Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 93-99). Available also in a digital version from Dissertation Abstracts.

The purpose of this dissertation is to provide a theoretical model to design RF coils using multiconductor transmission line (MTL) structures for MRI applications. In this research, an MTL structure is represented as a multiport network using its port admittance matrix. Resonant conditions and closed-form solutions for different port resonant modes are calculated by solving the eigenvalue problem of port admittance matrix using block matrix algebra. A mathematical proof to show that the solution of the characteristic equation of the port admittance matrix is equivalent to solving the source side input impedance is presented. The proof is derived by writing the transmission chain parameter matrix of an MTL structure, and mathematically manipulating the chain parameter matrix to produce a solution to the characteristic equation of the port admittance matrix. A port admittance matrix can be formulated to take one of the forms depending on the type of MTL structure: a circulant matrix, or a circulant block matrix (CB), or a block circulant circulant block matrix (BCCB). A circulant matrix can be diagonalized by a simple Fourier matrix, and a BCCB matrix can be diagonalized by using matrices formed from Kronecker products of Fourier matrices. For a CB matrix, instead of diagonalizing to compute the eigenvalues, a powerful technique called “reduced dimension method� can be used. In the reduced dimension method, the eigenvalues of a circulant block matrix are computed as a set of the eigenvalues of matrices of reduced dimension. The required reduced dimension matrices are created using a combination of the polynomial representor of a circulant matrix and a permutation matrix. A detailed mathematical formulation of the reduced dimension method is presented in this thesis. With the application of the reduced dimension method for a 2n+1 MTL structure, the computation of eigenvalues for a 4n X 4n port admittance matrix is simplified to the computation of eigenvalues of 2n matrices of size 2 X 2. In addition to reduced computations, the model also facilitates analytical formulations for coil resonant conditions. To demonstrate the effectiveness of the proposed methods (2n port model and reduced dimension method), a two-step approach was adopted. First, a standard published RF coil was analyzed using the proposed models. The obtained resonant conditions are then compared with the published values and are verified by full-wave numerical simulations. Second, two new dual tuned coils, a surface coil design using the 2n port model, and a volume coil design using the reduced dimensions method are proposed, constructed, and bench tested. Their validation was carried out by employing 3D EM simulations as well as undertaking MR imaging on clinical scanners. Imaging experiments were conducted on phantoms, and the investigations indicate that the RF coils achieve good performance characteristics and a high signal-to-noise ratio in the regions of interest.

A configuration-oriented circuit model for multiple coupled lines in an inhomogeneous medium is developed and presented in this thesis. This circuit model consists of a network of uncoupled transmission lines and is readily modeled with simulation tools like LIBRA�� and SPICE��. It provides an equivalent circuit representation which is simple and topologically meaningful as compared to the model based on modal decomposition. The configuration-oriented model is derived by decomposing the immittance matrices associated with an n coupled line 2n-port system. Time- and frequency-domain simulations of typical coupled line multiports are included to exemplify the utility of the model. The model is useful for the simulation and design of general single and multilayer coupled line components, such as filters and couplers, and for the investigation of signal integrity issues including crosstalk in interconnects associated with high speed digital and mixed signal electronic modules and packages. It is shown that multiconductor lossless structures in an inhomogeneous medium can be characterized by multiport time-domain reflection (TDR) measurements. A synthesis technique of an equivalent lossless (non-dispersive) uniform multiconductor n coupled lines (UMCL) 2n-port system from the measured discrete time-domain reflection response is presented. This procedure is based on the decomposition of the characteristic immittance matrices of the UMCL in terms of partial mode immittance matrices. The decomposition scheme leads to the discrete transition matrix function of a UMCL 2n-port system. This in turn establishes a relationship between the normal-mode parameters of the UMCL and the measured impulse reflection and transmission response. Equivalence between the synthesis procedure presented in this thesis and the solution of a special form of an algebraic Riccati matrix equation whose solution can lead to the normal-mode parameters and a real termination network is illustrated. In order to demonstrate the procedure, a typical microstrip structure with three lines is synthesized from the time-domain reflection (TDR) data. In order to compliment known field theoretic techniques for characterization of multiconductor structures a network analog method is employed to solve the magnetic vector potential equation to characterize multilayer Metal-Insulator-Semiconductor (MIS) transmission line structures. This approach leads to the frequency dependent distributed inductance and the resistance matrices of a multilayer MIS transmission line structure. It is shown that the frequency dependent transmission line parameters can be modeled by an efficient quasi-static formulation for all propagating modes including the slow-wave and skin-effect modes. To demonstrate the proposed approach for single and multilevel structures, the frequency dependent distributed inductance and resistance matrices corresponding to the propagating modes classified as the slow-wave and skin-effect modes are calculated and validated by comparison with full-wave solutions. / Graduation date: 1999

