On Apr 19, 12:02 am, Cecil Moore wrote:
Keith Dysart wrote:
I have stated that there is no re-reflection of the reflected wave at
the
source. Since the source is matched to the line, the reflection
coefficient is 0 and the wave just .... Well it must go into the
source
since tau is one. But at least it is not reflected when rho is zero.

But you are missing the point. You say the source is matched
to the line but the source is obviously re-reflecting 100% of the
reflected energy.

But the same can be said for experiment A, can't it? Measured
conditions on the line are identical.

Your special magic source is doing exactly
the opposite of what you claim it is doing. The calculated
physical reflection coefficient may be 0 but the virtual
reflection coefficient, SQRT(Pref/Pfor), is 1.0.

Please apply this calculation to Experiment A and check
your result. No difference. Oooopppps.

This is
the point I have been making ever since you started posting.

As you observe for Experiment B, the current is zero so as you
say "The source is not only not sourcing any forward power, it is
also not sinking any reflected power."

Of course the current is also zero at the same point for
Experiment A, so there as well, the source is not only not sourcing
any forward power, it is also not sinking any reflected power.

That's again where you are wrong. In Experiment A, the circulator
load resistor is sinking 100W, i.e. 100% of the reflected power.
A bit of modulation will show that the power being sunk by the
circulator load resistor has made a round trip to the end of
the transmission line short and back.

And if you did the same test with Experiment B you would get the
same result.

A bit more analysis for Experiment A yields some more questions.
Terminate the line with a 50 Ohm resistor. The source is now
providing power to the line, there is no reflection on the line and
the circulator dissipates nothing.
Remove the resistor. The reflection returns. The circulator once
again dissipates 100 W. But as you said, in this condition,
"The source is not only not sourcing any forward power, it is also
not sinking any reflected power." So where did that 100 W being
dissipated in the circulator come from?

In Experiment A, the source is sourcing 100 watts and the
circulator load resistor is sinking 100 watts after the
round trip delay to the end of the line and back. If the
source signal is modulated, the delay between the source
signal and the dissipated signal is obvious and can be
measured.

No different for B.

I suggest a further extension to both Experiment A and
Experiment B. Replace the 1/4 WL stub with a 1 and 1/4 WL
stub. Now, at each 1/4 WL along the line coming back from
the load, no energy is flowing because either the current is
0 or the voltage is 0. So this absence of energy flow happens
not just at the source but repeatedly along the line. This
makes it difficult to accomodate the thought that the
forward or reflected travelling waves are transporting energy
along the line (at least at the quarter wave points).

The "absence of energy flow" is an illusion. There is 100
joules/sec in the forward wave and 100 joules/sec in the
reflected wave. Since the waves are flowing in opposite
directions, you can argue that there is no *net* energy
flow, but the component wave energy flow is alive and well.

Well this is the point you lock up on and it is one of the root
causes of all subsequent errors. I suspect your refusal to
accept the common knowledge that the output impedance
of the generator can be well known, that this controls the
amount of reflection at the generator and that superposition
works is the realization that this will conflict with "energy in
the waves". I encountered the same dilemma when first
dealing with these questions, but came to the answer that
works.

Now back to the quibble. You said: "The source sources 100 watts
and the circulator resistor dissipates 100 watts which is all of the
reflected power."

Yes, in Experiment A but obviously not in Experiment B.
Your source has failed to perform the way you said it would.
As I said in the beginning, there will be re-reflections from
your source. In this case, there is 100% re-reflection.
Real world conditions are not as simple-minded as you say.

But, of course, your proof of re-reflections was your apriori
knowledge of the interior of the generator. I present you with
two 50 Ohm generators; one constructed with a circulator and
one constructed with a 50 Ohm resistor. How do you tell which
is which? The line conditions will be the same, so you can't.
Do you really want a theory of reflections that is dependent on
knowing the internals of the generator?

It would be more precise to say "The source sources 100 watts
and the circulator resistor dissipates 100 watts which is numerically
equal to the reflected power." I contend that it is this "numerical
equality" that has led many astray into believing that the
circulator is dissipating the "reflected power".

No, modulation on the reflected wave proves that it has made
a round trip to the end of the line and back. There is no
getting around that fact. There is also no getting around
the fact that the energy content of the stub is identical
in both experiments. The number of joules in the stub, in
both cases, is exactly the magnitude needed to support the
100W forward wave and the 100W reflected wave. The energy
in the stub in Experiment A is obviously real. The energy
in the stub in Experiment B is identical to Experiment A.

Yes indeed. All line conditions are exactly the same. The same
energy is stored. The output impedance is the same. Modulation
has exactly the same effects. The reflected modulated signal is not
re-reflected at the source for either case. They are
indistinguishable unless you dissassemble the generator.

But as we have seen,
no energy crosses the 0 current node into the generator so the
"reflected power" can not make it to the circulator (or the source
resistance, if the generator happens to have one).

Your "no energy crosses the 0 current node" is just an ignorant
illusion.

You can not possible be arguing that P is not equal to V times I,
can you?

And are you disputing that if V or I is at all times 0, there must be
no energy flowing.
If so, back to grade 11 science please.

The forward current and reflected current are alive
and well and simply superpose to a net current of zero at that
point. We are discussing EM wave energy and a boundary condition
for EM waves to exist is that they must travel at c(VF). If they
don't, they are no longer EM waves.

At a current node, forward current equals 1.414 amps at 0 deg.
Reflected current equals 1.414 amps at 180 deg. Of course, the
*net* current is zero but there is no physical impedance discontinuity
to cause any change in the forward and reflected waves at that
point.

Well it is pretty clear to me that if the net current is always 0,
then
no current is ever flowing and the power must be zero.

It seems to be a bit of a common fallacy to assign meaning to the
intermediate currents computed for the superposition solution to
a problem. Connect two equivalent batteries in parallel. The only
sensible answer is that no current is flowing since the voltages
are the same. (In another post you seem to accept this), though
if you use superposition to solve the problem, you get a very large
current flowing in one direction and an equally large current flowing
in the other. Only the resultant current is in any sense real. Same
for those waves on a transmission line. Just superposition. Just a
convenience to help reach the final solution. Don't over extend
and assign them meaning (or energy). In the end it will cause
deep conceptual difficulties.

....Keith