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Q. What do you call someone who can’t tell the difference between a dougnut and a teacup?
A. A topologist.
Q. Why didn’t Gauss invent group theory?
A. Because he wasn’t Abel.
Math majors hear jokes like this in college. They are inside jokes. Most people don’t understand them, because they are intended for people who are (or will become) mathematical professionals. Here are the explanations: A topologist is someone who studies topology, which is a branch of geometry that determines the properties of figures without regard to any deformation except cutting and joining. Some consider Gauss to be the greatest of all of the mathematicians in history. (Some of the other possible candidates for this honor are Newton, Archimedes, and Euler.) Abel was another outstanding mathematician. He died in this twenties, but he had established a great reputation during his short lifetime. Abel invented group theory.
I think I may have told something like an inside joke in the previous post in this thread. While everything I said is true, some readers may not have understood my point. This would not be fair, so I will explain what I meant.
I did not invent anything about the “No Field Antenna” I described, except the name. This antenna is better known as as the “X” antenna. It has been around for a very long time. The best-known relative of the “X” antenna is the “inverted L,” which has a vertical element attached to one end of a horizontal element. This antenna is very popular for the 160 meter ham band because it is at resonance when the total length of the vertical and horizontal elements is about a quarter wavelength. The inverted L is not as difficult to construct as a quarter wave vertical, and the horizontal element can fit in some confined spaces. The radiation is both horizontally and vertically polarized.
Another related antenna is the “T” antenna, in which a vertical element is attached to the center of a horizontal element. This antenna also produces vertically and horizontally polarized radiation, but the horizontally polarized radiation is weak because the RF currents in the two horizontal halves go in opposite directions, and the fields partially cancel each other out.
The “X” antenna has two horizontal elements that cross each other at right angles at their centers, and they are attached to a vertical element where they cross. The currents in the horizontal elements of the “X”antenna go in four different directions, and the fields nearly exactly cancel each other out. So the “X” antenna has vertically polarized radiation, but practically no horizontally polarized radiation. It is possible to cross more than two horizontal elements together to form a “star” antenna. The “star” antenna works about the same as an “X” antenna. It is possible to replace the horizontal “star” with a horizontal disk. In that case, we have a top-loaded antenna with a circular capacitive hat. This is also about the same as an”X” antenna with the same radius as the disk. Only the vertical elements of these last three antennas radiate. But, the horizontal elements still provide a very useful function. They increase the electical height of the vertical element and increase the radiation resistance. In these antennas, the vertical elements are true transmission lines, but they are transmission lines that radiate. It is not necessary for the top hat to be a disk. Any piece of metal that is comparable in horizontal dimensions to the disk will work as well as a disk.
The point I was trying to illustrate is that it is not necessary for a piece of metal you call an “antenna” to radiate at all if it is attached to a vertical “transmission line.” The antenna can be a poor radiator, or even a non-radiator, because practically all of the radiation is done by the vertical transmission line. This is the essence of the CFA, EH, and all the rest of the antennas of this type.