Theory, Analysis, and Applications of Multidimensional, Multiconductor Transmission-Line Metamaterials

  • Author / Creator
    Barth, Stuart E
  • The past few decades have seen incredible growth in the interest of using periodic structures to improve the efficacy of microwave-frequency devices, since they provide access to dispersion-engineered phenomena such as bandgaps, group- and phase-velocity control, and advanced resonance behaviors. Metamaterials - periodic, composite structures which may support novel wave phenomena not possible with natural materials - hold the promise of enabling many next-generation electromagnetic technologies in a broad array of fields, ranging from imaging to communications to wireless power transfer, among others. One of the more promising technologies for realizing metamaterials are those created using transmission-line techniques - i.e., those designed to interface with transmission-line modes. The use of these modes is highly desirable due to their ability to be manipulated with standard electronic components, their inherent ease of analysis, and their capacity to effect strong miniaturization.

    However, there are some serious analytical challenges facing systems which support multiple, coupled, transmission-line modes - as may be found in modern devices employing metamaterials, for example antennas, filters, and sensors. Multiconductor transmission-line theory provides a framework for analyzing these systems, but the theory is incomplete in at least one important aspect: it cannot predict all of the properties of a given set of transmission-line modes. Owing to this uncertainty, the theory has found limited use in the development of more elaborate networks, such as those required to enable advanced metamaterial phenomena.

    This thesis contributes to the completion of multiconductor transmission-line theory by providing a path forward for the computation of the modal properties of coupled transmission lines. It is demonstrated that transmission-line modes are ideally normal modes, and that as such their definitions in terms of sets of voltages and currents may be expressed as entirely real quantities. It is postulated that total charge (or, in the frequency domain, current) carried by the coupled lines is basis-invariant, which allows for expressions that uniquely determine the voltages and currents of the modes to within a sign - which, in turn, allows the modal properties to be uniquely determined.

    Having a process for determining multiconductor transmission-line modal properties, the work then develops novel processes with which to analyze more elaborate, multidimensional networks of multiconductor transmission-lines loaded with discrete circuit elements. A set of network parameters - M-Parameters - is rigorously defined and used throughout the work to assist with various derivations. A process for computing the dispersive properties of generalized, multidimensional networks is proposed and validated, along with a numerically-efficient process for assembling networks from their sub-components of multiconductor transmission line and other circuit elements.

    Applications of the theory and analyses explored in this work are given in the final chapter. A novel, fully-printed, dual-band quadrature hybrid coupler is designed and experimentally validated using new understandings of bandgap phenomena. Using knowledge of the underlying transmission-line modal properties, an electromagnetic bandgap structure is designed with inherent impedance matches and mismatches, to produce a fully printed common-mode filter that does not require a defected ground plane. The proposed multidimensional analysis is used to model and investigate the canonical uniplanar compact electromagnetic bandgap structure, where its dispersive properties are predicted to a much higher degree of agreement with full-wave solvers than previously proposed models. Lastly, various multidimensional metamaterial unit cells - a two-dimensional variant of a bandgap structure previously only modelled in one dimension, a two-dimensional hexagonal structure, and an isotropic primitive cubic lattice-based unit cell -- are modelled, where it is found that various Bloch modal properties are in agreement with those predicted by full-wave solvers.

  • Subjects / Keywords
  • Graduation date
    Fall 2021
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.