Today’s high-speed interconnects at the chip, package, and board levels of integration can be rigorously modeled with the boundary element method based on the surface discretization of the electric field integral equation (EFIE). The accuracy of such models critically depends on the surface impedance model, which has to accurately map the behavior of the electromagnetic field inside the wire volumes to their surfaces. This thesis proposes a surface impedance model, which casts the accurate but computationally intensive volumetric EFIE formulation to the boundary element framework. This is accomplished via approximating the volumetric current density as a product of the known exponential factor corresponding to the skin-effect behavior of the field inside the wires and the unknown surface current density on the conductor’s boundary. The reduction of the volumetric EFIE to its surface counterpart results in a physically consistent surface impedance model allowing to achieve the volumetric EFIE accuracy within the boundary element formulation. The method is initially introduced for lossy 2D interconnects and later generalized to 3D interconnects under magneto-quasistatic approximation. Finally, this work is extended to the Rao-Wilton-Glisson (RWG) method of moments (MoM) solution of the full-wave EFIE. The alternative models exhibit various limitations. For example, in the double-plane model the planar interconnect structure is replaced by two infinitely thin metal sheets at its top and bottom surfaces. This model succeeds for several practical scenarios where the conductor width is sufficiently larger than its thickness, or when the operating frequency is sufficiently low for the current distribution across the conductor cross section to be assumed uniform. The alternative”multi-sheet model” represents the interconnect by a number of infinitely thin metal sheets, which uniformly span its cross section such that the spacing between each two consecutive sheets is small compared to skin-depth. The model succeeds in accurately extracting conductor loss, however, it may require a large number of sheets, which makes the number of unknowns in MoM discretization of the same order as the number of unknowns in volumetric models.

<p>Transformation Optics is a design methodology that uses the form invariance of Maxwell's equations to distort electromagnetic fields. This distortion is imposed on a region of space by mimicking a curvilinear coordinate system with prescribed magnetoelectric material parameters. By simply specifying the correct coordinate transformation, researchers have created such exotic devices as invisibility cloaks, ``perfect'' lenses, and illusion devices.</p><p>Unfortunately, these devices typically require correspondingly exotic material parameters that do not occur in Nature. Researchers have therefore turned to complex artificial media known as metamaterials to approximate the desired responses. However, the metamaterial design process is complex, and there are limitations on the responses that they achieve.</p><p>In this dissertation, we explore both the applicability and limitations of metamaterials in Transformation Optics design. We begin in Chapter 2 by investigating the freedoms available to use in the transformation optics design process itself. We show that quasi-conformal mappings may be used to alleviate some of the complexity of material design in both two- and three-dimensional design. We then go on in Chapter 3 to apply this method to the design of a transformation-optics modified optic. We show that even a highly-approximate implementation of such a lens would retain many of the key performance feautures that we would expect from a full material prescription.</p><p>However, the approximations made in the design of our lens may not be valid in other areas of transformation optical design. For instance, the high-frequency approximations of our lens design ignore the effects of impedance mismatch, and the approximation is not valid when the material parameters vary on the order of a wavelength. Therefore, in Chapter 4 we use other freedoms available to us to design a full-parameter cloak of invisibility. By tailoring the electromagnetic environment of our cloak, we are able to achieve three distinct material responses with a singe metamaterial unit cell. We show the power of our design by experimentally demonstrating a cloak of ten wavelengths in diameter at microwave frequencies.</p><p>In addition to these specific examples, we seek a general method to simulate transformation optics devices containing metamaterial inclusions. In Chapter 5, we examine the discrete-approximation, and we apply it to the design of an electromagnetic cloak. We show that the point-dipole description of metamaterial elements allows us to correct for some aberrations that appear when the limits of homogenization are violated.</p><p>Finally, we examine so-called ``complementary metamaterials'' and their utility in transformation optics devices. Complementary metamaterials exchange the void and metallized regions of conventional metamaterial elements, and thereby offer a dual response to the electromagnetic field. This duality is attractive because it provides a straightforward method of creating broadband, highly-anisotropic magnetics. We analyze these elements and show that they may be incorporated into our discrete-dipole model. However, we show that the unique characteristics of complementary elements limit their functionality when used as effective materials.</p> / Dissertation

Today’s high-speed interconnects at the chip, package, and board levels of integration can be rigorously modeled with the boundary element method based on the surface discretization of the electric field integral equation (EFIE). The accuracy of such models critically depends on the surface impedance model, which has to accurately map the behavior of the electromagnetic field inside the wire volumes to their surfaces. This thesis proposes a surface impedance model, which casts the accurate but computationally intensive volumetric EFIE formulation to the boundary element framework. This is accomplished via approximating the volumetric current density as a product of the known exponential factor corresponding to the skin-effect behavior of the field inside the wires and the unknown surface current density on the conductor’s boundary. The reduction of the volumetric EFIE to its surface counterpart results in a physically consistent surface impedance model allowing to achieve the volumetric EFIE accuracy within the boundary element formulation. The method is initially introduced for lossy 2D interconnects and later generalized to 3D interconnects under magneto-quasistatic approximation. Finally, this work is extended to the Rao-Wilton-Glisson (RWG) method of moments (MoM) solution of the full-wave EFIE. The alternative models exhibit various limitations. For example, in the double-plane model the planar interconnect structure is replaced by two infinitely thin metal sheets at its top and bottom surfaces. This model succeeds for several practical scenarios where the conductor width is sufficiently larger than its thickness, or when the operating frequency is sufficiently low for the current distribution across the conductor cross section to be assumed uniform. The alternative”multi-sheet model” represents the interconnect by a number of infinitely thin metal sheets, which uniformly span its cross section such that the spacing between each two consecutive sheets is small compared to skin-depth. The model succeeds in accurately extracting conductor loss, however, it may require a large number of sheets, which makes the number of unknowns in MoM discretization of the same order as the number of unknowns in volumetric models.

