Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Electrical and Computer Engineering

Supervisor

Dr. Anestis Dounavis

Abstract

As operating frequencies increase, full wave numerical techniques such as the finite element method (FEM) become necessary for the analysis of high-frequency and microwave circuit structures. However, the FEM formulation of microwave circuits often results in very large systems of equations which are computationally expensive to solve. The objective of this thesis is to develop new parameterized model order eduction (MOR) techniques to minimize the computational complexity of microwave circuits. MOR techniques provide a mechanism to generate reduced order models from the detailed description of the original FEM formulation. The following contributions are made in this thesis:

1. The first project deals with developing a parameterized model order reduction to solve eigenvalue equations of electromagnetic structures that are discretized by using FEM. The proposed algorithm uses a multidimensional subspace method based on modified perturbation theory and singular-value decomposition to perform reduction directly on the finite element eigenvalue equations. This procedure generates parametric reduced order models that are valid over the desired parameter range without the need to redo the reduction when design parameters are changed. This provides significant computational savings when compared to previous eigenvalue MOR techniques, since a new reduced order model is not required each time a design parameter is changed.

2. Implicit moment match techniques such as the Arnoldi algorithm are often used to improve the accuracy of the reduced order model. However, the traditional Arnoldi algorithm is only applicable to first order linear systems and can not directly include arbitrary functions of frequency due to material and boundary conditions. In this work, an efficient algorithm to create parametric reduced order models of distributed electromagnetic systems that have arbitrary functions of frequency (due to material properties, boundary conditions, and delay elements) and design parameters. The proposed method is based on a multi-order Arnoldi algorithm used to implicitly calculate the moments with respect to frequency and design parameters, as well as the cross-moments. This procedure generates parametric reduced order models that are valid over the desired parameter range without the need to redo the reduction when design parameters are changed and provides more accurate reduced order systems when compared with traditional approaches such as Modified Gram Schmidt.

3. This project develops an efficient technique to calculate sensitivities of microwave structures with respect to network design parameters. The proposed algorithm uses a parametric reduced order model to solve the original network and an adjoint variable method to calculate sensitivities. Important features of the proposed method are 1) that the solution of the original network as well as sensitivities with respect to any parameter is obtained from the solution of the reduced order model, and 2) a new reduced order model is not required each time design parameters are varied.

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