Novel efficient integral-based techniques for characterization of planar microwave structures.

Abstract

The accurate analysis of complex planar microwave structures is not feasible without resorting to rigorous full-wave numerical techniques. Microwave CAD procedures seek numerical tools which are characterized by high degrees of computational efficiency as well as theoretical versatility. The integral equation technique is one of the most accurate and efficient approaches for the numerical modeling of electromagnetic problems. However, as the complexity of the structure under study and hence the size of the problem increase, the numerical implementation of this technique using the method of moments often leads to full matrices of prohibitive sizes, which in effect rule out the practical use of integral-based formulations for large-scale problems. To circumvent this major limitation, the present dissertation offers two different solutions. The first approach consists of the formulation of a new integral equation for planar dielectric structures. This formulation, named the integral transform technique, is based on the application of higher-order boundary conditions in an appropriate integral transform domain. By deriving integral equations of reduced dimensionality, this approach in effect reduces the dimensionality of numerical solution of the boundary value problem under study. The second approach, which is very general in nature, exploits the newly developed multiresolution expansions based on the theory of orthonormal wavelets. It has been demonstrated that using this type of expansions in the moment method treatment of integral equations leads to the generation of highly sparse moment matrices, which can be handled very efficiently using special sparse techniques such as the bi-conjugate gradient method. A variety of two- and three-dimensional planar microwave structures have been investigated through both space- and spectral-domain formulations. The results of the present research effort have opened new horizons for the application of the method of moments to large-scale electromagnetic problems.