While working on an energy-based presentation of W7EL's
data from the following web page, I came across an
instance where my energy analysis differed from W7EL's
results under the "Food for Thought: Forward and Reverse
Power" section. Assuming Roy was correct, I attempted to
find my error and failed to do so.

http://eznec.com/misc/Food_for_thought.pdf

**********begin quote**********

Zl fPa rPa Pa(tx) Pa(src) Pa(R0) Pa(Rl) frac R0 frac Rl
0 + j0 100 100 0 0 0 0 - -
infinite 100 100 0 0 0 0 - -

Not only that, but notice the last two cases. Here, the reverse power is
a full 100 watts. The source match is 1:1. Yet *none* of this reverse
power is dissipated in the source resistance. In fact, no power at all
is dissipated in the source resistance.

ANY MODEL PRESENTED TO ACCOUNT FOR WHAT HAPPENS TO "FORWARD" AND
"REVERSE" POWER AT TRANSMISSION LINE ENDS HAD BETTER GIVE RESULTS THAT
AGREE WITH THE ABOVE TABLE.

**********end quote**********

Unfortunately, my results do not agree.

In the line where ZL is zero, i.e. a short-circuit, the
dissipation in the source resistance is 400 watts, i.e.
all of the forward power and reflected power is dissipated
in the source resistor plus an additional 200 watts associated
with constructive interference. All 400 watts must be supplied
by the source so Pa(src) must also be 400 watts. It should read:

Zl fPa rPa Pa(tx) Pa(src) Pa(R0) Pa(Rl) frac R0 frac Rl
0 + j0 100 100 0 400 400 0 1.0 -
infinite 100 100 0 0 0 0 - -

For the ZL=0 case:
Pa(R0) = fPa + rPa + 2*SQRT(fPa*rPa) = 400 watts
This is *total constructive interference* as defined by
Hecht in "Optics".

For the ZL=infinite case:
Pa(R0) = fPa + rPa - 2*SQRT(fPa*rPa) = 0 watts
This is *total destructive interference* as defined by
Hecht in "Optics".

Since Roy doesn't read my postings or emails, could someone
please pass this information on to him.
--
73, Cecil http://www.w5dxp.com