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Re: [TowerTalk] Determining coax length?

To: towertalk@contesting.com
Subject: Re: [TowerTalk] Determining coax length?
From: Jim Brown <jim@audiosystemsgroup.com>
Reply-to: jim@audiosystemsgroup.com
Date: Tue, 12 Nov 2013 10:24:15 -0800
List-post: <towertalk@contesting.com">mailto:towertalk@contesting.com>
On 11/12/2013 8:29 AM, Jim Lux wrote:
There have been reports of the velocity factor varying substantially within a single spool of coax (other than a "once per turn on the spool").

Perhaps, or maybe it's simply that the reporter does not understand that Vf (and Zo) vary with frequency in a very well understood and predictable manner. Indeed, the transmission line equations predict it. See http://k9yc.com/Coax-Stubs.pdf

For example, Zo is NOT sqrt (L/C) at all frequencies. The full equation for Zo is sqrt [(R + jwL) / (G + jwC)] where w is greek omega, 2 pi f. The equation simplifies to sqrt (L/C) if f is large, but at MF and HF, one must use sqrt [(R + jwL) / ( jwC)] to get precise results. The difference is typically on the order of 1-2% on 160M, a bit less on 80M, and converges to sqrt (L/C) by 30 MHz.

The most accurate method to determine Vf and/or electrical length of a piece of transmission line is to measure it as a stub near the frequency where you care about its length. You can use TDR by the FFT method Jim describes, but the number you get will be for the frequency range where you have swept it, typically 100 MHz - 500 MHz. That's good enough for cutting precisely equal lengths of coax cut from the same roll, and maybe even of the same type if it's from a high quality manufacturer, but it's not good enough for coax with different part numbers, or from companies with poor manufacturing consistency.

Simple analyzers like the MFJ-259 are plenty good enough for finding the resonances in a stub if you read the null very carefully. I've done that by finding the zero reactance frequency, then finding the frequencies just either side where the digit changes from zero reactance, and take the average of the two, which should be quite close to the first center reading. I then carefully measure the physical length of the sample with a tape measure.

BTW -- the best bargain, by far, in a VNA is the VNWA 3e designed by DG8SAQ, built and sold by a UK ham. It's USB powered, runs via software from the USB port, full specs to 500 MHz, reduced dynamic range to 1.5 GHz, delivered to my door by post for $700 with calibration load and short. It does TDR by the FFT method Jim Lux described, and can be used as a spectrum analyzer. It reads and writes Touchstone files for use by Smith Chart and other design software. Control software is by DG8SAQ, who a university prof, and is being updated regularly to add features.

73, Jim K9YC




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