3 D capacitance extraction with the method of moments by TAO LI A

In this thesis, the Method of Moments has been applied to calculate capacitance between two arbitrary 3D metal conductors or a capacitance matrix for a 3D multi-conductor system. Capacitance extraction has found extensive use for systems involving sets of long parallel transmission lines in multi-dielectric environment as well as integrated circuit package including three-dimensional conductors located on parallel planes. This paper starts by reviewing fundamental aspects of transient electro-magnetics followed by the governing differential and integral equations to motivate the application of numerical methods as Method of Moments(MoM), Finite Element Method(FEM), etc. Among these numerical tools, the surface-based integral-equation methodology MoM is ideally suited to address the problem. It leads to a well-conditioned system with reduced size, as compared to volumetric methods. In this dissertation, the MoM Surface Integral Equation (SIE)-based modeling approach is developed to realize electrostatic capacitance extraction for 3D geometry. MATLAB is employed to validate its efficiency and effectiveness along with design of a friendly GUI. As a base example, a parallel-plate capacitor is considered. We evaluate the accuracy of the method by comparison with FEM simulations as well as the corresponding quasi-analytical solution. We apply this method to the parallel-plate square capacitor and demonstrate how far could the undergraduate result ′C = A ∗ ε/d’ be from reality. For the completion of the solver, the same method is applied to the calculation of line capacitance for twoand multi-conductor 2D transmission lines.