Cecil,

It's a slow day, so I thought I might take some time to help you out of
your dilemma.

Q: Where are the missing joules?

A: They are associated with the large standing wave supported by the
mismatched terminations of your transmission line.

As I have pointed out previously, standing waves are not inert. The
shape of the wave does not travel down the line, but the fields are
changing, and the charges are moving. Within each loop of the standing
wave the stored energy simply oscillates between magnetic energy when
the current is high and electrostatic energy when the voltage is high.
Very basic stuff.

The problem in your analysis is the initial axiom that RF waves always
move. This is simply incorrect, and it leads to the dilemma you face.
Traveling waves are fine if you do the math correctly, but the physical
situation is in the form of a standing wave. The model results need to
agree or there is a math error.

And as many people have pointed out, always add the voltages and
currents first and only consider power at the very end of the analysis.

Since you are also an optics guru you might want to check into the
details of laser cavity operation or Fabry-Perot etalon operation. These
are highly mismatched systems with very strong standing wave components
along with a little bit of net traveling wave. Definitely related to the
problem you posed.

73,
Gene
W4SZ


Cecil Moore wrote:

[snip]

After steady-state has been reached, the XMTR has output 300 more
joules than the load has accepted. A smaller real-world experiment
will easily verify that it is a fact that all energy sourced that
has not reached the load must necessarily be confined to circulating
energy or losses in the transmission line.

Question: In the above example, where are those 300 joules of energy
located and what is happening to them?

We know that 300 joules is wave energy and RF waves always move
at the speed of light, i.e. they cannot stand still. So please
determine how much energy is moving and in which of only two
possible directions.