## Contributions to guided wave theory.

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##### Date

1972##### Permanent Link

http://hdl.handle.net/10092/5708##### Thesis Discipline

Electrical Engineering##### Degree Grantor

University of Canterbury##### Degree Level

Doctoral##### Degree Name

Doctor of PhilosophyThere are many forms of structure for the guiding of electromagnetic waves. A review of these forms is given by Barlow (1964). He describes the well established parallel-wire and coaxial lines, and hollow uniform waveguides. He also considers waveguides containing solid materials and gaseous plasmas, and beam and surface waveguides. This thesis is a report on investigations into the numerical computations of the propagation characteristics of three types of guiding structures namely, the hollow waveguide, dielectric loaded waveguide and the dielectric clad azimuthal surface waveguide. The numerical solution of the hollow waveguide problem is considered in Part 1. Chapter 1 contains a comprehensive review of the methods used for the solution of the waveguide problem. This complements the only presently available review, given by Davies (1972) who compares and discusses the relative merits of some current methods (finite difference, finite element, point-matching, integral formulations and conformal transformation). Some useful criteria established by Davies in his review for the comparison of methods are used in Chap. 1 (Sec. 1.3). Chapter 2 is concerned with the numerical solution of waveguides of arbitrary cross-section by the null field method which was developed by Bates (1969b). Accurate results are obtained and it is demonstrated that for shapes possessing sharp reentrant corners, the computational accuracy is improved by explicitly satisfying the edge conditions at these corners. The detailed numerical investigation provides the supporting evidence for the computational viability of the null field method. The complete point-matching method is derived from the null field method and it provides an insight into the straightforward point-matching method (Bates 1969b). Chapter 3 considers point-matching methods of solution. Results obtained using the complete point-matching method show that accuracies of about 0.1% are obtainable for waveguide cross-sections which are convex. Less accurate results are obtained for cross-sections that are strongly reentrant. The alternative point-matching method (Bates 1969b) is also briefly considered. By comparing results for a rectangular waveguide, the alternative point-matching method is shown to be more error sensitive than the complete point matching method. When the straightforward point-matching method (Yee and Audeh 1965, 1966b; Bates 1969b) was proposed and used by Yee and Audeh for waveguide problems, doubts were raised as to its universal applicability (Harrington 1965; Bates 1967, 1969b; Millar and Bates 1970; Lewin 1970) and an example of its failure was given by Davies and Nagenthiram (1971). The detailed investigations in chapter 3 show conclusively that the straightforward point-matching method does sometimes break down and give erroneous wave functions. Chapter 3 also relates the applicability of the straightforward point-matching method to the validity or otherwise of an internal Rayleigh hypothesis which is introduced; 3 and shows that the straightforward point-matching method is unlikely to produce correct results when the waveguide cross-section has reentrant parts. An extended point-matching method is next introduced in chapter 3 and is employed to obtain accurate results for some cases for which the straightforward point-matching method fails. The success of the extended point-matching method is further illustrated by the prediction of a particular mode for the ridge waveguide (Sec. 3.5.1.4) which seems to have been missed by a previous analysis (Beaubien and Wexler 1970) using a high-order finite difference method. Part 2 is concerned with the cutoff characteristics of dielectric loaded waveguides. A specialised form of a general polarization source formulation (Bates 1970) is given in Chapter 4 and is used in Chapter 5 to obtain formulas for the cutoff characteristics of a waveguide of arbitrary cross-section loaded with a circularly cylindrical dielectric tube. The significance of the derivation given in chapter 5 is that the unknown field in the dielectric is eliminated and formulas are obtained that are line integral equations for the surface current densities on the waveguide wall alone. The computational convenience of the formulas is illustrated by results for a square waveguide loaded with a dielectric rod. Confirmatory experimental results are also reported. The numerical computation of the propagation of an azimuthal surface wave is presented in Part 3. In previous analyses of the azimuthal surface wave the attenuation is assumed to be small. This assumption is generally only satisfactory for very small curvatures. An investigation without such assumptions is given in Part 3. The general external field for any circular cylindrical guiding surface is considered in chapter 6 and universal tables for the surface impedance are given. These results are used in chapter 7 to obtain the accurate dependence upon curvature of the propagation characteristics of a dielectric clad circular cylindrical guiding surface. General conclusions are drawn in Part 4 which also gives some suggestions for further research. The results of chapters 2 and 3, for the null field method and point-matching methods, are new. The formulation and results of chapter 5 (dielectric loaded waveguides) are also new, as are the derivations and results of chapters 6 and 7 (azimuthal surface wave). All the computer programs used, except for one subroutine, were written by the author, in Fortran IV with 8-byte (64 bit) words, and run on the University of Canterbury IBM 360/44 machine which has 128 Kbytes of core memory. The Bessel functions of the first and second kind used were computed from the ascending series (Abramowitz and Stegun 1965, formulas 9.1.10 and 9.1.11). The Lommel polynomials required in Part 3 were computed using the recurrence relation given in Watson (1968, sec. 9.63) and a standard. IBM subroutine (IBM System 360, Scientific Subroutine Package 1968, p.367), modified to double precision by the author, was used to generate the modified Bessel function K1. The following papers, relevant to this thesis, have been produced: Bates, R.R.T. and Ng, F.L. (1971), “Contributions to the theory of the azimuthal surface wave", Alta Frequenza, 40, 658-666. Ng, F.L. and Bates, R.R.T. (1972), “Null field method for waveguides of arbitrary cross-section”, IEEE Trans., Microwave Theory Tech., in press. Bates, R.R.T. and Ng, F.L. (1972), “Point matching computation of transverse resonances”, submitted to: Int. Jour. for Numerical Methods in Engineering. Bates, R.R.T. and Ng, F.L. (1972), “Polarization source formulation of electromagnetism and dielectric loaded waveguides”, submitted to: Froc. IEE(London).