On Sat, 05 Jun 2004 10:14:09 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
But Cecil, take another look at Fig 6 on page 23-5 to note that those two waves
arrive 180 out of phase at point A, which means only that the E and H fields
cancel in the rearward direction only, resulting in a Zo match to the source.

Yes, and that is exactly my point. EXACTLY the same thing happens to the E-fields
and H-fields. That means exactly the same thing that happens to the rearward-
traveling voltages also happens to the rearward-traveling currents. Two equal-
magnitude/opposite-phase voltages cancel. Two equal-magnitude/opposite-phase
currents cancel. That doesn't happen at either an open or a short. If one
looks at just the voltages, it looks like a short. If one looks at just the
currents, it looks like an open.

Snip

J. C. Slater says that's what happens in the above quote. Voltages 1/2WL apart
in time cancel to zero. Currents 1/2WL apart in time cancel to zero.

Yep, but only in the rearward direction.

The rearward direction is what we are talking about. The point is that EXACTLY
the same thing happens to the two rearward-traveling current waves as happens
to the two rearward-traveling voltage waves. A short-circuit doesn't affect
voltages and currents in the same way. An open-circuit doesn't affect
voltages and currents in the same way. A match point affects the rearward-
traveling voltages and rearward-traveling currents in EXACTLY the same way.
The re-reflection at a match point is a conservation of energy reflection where
the rearward destructive interference energy supplies energy to constructive
interference in the opposite direction. For light, the equation a

Destructive Interference Irradiance = I1 + I2 - 2{SQRT[(I1)(I2)]} (9.16)

Constructive Interference Irradiance = I1 + I2 + 2{SQRT[(I1)(I2)]} (9.15)

_Optics_, by Hecht, fourth edition, page 388

Note the similarities to equations 13 and 15 in Dr. Best's QEX article,
Part 3.

PFtotal = P1 + P2 - 2{SQRT[(P1)(P2)]} (Eq 15)

PFtotal = P1 + P2 + 2{SQRT[(P1)(P2)]} (Eq 13)

Too bad he didn't label them as Hecht did, as "total destructive interference"
and "total constructive interference" equations.

Sorry, Cecil, in spite of their similarity with Hecht's, these equations are
totally invalid. Steve derived them from his Eq 9, which is also totally invalid
for use with reflected power. This equation is correct and valid when there are
two separate and individual sources. But here there is only one source, the
transceiver. When connecting two batteries in series Eq 9 works, because there
is enough energy there to support the additional current demanded with the
increased voltage. But not when the transceiver is the sole source of power.

With the transmission line system Steve's voltage V2 comes from the same source
as V1. The problem is that when the total forward power resulting from the
addition of reflected power and source power the total forward power is never
absorbed in the load, the power resulting from the reflection is subtracted from
the total power. This limitation does not occur when there are two separate
sources to maintain the increased current.

Because Steve used Eq 9 in an invalid way to derive Eqs 10 through 15, all of
these derived equations are also invalid. Try Eq 13 for example. It says 75 w
plus 8.33 w = 133.33 w, as you well know. This is absurd!

In addition, because the powers don't add up correctly using V1 and V2 at zero
phase relationship, he concocted the ruse that they must add vectorially, and he
goes through several values of phase relationships to show what the forward
power would be with the various phases. This is poppycock, because the phase
relationship between the source (V1) and re-reflected voltage (V2) is ALWAYS
ZERO on lossless lines.

His initial problem is that he misinterpreted Eq 6 in Part 1 to yield the
forward voltage Vfwd, where it actually yields the voltage E of the standing
wave at any point on the line, where the point on the line is determined by the
'L' term in the exponents on the right-hand side of the equation. In other
words, the summation of terms on the right-hand side of his Eq 6 does not equal
forward voltage Vfwd, as it indicates incorrectly, but instead equals the
voltage of the standing wave.

In addition to other errors, the entire right-hand column of page 46 is invalid.

Walt

On Sat, 05 Jun 2004 15:23:37 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
Yes, Cecil, I understand. However I don't particularly like the notion of saying
both fields go to zero, or both fields go to zero in the rearward direction.

