Cecil Moore wrote:
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.
While Pnet = Pfwd - Prev using the classic definitions
Pfwd = Vi^2/R0 and Prev = Vr^2/R0
works for lossless line, we do not yet have an equivalent set of
definitions for Pfwd and Prev on a lossy line.
When we do find appropriate definitions for Prev and Pfwd on a
lossy line such that Pnet = Pfwd - Prev, then
Prev/Pfwd
will not be greater than one and it definitely will not be equal
to rho^2 (which can be greater than one).
So we are still looking for appropriate definitions of Pfwd and
Prev on a lossy line.
Or we could just throw this whole power analysis thing away and
stick with voltage analysis which works just fine and lets us
compute everything of interest.
....Keith