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Re: LF: Mains Cable and other transmission lines

To: [email protected]
Subject: Re: LF: Mains Cable and other transmission lines
From: "James Moritz" <[email protected]>
Date: Thu, 08 May 2003 16:30:52 +0100
In-reply-to: <[email protected]>
References: <[email protected]> <[email protected]> <[email protected]>
Reply-to: [email protected]
Sender: <[email protected]>
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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