This thesis focuses on the analytical modeling of periodic structures which contain bands with multiple modes of propagation. The work is motivated by several structures which exhibit dual-mode propagation bands. Initially, transmission line models are focused on. Transmission line models of periodic structures have been used extensively in a wide variety of applications due to their simplicity and the ease with which one can physically interpret the resulting wave propagation effects. These models, however, are fundamentally limited, as they are only capable of capturing a single mode of propagation. In this work multiconductor transmission line theory, which is the multi-mode generalization of transmission line theory, is shown to be an effective and accurate technique for the analytical modeling of periodically loaded structures which support multiple modes of propagation. Many results from standard periodic transmission line analysis are extended and generalized in the multiconductor line analysis, providing a familiar intuitive model of the propagation phenomena. The shielded Sievenpiper structure, a periodic multilayered geometry, is analyzed in depth, and provides a canonical example of the developed analytical method. The shielded Sievenpiper structure exhibits several interesting properties which the multiconductor transmission line analysis accurately captures. It is shown that under a continuous change of geometrical parameters, the dispersion curves for the shielded structure are transformed from dual-mode to single-mode. The structure supports a stop-band characterized by complex modes, which appear as pairs of frequency varying complex conjugate propagation constants. These modes are shown to arise even though the structure is modeled as lossless. In addition to the periodic analysis, the scattering properties of finite cascades of such structures are analyzed and related to the dispersion curves generated from the periodic analysis. Excellent correspondence with full wave finite element method simulations is demonstrated. In conclusion, a physical application is presented: a compact unidirectional ring-slot antenna utilizing the shielded Sievenpiper structure is constructed and tested.

This thesis focuses on the analytical modeling of periodic structures which contain bands with multiple modes of propagation. The work is motivated by several structures which exhibit dual-mode propagation bands. Initially, transmission line models are focused on. Transmission line models of periodic structures have been used extensively in a wide variety of applications due to their simplicity and the ease with which one can physically interpret the resulting wave propagation effects. These models, however, are fundamentally limited, as they are only capable of capturing a single mode of propagation. In this work multiconductor transmission line theory, which is the multi-mode generalization of transmission line theory, is shown to be an effective and accurate technique for the analytical modeling of periodically loaded structures which support multiple modes of propagation. Many results from standard periodic transmission line analysis are extended and generalized in the multiconductor line analysis, providing a familiar intuitive model of the propagation phenomena. The shielded Sievenpiper structure, a periodic multilayered geometry, is analyzed in depth, and provides a canonical example of the developed analytical method. The shielded Sievenpiper structure exhibits several interesting properties which the multiconductor transmission line analysis accurately captures. It is shown that under a continuous change of geometrical parameters, the dispersion curves for the shielded structure are transformed from dual-mode to single-mode. The structure supports a stop-band characterized by complex modes, which appear as pairs of frequency varying complex conjugate propagation constants. These modes are shown to arise even though the structure is modeled as lossless. In addition to the periodic analysis, the scattering properties of finite cascades of such structures are analyzed and related to the dispersion curves generated from the periodic analysis. Excellent correspondence with full wave finite element method simulations is demonstrated. In conclusion, a physical application is presented: a compact unidirectional ring-slot antenna utilizing the shielded Sievenpiper structure is constructed and tested.

