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Numerical techniques for solving differential equations have been vigorously studied, and various techniques have been proposed and investigated for particular problems. Maxwell's equations are the system of partial differential equations which describe the behavior of electromagnetic fields. The methods for solving the equations should be properly chosen depending on the purpose of the analysis and the available computational resources. In this thesis, we propose a time-domain electromagnetic field modeling technique based on Haar wavelets. The multiresolution nature of the wavelets was used in the formulation, and a time stepping algorithm that is similar to the conventional finite-difference time-domain (FDTD) method was obtained. The proposed technique effectively models realistic structures by virtue of the multi-resolution property; the computational time is reduced approximately by half compared to the conventional FDTD method. In order to provide a comprehensive understanding of the proposed method, algorithms for one, two and three space dimensions were formulated, validated in terms of the accuracy, and actually applied to various realistic problems. Various boundary conditions have been formulated and implemented, and in addition, the following applications are addressed: S-parameter extraction for two-dimensional waveguide problems, combined with field singularity correction at metal edges and corners, resonant cavity analyses for validation purposes, and analyses of microwave passive devices with open boundaries such as microstrip low-pass filters and spiral inductors. An algorithm that needs half the computational effort is equivalent to hardware that is twice as fast. The purpose of this thesis is to make a contribution to the improvement of computational speed in electromagnetic time domain solutions. / Graduate

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Understanding the trajectories of particulate solids inside a flow-through reactor, such as the riser of a recirculating fluidized bed, is a basic requisite to accurately modelling the reactor. However, these trajectories, which are complicated by gross internal recirculation, are not readily measurable. Conventional means of measuring the residence time distribution can be applied to closed boundaries, such as the exit of the riser. Doing so, however, does not directly provide the details of the trajectories within the riser. In order to determine these trajectories, meaningful measurements must be made at the open boundaries between the adjacent axial regions which, in total, make up the riser. Transient tracer concentration measurements at open boundaries are ambiguous because, as tracer material recirculates past the sensor, its concentration is repeatedly recorded, with no distinction as to which region (above or below the boundary) it has just resided in. A method designed to eliminate this ambiguity at open boundaries is reported in this thesis. By repeatedly introducing single tracer particles into the riser, and measuring the time of passage through each axial region, the residence time distributions for each region can be obtained from the frequency density of these times. The crux of this approach is being able to sense individual tracer particles. The major thrust of this investigation has been to find a practical means to this end. The final sensor considered in this investigation is based on electromagnetic induction: a magnetic primary field induces an eddy current in a conductive tracer particle, and the resulting secondary field is sensed, indicating the presence of the tracer particle in the sensing volume. Noise, resulting from direct coupling between transmitter and receiver coils, electrostatics, and vibrations, determines the sensitivity of the device. The final prototype sensor is limited in sensitivity to relatively large tracer particles, and it is incapable of measuring tracer velocity. Nevertheless, the trajectory of large particles is of practical significance for circulating fluidized beds. Limited tests were conducted in a 0.15 m ID x 9.14 m tall acrylic riser where the tracer particles were injected opposite the solids re-entry point, and were sensed by a single sensor located at an open boundary 7.5 m downstream. At each of the two superficial gas velocities considered, and above a threshold solids flux, the time-of-flight frequency density between the injector and the sensor for these large tracer particles does not change with increasing flux of the fine solids. This result is incongruous with obvious changes in the macro-flow structure occurring in the riser. Recommended changes in the sensor would allow measurement of the direction and speed of the tracer, as it passes by the sensor, as well as potentially reducing noise. With these improvements, it would be useful to install multiple sensors along the full length of the riser. The information obtainable from such a configuration would greatly enhance understanding of the detailed trajectories within the riser. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

