Cecil Moore wrote:
Tom Donaly wrote:

Cecil's ability to add powers together, which he did in
this instance, isn't anything unique, and doesn't
really teach anything about the general case.


I'm glad you agree, Tom. Other experts on this newsgroup
will argue with you as they have with me for four years
ever since Dr. Best posted his infamous Z0-match equation:

Ptot = 75w + 8.33w = 133.33w

to which I objected back then, only to have most of
the rest of the posters agree with Dr. Best. I was
dumbfounded to see so many otherwise knowledgable
engineers agree to a violation of the principle of
conservation of energy. I was told not to worry about
conservation of energy - that it takes care of itself.

In fact, for a quarter wave transformer, you can
do the following trick: compute the value of the
power as it just comes through the impedance discontinuity
for the first time and call it Pa. Call Rho^2 at the
load P. Then the power delivered to the load will be
Pa( 1 + P + P^2 + P^3 + P^4 ....) which looks the
same as if the power reflection coefficient looking
back toward the generator was 1 and the power at the
load was the result of the addition of an infinite
number of reflections. Such an interpretation, though,
can be shown to be absolutely wrong. Can anyone see why?


Destructive interference between the external reflection
at the match point and the internal reflection from the
load supplies additional constructive interference
energy to the forward wave in the quarter wave transformer.
You didn't include that constructive interference energy
above. Hint: That virtual power reflection coefficient looking
rearward into the match point doesn't reach 1 until steady-
state is reached (wrong premise above). The virtual power
reflection coefficient looking forward into the match point
also doesn't reach 0 until steady-state is reached. Those
two virtual power reflection coefficients actually start out
the same value and proceed in opposite directions during
the transient buildup to steady-state.

Hi Cecil,
you come up with the right answer, but is your
interpretation correct? Can you do the same thing in a
general sense? If there is no Z0 match between the two
transmission lines, does your method still work? The
little conundrum I posed is an example of a procedure
that will actually give the right answer, but the
interpretation I gave of how it works is wrong. Can you
be sure your method doesn't have the same flaw?
73,
Tom Donaly, KA6RUH
(P.S. The method of using V and I and the junction of
the two xmission lines to find the forward and reverse
powers on a transmission line doesn't prove the powers exist.
It works just as easily with a pair of resistors and is
more an algebraic stunt that works than anything else. It
does agree with you, however.)