Comments interspersed. . .

Keith Dysart wrote:
Thanks for offering the two capacitor/one capacitor view of the middle
of the line. It took a bit of time to decide whether the commingling
of the charge in the single capacitor at the middle of the line would
solve my dilemma.

So I considered this one capacitor in the exact center of a perfect
transmission line. It is the perfect capacitor, absolutely
symmetrical. So as the exactly equal currents flow into it on
the exactly symmetrical leads, the charge is perfectly balanced
so that the charge coming from each side exactly occupies its
side of the conductor. As the two flows of charge flow over
the perfectly symmetrical plates, they meet in the exact
center, and flow no more. I conclude that a surface can
be found exactly in the center of this capacitor across
which no charge flows. Thus (un)happily returning me exactly
to where I was before; there is a line across which no
charge, and hence no energy, flows.

I'm ok with that. To me, it's the same as splitting the capacitor into
two separate ones, each with its own charge from one direction.

More comments below.

On Jan 2, 7:38 pm, Roy Lewallen wrote:
I'm top posting this so readers won't have to scroll down to see it, but
so I can include the original posting completely as a reference.

Keith, you've presented a very good and well thought out argument. But
I'm not willing to embrace it without a lot of further critical thought.
Some of the things I find disturbing a

1. There are no mathematics to quantitatively describe the phenomenon.
2. I don't understand the mechanism which causes waves to bounce.

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.

3. No test has been proposed which gives measurable results that will
be different if this phenomenon exists than if it doesn't. (I
acknowledge your proposed test but don't believe it fits in this category.)
4. I'm skeptical that this mechanism wouldn't cause visible
distortion when dissimilar waves collide. But without any describing
mathematics or physical basis for the phenomenon, there's no way to
predict what should or shouldn't occur.
5. Although the argument about no energy crossing the zero-current
node is compelling, I don't feel that an adequate argument has been
given to justify the wave "bouncing" theory over all other possible
explanations.

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?

One other one which I have seen and am not confortable with is the
explanation that energy in the waves pass through the point in
each direction and sum to zero. But this is indistinguishable from
superposing power which most agree is inappropriate. As well, this
explanation means that P(t) is not equal to V(t) times I(t),
something that I am quite reluctant to agree with.

I won't go there either.

The other explanation seen is that the voltage waves or the
current waves travel down the line superpose, yielding a total
voltage and current function at each point on the line which
can be used to compute the power.

This is done and graphically shown with the TLVis1 program demo. The
energy at each point is also calculated and shown.

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

So...

I can give up on pulses (or waves) moving energy. I am not
happy doing that.

I'm afraid you might have to.

I can give up on P(t) = V(t) * I(t). I am not happy doing
that either.

Fortunately, that's not necessary.

So the (poorly developped) "charge bouncing" explanation
seems like a way out, but I certainly would appreciate
other explanations for consideration.

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

None of these make an argument with your logical development, although I
think I might be able to do that too. But I'm very reluctant to accept a
view of wave interaction that's apparently contrary to established and
completely successful theory and one, if true, might have profound
effects on our understanding of how things work. So frankly I'm looking
hard for a flaw in your argument. And I may have found one.

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?

. . .


It would be instructive to see what happens as, for example, the load
resistance is increased toward infinity or decreased toward zero
arbitrarily closely, but not at the point at which it's actually there.
If the "bouncing" phenomenon is necessary only to explain the limiting
case of infinite SWR on a perfect line but no others, then an argument
can be made that it's not necessary at all. I suspect this is the case.

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.

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.

I agree with your argument about two sources energized in turn, and have
used that argument a number of times myself to refute the notion of
superposing powers. Once two voltage or current waves occupy the same
space, the only reality is the sum. We're free to split them up into
traveling waves or any other combination we might dream up, with the
sole requirement being that the sum of all our creations equals the
correct total. (And the behavior of waves you're describing seemingly go
beyond this.)

I sometimes think that this may actually be a debate about the
conceptual view of waves. If waves consist only of voltage and
current, then all is well, superposition works, the correct
answers are achieved. And if the power is computed after the
voltages and currents are arrived at, all is well.

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.

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'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.

Roy Lewallen, W7EL