Walter Maxwell wrote:
Cecil, please read me in the first paragraph. By Steve's own words he says the
re-reflected wave must equal the reflected wave.

No, he says that is a fallacy. He says the re-reflected wave equals the
reflected wave multiplied by the reflection coefficient. His example is:
reflected power = 33.33W, re-reflected power = 8.33W

re-reflected power = 33.33W(rho^2) = 33.33W(0.25) = 8.33W
Here's what Dr. Best said in his QEX article, Part 3: "When two forward-traveling
waves add, general superposition theory ... require(s) that the total forward
traveling voltage be the vector sum of the individual forward-traveling voltages
such that VFtotal = V1 + V2." He clearly implies that V2 is a forward-traveling
wave and it is. Numerically, it is equal to the voltage reflected from the load
multiplied by the reverse reflection coefficient. In S-parameter terms, V2 is
the s22(a2) term.

Concerning tau, I've seen it described in an HP App Note, which I didn't bring
to Michigan, but I've never used it. However, if the power transmission
coefficient is (1 - rho^2) the coefficient is 0.75 for rho = 0.5. Therefore, for
100 w forward only 75 w are delivered. This condition is shown valid
experimentally.

Yes, 100W(0.75) is perfectly consistent with 70.7V(1.5)^2/150 where Z0=150 ohms

Now let's use tau = 1 + rho as the voltage transmission coefficient. I interpret
this to mean tau x input voltage = forward voltage arriving at a mismatched
load.

No, no, no. Mistaken interpretation.

tau x input voltage = V1 (not the total forward voltage)

rho x reflected voltage = V2 (re-reflected)

V1 + V2 = forward voltage arriving at a mismatched load

V1 is proportional to the S-parameter term, s21(a1) where s21 is the forward-transmission
coefficient.

V2 is proportional to the S-parameter term, s22(a2) where s22 is the reverse-reflection
coefficient.

b2 is the total forward voltage arriving at a mismatched load.

VFtotal = V1 + V2 is virtually identical to b2 = s21(a1) + s22(a2)
--
73, Cecil http://www.qsl.net/w5dxp



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On Mon, 07 Jun 2004 09:56:04 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
Cecil, please read me in the first paragraph. By Steve's own words he says the
re-reflected wave must equal the reflected wave.

No, he says that is a fallacy. He says the re-reflected wave equals the
reflected wave multiplied by the reflection coefficient. His example is:
reflected power = 33.33W, re-reflected power = 8.33W

But when the system is matched the reflection coefficient is 1.0.

re-reflected power = 33.33W(rho^2) = 33.33W(0.25) = 8.33W
Here's what Dr. Best said in his QEX article, Part 3: "When two forward-traveling
waves add, general superposition theory ... require(s) that the total forward
traveling voltage be the vector sum of the individual forward-traveling voltages
such that VFtotal = V1 + V2." He clearly implies that V2 is a forward-traveling
wave and it is. Numerically, it is equal to the voltage reflected from the load
multiplied by the reverse reflection coefficient. In S-parameter terms, V2 is
the s22(a2) term.

Cecil, it is clear that you are not reading my posts!!!

You quoted Steve above, but I quoted the SAME quote earlier, explaining that he
is WRONG. Please reread my quote. General superposition theory does NOT require
that the forward voltage be the vector sum of the individual forward-traveling
voltages.

When are you going to understand that that superposition yields the standing
wave, NOT the forward wave? I've told you this over and over again, but you
apparently aren't listening.

Cecil, please go to Johnson as I pointed out earlier and become educated as to
where Steve screwed up.

Walt

Walter Maxwell wrote:

On Mon, 07 Jun 2004 09:56:04 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
Cecil, please read me in the first paragraph. By Steve's own words he says the
re-reflected wave must equal the reflected wave.

No, he says that is a fallacy. He says the re-reflected wave equals the
reflected wave multiplied by the reflection coefficient. His example is:
reflected power = 33.33W, re-reflected power = 8.33W

But when the system is matched the reflection coefficient is 1.0.

But if rho = 1.0, then tau = 2.0. Wasn't it 1.5 just a minute ago?

73, Jim AC6XG

Walter Maxwell wrote:
But when the system is matched the reflection coefficient is 1.0.

