On Mar 11, 11:07*pm, Cecil Moore wrote:
Keith Dysart wrote:
To be convincing, the various functions of time need to
align appropriately.

And one can tell that they indeed do "align appropriately"
just by looking at the graphs of the two voltages. We know
that the average power in the reflected wave is dissipated
in the source resistor.

Actually, we have shown that that is not the case. If the
instantaneous power is not dissipated in the source resistor,
then neither is the average of the instantaneous power. And
we have shown that the instantaneous power is not dissipated
in the source resistor.

You might like to visit
http://keith.dysart.googlepages.com/radio6
for a graph that shows the actual power dissipated in the
source resistor along with the power in the reflected
wave. It can be visually seen that the power dissipated in
the source resistor has no relationship to the sum of the
reflected power and the power that would be dissipated in
the source resistor if there was no reflection.

All that is left to understand is
how long the destructive interference energy is stored in
the transmission line before being dissipated in the source
resistor as constructive interference.

Graphing in ASCII is pretty difficult. Let's see if we
can do it with words. Take a piece of transparent film
and draw the forward voltage to scale. Take another piece
of transparent film and draw the reflected voltage to
scale. Now we have graphs of two voltages that can be
varied by phase. In ASCII, the best I can do is:

* * * *------ * * * * * * * * * * * * * * * *----
* * */ * * * *\ * * * * * * * * * * * * * */
* */ * * * * * *\ * *forward voltage * * /
/________________\____________________/_________
* * * * * * * * * * \ * * * * * * * */
* * * * * * * * * * * \ * * * * * */
* * * * * * * * * * * * \ * * * */
* * * * * * * * * * * * * ------

* * * * * * * *----------
* * * * * * */ * * * * * *\ * reflected voltage
__________/________________\_____________________
* * * * */ * * * * * * * * * *\ * * * * * * * */
* * * */ * * * * * * * * * * * *\ * * * * * */
----- * * * * * * * * * * * * * *----------

For the first 90 degrees of the above graph, the forward voltage
is positive and the reflected voltage is negative. That is
destructive interference so there's an excess of energy that
is stored in the transmission line. For the second 90 degrees,
the forward voltage is positive and the reflected voltage is
positive. That is constructive interference so the excess energy
from the first 90 degrees is sucked back out of the transmission
line and dissipated in the source resistor.

You have shown that for some of the time energy is delivered to
the line and sometimes it returns energy. This is
Pg(t) = 32 + 68cos(2wt)
which has nothing to do with reflected wave energy dissipated in
the source resistor.

Pg(t) is equal, however, to Pf.g(t) + Pr.g(t).

Given that the average
reflected energy is dissipated in the source resistor and assuming
we honor the conservation of energy principle, nothing else is
possible.

But the premise in the above sentence (average reflected energy is
dissipated in the source resistor) is wrong, so the conclusion
(nothing else is possible) is as well.

...Keith