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The easiest and most efficient way to tune a caged monopole is to first connect all the “fold” conductors both top and bottom. A return or ground side conductor connects at the common point at the top and runs down to the ground side of the feedline at the bottom (usually through the center of the antenna).
Then, a shorting ring is constructed so that it encircles the entire antenna horizontally connecting to all fold conductors at the same elevation. The point of the connection is determined by the feed impedance of the transmitter. This can closely impedance match the antenna to the transmitter.
The antenna constructed this way most often exhibits inductive reactance which can be tuned to resonance by a simple variable capacitor in series with the hot side of the feedline to the antenna feed connection (usually a feed ring similar to the shorting ring). This may eliminate the need for any coil in the feed to the antenna.
In broadcasting, this antenna design is called a folded monopole and can be used at any frequency. This antenna design is used to raise the antenna efficiency for systems that are very short radiators. This design would be a good choice for Part 15 AM BCB antennae. I have used a very similar design (with success) for the AM BCB, as well as, vhf and uhf antennae.
Examples and drawings of the construction and tuning of this antenna system is common place by doing a Google search on the web. This antenna can be made to exhibit a wide bandwidth and nearly any impedance required by the transmitter.
The picture shown previously on this thread is a simple example of a series feed system found on many AM station broadcast towers across the country. Just think of each vertical wire as a separate leg of the tower.