My, it sure didn't take long to get the discussion diverted from the
voltages, currents, and powers in the analysis. I'm sorry to say I
expected that.

Cecil Moore wrote:
Roy Lewallen wrote:

Well, Cecil, you've redefined Pref and Pfwd.


Nope, I haven't, Roy. You have somehow arrived at the equations for
a four-port network while dealing with what appears to be a two-port
network. Inadvertently, you seem to have calculated |s11|^2, |s12|^2,
|s21|^2, and |s22|^2 for what appears to be a two-port network. Is a
two-port lossy line network with inductive load really a four-port
network in disguise? Does the delay in the inductor returning energy
to the system constitute an 'a2' term in the s-parameter analysis?


I'll leave the philosophical question to you of when a transmission line
is an n-port network and when it isn't, and which s parameter I
inadvertently calculated. Was I unclear about what I did calculate? What
part of it don't you understand?

Pref used to be solely a function of the forward voltage and current
waves, and Pref a function of the reverse voltage and current waves.
But now you've chosen to add an extra term to one or the other of
those, or both -- a term which contains components of both forward and
reverse waves.


Roy, that is built right into the s-paramater analysis. For instance,
for a Z0 (image) matched system:

Forward Power = |s11|^2 + |s12|^2 + |s21|^2 + |s22|^2

For a matched system, Forward Power contains four power terms.
In fact, Forward Power can contain from one to four terms depending
on system configuration.


I don't know, and don't really care, where you're trying to go with your
S parameter analysis. But when you're all done, please translate all
that wonderful stuff to voltages, currents, and powers, using a finite
length transmission line, and present your analysis.

Are you having difficulty understanding what I've done simply with
voltages, currents, and powers?

You might recall from the analysis that I originally had two cosine
terms, one arising from the product of forward voltage and reverse
current, and the other arising from the reverse voltage and forward
current. Which of these do you assign to the "forward power" and which
to "reverse power"?


You are talking about |s12|^2 and |s21|^2. The sign and phase of their
power flow vectors will indicate whether they are forward power or
reverse power.

When combined into a product of two sine functions as I did in the
analysis, do you assign this combined function to Pref or Pfwd?


If the sign is positive, it is flowing toward the load, i.e. it will
superpose with the forward wave. If the sign is negative, it is flowing
toward the source, i.e. it will superpose with the reverse wave. The
conservation of energy principle will not allow the power in the reverse
wave to exceed the power in the forward wave for passive loads, no matter
what the value of rho.

So now when you say Pref and Pfwd, what do you mean?


What I have always meant. Pfwd is the total of all the coherent forward
components. Pref is the total of all the coherent reverse components.

So, you mean that the term containing the product of two sine functions
is part of Pfwd when the angles are such that the sine functions return
a positive value, and part of Pref when they return a negative value?

If you were to stick with the definition you've always used in the
past, i.e., powers calculated from solely forward or reverse voltage
and current waves, the answer is yes. For evidence I offer my
derivations.


All you have derived is the s-parameter analysis which is known to include
four power parameters. It is known that s11 doesn't always equal rho for
a four-ternimal network. You seem to have proven that to be true for what
appears to be a two-port network.

No, I did not derive an s parameter analysis. I derived voltages,
currents, and powers. Interpretation of this in terms of s parameters is
strictly your own doing, and it provides wonderful opportunities to
obscure and misinterpret what's really happening. If you're unable to
understand voltages, currents, and powers and want to argue instead
about s parameters (which indeed do represent voltages and powers, but
not necessarily in a one-to-one correspondence to those in the circuit I
analyzed), how many ports the circuit has, and the meaning of the power
reflection coefficient, have at it. But I won't participate. I'll simply
wait until you're done with your philosophising, calculations,
translation back and forth, and post your analysis with V, I, and P as
the variables.

Roy Lewallen, W7EL

Clears up what confusion?

Nowhere in my analysis is s11, s12, or s22 mentioned. I don't consider
s12 or s22 to be anything at all, and don't make any claim whatsoevera
about what they are or aren't. Which step or steps of my analysis is/are
incorrect? And in terms of voltages, currents, and powers, why?

Roy Lewallen, W7EL

Cecil Moore wrote:
Roy Lewallen wrote:

Again, I welcome an alternate solution that accounts for all the
voltages, currents, and powers, including one that does it with rho 1.


It dawned on me, just now in the shower, what is happening here. When
you introduced the 'x' parameter, the distance from the load, you
introduced a 2-port network analysis, be it an s-, h-, y-, z-, or
whatever-parameter analysis. And of course there are four power
terms in a 2-port analysis. There a

1. The power reflected from the network input back toward the source.
|s11|^2

2. The power transmitted through the network port toward the load. |s21|^2

3. The power re-reflected from the network output back toward the load.
|s22|^2

4. The power transmitted through the network port toward the source.
|s12|^2

These are the four powers you calculated and you consider only |s12|^2 to
be forward power. That is an error. |s22|^2 is also forward power. These
two forward power flow vectors have to be added to obtain the total
forward Poynting vector. I do believe that clears up the confusion.