This work is a study of the scattering of electromagnetic waves from random media of discrete scatterers. The object is primarily the investigation of existing general discrete-scatterer theories and the development of more accurate ones, the technique of Monte Carlo computer simulation being employed to provide "exact" experimental results for comparison with theoretical data. A one-dimensional model of randomly-positioned planar scatterers is used as a tool in the investigation and as a means of providing insight into the physical and statistical characteristics of discrete-scatterer media. The limitations of the one-dimensional forms of Twersky's theories for the coherent field are illustrated by a presentation of results for a wide range of scattering parameters, and requirements necessary for the approximate validity of these theories are given. Accurate series expressions for several average field functions of interest in the problem of plane-wave scattering from distributions of uniformly-random planar scatterers are presented and verified from simulation results. The asymptotic scattering behavior for a low average density of scatterers is emphasized; a modification to the one-dimensional form of Twersky's free-space theory for the coherent transmitted field to give exact asymptotic behavior is shown to be a considerable improvement for higher average densities also. The relation of the one-dimensional model theory and results to more complex three-dimensional models is discussed where possible. Simulation methods for the generation of a non-uniform distribution of planar-scatterer configurations weighted towards "periodicity" are presented. Based on the scattering results obtained, criteria for the assumption of a uniform distribution are given. The physical conditions necessary for the approximate validity of the bivariate Gaussian distribution in describing the total field statistics of the one-dimensional model are discussed and quantitative results based on the third and fourth field moments given. Also presented is a new physical model of a random medium of discrete spherical scatterers for use in controlled laboratory experiments at millimeter-wave frequencies. The main feature of this model is that the scatterer statistics are directly controlled by an application of the Monte Carlo method. The results of an experimental investigation into the suitability of the model are given. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The analyses presented in this thesis are based on a consideration of induction effects below transmission lines and the hazards as presented to the public. The rapid increase of transmission voltages has caused a great deal of concern among utilities about these hazards. The induction effects are a function of line height and at present there is conflict concerning-these dimensions. Primarily, this thesis is concerned with the establishment of the minimum line-to-ground clearances of EHV ac and dc transmission lines. These clearances are established in terms of the electric field under the line based on the "electric field recognition level". Equations are derived for the electric field, and potential at any point below the line in Chapter 2. These equations are then used in Chapter 3 to show the effect of conductor spacing, height and size on the field. Also, the effect of sky wires and bundle conductors is noted. Chapter 4 derives an allowable value of electric field which is used in Chapter 5 to derive the required heights. Chapter 6 considers a reduction of these clearances or induction effects using ground wires below the line conductors for shielding purposes. Experimental readings are obtained in Chapter 7 to verify the equations derived in Chapter 2 and the effects of sky wires and bundle conductors on the electric field below the line. Chapter 8 establishes right-of-way widths based on induction effects. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Most solutions for electromagnetic wave diffraction by obstacles and apertures assume plane wave incidence or omnidirectional local sources. Solutions to diffraction problems for local directive sources are needed. The complex source point representation of directive beams together with uniform solutions to high frequency diffraction problems is a powerful combination for this. Here the method is applied to beam diffraction by planar structures with edges, such as the half-plane, slit, strip, wedge and circular aperture. Previously used restrictions to very narrow beams and paraxial regions, are removed here and the range of validity increased. Also it is shown that the complex source point method can give a better approximation to broad antenna beams than the Gaussian function. The solution derived for the half-plane problem is uniform, accurate and valid for all beam orientations. This solution can be used as a reference solution for other uniform or asymptotic solutions and is used to solve for the wide slit and complementary strip problems. Uniform solutions for omidirectional sources are developed and extended analytically to become solutions for directive beams. The uniform theory of diffraction is used to obtain uniform solutions where there are no simple exact solutions, such as for the wedge and circular aperture. Otherwise rigorously correct solutions at high frequencies for singly diffracted far fields are used, such as for the half-plane, slit and strip. The geometrical theory of diffraction and equivalent line currents are used to include interaction between edges. Extensive numerical results including the limiting cases; e.g. plane wave incidence, line and point sources are given. These solutions are compared with previous solutions, wherever possible and good agreement is evident Beam diffraction by a wedge with its edge on the beam axis is analysed. This solution completes a previous asymptotic solution which is infinite on the shadow boundaries and inaccurate in the transition regions. Finally, the diffraction by a circular aperture illuminated by normally incident acoustic beam, is derived and the singularity along the axial caustic is removed using Bessel functions and a closed form expression for multiple diffraction is derived. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

