On Apr 9, 12:51*pm, Roger Sparks wrote:
On Wed, 9 Apr 2008 03:45:19 -0700 (PDT)

Keith Dysart wrote:
On Apr 7, 12:14*pm, Roger Sparks wrote:
On Sun, 6 Apr 2008 19:21:00 -0700 (PDT)

Keith Dysart wrote:
On Apr 5, 10:06*am, Roger Sparks wrote:
Pg(t) is the result of a standing wave, containing *power from Pf(x) and Pr(x+90). *

This is one way of thinking of it, but it is less misleading to
consider
that Pg(t) describes the actual energy flow, just as Vg(t) describes
the
actual voltage and Ig(t) describes the actual current. Using
superposition
Vf, If, Vr and Ir can be derived and from these Pf and Pr.

Your argument is correct to the extent that the power you describe is passing point Pg(t) at the instant (t). *It is the equivalent statement that an observer watching cars pass on the freeway would make, saying "one blue car moving left and one red car moving right, so two cars are passing". *Not wrong, just "how is the information useful"?

Pg(t) is the actual power at that point in the circuit. It can be
derived by simply multiplying the direct measurement of the actual
voltages and currents at that point in the circuit. One measures
the same voltages and currents regardless of whether it is a
transmission line to the right of point g, or the equivalent
lumped circuit element.

While Vf, Vr, etc. can be used to derive the same information and,
therefore is arguably just a different point of view, Vf and Vr,
If and Ir, etc., must always be used in pairs to arrive at the
actual circuit conditions. It is when one starts to look at them
separately, as if they individually represent some part of reality,
that confusion awaits.

Thus I strongly suggest that Vg, Ig, Pg, represent reality. The
others are a convenient alternative view for the purposes of
solving problems.

Typically we see Vg split into Vf and Vr, but why stop at two.
Why not 3, or 4? Analyzing a two wire telephone line will use
four or more, forward to the east, forward to the west, reflected
to east, reflected to the west, and sometimes many different
reflections. How do we choose how many? Depends on what is
convenient for solving the problem. The power of superposition.
But assigning too much reality to the individual contributors
can be misleading.

Good thoughts. *

By breaking Vg into Vf and Vr, we can explain

I am not sure that 'explain' is the correct word. It certainly
provides
a convenient technique for computing the voltate and current along the
line, but there are other ways to compute the result; differential
equations being one other way, though less convenient. But I am not
convinced that a convenient technique for solving the problem is
necessarily an 'explanation of why'.

why very long transmission lines, many wavelengths long, have repeating patterns of inductive and capacitive reactance as if they were lumped components. *If Vf and Vr work for long lines, they should work for short lines.

This is true. But when we descend to zero length lines, as some have
done, the rationale becomes quite a bit weaker.

So far as breaking Vg into many sequential/different Vf and Vr, we usually need to do that. *Cecil chose our simple example to prevent re-reflection (reflection of the reflection) but even then it is apparent that the voltage source will have a reactive component.

I still think of a voltage source as just being a voltage source, not
something
with resitance, reactance or impedance.

If we can't account for the power, it is because we are doing the accounting incorrectly.

And the error in the accounting may be the expectation that the
particular set of powers chosen should balance. Attempting to
account for Pr fails when Pr is the imputed power from a partial
voltage and current because such computations do not yield powers
which exist.

If we remove the transmission line from the circuit, we have an open circuit with no current. *Without current, there can be no power. How can power arrive at Rs if there is no power coming through the transmission line? *

There is power coming from the transmission line. Looking at Pg(t),
some of the time energy flows into the line, later in the cycle
it flows out. The energy transfer would be exactly the same if the
transmission line was replaced by a lumped circuit element. And
we don't need Pf and Pr for an inductor.

But this flow is quite different than the flow suggested by Pf and
Pr. These suggest a continuous flow in each direction. It is only
when they are summed that it becomes clear that flow is first in
one direction and then other.

I understand the delemma here. *It is like trying to both fill and empty the bottle at the same time. *We can't do that with physical objects and we like to think of energy as if it were a physical object. *So how can energy seemingly flow into a line at the same time it flows out?

Of course one way would be if Vf actually did reflect from Vr. *A reflection beginning at the point Vg, then propagating down the line as an artifact of the original wave. *So far as I have been able to figure, the result is the same as when we think of both Vf and Vr as actual waves, which are much easier to follow and calculate.

I agree that the final results are the same. The intermediate results
can
mislead in different ways.

Would it help to consider that before the "reflection from the short" arrives, power arrives via the transmission line path but the impedance is 100 ohms for our example, composed of Rs = 50 ohms and transmission line = 50 ohms? *After the "reflection from the short" arrives, the impedance drops to 70.7 ohms so the power to the circuit goes up (assuming a constant voltage source). *How can this happen if power is not carried via the "reflection from the short"?

It goes up because the impedance presented by the transmission
changes when the reflection returns. This change in impedance
alters the circuit conditions and the power in the various
elements change. Depending on the details of the circuit,
these powers may go up, or they may go down when the reflection
arrives.

Your comment almost makes the altered impedance sound like a resistance,

Impedance does have some similarity to resistance, but only for
single
frequency sinusoidal excitation, though I was not trying to say that.

probably not quite the picture you want to convey. *I think of power to Rs coming via two paths, one longer than the other. *In my mind, the changed impedance is the result of two power streams merging back together.

The impedance found when the reflection returns is dependent upon the line impedance, length of line, and conditons at the point of reflection. *The length of line is measured in terms of time and wave velocity. *While this is strong evidence supporting Vf and Vr,

The technique of breaking actual voltage into Vf and Vr certainly
works. But
I would not say this is evidence for the existance of Vf and Vr,
merely agreement
with superposition.

One of my text books drags the reader through the solution using
differential
equations, and then introduces Vf and Vr as a simpler way to solve the
problem.
The student is truly happy from learning that diffyQs will not be
required.

it does not rule out reflection between wave components.

I don't know how many people have seen an railroad engine starting a train from stop, when there is a small gap between each of the cars. *You can hear each of the cars bumping the adjacent car in a chain reaction going from engine to the end of the train. *Clearly, the reaction has a velocity of travel. *

Some what like hole flow in semiconductors. Electrons going forward
make the
holes flow backwards.

Our EM waves could do the same thing but we would never measure anything except the the resultant wave.

...Keith