Multipole accelerated macro basis functions analysis of printed antenna arrays

This paper presents a multipole expansion for the layered media Green's function (GF). It is obtained thanks to a closed-form expression of the GF as a finite sum of Hankel functions. This multipole expansion can be introduced in the framework of Mixed-Potential Integral Equation (MPIE) formulations and solved with the Method-of-Moments (MoM). Then, when applying the Macro Basis Function (MBF) technique, one can exploit the aforementioned expansion in order to provide a fast evaluation of the reaction integrals between the set of MBFs considered for the array radiating element. Moreover, the size reduction of the MoM system of equations achieved using MBFs, allows one to save resources in terms of memory and solution time.