On Jun 6, 10:13*pm, lu6etj wrote:
On 6 jun, 18:00, Keith Dysart wrote:
On Jun 6, 9:45*am, Cecil Moore wrote:
On Jun 5, 6:28*pm, Keith Dysart wrote:
There are indeed negative values. These occur when the energy is
flowing in the other direction, ...

Let's take a close look at the illusion that you are seeing and not
comprehending. Observe a snapshot of the instantaneous power envelope
of a traveling wave. It is a sinusoidal envelope with peak
instantaneous power levels and zero instantaneous power levels. When
it is traveling in the forward direction we consider that to be
positive power. When it is traveling in the reverse direction, we
consider that to be negative power. It is only a directional
*convention* not proof that negative power exists. The only waves that
can exist as waves on a transmission line are traveling waves.

Ahhh. I see part of your problem. You are thinking envelopes.

You need to change your point of view to be a particular point on the
line.
At this point, there is a function that describes the voltage: V(t).
It
may or may not be a sinusoid. There is a function for the current:
I(t).
And from these can trivialy be derived a function for power:
P(t)=V(t)I(t).

When I clip my instantaneous voltmeter across a line and measure 0 for
all time, I can confidently say that no energy is flowing, for there
is
not. I am curious as to what you would answer?

In "Optics", Hecht says instantaneous power is "of limited utility."
You seem to have discovered that limit, stepped over it, and stepped
in it. :-)

Well, Hecht may have his limitations when dealing with Optics, but
there
is no reason to expect these same limitations to apply to circuit
analysis.

...Keith

Hi folks, good night (from here).

I do not disagree with anything you have written, but I do think it
is much too early to introduce Poynting vectors and lossy conductors
to the discussion.

Hello Keith, Yes, I understand your comment, I introduced Poynting
vector only because both, energy and power, are scalars and we can not
talk about scalars having direction without get in conceptual
troubles; flux of power instead, have direction because surface vector
presence in its definition gives directive characteristics to power
crossing an imaginary surface.
Slanted flux of electromagnetic power (Poynting) due resistive
conductor simply seems to me a good example of a power flux in a TL
not totally coincident with axial direction to provide a little more
supporting to "directive" notion of Power Flux.
However IMHO power flux do not seems to me more complicated than
power, work, voltage, potential, energy, E and H fields, etc. All of
them -I believe- are not very simple stuff :(, but they are very
funny and interesting, indeed...!! :D. What do you think?

My interests lie in understanding the behaviour of transmission lines
to a level necessary to predict their basic behaviour. I did not find
that I needed power flux to achieve this so I have not explored it. I
suspect that you are right and it is an interesting topic.

.....
Please would you mind tell me why "sine wave" it is not a correct use
of "wave" word. The only dictionary I have = "Oxford *advanced
english dictionary of current english defines wave as: "move to and
fro, up and down", I believe also in english there are word qualifiers
(sine, traveling, standing, etc) who specify the precise meaning of
them in diverse contexts. Am I wrong about this?.

Sine wave. Square wave. Triangle wave. Sawtooth wave. Waveform.
Waveshape. 'Wave' seems to fit well with many words. I do not see a
problem.

....
Sorry by my insistence about convenience of discuss about "models".
Please let me bring a citation:
"At times, two quite differents models may serve equally well, but
eventually one is usually found to prevail, not because it is right,
but because it is both more convenient and more logically constructed.
After all, models are constructed for convenience in thinking and
recording, not as photographic images of nature"
(From "Electromagnetic Engineering", Ronold W.P. King (PhD), page 94.
McGraw Hill.1946).

It seems to me that all is well as long as the model is used properly
in the contexts in which it yields answers which are adequately
accurate.

....
I studied "Principle of Conjugates Impedance Matching" in my early
student days and the "mirror reflection" explained by Walter Maxwell
in his article agree with my undestanding about "where the reflected
waves go" because to balance magnitudes it is necessary that they
found a full mismatch on its way (path?) to generator. My own limited
analisis led me to the same notion even without conjugate match if I
calculate Incident and reflected voltages values in a half wave TL (as
my early thread example),
As I said, reading Cecil's web page quarter wave line examples led me
to considerate another possible representations of the problem, in
addition Owen's own ideas about it also made me consider the issue
from another point of view.

When I was trying to understand the behaviour of reflections in
transmission lines, I found it extremely valuable to consider
waveforms
other than sinusoids. Step functions into open, shorted and properly
terminated lines were quite enlightening. The arithmetic is much
easier to perform than for sine waves and some of the results rather
surprising.

For example, apply a step function from a matched generator to an
open transmission line. After the step makes one round trip, there
will be a constant voltage everywhere on the line and the current
will be zero everywhere. The wave reflection will show that there
is a constant forward wave which is summed with a constant reflected
wave to produce the constant voltage on the line. This is a strong
example of why there is not necessarily power in the forward and
reflected wave.

Other interesting thought experiments are pulses and pulse trains.
Arrange the timing so that a forward pulse collides with a reflected
in the middle of the line. What are the voltages and currents that
would be observed? Try alternating positive and negative pulses.

And lastly, inject signals simultaneously from both ends of a
transmission line. What is the result?

When doing these, I would compute the power provided by the source
and dissipated in the source resistor (I tend towards ideal
Thevenin generators to simplify the analysis, though it is
worth occasionaly doing the same with Norton), the energy stored
in the line and the energy being dissipated in the load resistor,
if there is one. Dealing with all of this in the time domain can
help make the energy flows clear.

These simple thought experiments definitely helped my understanding.
Some of the assertions that have been made can be shown to be false
when tested with these waveforms and analysis.

....Keith