Fast construction of the MoM matrix for reflectarrays through a smart tabulation

A novel and efficient analysis technique for reflectarrays of variable element sizes was previously proposed by the authors. The technique relies on using the scaled version of a reference mesh for all elements and reusing the dominant characteristic mode of the resonant sized patch for all differently sized patches on the reflectarray. The number of unknowns is reduced to the number of elements by constructing a reduced matrix form through the use of the dominant characteristic mode as a macro basis function. In this study, an accurate and efficient method for the construction of this reduced MoM (Method of Moments) matrix is proposed. An entry of the reduced matrix corresponds to the interaction of two patches and it is a function of horizontal and vertical displacements and sizes of these patches. The efficiency of the proposed method is based on our observation that, except for near field interactions, the displacement and size dependencies are separable such that the matrix entries can be expressed as the product of two functions. Therefore it becomes sufficient to tabulate the reduced matrix entry for two cases, one for a fixed pair of source and observer patch sizes, whereas the other is for a fixed pair of horizontal and vertical displacements. When the tabulations are available, it takes 0.38 seconds to compute the current density on a reflectarray with 1000 elements, on a personal computer with 3.3 GHz clock speed.