May 2013 Archives

Measuring Coax Length

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I had a bundle of coax of some known type but an unknown length. I knew the previous application of the coax -- it had been used to connect from inside the car to the trunk of the car or to the roof. Noticing a part of the coax marked with silicone caulk, I knew exactly where that part had been in the vehicle in relation to everything else. Of note, the coax has one connector installed, and the other end of the coax is unterminated.

I measured the coax using a MFJ-269 Antenna Analyzer, carefully tuning up through the HF bands to find a point of resonance. I didn't find one, but I did note a large, slow sweep area where R (resistance) was approaching zero at the same time that X (Reactance) was approaching 50-ohms. At 35.210 MHz, I noted that the RG-58 had a Rs of 0 and a Xs of 50, and an infinite SWR. However, this was not the "reflected" short I was expecting to see at the opposite end of 1/4-wave of an open-circuit coaxial stub. What I later realized upon reading is that the conditions I observed are indicative of a perfectly inductive match, with zero power transferred to the load. At any rate, I had a few known figures:

Around 7.66MHz, I noted a Rs=1 and Xs=0. At 23.403, I noted Rs=2 and Xs=1. These were the minimum voltage points of the VSWR (a dead short can have no voltage present). 23.403 is within a few percent of 3 * 7.66.

Some sort of resonance at 7.66MHz and 23.4MHz.

Velocity factor of 0.66% -- both assumed and verified at the manufacturer's website.

At 7.66 MHz, the wavelength is 128.4 ft or 32.1 ft per quarter-wave; at 23.403 it is 42.028 feet or 10.507 per quarter-wave. So we know that the coax is electrically some common factor of these two lengths, likely related to multiples of 1/4-wave but not 1/2-wavelengths.

Right away we can see that 10.5 * 3 = 31.5, which is 3/4 wave at 23.4MHz and 1/4 wave at 7.66MHz. But the coax will not be that long; it will be 0.66 times the length because of the velocity factor. 31.5 feet * .66 = 20.79 feet.

Which is approximately the actual length of the cable, which I later measured to verify this post.

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