wrote:
Cecil Moore wrote:
Assuming a single source, single feedline, a passive load,
RMS voltage, and a real Z0, yes, average Prev can never be
greater than average Pfwd, i.e. the total Poynting vector
can never point away from the load. Such would be a violation
of the conservation of energy principle.

Yes indeed. But in the original example Z0 was complex. So once
again, with the clarification that the following question was
phrased in general terms and not constrained to lines where
Z0 is real...

I believe my statement holds true for any possible Z0. Here's the
logical proof. Replace the following:

source---Z01 lossy line---x--passive load
Pfwd1--
--Pref1

with an extra 1WL of lossless line that doesn't change anything.
The lossy line still sees the same impedance looking into point 'x'.

source---Z01 lossy line---x---1WL lossless Z02---+--passive load
Pfwd1-- Pfwd2--
--Pref1 --Pref2

Pfwd1 and Pref1 exist just to the left of point 'x'. We know that
(Pfwd1-Pref1) has to equal (Pfwd2-Pref2) which equals the power
delivered to the load. Everything to the right of point 'x' is easy
to analyze. We know that Pfwd2 Pref2 if there is any resistance
in the load. If resistance in the load is zero, Pfwd2 = Pref2. In
any possible case of a passive load, Pref2 cannot be greater than
Pfwd2. Therefore, just to the left of point 'x', Pref1 cannot be
greater than Pfwd1. Backtracking from the load, the lossy line really
doesn't enter into the discussion at all.

Note that Pfwd1 will not equal Pfwd2 and Pref1 will not equal Pref2
but the difference between forward power and reflected power must be
equal to the power delivered to the load in order to satisfy the
conservation of energy principle.
--
73, Cecil http://www.qsl.net/w5dxp



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