This thesis presents a method to obtain the per-unit-length electrical parameters of a given overhead transmission line or underground cable in an unbounded space considering the effect of the ground. This is achieved using a two-dimensional conformal mapping technique, which consists of a modified bilinear transformation to map a semi-open half-space problem into a unit circle. The Helmholtz equations describing the quasi-stationary approximation for the electromagnetic field behaviour are solved using finite element method, with the aid of commonly used commercial software program, COMSOL Multiphysics. The per-unit-length resistance, inductance and capacitance are calculated using the proposed mapping method, the truncation of the original space method and then compared with the analytical solution obtained from Carson's approximation for the overhead lines and Wedepohl's formulation for the underground cables. / October 2016

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Thesis (M.App.Sc.) - Carleton University, 2005. / Includes bibliographical references (p. 115-121). Also available in electronic format on the Internet.

Thesis (M.App.Sc.) - Carleton University, 2006. / Includes bibliographical references (p. 103-107). Also available in electronic format on the Internet.

Ces travaux de thèse portent sur la détection de défauts non francs dans des structures filaires particulières : les lignes de transmission a multiconducteurs (MTL), aussi appelées torons de câbles. Couramment employées pour le diagnostic de réseaux filaires, les méthodes par réflectométrie ne sont, pour l'heure, pas suffisamment performantes pour détecter de tels défauts. Par ailleurs, elles n'ont, en général, été étudiées et développées que pour des lignes simples, ou les phénomènes de couplages électromagnétiques entre les conducteurs (diaphonie) ne sont pas présents. Ces derniers sont cependant porteurs d'information supplémentaire sur l'état du câble. Les utiliser permettrait d'accroître la sensibilité de détection aux défauts. L'objectif est de proposer une nouvelle méthode de réflectométrie, tirant profit des signaux de diaphonie pour détecter les défauts non francs. Une telle méthode présente également l'avantage d'être adaptée aux structures en toron. Après avoir étudié l'impact d'un défaut non franc sur les paramètres caractéristiques d'une MTL et sur les signaux de diaphonie, une méthode, la "Cluster Time Frequency Domain Reflectometry ", a pu être proposée. Il s'agit d'un procédé en trois étapes. Des mesures par réflectométrie temporelle sont tout d'abord réalisées à l'entrée de la ligne à diagnostiquer. Tous les signaux présents, y compris ceux de diaphonie, sont enregistrés. Un traitement temps-fréquence leur est ensuite appliqué afin d'amplifier la présence d'éventuels défauts. Enfin, un algorithme de clustering, spécifiquement développé pour le diagnostic filaire, est utilisé de manière a bénéficier de l'ensemble de l'information disponible / Research works presented in this thesis rely on detecting soft faults (incipient faults) in specic wiring structures : multiconductor transmission lines (MTL), also known as bundles of wires. Reflectometry methods, often used for the diagnosis of wiring networks, aren't for now efficient enough at detecting such defects. Besides, they have been designed for single lines only, where electromagnetic coupling between conductors (crosstalk) is not to be considered. However such phenomenon can provide more information about the state of the cable. Using this information could enable us to detect soft faults more easily. Our goal is to propose a new reflectometry method, which takes advantage of crosstalk signals in order to detect incipient faults. Such a tool has also the advantage of being well-adapted to bundles of cables. Thanks to the preliminary study of the impact of soft faults on the characteristic parameters of a MTL and on crosstalk signals, a method called "Cluster Time Frequency Domain Reflectometry ", has been proposed. It is a three step process. Firts temporal reflectometry measurements are made at the beginning of the line under test. All the available signals, even crosstalk ones, are recorded. A time-frequency process is then applied on them, in order to amplify the presence of defects. Finally, a clustering algorithm, that has been specically developed for wiring diagnosis, is used to benefit from the whole available information