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.

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.

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.

...Keith