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

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

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

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

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

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

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