Not in an S-parameter analysis which is essentially what Dr. Best is doing.
He is dealing with the PHYSICAL reflection coefficient, (Z2-Z1)/Z2+Z1), not
the virtual reflection coefficient based on reflected power being zero. This
may be the source of the misunderstanding between you two. His reflection
coefficients, like the S-parameter reflection coefficients, don't change from
startup to steady-state. They remain constant even when no signal is present.

General superposition theory does NOT require
that the forward voltage be the vector sum of the individual forward-traveling
voltages.

Superposition of two individual forward-traveling voltages requires that the
sum be the vector sum as long as the interference energy requirements are met.

When are you going to understand that that superposition yields the standing
wave, NOT the forward wave? I've told you this over and over again, but you
apparently aren't listening.

I am listening, Walt, and still telling you that you are wrong about that
concept. Superposition of two waves traveling in opposite directions yields
the standing wave. Superposition of two coherent waves traveling in the same
direction yields DESTRUCTIVE/CONSTRUCTIVE INTERFERENCE, not standing waves.

Cecil, please go to Johnson as I pointed out earlier and become educated as to
where Steve screwed up.

I know where Steve screwed up, Walt, and he did screw up. But it wasn't in the
area of an S-parameter analysis in the forward direction. It was in the rearward
direction that he screwed up royally.

In the afore-mentioned example, the four powers associated with the four
superposition voltages are P1, P2, P3, and P4. P1=75W, P2=8.33W, P3=25W,
and P4=25W.

P1+P3 = 100W = generated power

P2+P4 = 33.33W = power reflected from the load

Dr. Best tell us that 75W+8.33W+2*SQRT(75*8.33)=133.33W and that is
mathematically true.

What Dr. Best doesn't tell us is that 2*SQRT(75*8.33) = P3+P4 and that
they are the interference component powers from classical optics theory.

You are grouping the powers together in this manner, (P1+P3)+(P2+P4)=133.33W
and that is perfectly true mathematically.

Both of you are doing essentially the same thing but neither one of you
realizes it. You guys are two inches apart and don't know it. It feels like
I am listening to two flatlanders argue about the third dimension.
--
73, Cecil http://www.qsl.net/w5dxp



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Jim Kelley wrote:

Walter Maxwell wrote:
But when the system is matched the reflection coefficient is 1.0.

But if rho = 1.0, then tau = 2.0. Wasn't it 1.5 just a minute ago?

Dr. Best is using physical reflection coefficients, aka an S-parameter
analysis, which are never 1.0 in a system with a mismatched load.
--
73, Cecil http://www.qsl.net/w5dxp



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On Mon, 07 Jun 2004 15:28:01 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
But when the system is matched the reflection coefficient is 1.0.

Not in an S-parameter analysis which is essentially what Dr. Best is doing.
He is dealing with the PHYSICAL reflection coefficient, (Z2-Z1)/Z2+Z1), not
the virtual reflection coefficient based on reflected power being zero. This
may be the source of the misunderstanding between you two. His reflection
coefficients, like the S-parameter reflection coefficients, don't change from
startup to steady-state. They remain constant even when no signal is present.

General superposition theory does NOT require
that the forward voltage be the vector sum of the individual forward-traveling
voltages.

Superposition of two individual forward-traveling voltages requires that the
sum be the vector sum as long as the interference energy requirements are met.

When are you going to understand that that superposition yields the standing
wave, NOT the forward wave? I've told you this over and over again, but you
apparently aren't listening.

I am listening, Walt, and still telling you that you are wrong about that
concept. Superposition of two waves traveling in opposite directions yields
the standing wave. Superposition of two coherent waves traveling in the same
direction yields DESTRUCTIVE/CONSTRUCTIVE INTERFERENCE, not standing waves.

Cecil, please go to Johnson as I pointed out earlier and become educated as to
where Steve screwed up.

I know where Steve screwed up, Walt, and he did screw up. But it wasn't in the
area of an S-parameter analysis in the forward direction. It was in the rearward
direction that he screwed up royally.

Cecil, you're not even close to knowing where Steve screwed up. And you won't
know until you follow my directions and go to Johnson and read what I said to
read. I can't understand why you refuse to go in that direction. Because you
refuse we're going around in circles. This has to stop.

What Johnson and I are trying to tell you is that the superposition of the
source voltage and the re-reflected voltages DO NOT establish the forward
voltage. Steve used Johnson's Eq for determining the standing wave voltage at
any point on the line incorrectly as the forward re-reflected voltage wave V2.
THIS IS WHERE HE SCREWED UP, CECIL., SCREWING UP THE ENTIRE ARTICLE !!