A detailed study of electromagnetic induction in a sequence of conductive layers has been completed for the case when the inducing fields are generated by an alternating current in a horizontal loop. The study was undertaken with a view to the development of a computer program to perform automatic inversion of horizontal loop electromagnetic (HLEM) frequency soundings taken over horizontally stratified ground. The program constitutes a new implementation of the general approach of Backus and Gilbert (1967, 1968, 1970). By means of a linearised iterative scheme, it constructs layered conductivities which satisfy a given set of observations to an accuracy consistent with the observational uncertainties. Subsequently, the non-uniqueness admitted by the limited amount of data can be appraised by computing averages of the original constructed model and comparing them with averages corresponding to other dissimilar models which also satisfy the data. In examples the Backus-Gilbert averages faithfully reflect the character of the "true" conductivity in regions of high conductivity, but they are of limited value in delineating resistive zones. The program has been applied successfully to the inversion of real data from Grass Valley, Nevada. A uniqueness theorem is presented for inversion of HLEM frequency soundings. It has been proved that an unlimited quantity of perfectly accurate HLEM frequency soundings (at a fixed receiver location) suffices to completely determine the conductivity as a function of depth. This result, which is believed to be new, enhances the credibility of conclusions based on inversion of HLEM soundings. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Ocean bottom magnetometer data from a site on the Pacific plate above 3 my old lithosphere are inverted for electrical conductivity as a function of depth. Magnetotelluric impedances are calculated by the vertical gradient method using the fields at the OBM in conjuction with those measured at the Victoria Geomagnetic Observatory. The approximations involved are examined. Winnowing criteria are proposed which isolate those impedances compatible with all the model and source field assumptions. These then define the best possible data set. A number of inversion algorithms are applied to the data and a wide range of acceptable conductivity profiles are constructed. All profiles exhibit a uniform, relatively high conductivity of about 0.2 S/m from the surface down to a depth of 100 km. Exact and approximate bounds on the conductance are calculated in an effort to quantify the non-uniqueness of the diverse conductivity models. Profiles with a minimum of structure are used to calculate the partial melting and temperature variations beneath the 3 my old site. All results are compared with three other magnetotelluric analyses above 1, 30 and 72 my old lithosphere. The 3 my old datum is discordant and does not fit the trends interpreted from the other three studies. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

The advent of the integration of discrete passive components is a direct result of the drive towards the minimisation of power electronic converters and filters. To this end Integrated Power Passive Modules (IPPMs) have been utilised in the past. The IPPMs discussed in this dissertation refer to structures consisting of dielectric layers sandwiched between layers of conductive material. The use of these types of structures in various applications has been well documented. However, the applications have been single-phase in nature and the exact configuration of the IPPMs has been largely dependent on the designers’ past experience with the modules. The development of a synthesis procedure to identify the required configuration for any particular application would be of great benefit to designers. The foundation of such a synthesis procedure was laid through an exhaustive search of all possible configurations that can be realised with a three conductive layer IPPM. From this exhaustive search a number of general trends, between the configurations and their associated frequency response, were observed. Furthermore, a number of principles underlying the functionality of the configurations were highlighted during the course of the exhaustive search. The validity of some of these results was experimentally investigated through the design and implementation of an integrated EMI filter. The EMI filter considered in this study differed from integrated EMI filters, previously reported on, through the fact that the filter considered herein was to be implemented in a three-phase application. To this end a set of configurations that realise low pass filters were identified from the results of the exhaustive search. The application of these configurations was expanded from single-phase to three-phase by mapping the configurations onto a building block component used to realise the three-phase application. Simulations of these three-phase filters were used to analyse the filter performance. From this analysis a subset of configurations were identified as displaying the best performance characteristics. The configurations within this subset were further analysed using the results of the exhaustive search. In so doing two configurations were isolated for use in a practical realisation of the three-phase filters. The physical design and construction of the integrated three-phase filters, as well as the test bench, was considered. The performance of the filters was investigated through comparative measurements of common mode and differential mode currents, in the test bench, in the presence and absence of the filters. From this investigation significant reduction in the conducted EMI noise was seen through the introduction of the filters into the system. / Dr. I. W. Hofsajer