Efficient Modeling of Transmission Lines With Electromagnetic Wave Coupling by Using the Finite Difference Quadrature Method

Abstract—This paper proposes an efficient numerical technique, called the finite difference quadrature (FDQ) method, to model the transmission line with radiated electromagnetic (EM) wave noise coupling. A discrete modeling approach, the FDQ method adapts coarse grid points along the transmission line to compute the finite difference between adjacent grid points. A global approximation scheme is formulated in the form of a weighted sum of quantities beyond the local grid points. Unlike the Gaussian quadrature method that computes numerical integrals by using global approximation framework, the FDQ method uses a global quadrature method to construct the approximation schemes for the computation of, however, numerical finite differences. As a global approximation technique, the FDQ method has superior numerical dispersion to the finite difference (FD) method, and, therefore, needs much sparser grid points than the FD method to achieve comparable accuracy. Equivalent voltage and current sources are derived, exciting the transmission line at the grid points. Equivalent circuit models are consequently derived to represent the transmission line subject to radiated electromagnetic wave noise. The FDQ-based equivalent models can be integrated into a simulator like SPICE. Index Terms—Electromagnetic (EM) wave illuminating, external field coupling, finite difference quadrature (FDQ) method, interconnect modeling, transient simulation, transmission lines (TL). I