An efficient MoM formulation for finite-by-infinite arrays of two-dimensional antennas arranged in a three-dimensional structure

In strongly coupled antenna arrays, the behavior of the elements near the edge can exhibit very large deviations with respect to the infinite periodic array solution. Insight into these truncation effects can be obtained by simulating finite-by-infinite arrays. This paper describes an efficient method-of-moments (MoM) scheme for simulating such arrays. This scheme is capable of handling arrays of two-dimensional metallic antennas placed perpendicularly to the array plane, in lossless media. This formulation relies on the free-space Green's function related to arrays infinite in one direction only, with linear phase excitation. After extraction of its singular part, this function is tabulated. Then, the elements of the MoM impedance matrix are computed in the space domain, with the help of a limited number of integration points. The computation time needed for establishing the MoM system of equations and for solving it is comparable to the time needed in the linear array case. An extension of this formulation is also developed to study infinite-by-infinite arrays and semi-infinite arrays. The latter solutions also provide standard current distributions, which are used to obtain a fast approximate solution of the MoM system of equations. Simulation results are shown for broadband arrays, made of tapered slot antennas consisting of metallic plates