But Walt, that's exactly what happens when total destructive interference
occurs as explained by J. C. Slater in _Microwave_Transmission_.

I believe voltage 180 out defines a short--period.

That same belief is what got Dr. Best into trouble. He never considered
what happens to the reflected current waves. In a sense, your and his
disagreements are because you both made the same conceptual mistake and
arrived at different conclusions because of that common mistake. If you
and he had not made that shared mistake, you both would have arrived at
the same conclusions.

Cecil, how do you figure I made a mistake in this issue? I have always
considered voltage 180 out as a short. And my writings show voltage at 180 as a
short, as stated on page 23-9. I agree that the opposite phases of both voltage
and current in that discussion resulted in the cancelation of reflected power
traveling in the 225-ohm section of line. And during the last day or two I
leaned toward thinking the out of phase current implied an open circuit. But you
can see from my words above that voltage rules--when the voltages are 180 out of
phase it defines a short circuit. My zip cord example is evidence to that.
Consequently, I don't agree that Steve and I made the same mistake. My writings
delivered the correct mathematical answers--Steve's does not. The mistake I made
on page 23-9 is in overlooking that it is the effective open circuit condition
seen looking in the rearward direction by the reflected waves at point A is what
gave both the voltage and current waves the reversal and phase change to zero
relative to the source waves.

Another scenario with the same initial conditions and results: Take two
identical generators delivering the same level of harmonically related output
voltages. Connect their terminals in phase.Voltages in phase--currents in phase.
Result? No current flow. Why? Zero voltage differential. Open circuit to
voltage--open circuit to current.

Now reconnect their terminals in the opposite manner. Voltages 180 out--currents
180 out. Do we have current flow? You bet--dead short! Because current results
from voltage, if voltages are 180 out of phase we have a short to both voltage
and curent. No open circuit to current.

This is the problem with trying to use circuit analysis to replace network analysis.
Put the two sources at the two ends of a transmission line and please reconsider
the outcome. Equip the two sources with circulators and dummy loads so the outcome
cannot be in doubt.

Cecil, I don't believe the outcome is in doubt.

Walt

Walter Maxwell wrote:
Sorry, Cecil, in spite of their similarity with Hecht's, these equations are
totally invalid.

Before we go any farther, Walt, please reference a copy of _Optics_,
by Hecht. Dr. Best's equations are valid. He just didn't understand what
he was dealing with and presented them improperly. Hecht presents them
properly. Dr. Best's equations are the classical physics equations for
the destructive interference and constructive interference.

With the transmission line system Steve's voltage V2 comes from the same source
as V1.

Yes, V1 comes from the generator and V2 comes from reflections from the
load which come originally from the generator. Dr. Best didn't understand
the S-parameter analysis and presented his material in an invalid way. But
even though he didn't understand what he was saying, his equations are
valid. He was completely off base in his explanations. It was like
Einstein coming up with E = MC^2 and then completely blowing the
explanation.

In an S-parameter analysis, b2 = s21(a1) + s22(a2)

In Dr. Best's analysis, VFtotal = V1 + V2 whe
V1 = V1F*(transmission coefficient) + V2R*(reflection coefficient)

V1F is the voltage incident upon the impedance discontinuity from the left. (port1)
V2R is the voltage incident upon the impedance discontinuity from the right. (port2)

There's a one-to-one correspondence above. If the S-parameter analysis is
valid, then Dr. Best's equations are valid. He just didn't present them
in a valid manner.

Because Steve used Eq 9 in an invalid way to derive Eqs 10 through 15, all of
these derived equations are also invalid. Try Eq 13 for example. It says 75 w
plus 8.33 w = 133.33 w, as you well know. This is absurd!

His equations are valid. His knowledge is what was invalid. It is true that

75w + 8.33W + 2*SQRT(75W*8.33W) = 133.33W

P1 + P2 + interference power = PFtotal

I presented this to Dr. Best 9 months before his Part 3 was
published. He simply didn't pay any attention.

