t) + Ptop(t)

For the specific situation you describe above:
"energy flowing out of both ends at the same time"
means that the energy stored in the ooil is being
reduced to supply the energy leaving the top and
the bottom. The sum of the energy flows out of
the top and the bottom is exactly equal to the rate
at which the stored energy is being reduced.

Lumped or not lumped is moot.
The same analysis can be applied to a transmission
line. The energy flow into the left is exactly
equal to the energy flow out on the right plus
the rate of increase in the energy stored in the
line.

Energy flows (aka power) do indeed balance, though
you certainly have to correctly pick the flows that
should balance.

...Keith

The Rest of the Story
 

Keith Dysart wrote:
For the specific situation you describe above:
"energy flowing out of both ends at the same time"
means that the energy stored in the ooil is being
reduced to supply the energy leaving the top and
the bottom. The sum of the energy flows out of
the top and the bottom is exactly equal to the rate
at which the stored energy is being reduced.

Yes, the energy obviously balances but the instantaneous
powers are in opposite directions and therefore cannot
balance.

Lumped or not lumped is moot.

Energy cannot flow out of both ends of a lumped circuit
inductor. The current is, by definition, exactly the
same at both ends as it is for the lumped inductors in
EZNEC. You might find these class notes informative.

http://www.ttr.com/corum/
--
73, Cecil http://www.w5dxp.com

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On Apr 13, 9:45*am, Cecil Moore wrote:
Keith Dysart wrote:
For the specific situation you describe above:
"energy flowing out of both ends at the same time"
means that the energy stored in the ooil is being
reduced to supply the energy leaving the top and
the bottom. The sum of the energy flows out of
the top and the bottom is exactly equal to the rate
at which the stored energy is being reduced.

Yes, the energy obviously balances but the instantaneous
powers are in opposite directions and therefore cannot
balance.

Lumped or not lumped is moot.

Energy cannot flow out of both ends of a lumped circuit
inductor. The current is, by definition, exactly the
same at both ends as it is for the lumped inductors in
EZNEC. You might find these class notes informative.

It is well known that if one builds the wrong model one
will get the wrong answer. You build the wrong model,
then claim that flows do not balance. Unbalanced flows
are the expected result from incomplete models.

Your imcompleteness is that you forgot to include the
energy flow into the electric and magnetic fields around
the coil. When one does not forget this flow, all of
the flows will balance at every instant.

...Keith

The Rest of the Story
 

Keith Dysart wrote:
Your imcompleteness is that you forgot to include the
energy flow into the electric and magnetic fields around
the coil. When one does not forget this flow, all of
the flows will balance at every instant.

Sorry, it may or may not be a coil. It is in a black box
whose contents are unknown. Including the energy flows
inside the black box is impossible. The instantaneous
power into the black box does not balance the instantaneous
power out of the black box.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Apr 13, 8:41*pm, Cecil Moore wrote:
Keith Dysart wrote:
Your imcompleteness is that you forgot to include the
energy flow into the electric and magnetic fields around
the coil. When one does not forget this flow, all of
the flows will balance at every instant.

Sorry, it may or may not be a coil. It is in a black box
whose contents are unknown. Including the energy flows
inside the black box is impossible. The instantaneous
power into the black box does not balance the instantaneous
power out of the black box.

Black boxes are an excellent way to set problems which help us
learn about the meaning of theories.

Conservation of energy and its corollary, conservation of power,
is used in a different way for analyzing black boxes than it
is when we analyzed the fully specified circuit in your Fig 1-1.

With the black box, knowing the power function on the two ports,
we can compute the energy flow into the storage elements within
the box. If the flow out of one port is not always exactly
balanced by the flow into the other, then we know that the black
box is storing some energy and therefore that it has some elements
which store energy. In a more typical situation, we do not have
a completely black box, but we know some of its elements. We can
use the balance of energy flows to help us decide if we have all
the elements. If some of the energy flow is unaccounted for, then
we have not yet found all the elements.

If the box is truly opague, then all we can say is that it has
some energy storage elements and that collectively, the flow
into these elements is described by
Pport1(t) - Pport2(t)

The situation is somewhat different in Fig 1-1. All the elements
of the system are completely specified in Fig 1-1 and we used
circuit theory to compute the energy flows. Not surprisingly, they
completely balanced:
Ps(t) = Prs(t) + Pg(t)
Associated with Fig 1-1, there is a secondary hypothesis that it
should be possible to account for another energy flow, the imputed
flow in the reflected wave on the line. The inability to account
for this flow, given the conservation of power corollary to the
conservation of energy law, is a very strong indicator that the
energy flow imputed to the reflected wave is not an actual energy
flow.

...Keith

The Rest of the Story
 

Keith Dysart wrote:
All the elements
of the system are completely specified in Fig 1-1 and we used
circuit theory to compute the energy flows. Not surprisingly, they
completely balanced:
Ps(t) = Prs(t) + Pg(t)

Yes, but that is only *NET* energy flow and says nothing
about component energy flow. Everything is already known
about net energy flow and there are no arguments about it
so you are wasting your time. Your equation above completely
ignores reflections which is the subject of the thread.

You object to me being satisfied with average energy flow
while you satisfy yourself with net energy flow. I don't see
one iota of conceptual difference between our two positions.

After hundreds of postings, all you have proved is that
Eugene Hecht was right when he said instantaneous powers
are "of limited utility", such that you cannot even tell
me how many joules there are in 100 watts of instantaneous
power when it is the quantity of those very joules that
are required to be conserved and not the 100 watts.

The limit in your quest for tracking instantaneous energy
is knowing the position and momentum of each individual
electron. Good luck on that one.

I am going to summarize the results of my Part 1 article
and be done with it.

In the special case presented in Part 1, there are only
two sources of power dissipation in the entire system,
the load resistor and the source resistor. None of the
reflected energy is dissipated in the load resistor
because the chosen special conditions prohibit reflections
from the source resistor. Therefore, all of the energy not
dissipated in the load resistor is dissipated in the source
resistor because there is no other source of dissipation
in the entire system. Only RL and Rs exist. Pr is not
dissipated in RL. Where is Pr dissipated? Even my ten year
old grandson can solve that problem and he's no future
rocket scientist.
--
73, Cecil http://www.w5dxp.com