Date of Award

Spring 1972

Document Type

Dissertation

Degree Name

Doctor of Engineering Science in Electrical Engineering

Department

Electrical Engineering

First Advisor

Garland E. Ching

Second Advisor

Frederick A. Russell

Third Advisor

Gideon Peyser

Fourth Advisor

Joseph J. Padalino

Abstract

The analysis of nonuniform waveguides is formulated in terms of non-orthogonal generalized coordinates by utilizing the Hertz vector potentials and the Riemann metric tensor.

When the Hertz potential is expressible as a function of the propagation coordinate times a function of the transverse coordinates, then the nonuniform waveguide may be represented by transverse equations and a set of uncoupled nonuniform transmission lines. This decomposition facilitates studying propagation along the propagation coordinate. Sufficient conditions to achieve this decomposition are investigated. It is demonstrated that these constraints may provide guidelines for selecting a useful coordinate system to describe the nonuniform waveguide. In terms of this coordinate system the nonuniform waveguide analysis may be reduced to solving uncoupled nonuniform transmission lines if the eigenvalues of the transverse equations can be determined. This allows nonuniform transmission line theory to be applied to the study of certain nonuniform waveguides. It is also shown that when the diagonal element of the metric tensor (the element associated with the propagation coordinate) is unity, terms in the nonuniform transmission line differential equation and nonuniform transmission line parameters (such as characteristic impedance, and the per length admittance and impedance) are related to the logarithmic derivative of the transverse surface area.

For more general waveguides it is suggested that the nonuniform waveguide may sometimes be approximated by a cascade of solvable nonuniform waveguides. In this cascade approximation, the study of the junction between nonuniform waveguides is important because the nature of the coupling between the various waveguide modes lies in an understanding of the waveguide junction analysis. A junction, as defined in this dissertation, is the joining of two different coordinate systems. It may (or may not) have an associated edge in the waveguide wall. A junction analysis formulation is undertaken with approximations that allow the modal field expansions on both sides of the junction to be equated. As a convenient artifice, the modes on the load side of the junction are subdivided into a constituent that is related to the totality of E-modes on the source side of the junction and a constituent that is related to the totality of H-modes on the source side of the junction. The resulting formulation considers multimode propagation and cross-coupling between E-and H-modes. The special case in which one can choose the Hertz vector potential to be in the same direction on both sides of the junction and there is no cross-coupling between E-modes and H-modes is also considered and illustrated.

A method for obtaining the scatter parameters for the propagating modes relative to surfaces sufficiently far from the junction is also indicated.

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