From a voltage standpoint where ci means constructive interference:

V1^2/Z02 + V2^2/Z02 + Vci^2/Z02 = VFtotal^2/Z02

For a Z02 equal to 150 ohms (if I remember correctly)

106.07v^2 + 35.35v^2 + 86.6v^2 = 141.42v^2 So

V1^2 + V2^2 + Vci^2 = VFtotal^2

This is exactly what you have been saying all along, something that Dr.
Best simply didn't understand. He completely ignored the interference
term without which the voltage equation cannot balance.

2*SQRT(75W*8.33W) is the constructive interference term supplied by the
destructive interference event on the other side of the match point which
Dr. Best completely ignored in his article.

In addition, because the powers don't add up correctly using V1 and V2 at zero
phase relationship, he concocted the ruse that they must add vectorially, and he
goes through several values of phase relationships to show what the forward
power would be with the various phases. This is poppycock, because the phase
relationship between the source (V1) and re-reflected voltage (V2) is ALWAYS
ZERO on lossless lines.

Only if the system is perfectly matched. If the system is not matched, V1 and
V2 can have any phase relationship. Dr. Best's equations are valid but he just
didn't comprehend their meaning. When I called him on it, he seemed never to have
heard of destructive/constructive interference. That's what set me to researching
EM waves in the arena of optics.

I looked at the situation assuming that you two guys are both knowledgeable and
intelligent and I arrived at the conclusion that the two of you are only two inches
apart. But (IMO) neither one of you is willing to move that one inch to bridge the
gap. (I have said this before in private email to Walt.)
--
73, Cecil http://www.qsl.net/w5dxp



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Walter Maxwell wrote:
But you
can see from my words above that voltage rules--when the voltages are 180 out of
phase it defines a short circuit.

This is exactly the same mistake that Dr. Best made. *VOLTAGE DOESN'T RULE!*
Current is *equally* important to voltage. If you had assumed that "current
rules", you would be saying - "when the currents are 180 out of phase it
defines an open circuit".

My argument is actually a minor point but bridges part of the gap between
you and Dr. Best. (And absolutely nothing being discussed here concerns
the source impedance of a transmitter. All we are discussing is what
happens at a match point in a transmission line or at a tuner.)
--
73, Cecil http://www.qsl.net/w5dxp



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On Sat, 05 Jun 2004 19:11:32 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
Sorry, Cecil, in spite of their similarity with Hecht's, these equations are
totally invalid.

Before we go any farther, Walt, please reference a copy of _Optics_,
by Hecht. Dr. Best's equations are valid. He just didn't understand what
he was dealing with and presented them improperly. Hecht presents them
properly. Dr. Best's equations are the classical physics equations for
the destructive interference and constructive interference.

I'm trying to locate my Hecht paper, but can't at the moment. Let's make sure
we're talking about the same set of of equations. The ones I'm saying are
invalid as stated in his article appear on Page 46, Col 2. These equations are
all being used invalidly as a result of his Eq 9, Part 3 being invalid for use
with reflected power with only one source. This a concept you're just going to
have to learn to accept. This equation is valid ONLY when there are two separate
sources--the rearward traveling reflected wave is NOT a second source, and it
will NOT work on power contained in the reflected wave. You must understand why
the invalidity of his Eq 6 in Part 1is responsible for the entire problem. Once
you understand this point you'll understand why the equations on Page 46 are
invalid.

Cecil, Steve's Eq 9 is valid only if there is more than one source. In this case
there is only one, the transceiver. This a concept that you apparentely aren't
getting, and Steve didn't either. Because Steve derived his Eqs 10 thru 15 from
an invalid premise concerning Eq 6 those equations are invalid. Just plug his
values for P1 and P2 into any of those equations and you'll get invalid answers.

With the transmission line system Steve's voltage V2 comes from the same source
as V1.

Yes, V1 comes from the generator and V2 comes from reflections from the
load which come originally from the generator.

But Cecil, you CAN'T add V1 and V2 in any manner to obtain forward power,
because adding V1 and V2 does not yield forward voltage. This is the first place
Steve erred in Part 1. Go back and review my previous msg where I explain why
his Eq 6 in Part 1 is invalid.