Walt

Walter Maxwell wrote:
What Johnson and I are trying to tell you is that the superposition of the
source voltage and the re-reflected voltages DO NOT establish the forward
voltage.

If Johnson really said that, he screwed up because he is in direct
contradiction to the S-parameter analysis described in Ramo, Whinnery,
and Van Duzer in _Fields_and_Waves_in_Communications_Electronics_, (c)
1965, page 603, Section 11.09 "Scattering and Transmission Coefficients".

You and Dr. Best obtain the same component powers. You just group them
differently. You guys are two inches away from agreeing.

Please provide the location of the Johnson quote details again. I sort
by date and cannot find your Johnson reference even when sorting by
threads.
--
73, Cecil http://www.qsl.net/w5dxp



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On Mon, 07 Jun 2004 16:52:15 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
What Johnson and I are trying to tell you is that the superposition of the
source voltage and the re-reflected voltages DO NOT establish the forward
voltage.

If Johnson really said that, he screwed up because he is in direct
contradiction to the S-parameter analysis described in Ramo, Whinnery,
and Van Duzer in _Fields_and_Waves_in_Communications_Electronics_, (c)
1965, page 603, Section 11.09 "Scattering and Transmission Coefficients".

No Cecil, Johnson didn't screw up. Incidentally, the equation in question is his
Eq. 4.23, derived on Pages 98 and 99, and displayed on Page 100. Steve screwed
up because, as I've been repeating, he misinterpreted the equation to determine
the forward wave instead of the standing wave.

From all of your statements so far, it appears you may have misunderstood what
the forward wave really is. Here's a clue. When a tuner is properly adjusted in
matching a 50-ohm line to a 150 + j0 resistance and the output voltage of the
source is 70.71 v. the forward voltage is 70.71 x 1.1547 = 81.65 v. Do you
recognize it or know where the 1.1547 came from ? Steve doesn't have a clue.

Walt

Cecil,

I am happy to see that we are in agreement on this long-standing argument.

I explained this to Walt in some private e-mails about 18 months ago,
and I wrote similar explanations in this group. I was vilified by both
Walt and you.

I will summarize once again.

Both the Walter Maxwell model and the Steve Best model for this
transmission line problem work correctly. They are internally self
consistent, and they give the same physical answers. They obey the
standard laws of physics and mathematics. However it is not possible to
mix-and-match the models, using equations and definitions from one model
in the other.

Walt continues to mis-read Steve Best's QEX articles. He needs to throw
away all of his pre-conceived definitions about the meaning of specific
Vx components and read exactly what Steve wrote.

73,
Gene
W4SZ

Cecil Moore wrote:


You and Dr. Best obtain the same component powers. You just group them
differently. You guys are two inches away from agreeing.

Walter Maxwell wrote:
No Cecil, Johnson didn't screw up. Incidentally, the equation in question is his
Eq. 4.23, derived on Pages 98 and 99, and displayed on Page 100. Steve screwed
up because, as I've been repeating, he misinterpreted the equation to determine
the forward wave instead of the standing wave.

On page 99, in between equations 4.22 and 4.23 is an equation presented by
Johnson that is close to Steve's equation to which you are objecting.

From all of your statements so far, it appears you may have misunderstood what
the forward wave really is. Here's a clue. When a tuner is properly adjusted in
matching a 50-ohm line to a 150 + j0 resistance and the output voltage of the
source is 70.71 v. the forward voltage is 70.71 x 1.1547 = 81.65 v. Do you
recognize it or know where the 1.1547 came from ? Steve doesn't have a clue.

The forward voltage wave equals s21(a1)+s22(a2) which is virtually the same
as V1+V2 because V1/[SQRT(Z0)] + V2/[SQRT(Z0)] = s21(a1) + s22(a2). It's the
old one-to-one correspondence rule.

As I said before, Walt, the 1WL section of 50 ohm line in Steve's example
is *completely irrelevant* to the discussion. Steve only included that line
so the forward/reflected power could be measured and the impedance reproduced.
As long as you allow that 1WL of 50 ohm line to enter into your thinking and
calculations, you will never understand what he was trying to say. Please remove
the 1WL of 50 ohm line and please re-think your position. All the conditions
discussed by Steve occur at the *MATCH POINT* which, I think you will agree,
is NOT on the 50 ohm line.
--
73, Cecil http://www.qsl.net/w5dxp



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