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

• Published in: IEEE transactions on very large scale integration (VLSI) systems Vol. 15; no. 12; pp. 1289 - 1302
• Main Authors: Qinwei Xu, Mazumder, P.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.12.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Design. Technologies. Operation analysis. Testing; Distributed parameter circuits; Electromagnetic (EM) wave illuminating; Electromagnetic coupling; Electromagnetic interference; Electromagnetic modeling; Electromagnetic radiation; Electromagnetic scattering; Electromagnetic waves; Electronic equipment and fabrication. Passive components, printed wiring boards, connectics; Electronics; Exact sciences and technology; external field coupling; Finite difference methods; finite difference quadrature (FDQ) method; Fluid dynamics; Grid computing; Integral equations; Integrated circuits; interconnect modeling; Mathematical analysis; Mathematical models; Noise; Quadratures; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Studies; transient simulation; Transmission lines; transmission lines (TL); Very large scale integration; interconnect modeling; finite difference quadrature (FDQ) method; external field coupling; transient simulation; transmission lines (TL); Electromagnetic (EM) wave illuminating; Current source; External field; Equivalent current; Noise shaping; Modeling; Electromagnetic wave; Electromagnetic noise; Electromagnetic coupling; Wave coupling; Voltage source; Transmission line; Interconnection; Integrated circuit; Equivalent circuit; SPICE; Simulator; Finite difference method
• ISSN: 1063-8210; 1557-9999
• DOI: 10.1109/TVLSI.2007.904105

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.