[TowerTalk] Determining coax length?

[Jim Brown]

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