Fig. 1. Geometry of Problem for N-element Dipole Antenna Array. (4)

in this paper may be used as a design t.ool to predict the general pattern behavior of multimode slow wave spiral antennas. where .Z<jim is a generalized self-or mut.ual impedance defmed between two current functions f i t (~ <) and fp(zj). Solving (2) with rmpect to [. J i t J , we express them as Let Qj(9) represent the radiation pattern obtained when a unit voltage is applied to the jth input, and all other inputs are shorti circuited. Absfracf-The exact method of designing an array of dipole antennas with the prescribed radiation patterns in the magnetic plane is described. The integral of the current distribution, which is expressed according to the improved circuit theory, is set equal to the magnitude of the point source, which is given by the conventional synthesis method. The current distributions and the correct set of driving voltages or currents are sought to the prescribed radiation pattern simultaneously by the present method. It was found by Heines et aZ. [l] that the usual method of array design does not predict the pattern of the array with sufficient accuracy in cases where the array is designed for very low sidelobes. Eing and Sander [a], [3] analyzed the array of dipole antennas and showed the deformed pat.terns which are obtained when the input currents or volt,ages are specified according to the usual method. Heines et al. [4] int.roduced a rigorously correct, method of designing t,he array experimentally. This communication is intended to introduce an exact design method for the array of dipole antennas without any experimental means. Consider an ,Y-eIement antenna as shown in Fig. 1. The current distribution of the it.h element is expressed, according to the improved circuit theory [SI, as vj = 1. Heines et al. determined Q j (p) by the experiment for the array of traveling-wave slot antennas, and determined (Vil so that the following added pattern vi11 give the desired pattern [4]: Here we derive Q j (9) from the above theory. Integrating Ji(zi) nith respect to zi and adding them up, we get Then it follows from the principle of superposition, that the magnitude of an equivalent point source when all the elements me