On Dec 30 2007, 6:18 pm, Roy Lewallen wrote:
Keith Dysart wrote:

I predict that the pulse arriving at the left end will
have the same voltage, current and energy profile as
the pulse launched at the right end and the pulse
arriving at the right end will be similar to the
one launched at the left.

They will appear exactly AS IF they had passed
through each other.

The difficulty with saying THE pulses passed
through each other arises with the energy. The
energy profile of the pulse arriving at the left
will look exactly like that of the one launched
from the right so it will seem that the energy
travelled all the way down the line for delivery
at the far end. And yet, from the experiment above,
when the pulses arriving from each end have the
same shape, no energy crosses the middle of the
line.

So it would seem that the energy that actually
crosses the middle during the collision is
exacly the amount of energy that is needed to
reconstruct the pulses on each side after the
collision.

If all the energy that is launched at one end
does not travel to the other end, then I am
not comfortable saying that THE pulse travelled
from one end to the other.

But I have no problem saying that the system
behaves AS IF the pulses travelled from one
end to the other.

You said that:

What will happen? Recall one of the basics about
charge: like charge repel. So it is no surprise
that these two pulses of charge bounce off each
and head back from where they came.

Yet it sounds like you are saying that despite this charge repulsion and
bouncing of waves off each other, each wave appears to be completely
unaltered by the other? It seems to me that surely we would detect some
trace of this profound effect.

. . .

Is there any test you can conceive of which would produce different
measurable results if the pulses were repelling and bouncing off each
other or just passing by without noticing the other?

There are equations describing system behavior on the assumption of no
wave interaction, and these equations accurately predict all measurable
aspects of line behavior without exception. Have you developed equations
based on this charge interaction which predict line behavior with
equal accuracy and universal applicability?

No equations. I expect that such equations would be more complex
than those describing the behaviour using superposition. Since
the existing equations and techniques for analysis are tractable
and produce accurate results, I am not motivated to develop an
alternate set with lower utility.

And yet the "no interaction" model, while accurately predicting
the behaviour has some weaknesses with explaining what is
happening. It is, I suggest, these weaknesses that help lead
some so far astray.

To illustrate some of these weaknesses, consider an example
where a step function from a Z0 matched generator is applied
to a transmission line open at the far end. Charge begins to
flow into the line. The ratio of the current to voltage on
the line is defined by the distributed inductance and
capacitance. The inductance is resisting the change in current
which causes a voltage to charge the capacitance. A voltage
step (call this V for later use) propagates down the line
at the speed of light. In front of this step, the voltage,
current and charge in the line is zero. After the step, the
capacitance is charged to the voltage and charge is flowing
in the inductance.

The step function eventually reaches the open end where
the current can no longer flow. The inductance insists
that the current continue until the capacitance at the
end of the line is charged to the voltage which will stop
the flow. This voltage is double the voltage of the step
function applied to the line (i.e 2*V). Once the
infinitesimal capacitance at the end of the line is
charged, the current now has to stop just a bit earlier
and this charges the inifinitesimal capacitance a bit
further from the end. So a step in the voltage propagates
back along the line towards the source. In front of this
step, current is still flowing. Behind the step, the
current is zero and voltage is 2*V. The charge that
is continuing to flow from the source is being used
to charge the distributed capacitance of the line.

The voltage that is propagating backwards along the
line has the value 2*V, but this can also be viewed as
a step of voltage V added to the already present voltage
V. The latter view is the one that aligns with the "no
interaction" model; the total voltage on the line is
the sum of the forward voltage V and the reverse
voltage V or 2*V.

In this model, the step function has propagated to the
end, been reflected and is now propagating backwards.
Implicit in this description is that the step continues
to flow to the end of the line and be reflected as
the leading edge travels back to the source.

And this is the major weakness in the model. It claims
the step function is still flowing in the portion of
the line that has a voltage of 2*V and *zero* current.

Now without a doubt, when the voltages and currents
of the forward and reverse step function are summed,
the resulting totals are correct. But it seems to
me that this is just applying the techniques of
superposition. And when we do superposition on a
basic circuit, we get the correct totals for the
voltages and currents of the elements but we do
not assign any particular meaning to the partial
results.

A trivial example is connecting to 10 volt batteries
in parallel through a .001 ohm resistor. The partial
results show 10000 amps flowing in each direction
in the resistor with a total of 0. But I do not
think that anyone assigns significance to the 10000
amp intermediate result. Everyone does agree that
the actual current in the resistor is zero.

The "no interaction" model, while just being
superposition, seems to lend itself to having
great significance applied to the intermediate
results.

Partially this may be due to poor definitions. If the
wave is defined as just being a voltage wave, then
all is well.

But, for example, when looking at a solitary pulse,
it is easy (and accurate) to view the wave as having
more than just voltage. One can compute the charge,
the current, the power, and the energy. But when
two waves are simultaneously present, it is only
legal to superpose the voltage and the current.
But it is obvious that a solitary wave has voltage,
current, power, etc. But when two waves are present
it is not legal to.... etc., etc.
The "no interaction" model does not seem to resolve
this conflict well, and some are lead astray.

And it was this conflict that lead me to look for
other ways of thinking about the system.

Earlier you asked for an experiment. How about this
one....

Take two step function generators, one at each end
of a transmission line. Start a step from each end
at the same time. When the steps collide in the
middle, the steps can be viewed as passing each
other without interaction, or reversing and
propagating back to their respective sources. We
can measure the current at the middle of the line
and observe that it is always 0. Therefore the
charge that is filling the capacitance and causing
the voltage step which is propagating back towards
each generator must be coming from the generator
to which the step is propagatig because no charge
is crossing the middle of the line.

Do you like it?

....Keith