Roy Lewallen wrote:
I'm trying to stay out of this, but can't avoid mentioning that although
Cecil insists on only one Pref and one Pfwd, he has different criteria
for voltage waves, and requires multiple Vfwd and Vref. So there are
four directions for voltage, but only two for power?

There are four voltage components flowing in two directions. Add up the
two voltages flowing in the forward direction and you have total forward
voltage. Add up the two voltages flowing in the reverse direction and
you have total reverse voltage. From the total forward voltage, you can
calculate the total forward power. From the total reverse voltage, you
can calculate the total reverse power. There are no magic third terms
after superposition.

Vfwd2 = Vfwd1(tau1) + Vref2(rho2)

Vref1 = Vfwd1(rho1) + Vref2(tau2)

Four voltage components, two total voltages, two directions.
--
73, Cecil http://www.qsl.net/w5dxp



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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.

The fact that the Poynting vector still points toward the
load in Roy's example means that reverse power cannot be
greater than forward power.
--
73, Cecil http://www.qsl.net/w5dxp



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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

Cecil Moore wrote:

wrote:
But without some equations defining Pfwd and Prev, the concept is
not particularly useful since there are no predictions which you
can make from it.

The equations are to be found in Dr. Best's Nov/Dec 2001 QEX article,
"Wave Mechanics of Transmission Lines: Part 3" and in _Optics_, by
Hecht. When the characteristic impedances are real:

Do recall that this discussion started with a line whose characteristic
was complex not real, so all that follows here is moot.

V1 = Vfwd1(tau1) V2 = Vref2(rho2) V3 = Vfwd1(rho1) V4 = Vref2(tau2)

Vfwd2 = V1 + V2 Vref1 = V3 + V4

P1 = Pfwd1(1-|rho|^2) P2 = Pref2(|rho|^2) forward components

P3 = Pfwd1(|rho|^2) P4 = Pref2(1-|rho|^2) reverse components

Pfwd2 = P1 + P2 + 2*Sqrt(P1*P2)cos(delta-1)

Pref1 = P3 + P4 + 2*Sqrt(P3*P4)cos(delta-2)

where (delta-1) is the angle between V1 and V2, (delta-2) is the angle
between V3 and V4, and that last term is called the interference term.

In _Optics_, average power is called irradiance (I) and the equation is:

I1 + I2 + 2*Sqrt(I1*I2)cos(delta)

For further information, check out my Part 1 energy analysis article
on my web page. Part 2 will appear shortly.

But, going back to the original question, is Pfwd and Prev on a line
with complex Z0?

....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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wrote:
But, going back to the original question, is Pfwd and Prev on a line
with complex Z0?

See my logical proof in another posting.
--
73, Cecil http://www.qsl.net/w5dxp



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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.

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

On 6 Sep 2003 22:19:39 -0700, (Dr. Slick) wrote:

wrote in message ...

But, going back to the original question, wbat is Pfwd and Prev on a
line with complex Z0?

...Keith

I'd like to know the answer to this question too!

Hi Fellows,

Such intense interest and no comments to SV7DMC for his work to this
matter?

73's
Richard Clark, KB7QHC

wrote:
So we have the following requirements
Pload = Pfwd - Prev
Prho = Prev/Pfwd

There is still a very large selection of pairs which will satisfy
these constraints.

Nope, there are not. Assuming Pload is known and Prho is known, you
have two equations and two unknowns which can be solved for with
unique solutions. For instance, in my previous example:

Pload = 100 watts, Prho = 0.25. Prho can be calculated.

Prev = Pfwd*Prho and substituting, we have: 100W = Pfwd - 0.25*Pfwd
100W = 0.75*Pfwd, therefore Pfwd = 133.33W, a unique solution.

Incidentally, if you want a reference for losses in low-loss lines,
_Fields_and_Waves_... by Ramo, Whinnery, and Van Duzer has a section
1.22 on page 41 titled, "Physical Approximations for Low-Loss Lines".
They assume an average loss per unit length. I won't even try to
reproduce the equations in ASCII.
--
73, Cecil http://www.qsl.net/w5dxp



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