Diakoptic theory for multielement antennas

A theory is presented for the analysis of multielement antennas which consist of interconnected, conductive structure elements of electrically small dimensions. The theory is based on the retarded electromagnetic potentials which permit a diakoptic approach to the problem. The antenna is broken up into its individual structure elements. Each element is assumed to be excited by currents which are impressed at its terminals, i.e., junctions with adjacent elements (current coupling) and by the electric fields of the currents and charges on all the other elements (fieid coupling). Both excitations are treated independently. Each impressed current produces a "dominant" current distribution, a characteristic of the element, which can be readily computed. Current coupling is formulated by "intrinsic" impedance matrices which relate the scaler potentials at the terminals of an element, caused by its dominant current distributions, to the impressed currents of the element. Field coupling produces "scatter" currents on all the elements and is formulated by a "fieid-coupling" matrix which relates the scalar potentials at the terminals, caused by field coupling, to the impressed currents at all the terminals. Intrinsic and "field-coupling" matrices are combined to form the "complete" impedance matrix of the diakopted antenna. Enforcing continuity of the currents and equality of the scalar potentials at all the interconnections between the elements yields a system of linear equations for the junction currents and the input impedance of the antenna. Current coupling dominates field coupling. Fieid coupling is primarily affected by the dominant current distributions of the elements, and in general the scatter currents have negligible effect on it. Although detailed numerical investigations will be presented in another paper, a simple example is included here to demonstrate that the diakoptic theory yields very good results even if greatly simplified assumptions are made.