Roy Lewallen wrote:

My, it sure didn't take long to get the discussion diverted from the
voltages, currents, and powers in the analysis. I'm sorry to say I
expected that.

Please calm down, Roy. Disagreeing with you is not a diversion. You made
a simple error. When you introduced the 'x' term, the distance away from
the load, you introduced a 2-port analysis. It is a well known fact that
there are four power terms involved in a 2-port analysis as explained in
another posting.

Was I unclear about what I did calculate?

Yes, you were, but it was inadvertent.

I don't know, and don't really care, where you're trying to go with your
S parameter analysis. But when you're all done, please translate all
that wonderful stuff to voltages, currents, and powers, using a finite
length transmission line, and present your analysis.

I'm just showing you what small error you made when you assumed that only
one of the four power terms was the forward power. There are four power
terms. They divide up and add to obtain the forward power and reflected
power. You neglected to do that.

Are you having difficulty understanding what I've done simply with
voltages, currents, and powers?

Nope, I recognize the tiny error you made and am trying to explain it
to you. You didn't include all the forward voltages in your forward
voltage. There are four voltage terms, two forward and two reflected.
You left out half the terms and got the wrong forward or reflected
voltage or both. The mistake is in assuming that rho = s11. It doesn't
in this case.

So, you mean that the term containing the product of two sine functions
is part of Pfwd when the angles are such that the sine functions return
a positive value, and part of Pref when they return a negative value?

No, after further thought, I think you should NOT have combined those two
terms. Four terms is what exists in the analysis so just leave it at
four terms. All the terms with a plus sign combine and all the terms
with a minus sign combine. Please publish the four term power equation
before you used a trig identity to combine the terms. Two of those terms
are forward power and two of those terms are reflected power.

No, I did not derive an s parameter analysis. I derived voltages,
currents, and powers.

You obviously did a something-parameter analysis (maybe a z-parameter
analysis?). Whatever you did results in four power terms, not two plus
a third. When you introduced 'x' you introduced an analysis that produces
a reflected wave on each side of 'x' and a forward wave on each side of
'x'. That's four waves. You went too far when you combined two of those
waves into one especially since one is a forward wave and one is a
reflected wave.
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore wrote:
Roy Lewallen wrote:

I didn't, and don't, claim to have derived a "power reflection
coefficient". What I calculated was the ratio of reflected voltage to
forward voltage at the load, and called its magnitude rho. If there's
any step in the analysis that's unclear, I'll be happy to explain it
in more detail.


What you apparently calculated is s11 which is not always equal to rho.

I calculated the ratio of the reflected to forward voltage at the load,
and called its magnitude rho. If you have some other "rho" you want to
argue about, please call it something else.


What I have calculated is the ratio of reflected voltage to forward
voltage at the load, no more and no less.


No, you have calculated the ratio of one of the reflected voltages to
one of the forward voltages. I believe you have calculated the ratio
of s21*a1 to s12*a2 when you should be calculating the ratio of
(s11*a1+s12*a2) to (s21*a1+s22*a2). You simply omitted half the terms.


Please repeat my analysis, including the voltages or currents which were
omitted, and explain why they should be included. I used standard steady
state analysis, which infers one forward traveling voltage and current
wave, and one reverse traveling voltage and current wave. Although the
physical meaning of multiple traveling forward and reverse waves in
steady state gets a little hazy to me, I don't think there's anything in
principal that prevents you from assuming any number of forward and
reverse voltage an current waves you'd like, calculating reflection
coefficients for each pair, and adding them all up to get the total.
It'll be interesting to see how you choose to do it.

Of course, by choosing the pairs carefully, you can probably assure that
the magnitude of the reflection coefficient for any pair doesn't exceed
one. I'm not sure what that means or proves, but by all means have at it.

. . .

I'm sure that with enough s parameter and optics references, the facts
of the matter can be satisfactorily obscured.


It is you who is using an s-, h-, y-, z-, or other-parameter analysis
and are inadvertently obscuring the facts. You left out half the voltage
terms that should be included in the forward voltage and reflected
voltage. Add all the reflected voltages together. Add all the forward
voltages together. Divide the total reflected voltage by the total
forward voltage.

What the heck are you talking about? Just where in the analysis do you
see any s, h, y, or z parameter? I did calculate an impedance here and
there from voltages and currents -- is that some kind of a no-no in your
eyes?

Again, please show your analysis with the "missing" terms (that is,
voltages and currents) included.

Your view of how average powers add and travel do force that
restriction. I'm looking forward to your alternative analysis, which
shows the voltages, currents, and powers at both ends of the line
while simultaneously satisfying your notion of how average powers
interact.


I think all that is built into your analysis. When you include all the
necessary terms, I will be surprised if everything doesn't fall out
consistently.

