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A capacitive hat improves antenna efficiency by increasing the radiation resistance of the antenna and increasing antenna capacitance. Increasing the diameter of an antenna does not increase radiation resistance much, but it does increase antenna capacitance.
I recently received a message addressed to me personally that claims that radiation resistance alone determines antenna efficiency, and antenna capacitance merely increases the antenna bandwidth. I’ve heard this opinion expressed before.
Increasing the diameter of an electrically short antenna improves efficiency by reducing the loading coil inductance needed to tune the antenna to resonance. A smaller inductance coil can be made with less loss resistance. Loading coil loss is a major component of Part 15 AM antenna inefficency, and the higher the antenna capacitance, the better.
The Rangemaster uses a CB whip, which has a small diameter. Using a larger diameter pipe would allow the transmitter to be tuned to a smaller inductance tap on the secondary winding of the output transformer, which is the loading coil. This would improve the efficiency of the transmitter. The certification issue was already discussed. Rangemaster would need to design a fatter antenna for the AM 1000, and re-certify, in order to make the larger diameter antenna legal.