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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