Current distribution and driving point impedance for a rhombic antenna

Abstract

From Maxwell's equations, the differential equations are derived for an open wire line. The resulting classical transmission line theory is correlated with the generalized circuit theory. In fact, it is shown that the radiation impedance of a rhombic antenna may be derived from the classical theory, and the concept of radiation impedance is clarified. It is further shown that the customary usage of the difference in scalar potential for the driving point voltage is equivalent to replacing the drop across the terminal reactance, for a circuit assumed to be in a self sustained steady state oscillation, with the generator voltage. Methods for approximating the driving point impedance of a rhombic antenna are discussed. For determining the current distribution in a rhombic antenna, the Hallen integral equation technique is briefly considered and, because of its complexity, is discarded in favor of the nonuniform transmission line technique. The current distribution is found by dividing the rhombus into four intervals, namely, 0<x<λ/2, λ/2<x<l, l<x<2l-λ/2, 2l-λ/2<x<2l, and applying the nonuniform line theory. Graphs for the radiation impedance of a rhombic antenna are presented. Also, curves for the current distribution along a single wire rhombic antenna are given.