At 13:55 04/05/2003 +0100, you wrote:
After reading Jim's e-mail I searched through all my radio books
(Terman, Kraus et al) for enlightenment and the reason for 50ohms as a
standard is not discussed at all.
Any references Jim?
Dear Peter, LF Group,
I can't remember where I originally heard this - it gets a vague mention in
several reference books, but the only discussion in any detail I could find
was in a small book called "High Frequency Transmission Lines" by Willis
Jackson, published in about 1945. The Zo for minimum loss is dependent
mainly on the materials used for the conductors in the coax - for copper
inner and outer it is 77ohms, but with copper inner and lead outer (I guess
lead sheathed cables were popular then), it comes out to 93ohms. However,
loss does not vary greatly with Zo. But this applies to an air dielectric;
with a polythene dielectric, the optimum ratio of conductor sizes stays the
same, but the presence of the polythene reduces the impedance. This would
appear to make a Zo of 51ohms optimum for solid polythene insulated coax. I
have some samples of old trans-atlantic telephone coax cable - according to
the labels, they are from the TAT-1, TAT-II and CANTAT-2 cables. Measuring
the dimensions of these, they work out to Zo of 57, 45, and 55 ohms
respectively. I imagine they must have been designed with low loss in mind;
which would tend to support the 51ohm figure.
The calculation for max power handling is not straightforward - it depends
on what the limiting factor is. In an air-dielectric cable limited by
voltage breakdown , the optimum is 30ohms. But if the cable has solid
dielectric, the breakdown voltage is higher, and other factors such as heat
dissipation may be more important, favouring a higher Zo like 50ohms.
The fact that Zo is proportional to the log of the ratio of diameters of
outer and inner conductors severely limits the practical range - eg. if you
wanted 600 ohm coax, then with a 1mm inner conductor, the outer would have
to be about 4km in diameter! Low Zo is a bit more practical; a 4ohm cable
would have the outer only about 10% greater in diameter than the inner,
requiring a very thick inner conductor. I suppose this is why most coax is
between 25 and 100 ohms.
Cheers, Jim Moritz
73 de M0BMU
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