pez wrote:
Dear Mr. Cecil Moore,

I am terribly sorry but I am not so sure that
I am in position to follow your argument,
except perhaps that the equation

| ...
| |b1|^2 = |s11*a1|^2 + |s12*a2|^2 + 2*s11*a1*s12*a2
| ...

needs a modification to
the third term on its right hand side,
in which, instead of

2*s11*a1*s12*a2

we have to set

2*Re{[s11*a1]*Conjg[s12*a2]}

That is taken care of by the cosine of the angle between
a1 and a2. Note no magnitude bars around that term in my
equation. a1*a2 is phasor multiplication, a1*a2*cos(theta).

Therefore,
I can only guess that
this subtle distinction is the source of the trouble
because this is maybe due to the sure existence of two,
after Kurokawa, different physical meanings
for the same physical phenomenon.

And finally, unfortunately enough,
it seems that there are maybe more than a finite number
of possible such physical meanings for the same physical phenomenon...

What I was trying to point out is the similarities between
Dr. Best's QEX article term, 2*sqrt(P1)*sqrt(P2)*cos(theta),
In _Optics_, Hecht's interference term 2*sqrt(I1*I2)*cos(theta),
and the above 2*s11*s12*a1*a2(cos theta) term. Seems to me, they
are all interference terms. If (0 deg = theta 90 deg) then the
interference is constructive. If (90 deg theta = 180 deg) then
the interference is destructive.
--
73, Cecil, W5DXP

Cecil Moore wrote:
What I was trying to point out is the similarities between
Dr. Best's QEX article term, 2*sqrt(P1)*sqrt(P2)*cos(theta),
In _Optics_, Hecht's interference term 2*sqrt(I1*I2)*cos(theta),
and the above 2*s11*s12*a1*a2(cos theta) term. Seems to me, they
are all interference terms. If (0 deg = theta 90 deg) then the
interference is constructive. If (90 deg theta = 180 deg) then
the interference is destructive.
--
73, Cecil, W5DXP

(a + b) * (a + b) = a^2 + 2ab + b^2

Wow, I made my own "interference term"!

73 de jk

Jim Kelley wrote:

Cecil Moore wrote:
What I was trying to point out is the similarities between
Dr. Best's QEX article term, 2*sqrt(P1)*sqrt(P2)*cos(theta),
In _Optics_, Hecht's interference term 2*sqrt(I1*I2)*cos(theta),
and the above 2*s11*s12*a1*a2(cos theta) term. Seems to me, they
are all interference terms. If (0 deg = theta 90 deg) then the
interference is constructive. If (90 deg theta = 180 deg) then
the interference is destructive.

(a + b) * (a + b) = a^2 + 2ab + b^2

Wow, I made my own "interference term"!

Yep, assuming those are phasor voltages normalized to the
square root of Z0, you sure did. That's one of the advantages
of an s-parameter analysis. With the voltages normalized to
the square root of Z0, the square of any voltage equals
V^2/Z0 = power.

a^2 would be P1, b^2 would be P2, and 2ab would equal to
2*sqrt(P1)*sqrt(P2)*cos(theta) [phase angle between a and b]
--
73, Cecil, W5DXP

"Cecil Moore" wrote in message
...
Jim Kelley wrote:
(a + b) * (a + b) = a^2 + 2ab + b^2

Wow, I made my own "interference term"!

Yep, assuming those are phasor voltages normalized to the
square root of Z0, you sure did.

a^2 would be P1

I call the a^2 term Cecil. :-)

73 jk

Dear Mr. Cecil Moore,

I think now I understand the notation.
If

| ...
| a1*a2 is phasor multiplication, a1*a2*cos(theta)
| ...

then s11*a1*s12*a2
is s11*a1*s12*a2*cos(phi)

which has the same meaning as the

Re{[s11*a1]*Conjg[s12*a2]}

and the only thing which remains
is the specification of the phi range of values.

I think also,
I grasped your point of view
for the existence of a deeper, common, base between
these different physical phenomena,
with which anyone hardly disagrees.

Finally,
I would ask you to tell me please,
the reference details to
Dr. Best's QEX article and Hecht's _Optics_.

Thanking you in advance,

pez
SV7BAX
TheDAG

pez wrote:
I would ask you to tell me please, the reference details to
Dr. Best's QEX article and Hecht's _Optics_.

_Optics_ by Eugene Hecht, fourth edition, ISBN 81-7808-617-4

"Wave Mechanics of Transmission Lines, Part 3", Dr. Steven R. Best,
VE9SRB, _QEX_, Nov/Dec 2001
--
73, Cecil http://www.qsl.net/w5dxp



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