On Jan 15, 6:03*am, Roy Lewallen wrote:
Comments interspersed. . .

Keith Dysart wrote:
[snip]
I take this to imply that you are not happy with the simple "like
charge
repels"?

That's right. Although it's a true statement, I haven't seen any
explanation of why it would cause waves to bounce off each other.

And Roger suggested the counter-example which may mark the end of
the line for "bounce".

[snip]
I would really appreciate seeing some other possible explanations.

How about this: During the initial turn-on of the system, energy does
cross the magic node. It's only in the theoretical limiting case of
steady state that the energy goes into and out of the node but doesn't
cross it. I'll argue that the limiting case can never be reached --
since this whole setup is a perfect construct to begin with. Or, if
that's not adequate by itself, what's the problem with energy being
trapped between nodes once the line is charged and steady state is reached?

I do use the view that the energy is trapped. The difficulty is: What
is the mechanism that traps the energy?

[snip]
With this explanation, P(t)
is definitely equal to V(t) time I(t), which I do appreciate.
The weakness of this explanation is that it seems to deny
that the wave moves energy. And yet before the pulses collide
it is easy to observe the energy moving in the line, and if
a pulse was not coming in the other direction, there would
be no dispute that the energy travelled to the end of the
line and was absorbed in the load. Yet when the pulses
collide, no energy crosses the middle of the line. Yet
energy can be observed travelling in the line before
and after the pulses collide.

I think the basic problem here is assigning energy to each traveling
wave.

I agree. And when looking at sinusoidal excitation with "standing
waves", it easy not to assign energy.

But when looking at pulses, the energy in the pulse seems to jump
out at me, and it is hard to ignore.

It's taking you into exactly the same morass that Cecil constantly
finds himself in.

I know. And I definitely do not want to go there.

And yet, when I look at pulses, where the energy is clearly visible,
I develop some sympathy for Cecil's position.

He also concluded some time back that two waves which
collide had to reverse direction in order to conserve power, energy,
momentum, or something. Energy in the system is conserved; but nowhere
is it written that each wave has to have individually conserved energy.

[snip]
I think you need to take a closer look at what it's getting you out
from. I believe the problem lies there.

Possibly.

[snip]
So I am not convinced that it any way goes against established theory.
I have not seen established theory attempt an explanation of how the
waves can both transport energy as well as not do so when waves of
equal energy collide.

Perhaps that's because individual waves don't transport energy that has
to be conserved?

Possibly, but the energy is so clearly visible in the pulses before
and
after they collide.

[snip]
The same concern that arises for pulses of equal voltage also
occurs for pulses of different voltage. While the mid-point no
longer has zero current, the actual current is only the difference
of the two currents in the pulses, the charge that crosses is only
the difference in the charge between the two pulses, and the
power at the mid-point is exactly the power that is needed
to move the difference in the energy of the two pulses.

Sorry, I'm having trouble following that. Voltage, current, charge, and
energy all in two sentences has too high a concept density for me to handle.

I'll try with a better description. Consider a line 4 sec long with
a matched pulse generator at each end. There is an instantaneous power
(p(t)=v(t)*i(t)) meter at the 1, 2 and 3 sec points on the line.
Call them the left, middle and right meters.
The left generator launches a 1 sec pulse of 100 volts and 2 amps (it
is
50 ohm line). This pulse is 200 W and contains 200 J.
Simultaneously the right generator launches a 1 sec pulse of 50 volts
and 1 amp (50 W and 50 J).
At 1 sec the left power meter reads 200 W for 1 sec as 200 J pass,
then at 3 sec the right power meter reads 200 W for 1 sec as 200 J
pass. It sure looks like the pulse has travelled down the line.
At 1 sec the right power meter reads -50 W for 1 sec as 50 J pass,
then at 3 sec the left power meter reads -50 W for 1 sec as 50 J
pass. It sure looks like this pulse has travelled up the line.
The total energy transfer measured by the left meter is 150 J and
by the right meter is also 150 J.
At second 2, when the pulses collide in the middle, the middle meter
reads 150 W for 1 second. So the total energy transfer at the middle
is 150 J, which is good since it agrees with the totals in the other
meters.

