Efficient, numerically robust characterisation of a large, double-loop antenna array

Abstract

Arrays of circular, double-loops are treated via a semi-analytical technique, on the basis of a Method of Moments formulation. A Pocklington-type integral equation for the current is derived and discretised via a suitable set of basis functions. The matrix corresponding to the pertinent linear system is found to consist of circulant blocks. The system is therefore analytically solvable, and hence, potential ill-conditioning, encountered in large geometry cases, cannot possibly introduce any numerical instabilities to the calculations. Introduction of a delta gap source as excitation facilitates very efficient computation of the current and input admittance. The algorithm exploits almost exclusively elementary functions and yields results in terms of a set of rapidly convergent series, applicable to extremely large loops. Data for such loops are presented for the first time in literature. The method is expected to lead in the future to very efficient designs of multi-loop arrays.