Dr. Best didn't understand
the S-parameter analysis and presented his material in an invalid way. But
even though he didn't understand what he was saying, his equations are
valid. He was completely off base in his explanations. It was like
Einstein coming up with E = MC^2 and then completely blowing the
explanation.

In an S-parameter analysis, b2 = s21(a1) + s22(a2)

In Dr. Best's analysis, VFtotal = V1 + V2 whe
V1 = V1F*(transmission coefficient) + V2R*(reflection coefficient)

How many times do I have to explain that V1 + V2 does NOT equal VF total? This
concept cannot be fudged into the S- parameter analysis, because V1 + V2 = VF
total is an invalid premise.

V1F is the voltage incident upon the impedance discontinuity from the left. (port1)
V2R is the voltage incident upon the impedance discontinuity from the right. (port2)

I repeat, Cecil, V1 + V2 yields only the swr, not VF total forward voltage.

There's a one-to-one correspondence above. If the S-parameter analysis is
valid, then Dr. Best's equations are valid. He just didn't present them
in a valid manner.

The S-parameter analysis would be valid if the premise that V1 + V2 = VF were
valid, which it is not. Please review my explanation why his Eq 6 in Part 1 is
invalid. This is the crux of the entire case, which has made the Eqs that I say
are invalid, invalid.

Because Steve used Eq 9 in an invalid way to derive Eqs 10 through 15, all of
these derived equations are also invalid. Try Eq 13 for example. It says 75 w
plus 8.33 w = 133.33 w, as you well know. This is absurd!

His equations are valid. His knowledge is what was invalid. It is true that

75w + 8.33W + 2*SQRT(75W*8.33W) = 133.33W

This is Steve's Eq 12, which appears to be correct when theta = zero, but he
qualifies this equation, saying tghat when V1 and V2 are in phase the total
power can be determined by Eq 13. NOT SO. The ironic part of this is that when
the system is matched V1 and V2 are always in phase on lossless lines.

P1 + P2 + interference power = PFtotal

This fact is precisely what Steve emphatically denies,

I presented this to Dr. Best 9 months before his Part 3 was
published. He simply didn't pay any attention.

From a voltage standpoint where ci means constructive interference:

I don't understand the ci term--please explain.

V1^2/Z02 + V2^2/Z02 + Vci^2/Z02 = VFtotal^2/Z02

V1^2/Zo + V2^2/ Zo = total forward power. The left -hand terms of the above
equation are power terms that do not equal VFtotal^2/Zo, because V1 + V2 does
not equal VFtotal.

For a Z02 equal to 150 ohms (if I remember correctly)

106.07v^2 + 35.35v^2 + 86.6v^2 = 141.42v^2 So

V1^2 + V2^2 + Vci^2 = VFtotal^2

Again, if V1 + V2 does not equal VFtotal, then the sum of the squares of V1 and
V2 cannot equal the square of VFtotal, unless Vci^2 is a large negative number.

This is exactly what you have been saying all along, something that Dr.
Best simply didn't understand. He completely ignored the interference
term without which the voltage equation cannot balance.

2*SQRT(75W*8.33W) is the constructive interference term supplied by the
destructive interference event on the other side of the match point which
Dr. Best completely ignored in his article.

In addition, because the powers don't add up correctly using V1 and V2 at zero
phase relationship, he concocted the ruse that they must add vectorially, and he
goes through several values of phase relationships to show what the forward
power would be with the various phases. This is poppycock, because the phase
relationship between the source (V1) and re-reflected voltage (V2) is ALWAYS
ZERO on lossless lines.

Only if the system is perfectly matched. If the system is not matched, V1 and
V2 can have any phase relationship.

Yeah, but if V1 and V2 have any relationship other than zero the system is NOT
perfectly matched.

Dr. Best's equations are valid but he just
didn't comprehend their meaning. When I called him on it, he seemed never to have
heard of destructive/constructive interference. That's what set me to researching

But Cecil, why would we be considering any condition other than perfectly
matched? All of his equations from 9 thru 15 specifiy the route to obtain either
PF or VF. This means conditions are for a matched system.
EM waves in the arena of optics.

