An efficient method for wide band characterization of periodic structures using a modified Z matrix interpolation

The method of moments (MoM) is the most popular numerical technique for periodic structures such as frequency selective surfaces (FSS). The solution time for MoM in FSS applications is usually dominated by the calculation of the Z matrix elements rather than the matrix inversion. Therefore, reducing the time involved in calculating the Z matrix elements can significantly reduce the total solution time. One way to reduce the calculation time of the Z matrix elements is interpolation. The idea is to first sample the matrix at N (usually 3) distinct frequency points, and then interpolate the matrix elements at all other frequencies in the interpolation band. Once the matrix is found using interpolation, the matrix is inverted to find the induced currents, from which the scattered field can be calculated. The concept of interpolating the Z matrix was first proposed by Newman (1988). We fine tune this technique to FSS, in order to maximize the accuracy over the largest possible bandwidth (as much as an 8:1 bandwidth with only 3 samples).