Linear arrays: Currents, impedances, and fields, I

The radiation field of dipoles is usually expressed in the form of a product of a field factor and one or more array factors. Actually, such a formulation depends on the implicit assumption that the distributions of current along all elements are the same regardless of the location in the array or differences in driving conditions. Since this is a satisfactory approximation only when the elements are near a half-wavelength long, a study of the fields of arrays of longer elements in terms of the actual distributions of current is indicated. The available solutions of the simultaneous integral equations for the distributions of current in a circular array ofN-parallel elements are adequate in a quantitative sense only for arrays of approximately half-wave elements. Moreover, the form of the solution as a series of complicated terms is quite useless (except in the leading sinusoidal term) when the determination of the radiation field is desired. For this reason, a new solution for the currents, which provides a good approximation for the currents in arrays of elements that may be a full wavelength long or longer, and which is expressed in terms of combinations of simple trigonometric functions, is derived. The new solution is used to determine the currents in and the fields of isolated half-wave and full-wave dipoles more accurately than with the conventional sinusoidal currents. The currents, impedances, and fields of a two-element array of full-wave elements are studied under various driving conditions including the broadside, bilateral end-fire, unilateral end-fire or couplet, and the case when one of the elements is parasitic. It is shown that the null in the conventional pattern for the couplet with identically distributed currents becomes a minor maximum with an amplitude equal to half that of the principal maximum when the more accurate distributions of current are used. The significance of this fact in its application to the minor lobe structure of more general arrays is considered. The usefulness of the new theory in determining the radiation field of parallel arrays, in general and when scanned, is discussed, and plans for further work are outlined.