So the middle meter reads 150 W.
The left meter reads 200 W and later -50 W.
And the right meter reads -50 W and later 200 W.

So how does a pulse that measurably is 200 W (measured at both right
and left meters) move through a point that only measures 150 W.

Numerologically it surely does appear that one can superpose powers
since 200+(-50) is 150.

The main difference between this experiment and one with steady state
sinusoidal waves is that in the latter the component forward and
reverse waves in are derived by arithmetic from the actual conditions
on the line and it is easy to wave the issues away by saying that the
component waves have no reality. They are just intermediate results
in some arithmetic.

This waving away is much harder to do for the pulse case because
the pulses can be individually observed as actual conditions on the
line.

So the challenge is not so starkly obvious as it is when the
power at the mid-point is always 0, but P(t) = V(t) * I(t) can
still be computed and it will not be sufficient to allow
the energy in the two pulses to cross the mid-point (unless
one likes superposing power, in which case it will be
numerologically correct).

No, it'll have to be done without superposing power. Simple calculations
clearly show where the power is and where the energy is going, without
the need to superpose power or assign power or energy to individual waves.

Yes. And I find it easy to obscure for the sinusoid case. But the
pulses
seem to make it easy to measure and not so easy to refrain from
assigning
energy and power to the pulses.

[snip]
But if one conceives waves as also including energy, then it
seems that the question 'where does the energy go' is valid
and the common explanations do not seem to hold up well.

I think you're partially right about that. Partially, because I think
there's an underlying assumption that the power in an individual wave
has to be conserved. If you do insist on assigning energy to individual
traveling waves, I think you have to be willing to deal with the fact
that the energy can be swapped and shared among different waves, and
stored and returned as well.

But then, what is the mechanism that swaps the power between the
pulses
and changes the direction of the energy flow?

Our common analytical techniques deal with E and H fields which we can
superpose. In a transmission line, these are closely associated with
voltages and currents. They add nicely to make a total with properties
we can measure and characterize, and the total can neatly be created as
the sum of individual traveling waves from turn on until steady state.
It all works very well. Two fields, voltages or currents can easily add
to zero simply by being oriented in opposite directions -- and they do,
all along a transmission line. But how are the energies they supposedly
contain going to add to zero? You'll have to construct a whole new model
if you're going to require conservation of energy of individual
traveling waves.

I agree. And it especially will fail if instead of dealing with
the sum of the reflected waves, we try to sum the power of each
reflection
individually.

And yet, the power and energy are so visible when looking at pulses.

I'm absolutely certain that after all the work of
developing a self-consistent model with all interactions quantitatively
and mathematically explained and accounted for, we'll find a testable
case where some measurable result will be different from the
conventional viewpoint. (Google "ultraviolet catastrophe".) That would
then establish the validity of the new model. But I'm just as certain
that no such mathematical model will ever be forthcoming.

The advantage to the non-interacting traveling wave model
is that it so neatly predicts transient phenomena such as TDR and run-up
to steady state. I spent a number of years designing TDR circuitry,
interfacing with customers, and on several occasions developing and
teaching classes on TDR techniques, without ever encountering any
phenomena requiring explanations beyond classical traveling wave theory..
So you can understand my reluctance to embrace it based on a problem
with energy transfer across a single infinitesimal point in an ideal line.

Yes, indeed. Though any (new) explanation would have to remain
consistent with the existing body of knowledge which works so well.

Either that, or be able to demonstrate where the existing knowledge
fails. I'm not holding my breath.

I do not expect that to happen. But how is the energy in the left
travelling
50 W pulse turned around at the middle to add to the 150 W that is let
through
to complete the 200 W right travelling pulse?

...Keith