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Rigorous analysis of TM modes in arbitrary shaped closed and slotted waveguides

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posted on 28.03.2022, 11:33 by Turker Topal
In this thesis, we use Method of Regularization (MoR) to analyse TM modes of closed and slotted waveguides. Cross section of waveguides can be of arbitrary shape assuming that a smooth parametrization is defined. MoR provides us with tools for transforming the corresponding boundary value problems to a functional equation of the second kind. We start with the standard integral representation of the total or scattered field as appropriate in terms of surface quantities. Using Green’s function approach, we obtain a first kind Fredholm integral equation, and convert it into a second kind Fredholm integral equation. The resulting system of infinite linear algebraic equations can be solved effectively using the truncation method, which produces algebraic systems with uniformly bounded condition numbers, when system size tends to infinity. This allows us to predefine truncation number to achieve desired accuracy. Using the connection between cut-off frequencies and normal eigenmodes of a hollow waveguide and the corresponding resonance properties of two-dimensional resonator, we adopt MoR to waveguide problems. We investigate physical features of hollow waveguides of various shapes. Finally, we provide numerical results which show the impact of slot width and wall thickness as well as the qualitative features of the method.


Table of Contents

1. Introduction -- 2. State of the art in waveguide problems -- 3. Method of regularisation - theoretical background -- 4. Numerical investigation of the spectrum for closed and slotted waveguides -- 5. Conclusions -- A. Numerical results -- Bibliography.


Bibliography: pages 63-65 Empirical thesis.

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


MRes, Macquarie University, Faculty of Science and Engineering, Department of Mathematics

Department, Centre or School

Department of Mathematics

Year of Award


Principal Supervisor

Elena Vynogradova


Copyright Turker Topal 2017. Copyright disclaimer: http://mq.edu.au/library/copyright




1 online resource (ix, 65 pages) colour illustrations

Former Identifiers

mq:70274 http://hdl.handle.net/1959.14/1261984