"Roy Lewallen" wrote in message
...
Z0 = 68 - j39 ohms.
Zl = 10 + j50 ohms.

Zl is certainly physically possible. I believe Z0 is also.


According to A/C/F the angle of Zo is constrained to +/- 45 degrees.

Cecil Moore wrote:
Using deductive reasoning, since the real part of the voltage
reflection coefficient cannot be greater than 1.0, ...

So much for my deductive reasoning - A kind soul has furnished proof
by email that the real part of the voltage reflection can be greater
than 1.0.

Z_0 = 50 - 25j (which is well within the - 45 to 45 degree angle bounds)
Z_L = 50 + 250j (chosen to make the arithmetic easy; there are lots more)

Then Z_L - Z_0 = 275j and Z_L + Z_0 = 100 + 225j so that
gamma = 11j/(4 + 9j) = 11j(4 - 9j)/(16 + 81) = (99 + 44j)/97.
--
73, Cecil http://www.qsl.net/w5dxp



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Well, Cecil, I think we're zeroing in on the flaw in your perception of
how the powers add. I hope you won't just keep saying it's impossible,
and will instead sharpen your pencil to show, as I have, the forward,
reverse, and total voltages, currents, and powers at both ends of the
line. And how everything can work together consistently to fit into your
view of power addition and subtraction.

A number of people have been trying for a long time to convince you
there's a flaw in your logic, but so far you haven't been able to see
it. Hopefully, in the process of deriving the values for this circuit,
you'll see where your logic has gone astray. Or, perhaps, you'll come up
with a completely consistent set of voltages, currents, and powers that
do fit within your view. And we'll all learn from it as we see where the
difference arises between your analysis and mine. Until you come up with
your analysis, though, I won't pay much attention to your complaints
that it's wrong unless you're able to show where in the analysis the
error lies.

I've posted the derivation of the total power formula on this thread. In
going through it, I found an error in the formula posted with my
numerical example. I've posted a correction for that on the same thread
as the example. In the correction posting, I also show how the formula
produces the same result as I got by directly calculating the total
power from the load voltage and current.

A closing quotation, from Johnson's _Transmission Lines and Networks_:

"[For a low loss line] P = |E+|^2 / Z0 - |E-|^2 / Z0. We can regard the
first term in this expression as the power associated with the
forward-traveling wave, and the second term as the reflected power. This
simple separation of power into two components, each associated with one
of the traveling waves, can be done only when the characteristic
impedance is a pure resistance. Otherwise, the interaction of the two
waves gives rise to a third component of power. Thus, the concept
applies to low-loss lines and to distortionless lines, but not to lossy
lines in general."

Something for you to think about. Or maybe you subscribe to Reg's view
that these texts are written by marketeers and salesmen. After all, as
Chairman of Princeton's EE department, I suppose Johnson's job was
primarily PR.

I'm quite sure that if you look carefully at any text where the author
subtracts "reverse power" from "forward power" to get total power, that
somewhere prior to that the assumption is made that loss is zero and/or
the line's characteristic impedance is purely real.

Roy Lewallen, W7EL

Cecil Moore wrote:
Roy Lewallen wrote:

No, the average Poynting vector points toward the load.


That automatically says Pz- is not larger than Pz+. There are only
two component Poynting vectors, 'Pz+' forward and 'Pz-' reflected.

If so, surely you came up with the same result, including the third
power term. If you haven't done the derivation, or if you'd like to
compare your derivation of total average power with mine, I'll be glad
to post it.


Assuming coherent waves, all wave components flowing toward the load
superpose into the forward wave and all wave components flowing away
from the load superpose into the reflected wave. Since there are only
two directions, there cannot exist a third wave. If your average Poynting
vector points toward the load, Pz- cannot possibly be larger than Pz+.
But feel free to post the derivation.

I believe that, and the value I used is within that range.

Roy Lewallen, W7EL

Tarmo Tammaru wrote:
"Roy Lewallen" wrote in message
...

Z0 = 68 - j39 ohms.
Zl = 10 + j50 ohms.

Zl is certainly physically possible. I believe Z0 is also.



According to A/C/F the angle of Zo is constrained to +/- 45 degrees.

Roy Lewallen wrote:

Well, Cecil, I think we're zeroing in on the flaw in your perception of
how the powers add.

I don't see how this thread is relevant to the treatment of powers in
lossless lines. Perhaps you have misunderstood what I said.

A number of people have been trying for a long time to convince you
there's a flaw in your logic, but so far you haven't been able to see
it.

If there's a flaw for lossless lines with purely resistive characteristic
impedances, please present it. So far, nobody has. Here's what I said in
my magazine article on my web page"

"For the purpose of an energy analysis involving *LOSSLESS* transmission
lines, we do not need to know anything about the source or the load or
the length of the transmission lines."

I'm quite sure that if you look carefully at any text where the author
subtracts "reverse power" from "forward power" to get total power, that
somewhere prior to that the assumption is made that loss is zero and/or
the line's characteristic impedance is purely real.

Of course, that's why my previous assertions have been only about lossless
lines. Do you happen to have a lossless example that proves my concepts
about lossless lines are wrong? I have no concepts about lossy lines
except that they obey the conservation of energy principle.
--
73, Cecil http://www.qsl.net/w5dxp



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Roy Lewallen wrote:
P1 = fP - rP + (|fE1|^2 / |Z0|) * rho * exp(-2 * ax) * 2 *
sin(delta) * sin(2 * bx - 2 * psi).

