Roger Sparks wrote:
The overriding issue is to account for all the power, which we are having a hard time doing. The current is flowing the wrong way for the source voltage at Ps(91) so
the source is absorbing power. That negates the idea that the source
has an impedance of zero when we also assign the source a voltage.

Consider that what you are seeing is the flip side of the
interference at the source resistor. When a local source is
present, it can certainly absorb destructive interference
energy and supply constructive interference energy. The
following example has identical steady-state conditions
but brings Pfor1 and Pref1 into play for the instantaneous
values. I suspect that Pref1 is being completely ignored
in the present analysis.

Vs(t)---1WL 50 ohm---Rs---1WL 50 ohm---+j50
Pfor1-- Pfor2--
--Pref1 --Pref2

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

Try the above example and maybe it will become clear.

Pref1 = Pfor1(rho1^2) + Pref2(1-rho2^2) + interference1

Pfor2 = Pfor1(1-rho1^2) + Pref2(rho2^2) + interference2

The source power doesn't appear directly in the equations
and need not be considered at all.

Pfor1 + Pref2 + P.Rs = Pfor2 + Pref1 (all average)

I suspect the above equation will account for all the
energy components even at the instantaneous level such
that:

Pfor1(t) + Pref2(t) + P.Rs(t) = Pfor2(t) + Pref1(t)

Please note that all of these power components exist
when the two transmission lines are removed so this
analysis is probably the key to understanding what
is wrong with the earlier analysis.
--
73, Cecil http://www.w5dxp.com