Numerical and analytical approaches to electromagnetic modeling and simulation

Multiwavelets based moment method (MBMM) exhibits a very attractive performance in 2D EM simulation problems. The first part of this thesis extends such a method to the scattering problems of arbitrary 3D objects with smooth surface. First, the surface of an arbitrary object is divided into parallel patch cells which are mapped onto reference cells. Then the tensor form of multiscalets are employed to form the basis functions to expand the unknown surface current density. By using the discrete Sobolev inner product to test the integral equations, the MBMM creates a point-matching-like process, in which the derivative of the unknown is also tracked to assure the accuracy and fast convergence. Because of their interpolation properties on the function and derivative, the multiscalets represent the unknown functions in the EM integral equations in an optimal manner, leading to a coarser discretization and fast convergence of the solution in.;Complex permittivity of the substrate is an essential parameter in the design of microwave circuits, high speed digital circuits, multichip modules (MCMs), packaging, etc. The most widely used measurement techniques in the microwave region are: cavity resonators, transmission line, free space, open-ended coaxial probe. In the second part, a novel simple method for determination of the permittivity and loss tangent of low loss dielectrics is presented, using printed circuit board (PCB) circular disks. Because it utilizes multiple resonances, this method is in high precision and broadband (500 MHz - 12 GHz) based on closed form analytic expressions of cylindrical symmetry, taking into account of disk rim fringing fields and radiation loss. Numerical results are conducted for popular PCB material, FR4, and the self consistent Kramers-Kronig relation is verified.;Via structures are predominantly used in multilayered packages to connect traces residing in different layers. Higher density, faster operating speed and complex routing complexity have introduced unwanted coupling among vias in the naturally formed parallel plate waveguide environment. Full wave characterizations of vias is absolutely necessary. In the third part, a simplified full-wave modeling of massive number of vias with or without circular pads is formulated based on equivalent magnetic frill array and Galerkin procedure. The proposed method employs equivalent principle, image theory and Fourier transformation to simplify the problem and takes advantage of circular cylindrical shapes with Bessel's functions and addition theorem to solve 2D EFIE equations without resorting numerical discretization. As a result, it is a fast and accurate algorithm. Numerical examples demonstrate good agreement between the analytical results and that of commercial software HFSS.