Well, good. So show us.

Roy Lewallen, W7EL

So do it right and show us how it really should be done.

Roy Lewallen, W7EL

Cecil Moore wrote:

You obviously did a something-parameter analysis (maybe a z-parameter
analysis?). Whatever you did results in four power terms, not two plus
a third. When you introduced 'x' you introduced an analysis that produces
a reflected wave on each side of 'x' and a forward wave on each side of
'x'. That's four waves. You went too far when you combined two of those
waves into one especially since one is a forward wave and one is a
reflected wave.

Yuck.

That should, of course, be "principle", not "principal". Sorry, I really
do know better!

Roy Lewallen, W7EL

Roy Lewallen wrote:
. . .
steady state gets a little hazy to me, I don't think there's anything in
principal that prevents you from assuming any number of forward and
reverse voltage an current waves you'd like, . .

Dear Cec,

Your arithmetic is abominable. ;o) Dr Slick's
vanishing-act was a better tactic.

Your only avenue of escape is to prove the | rho |
meter gives incorrect meter readings.

That's likely to be difficult.

The meter is based on precisely the same simple
principle as your common-or-garden SWR+Fwd Power+Refl
Power meter. In fact, its scale, instead of | rho |,
can be simultaneousy calibrated in terms of SWR from 1
to infinity. And 1 million professional housewives
supported by trusted ARRL handbooks can't be wrong.

By the way, does that Texas vinyard you mentioned have
a website? ;o)

---
Yours, Reg, G4FGQ

Modify what I believe to be a correct analysis in order to satisfy your
view of reality? You must be kidding again -- sometimes it's hard to tell.

Somehow I expected that an alternative analysis or any specific
correction wouldn't be forthcoming. I'm glad you've got it all sorted
out in your own mind, Cecil.

I'll now bow out, unless a coherent alternative analysis, or specific
corrections to the one I posted, are presented.

Roy Lewallen, W7EL

Cecil Moore wrote:
Roy Lewallen wrote:

Clears up what confusion?

Nowhere in my analysis is s11, s12, or s22 mentioned. I don't consider
s12 or s22 to be anything at all, and don't make any claim whatsoevera
about what they are or aren't.


Those are the reflection and transmission coefficients that represent
the effect the forward waves have on the reflected waves and vice versa.
You said your analysis included that effect so you are performing an
s-parameter-like analysis whether you realize it or not.

Which step or steps of my analysis is/are incorrect? And in terms of
voltages, currents, and powers, why?


Please publish your four term power equation and I will show you exactly
what is wrong. Please don't say rP and fP in that equation but show
the voltage, current, and impedance terms that make up what you think is
rP and fP. Hint: rP is not the total reflected power that you think
it to be. Neither is fP.

Roy Lewallen wrote:
I calculated the ratio of the reflected to forward voltage at the load,
and called its magnitude rho.

No you didn't. The voltage that you think is the reflected voltage
is only one term of two. The voltage that you think is the forward
voltage is only one term of two.

Please repeat my analysis, including the voltages or currents which were
omitted, and explain why they should be included.

I have already done that, Roy. There are four waves. You must combine
the four waves to get the forward wave and the reflected wave. You
didn't do that. You declared one of the four waves to be the forward
wave and one to be the reflected wave and added the other two to get
a "third wave". That is an error.

What the heck are you talking about? Just where in the analysis do you
see any s, h, y, or z parameter? I did calculate an impedance here and
there from voltages and currents -- is that some kind of a no-no in your
eyes?

OK, let me do it in a way that you can understand. When you introduced
'x', you introduced a 2-port analysis whether you realize it or not.
In a 2-port analysis, there are four waves, two forward and two reflected.
The four power waves are proof that you are inadvertently using a 2-port
analysis. There are forward and reflected waves on the left side of 'x'
and there are forward and reflected waves on the right side of 'x'.
Let's look at only the voltages for now where rho is a reflection
coefficient and tau is a transmission coefficient.

V1 = Vfwd1*tau1 similar to s21*a1

V2 = Vref2*rho2 similar to s22*a2

V3 = Vfwd1*rho1 similar to s11*a1

V4 = Vref2*tau2 similar to s12*a2

You are saying that one of these voltages is the forward voltage.
That's just not true.

V1+V2 = forward voltage similar to b2=s21*a1+s22*a2

V3+V4 = reflected voltage similar to b1 = s11*a1+s12*a2

Again, please show your analysis with the "missing" terms (that is,
voltages and currents) included.

Please publish your raw four term power equation, omitting the rP
and fP terms which you are wrong about. If you have already published
that equation, please tell me the date so I can go look it up.
--
73, Cecil http://www.qsl.net/w5dxp



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Roy Lewallen wrote:
So do it right and show us how it really should be done.

Sorry, that diversion won't work. Correct your error first
and effort on my part will be avoided.
--
73, Cecil http://www.qsl.net/w5dxp



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