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Old September 2nd 03, 03:36 AM
Peter O. Brackett
 
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Roy:

[snip]
"Roy Lewallen" wrote in message
...
I'm sorry I'm having such a hard time communicating, and maybe the
trouble is that I've been misunderstanding what has been said. Here's
how it looks to me.

[snip]

Heh, heh... don't feel bad, that is common in any discourse using the medium
of USENET Newsgroup postings!

[snip]
So what's bothering me is that I'm completely unable to start with what
I believe to be true about the relationships between voltages, currents,
and characteristic impedance of a transmission line (itemized as three
assumptions in a recent posting), and arrive at anything but the
classical equation which is universally used for transmission line
analysis.

[snip]

I'm with you man! I like and, only use, the classical definitions of rho
and
the Scattering Matrix wich correspond to the "actual" waves supported by
the wave equation [The Telegraphist's Equations] on passive transmission
lines.

I simply don't like the version of rho/Scattering matrix which uses the
complex
conjugate of the "reference impedance" or what ever else you wish to call
the charateristic or surge impedance simply because the transition between
Z and conj(Z) represents an impedance discontinuity, a big one in fact, and
physical intuition tells me that there will alwasy be some effect on waves
which
have to transit such a discontinuity.

I am not a bigot about this use of the conj(Z) and I can quote several
excellent
authoritative references that do so. I don't however agree with Slick's use
of
conj(Z) in the numerator and just Z in the denominator, I believe that to be
the result of some typographical error or complete errors in
misunderstanding.

I do understand that for special kinds of problems it may be convenient to
adopt
different definitions for rho and the Scattering Matrix, and that is fine
just as long
as the definers remain consistent thereafter and indicate their departure
from the
more common usual definitions. Confusion sets in when there are proponents
of
the different definitions discussing/arguing about results without first
agreeing on
the definitions.

[snip]
I've posted both a detailed derivation of the formula for reflection
coefficient and a numerical example of a terminated transmission line
with complex Z0.

[snip]

You do good work Roy.

[snip]
elements or "semi-infinite" transmission lines -- or no derivation at
all. The alternate dervivations, it seems, can't for some reason
withstand the condition that a simple, finite length transmission line
be involved. Rather than presenting a simple analysis of a system with a
transmission line (as I did), all I've seen in response is lumped
element or "semi-infinite" transmission line analyses with indignant
protestations if I question the possibility that the presented models
don't accurately represent a finite transmission line.

[snip]

Because Roy, the use of semi-infinite transmission lines in a simple
"theoretical"
derivation is easier to communicate in short NG postings and easier to
understand
and manipulate than complex long "arithmetical" developments, no matter how
practical.

I too can give the group numerous practical Engineering design calculations
of real
problems that many have solved over the years in the communications
industry, not
made up problems like yours, but real ones involving complex Zo transmission
lines
with highly variable Zo's of lengths up to 18,000 feet operating with very
little
"talker echo" [reflection coefficient] over frequency ranges of a handful of
decades,
using very economical lumped approximations to Zo in the balancing networks.
There
are several patents issued in this area. But I am sure that most would get
glassy eyed
with those detailed Engineering calculations.

Which would you rather have, some detailed long drawn out Engineering
calculations
or a simple two line theoretical proof that using Zo and not conj(Zo)
results in no talker
echo only for an image matched line.

The theory of "image matching" was developed by Campbell and Zobel in the
time
frame of the early 1920's, why are we trying to prove it again now using
arithmetic?

[snip]
I really think that by now, anyone who is able to benefit from the
discussion has done so, and those who remain will continue to hold their
views no matter what. So I won't further waste the time of either group
by continuing to question the issue. I hope that the derivations I've
posted are helpful to those people who are interested in seeing where
the common formulas and equations come from.

[snip]

Thanks for all of your efforts Roy. As you know I agree completely with
your
results and conclusions.

But I must re-iterate I don't agree with your methods. The use of
arithmetic where
a little algebra and mathematical theory of trasmission lines will suffice.
is not my ideal of good communications.

Kraus, Balmain and all of your "other heros" make use of semi-infinite lines
in their
developments and descriptions of the meaning of Zo, I just don't see what
*your*
problem is with that approach. I can assure you that Maxwell did not use
"arithmetic"
in the development of his equations, nor did the first person to "define" a
reflection
coefficient!

I am perplexed by your approach to say the least, but perhaps I just don't
understand...

--
Peter K1PO
Indialantic By-the-Sea, FL.