Seems to me, all the terms with a '+' sign would be forward power, by
definition, and all the terms with a '-' sign would be reflected power,
by definition. I don't see any violation of the conservation of energy
principle. The power equation balances.
--
73, Cecil http://www.qsl.net/w5dxp



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I apologize. I thought your view of power waves was alleged to hold true
even with loss. If it's restricted to lossless lines (which have purely
real Z0), then the total average power does equal "forward power" minus
"reverse power".

So please don't bother yourself with trying to explain the component of
power that's neither the "forward power" nor "reverse power".

Roy Lewallen, W7EL

Cecil Moore wrote:
Roy Lewallen wrote:

Well, Cecil, I think we're zeroing in on the flaw in your perception
of how the powers add.


I don't see how this thread is relevant to the treatment of powers in
lossless lines. Perhaps you have misunderstood what I said.

A number of people have been trying for a long time to convince you
there's a flaw in your logic, but so far you haven't been able to see it.


If there's a flaw for lossless lines with purely resistive characteristic
impedances, please present it. So far, nobody has. Here's what I said in
my magazine article on my web page"

"For the purpose of an energy analysis involving *LOSSLESS* transmission
lines, we do not need to know anything about the source or the load or
the length of the transmission lines."

I'm quite sure that if you look carefully at any text where the author
subtracts "reverse power" from "forward power" to get total power,
that somewhere prior to that the assumption is made that loss is zero
and/or the line's characteristic impedance is purely real.


Of course, that's why my previous assertions have been only about lossless
lines. Do you happen to have a lossless example that proves my concepts
about lossless lines are wrong? I have no concepts about lossy lines
except that they obey the conservation of energy principle.

Roy:

[snip]
There are a lot of opportunities for typos in a derivation like this,
especially when restricted to plain ASCII characters. I'd appreciate
very much if anyone finding an error, either in concept, fact,
assumption, or just typo, to call it to my attention so it can be
corrected.

Roy Lewallen, W7EL
[snip]

Wow! You said it Roy.

BTW... thanks for all of your nice work.

But for my taste it's far too detailed and seems filled with gratuitously
long
symbols for ASCII text consumers.

My eyes glazed over and I nearly fell asleep and had to stop following after
a couple of screens of what seemed to turn into gibberish before my eyes.

Not your fault mind you, it's mine.

On the other hand, ASCII NewsGroup postings are hardly the media for
sharing such detailed algebraic/numeric developments!

I just don't get the point of all of your wonderful efforts!

Thoughts, comments,

--
Peter

"Peter O. Brackett" wrote:
On another whole level it simply DOES NOT MATER which defiinition
of the reflection coefficient one uses to make design calculations though,
as long as the definition is used consistently throughout any calculations.

One can convert any results based on the non-conjugate version of rho to
results based on the conjugate version of rho and vice versa.

In other words, neither version is "RIGHT" or "WRONG" as long
as the results from using that particular definition are interperted
correctly in terms of the original definition.

While true, this is not what is occuring in the 'revised rho' debate.

Their claim is simply that 'classical rho' has been mis-calculated all
these years and we should start using the 'proper' calculation. There
is no acknowledgement that 'revised rho' will have different properties
than 'classical rho' and that, therefore, they are introdcing a new
entity.

Their claim of incorrectness derives from the fact that 'classical rho'
can have a magnitude greater than 1 and a belief that this means
reflected power is greater than incident. This belief is inconsistent
with generally accepted knowledge, so rather than modifying the belief,
the derivation of 'classical rho' is rejected.

Their second difficulty derives from not being able to separate
the behaviour at a particular interface from the system behaviour.
They do not recognize that a reflection at a particular interface
(which would reduce energy transfer at that interface), can
improve overall system energy transfer by improving the energy
transfer at another interface. This being what a transmission line
transformer does, for example.

Once they overcome these two hurdles, they will have no problems
with the classical definition of rho.

So... who gives a damm about the defintion of rho as long as you are
consistent in it's use. It simply doesn't matter! [Unless you choose
M to be singular. ;-) ]

There is no problem if this is what the 'revised rho' crowd really is
attempting to do, but they should clearly state this and have the
courtesy to pick a new name (despite Humpty-Dumpty's assertions) to
facilitate clear communication.

Really though, you are thinking several levels above them when you
hypothesize the existence of other, self-consistent, definitions of
rho.

They are still at the 'classical rho computation is just plain wrong'
level.

....Keith

Roy Lewallen wrote:
Well, shucks, that makes it easy.

Just being logical. There are only two directions in a transmission
line, forward and reverse. If all the waves are coherent, all forward
waves superpose to one wave and all reverse waves superpose to one
other wave. Your net forward power is greater than your net reflected
power by the net amount of power accepted by the load. This happens
locally at the load no matter what is happening elsewhere in the
transmission line.

Cecil Moore wrote:
Seems to me, all the terms with a '+' sign would be forward power, by
definition, and all the terms with a '-' sign would be reflected power,
by definition. I don't see any violation of the conservation of energy
principle. The power equation balances.
--
73, Cecil http://www.qsl.net/w5dxp
"One thing I have learned in a long life: that all our science, measured against
reality, is primitive and childlike ..." Albert Einstein



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