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It’s true that the gain of a lossless electrically short monopole is only .37 dB less than that of a lossless quarter wave monopole, but we know from our experience with Part 15 AM that the actual gain of a short monopole with losses can be enormously less than that of a quarter wave monopole. Gain is directivity times efficiency. The losses do not change the directivity of a short antenna, but they certainly reduce the efficiency.
The philosophy behind the regulations for licensed AM (Part 73) is opposite to the philosophy behind the regulations for Part 15 AM. The FCC wants a licensed AM station to use an antenna that has high efficiency. The FCC doesn’t want a Part 15 AM transmitter to cause interference to licensed stations, and so they have imposed severe restrictions in Sections 15.209, 15.219, and 15.221. On the contrary, a licensed AM station is supposed to be heard well within its coverage area. Section 73.189 requires a minimum antenna height of 45 meters for a Class C stations. The height of the building the antenna may be mounted on is not counted as part of the antenna height. Note that Section 15.219 specifies a maximum antenna height, while Section 73.189 specifies a minimum height. The FCC will allow an antenna shorter than 45 meters to be used if it can be shown that the effective field strength at 1 km is at least 241 mv/m for 1KW input. This is 2.28 dB below a lossless quarter wave monopole.
Trainotti indicated that the gain of a well-designed short monopole may be as little as 1.5 dB below a perfect quarter wave monopole. The theoretical minimum gain difference of .37 dB cannot be achieved because of the lower radiation resistance to ground resistance ratio of short monopoles. Trainotti says that the radials used for full-sized antennas are not good enough when short monopoles are used. A metallic ground plane is needed at short distances from the antenna base in order to get a low enough ground resistance in relation to radiation resistance.
I should point out that a “short” antenna operating under Part 73 is quite a bit longer than what is allowed in Part 15.219. It is unlikely that a Part 73 antenna would be less than about 15 m in height.