Cecil Moore wrote:

Jim Kelley wrote:

A column marked 'energy from source' is crucial to proving your point.


Jim, I was hoping you were capable of multiplying 100 joules/sec
by the number of seconds to get the total number of joules
delivered to the system over time by the source. My 1000 joules
after ten seconds is 100 joules/sec multiplied by ten seconds.
Is that math too difficult for you? :-)

:-) My contention is that it's too remedial. What you require is faith,
not math. Is the source supposed to be a virtual fire hydrant of
constant energy, or is it more like a real system? You seem to be
assuming a constant 100 Joules per second input, regardless of the fact
that the impedance the source sees is changing over the interval.
That's not particularly realistic, hence a need for the empirical. But
we could assume that the source is constant, and continue.

Maybe you need a simpler example. Here it is:

100w SGCL source----one second long feedline----load

The SGCL source is a signal generator equipped with a circulator
and circulator load. The circulator load dissipates all the
reflected power incident upon the signal generator. The signal
generator outputs a constant 100 watts.

The load is chosen such that the power reflection coefficient
is equal to 0.5, i.e. half the power incident upon the load
is reflected and half accepted by the load.

This configuration reaches steady-state in 2+ seconds. After 2+
seconds, the forward wave contains 100 joules and the reflected
wave contains 50 joules. 50 watts is being dissipated by the
load and 50 watts is being dissipated by the circulator load.
The source has output 150 joules of energy that has not been
dissipated by the load or the circulator load.

You have provided a lot of detail about where it all resides and in what
proportions, but you still haven't shown how much energy a source would
actually produce under such circumstances. Further, you're assuming
that energy would move forward in a transmission line at a rate higher
than the rate at which it is provided by the source. This is highly
speculative and suspect. What we know for sure is, once steady state is
achieved, energy is absorbed by the load(s) at the same rate at which it
is generated, all the energy from the source goes to the load(s). Given
that, there's very little impetus to believe that there need be any more
than one second's worth of energy held within a one second long
transmission line. It is therefore reasonable to contend that in the
first scenario, 100 Joules of energy is held within the transmission
line as it propagates toward the load. And in this latest scenario, 50
Joules is heading toward the load, and 50 is in the path to the
circulator for a total of 100 Joules stored within the one second long
transmission line.

The way to prove that there's any greater surplus of energy held within
the transmission line would be to make the energy vs. time measurements
at each end of such a transmission line. Absent that, it's purposeful
speculation.

73, AC6XG