I looked at the situation assuming that you two guys are both knowledgeable and
intelligent and I arrived at the conclusion that the two of you are only two inches
apart. But (IMO) neither one of you is willing to move that one inch to bridge the
gap. (I have said this before in private email to Walt.)

Sorry, Cecil, we're miles apart, and will be until the erroneous Eq 6 in Part 1
is corrected.

I know I've rambled all over the place with redundancies, but I tried to respond
to each of your paragraph statements as they occurred.

Walt

On Sat, 05 Jun 2004 19:20:18 -0500, Cecil Moore wrote:

Walter Maxwell wrote:
But you
can see from my words above that voltage rules--when the voltages are 180 out of
phase it defines a short circuit.

This is exactly the same mistake that Dr. Best made. *VOLTAGE DOESN'T RULE!*
Current is *equally* important to voltage. If you had assumed that "current
rules", you would be saying - "when the currents are 180 out of phase it
defines an open circuit".

Then how can you explain what happens when you reverse the zip cord, plugging
one end in one way and the other with the prongs reversed ? Are you saying the
currents in this condition are seeing an open circuit?

My argument is actually a minor point but bridges part of the gap between
you and Dr. Best. (And absolutely nothing being discussed here concerns
the source impedance of a transmitter. All we are discussing is what
happens at a match point in a transmission line or at a tuner.)

Walter Maxwell wrote:
I'm trying to locate my Hecht paper, but can't at the moment. Let's make sure
we're talking about the same set of of equations. The ones I'm saying are
invalid as stated in his article appear on Page 46, Col 2.

Walt, I'm sorry, all I have is the QEX CD and the pages are not the same as
they were in QEX magazine. Dr. Best's equations 13 and 15 are the classical
physics interference equations virtually identical to the irradiance equations
in _Optics_, by Hecht.

But Cecil, you CAN'T add V1 and V2 in any manner to obtain forward power,
because adding V1 and V2 does not yield forward voltage.

Yes, it does, Walt. Consider the following matched system similar to the
example in Dr. Best's article.

100w XMTR-----50 ohm line---x---1/2WL 150 ohm line---50 ohm load

P1 = 100W(1-rho^2) = 100(1-.25) = 75W

P2 = 33.33W(rho^2) = 33.33W*.25 = 8.33W

P1 = 75W, P2 = 8.33W, PFtotal = 133.33W

V1 = 106.07V, V2 = 35.35V, VFtotal = 141.4V

V1 + V2 = VFtotal, 106.07V + 35.35V = 141.4V

How many times do I have to explain that V1 + V2 does NOT equal VF total?

But it does, Walt. See above.

75w + 8.33W + 2*SQRT(75W*8.33W) = 133.33W (Equation 13)

This is Steve's Eq 12, which appears to be correct when theta = zero, but he
qualifies this equation, saying that when V1 and V2 are in phase the total
power can be determined by Eq 13. NOT SO.

Yes, it is, Walt. Equation 13 is valid for any matched system. That's
equation 13 just above. Perhaps you don't understand what Dr. Best means
by P1 and P2.

PFtotal = P1 + P2 + 2*SQRT(P1*P2) total forward power

133.33W = 75W + 8.33W + 50W

There's 50W of constructive interference and the equation balances perfectly.
--
73, Cecil http://www.qsl.net/w5dxp



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Walter Maxwell wrote:
Then how can you explain what happens when you reverse the zip cord, plugging
one end in one way and the other with the prongs reversed ? Are you saying the
currents in this condition are seeing an open circuit?

I'm sorry, Walt, you lost me. What zip cord?
--
73, Cecil http://www.qsl.net/w5dxp



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On Sat, 05 Jun 2004 23:39:35 -0500, Cecil Moore
wrote:
What zip cord?
:-)
A point offered that is not even half a day old... Symptoms of two
conversations running under the impression they are on the same
planet.

On Sat, 05 Jun 2004 20:06:48 GMT, Walter Maxwell wrote:
Cecil, I hope we're both still on the same page on this one;
Same page, different books....

Hi Walt,

Let's see, the score is one argument, two correspondents, and three
explanations. Do you know where Cecil is? Used to be "Find Waldo."

73's
Richard Clark, KB7QHC