Cecil Moore wrote:

wrote:
Just to make sure I understand correctly, are you saying that
Vrev^2/Z0 can never be greater than Vfwd^2/Z0
(these being the common definitions of Prev and Pfwd) or did
you have another set of defintions in mind for Prev and Pfwd
when you state that Prev can never be greater than Pfwd?

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...

Just to make sure I understand correctly, are you saying that
Vrev^2/Z0 can NEVER be greater than Vfwd^2/Z0
(these being the common definitions of Prev and Pfwd) or did
you have another set of defintions in mind for Prev and Pfwd
when you state that Prev can NEVER be greater than Pfwd?

....Keith

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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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

wrote in message ...
Vrev^2/Z0 can NEVER be greater than Vfwd^2/Z0
(these being the common definitions of Prev and Pfwd) or did
you have another set of defintions in mind for Prev and Pfwd

this is another of the basic misconceptions that is being applied over and
over on there. note from my big message about powers a couple days ago that
from phasor notation there are really only two types of power that can be
discussed:

average power:
Pav= .5 |I|^2 Re[Z] = .5 |V|^2 Re[Y]

and complex power.
P=.5 V I*

now, note that given Pav you can NOT recover enough information about V to
know its proper phase and magnitude in order to be able to compare it with
anything properly. Complex power on the other had requires the conjugate of
the current, which when expanded gives an equation like:
P=.5 |V| |I| cos(/_V-/_I) + j.5 |V| |I| sin(/_V-/_I)

where again, it is not possible to back up from the power to the full phasor
description of the voltage to be able to use it in calculations or
comparisons.

now, you CAN do this if you restrict Z0 to be purely real, you can NOT do it
if you use a complex Z0 because you can't extract the imaginary term back
out of a power calculation that has specifically removed it.

so all these places where you guys start doing sqrt(Pref/Pfwd)=Vfwd/Vref or
Vrev^2/Z0/Vfwd^2/Z0 are worthless in the general case.