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