Re: Standing-Wave Current vs Traveling-Wave Current

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.

More comments below.

On Jan 2, 7:38 pm, Roy Lewallen <w...@xxxxxxxxx> 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 are:

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"?

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.

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.

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. 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.

So...

I can give up on pulses (or waves) moving energy. I am not
happy doing that.
I can give up on P(t) = V(t) * I(t). I am not happy doing
that either.

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

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.

A large part of the argument seems to revolve around a single point in a
perfect transmission line, where the current is exactly zero. This is an
infinitesimal point on a perfect line, so some anomalous things might be
expected to happen there.

Let's consider a transmission line as a huge number of series inductors
and shunt capacitors, each an ideal lumped device. In the ideal case, of
course, there would be an infinite number of each, and each would have
an infinitesimal value. However, the LC product and ratio must remain
correct even in the limiting case. Each L and C is an ideal device, so
the current into one terminal of an inductor has to equal the current
out of the other. A consequence of this is that either we have a whole
inductor with zero current, or the zero current point occurs between
inductors, at a node to which a capacitor is connected. I think we'll
get the same result using either scenario, but let's consider the second.

If we analyze this situation carefully, we'll find that the inductor on
each side of the zero-current point does have a finite current, equal in
amplitude and flowing in opposite directions. So for half of the cycle,
both are putting positive charge in the capacitor, and for the other
half of the cycle, both are removing charge. The capacitor voltage goes
up and down as a result, as we can also see by looking at the voltage at
this zero-current point. So current from both sides is contributing to
the capacitor charge, and turning off either one would change the line
conditions. Any change in the current from the inductor on one side
would change the capacitor voltage, and hence the current on the other
side. So there is an interchange of information from one side to the
other. Each inductor is conveying energy to the capacitor, which is
storing and returning it.

Ok, so let's break the capacitor into two, each being half the original
value, and constrain each inductor to deliver charge only to "its"
capacitor. The wire between the capacitors carries no current because
the capacitors always have equal voltages, and can be cut with no effect.

When there was one capacitor, it shared energy from both sides. When we
broke it into two, there was no mixing of energy from either side. Why
might one be a better description of reality than the other? It looks to
me like the argument devolves into speculation about how small the
"point" is at which the current drops to zero.

It is very, very small.

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.

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).

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.

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.

....Keith

Roy Lewallen, W7ELKeith Dysart wrote:
On Dec 30 2007, 6:18 pm, Roy Lewallen <w...@xxxxxxxxx> wrote:
Keith Dysart wrote:
[snip]
.

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