Novel single-source surface integral equations for scattering on 2-D penetrable cylinders and current flow modeling in 2-D and 3-D conductors

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2012-06, 2012-05, 2013-01
Menshov, Anton
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Accurate modeling of current flow and network parameter extraction in 2-D and 3-D conductors has an important application in signal integrity of high-speed interconnects. In this thesis, we propose a new rigorous single-source Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) for magnetostatic analysis of 2-D transmission lines and broadband resistance and inductance extraction in 3-D interconnects. Furthermore, the novel integral equation can be used for the solution of full-wave scattering problems on penetrable 2-D cylinders of arbitrary cross-section under transverse magnetic polarization. The new integral equation is derived from the classical Volume Electric Field Integral Equation (V-EFIE) by representing the electric field inside a conductor or a scatterer as a superposition of the cylindrical waves emanating from the conductor’s surface. This converts the V-EFIE into a surface integral equation involving only a single unknown function on the surface. The novel equation features a product of integral operators mapping the field from the conductor surface to its volume and back to its surface terming the new equation the Surface-Volume-Surface EFIE. The number of unknowns in the proposed SVS-EFIE is approximately the square root of the number of degrees of freedom in the traditional V-EFIE; therefore, it allows for substantially faster network parameter extraction and solutions to 2-D scattering problems without compromising the accuracy. The validation and benchmark of the numerical implementation of the Method of Moment discretization of the novel SVS-EFIE has been done via comparisons against numerical results obtained by using alternative integral equations, data found in literature, simulation results acquired from the CAD software, and analytic formulas.
computational electromagnetics, network parameter extraction, current flow modeling, scattering problems, integral equations, resistance and inductance
A. Menshov and V. Okhmatovski, “Novel surface integral equation formulation for accurate broadband RL extraction in transmission lines of arbitrary cross-section,” Microwave Symposium Digest (MTT), 2012 IEEE MTT-S International, pp. 1-3, 17–22 June 2012.
A. Menshov and V. Okhmatovski, “Method of moment solution of Surface-Volume-Surface Electric Field Integral Equation for two-dimensional transmission lines of complex cross-sections,” Signal and Power Integrity (SPI), 2012 IEEE 16th Workshop on, pp. 31–34, 13–16 May 2012.
A. Menshov and V. Okhmatovski, “New Single-Source Surface Integral Equations for Scattering on Penetrable Cylinders and Current Flow Modeling in 2-D Conductors,” IEEE Trans. Microw. Theory Techn., Vol. 61, No. 1, pp. 341-350, Jan. 2013.