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As we say in America, “We are in the ballpark.” Just in case France doesn’t know that figure of speech, it means we have reached the best part of the topic. SCWIS has given a starting formula for building a loading coil for the 21-meter band, home of the 13mHz frequencies.
I’ve been searching through a big thick book from William I. Orr, W6SAI, the Radio Handbook, 20th Edition, from 1975. It covers everything to do with amateur radio, except there is no section on loading coils for the short indoor antenna. BUT, there is a great section on MOBILE AND PORTABLE EQUIPMENT, and, as it turns out, the mobile whip on a car or truck is an undersized antenna totally dependent on a loading coil for efficiency.
I will pick out a few points that might add to this discussion.
For example, it says the transmission line from transmitter to antenna should be “exactly odd multiples of one-quarter wavelength long electrically.” If the antenna is located right at the transmitter there will be no transmission line.
Another notable fact is that the majority of whip antennas at 14mHz and below are CENTER-LOADED, meaning that the loading coil goes at the center of the vertical antenna rather than at its bottom.
A CAPACITY HAT may be added to a loaded whip antenna to improve the efficiency. “The capacitance added above the loading coil requires a reduction in the number of turns in the coil to reestablish resonance.
Here now is something different than I have ever seen before about mounting a loading coil to the vertical antenna. “It was found that mounting the center-mounted loading coil at RIGHT ANGLES to the whip greatly improves the Q (efficiency).”