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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