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November 23rd 04, 03:36 PM

(Robert Lay W9DMK) wrote in message ...

The condition for which Zo of a transmission line is always purely resistive
(Zo = Ro) is extremely simple. It is -

G = C * R / L

where G is shunt conductance, C is shunt capacitance, R is series
resistance, L is series inductance, all per unit length of line.

Well, that is pretty entertaining and
interesting, i will admit. However, the
result isn't very practical...

Most texts just assume lossless conditions,
so that R and G equal zero, so that Zo is
again, always purely real, and only dependant
on the distributed inductance and capacitance
of the transmission line.

Which applies to any line length, at any frequency from DC to UHF.

It is a shortcoming of the Smith Chart, with Zo always equal to Ro, that it
does not make you aware of this and can lead you up the garden path if you
are not careful. As has recently occurred on this newsgroup.

Don't get me wrong. I'm not against Smith Charts. They are graphically
educational within their limitations.
----
Reg, G4FGQ

Dear Reg,

You say that it is a shortcoming of the Smith Chart that Zo equals Ro.
However, I think that is either a misunderstanding or just misleading.
The Smith Chart only constrains the normalizing quantity to be purely
resistive - not the characteristic impedance of a particular
transmission line being shown on that chart. My program, SmartSmith,
for example, allows the user to specify both an Ro and an Xo term for
all transmission line sections.

When it's all said and done, the Smith Chart only implements the
transmission line equation (as shown on pages 24-10 and 27-29 in the
17th Edition of The ARRL Antenna Book).

You know, this seems to be quite a theory
problem regarding the Smith Chart. This goes back to
the heated argument on the Gamma reflection
coefficient using the conjugate of Zo in the
numerator.
Since i trust Les Besser more than
other people, i'm gonna assume that
you indeed CAN normalize a Smith chart
to a complex Zo. That is, a Zo that
is not a purely real impedance.

Slick

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