Accelerated Macro Basis Functions Analysis of Finite Printed Antenna Arrays Through 2D and 3D Multipole Expansions

An efficient technique is presented for the analysis of finite printed antenna arrays made of identical elements. It is based on a closed-form expression for the spatial-domain Green's function (GF) given as a finite sum of cylindrical waves (obtained through rational function fitting) plus one spherical wave. From there, a multipole expansion can be obtained for planar layered medium GFs. The macro basis function (MBF) technique is applied to the method of moments (MoM) solution of a mixed-potential integral equation, this reduces the size of the MoM impedance matrix and allows for a direct solution. However, the evaluation of the entries of this reduced matrix becomes the dominant contribution to the total computation time. The aforementioned multipole expansion is exploited to provide a fast construction of the reduced MoM matrix, whose elements are the reaction integrals between the MBFs considered to characterize the currents on the array element. The complexity of evaluating the interactions between MBFs is found to be dominated by the calculations related to the spherical wave term. Thus, taking into account the layered medium does not increase the order of the complexity with respect to a multipole-accelerated computation of reaction integrals in a homogeneous medium.