The Impedance of Short, Long, and Capacitively Loaded Antennas with a Critical Discussion of the Antenna Problem

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Abstract
In Part I curves computed from Hallén's formula for the self‐impedance of a center‐driven antenna of half‐length h and radius a are given for Ω=2 ln (2h/a)=7, 10, 20, 30 for values of h from zero to two wave‐lengths. A simple formula for the impedance of short antennas is obtained; the reactance is shown to agree with that computed from the static capacitance between the two halves of the antenna. The effect of a capacitive reactance connected across the input terminals of the antenna is investigated. It is shown that the resistance at anti‐resonance is reduced, the capacitive lobes of the curve for reactance relatively increased, the inductive lobes relatively very much decreased, and curves for both resistance and reactance shifted to shorter lengths. In Part II the differences between various methods used by different investigators to compute the impedance of an antenna are examined critically. It is concluded that Hallén's formula probably is a better approximation for an antenna consisting of two sufficiently thin ellipsoids each of semi‐minor axis a placed end to end than for cylinders, but that cylindrical antennas driven in various ways can be approximated by using an effective value of h/a and a suitably chosen capacitance across the input terminals.