Sparse Matrix/Canonical Grid (SMCG) Method For Microstrip Circuits

In this paper, we illustrate the analysis of microstrip structures using the sparse-matrix/canonical grid method. This fast Fourier transform (FFT) based iterative method reduces both CPU time and computer storage memory requirements. We employ the Mixed-Potential Integral Equation (MPIE) formulation in conjunction with the RWG triangular discretization. The required spatial-domain Green's functions are obtained efficiently and accurately using the Complex Image Method (CIM). The impedance matrix is decomposed into a sparse-matrix, which corresponds to near interactions and its complementary matrix, which corresponds to far interactions among the subsectional current elements on the microstrip structures. During the iterative process, the near-interaction portion of the matrix-vector multiplication is computed directly as the conventional MPIE formulation. The far-interaction portion of the matrix-vector multiplication is computed indirectly using fast Fourier transforms (FFTs). This is achieved by a Taylor series expansion of the Green's function overlaying the triangular discretization.