Theory of Antennas of Arbitrary Size and Shape

In this paper there are presented (1) a quite general method of antenna analysis; (2) a physical picture of transmission phenomena in antennas, based on this method; and (3) an expression for the input impedance of antennas of any shape, whose transverse dimensions are small compared with the wavelength. In a brief historical sketch of the antenna problem the factors which must be taken into consideration in solving the problem are discussed. While in ordinary transmission lines the voltage is proportional to the charge, this is not the case in antennas. The explanation lies in the fact that antennas are multiple transmission lines (like wave guides) and not simple, that is, single-mode transmission lines. Our present theory is based on the voltage-current equations since these appear to be considerably simpler than charge-current equations. The latter are considered only briefly. In the absence of dissipation and in so far as the total voltage wave and the "principal" current wave are concerned, radiation is strictly an end effect. In so far as the total current and the total charge waves are concerned, radiation effects are distributed (nonuniformly) along the entire antenna. In the first approximation, regardless of the shape of the wire the charge is proportional to the voltage and waves are sinusoidal, the current wave having nodes while the voltage wave and the charge wave antinodes at the ends of the antenna.