abstract: Artificial magnetic conductor (AMC) surfaces have the unique electromagnetic property that the phase of the reflected fields imitate those of perfect magnetic conductors (PMCs). When a perfect electric conductor (PEC) and an AMC surface are placed on the same plane and illuminated by a plane wave, destructive interference occurs between the fields (due to 180 degrees phase difference between the reflected fields of each surface). In this dissertation, a design procedure is introduced where a refined algorithm is developed and employed on single-band AMCs leading to a 10-dB RCS-reduction bandwidth of 80%. The AMC circuit model is judiciously utilized to reduce the substrate thickness while simultaneously increasing the bandwidth of the AMC surfaces. Furthermore, dual-band AMC surfaces are synthesized and utilized in combination with single-band AMC surfaces to extend the 10-dB RCS-reduction bandwidth from 80% to about 99%. Employing the proposed design procedure, a 99% bandwidth of 10-dB RCS-reduction bandwidth is achieved while reducing the thickness of the substrate by 20%. The second topic of this dissertation aims at analytically modeling the scattering of planar checkerboard surfaces. The high-frequency asymptotic method, Physical Optics (PO), is utilized to analyze the scattering characteristics of complex structures since the PO is computationally efficient and provides intuitive physical insight. Closed-form formulations developed using PO are used to predict the scattering patterns of checkerboard planar surfaces. The PO-based data compare well, along and near specular directions, with simulations by the full-wave Finite Element Method (FEM). Finally, a Van Atta retrodirective reflector with low backscattering is designed and developed using a microstrip antenna array. Conventional retrodirective reflectors are sensitive to interference by the fields scattered by the antenna structure. By using a virtual feeding network, structural mode scattering is identified and canceled using AMC technology. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

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The constant-phase-angle (CPA) impedance observed in electrochemical cells is often thought to be due to fractal roughness on the electrode surface. This idea was pursued by numerous theoretical and experimental studies in the last decade but there is no consensus on the quantitative relationship between the roughness and the impedance. In this study, we consider the partial differential equations that govern the electrostatic potential and the concentrations of anions and cations between two blocking electrodes which have no chemical reactions. We assume that diffusion and conduction are the only transport mechanisms and the Poisson-Boltzmann equation is obeyed. These equations are linearized and solved analytically in one dimension and numerically in two dimensions. For the latter, we used electrodes shaped like Koch curves and saw-tooth curves. A special grid was generated by conformal mapping to fit these boundaries with singularities and the equations are solved by finite-difference method on this grid. The numerical results are compared to the one-dimensional solution that give the behavior of the flat electrode. We find that the only observable effect of surface roughness is that it increases the interfacial capacitance due to the increased surface area. No evidence of the CPA impedance could be seen in our numerical data. We also studied the problem with the boundary-element method. It confirms that the numerical results are rigorously correct in the high and low frequency limit. Requiring the impedance in the intermediate frequency regime to match smoothly with these limits rule out the possibility of a CPA impedance. We suggest that the CPA impedance observed in many experiments is caused either by the adsorption and desorption of ions on the surface, or by oxidation and corrosion on the surface that changed the boundary conditions in the system.

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Arrays of edge magnetic coils and an insertable magnetic probe have been used to study the behaviour of the magnetic fluctuations in the HBTX1A Reversed Field Pinch. EDGE COILS: In the sustainment phase of the discharge poloidal arrays of edge coils show that the superficially random fluctuations can be attributed almost entirely to global modes of poloidal mode number m &ap; 0 and 1 provided account is taken of the toroidal distortion of these instabilities. A toroidal array of edge coils discloses a broad spectrum of toroidal mode numbers with a peak at |n| &ap; 10 and significant variation with time and frequency. Cross correlation between signals from poloidal and toroidal edge coil arrays establishes that the |n| &ap; 10 is m = 1, a set of helical modes resonant inside the reversal surface and also shows the presence of m = 0, |n| &ap; 0. Timescales of the measured fluctuations indicate that the instabilities are probably resistive in character and mode amplitudes are such that island overlap and magnetic field ergodization should occur. The energy confinement time due to stochastic transport, estimated directly from the measured fluctuations, is consistent with that experimentally observed. Studies of the edge magnetic fluctuations have been applied to discharges of differing conditions and in the termination and current set-up phases. Results show that, although systematic trends in the amplitude of the fluctuations occur, mode numbers and frequencies appear invarient with respect to changes in plasma current and filling pressure. At high values of [theta] an |n| &ap; 3 mode becomes of equal significance to the m = 1, |n| &ap; 10 modes. Estimates of the safety factor indicate that, although the observed timescale of this mode would label it resistive, it is not resonant. The structure of the global fluctuations in the current set-up phase appears very similar to that during sustainment, although the amplitude is higher. In the termination phase the fluctuations show several differences in the frequency and mode numbers. However, after reversal is lost, the observed frequencies correspond to resistive timescales rather than the Alfven timescale expected for ideal modes. INSERTABLE PROBE: A statistical method for determining the radial amplitude distributions of instabilities is presented. This is used to analyse probe data from which it is possible to distinguish three types of instability. At low frequencies (4 20 kHz) the dominant internal fluctuations are to be associated with the global m = 1, |n| &ap; 10 resistive modes seen by the edge coils. These modes possess a radial structure in agreement with that predicted by a linear tearing mode stability analysis of the measured equilibrium. At similar amplitudes to these modes there is also a short correlation component ([lambda]r = 3 cm) which is peaked in the central regions of the discharge. At high frequencies ( > 30 kHz) this local turbulence dominates over the global modes. Finally, at about the peak power of the dominant global modes and with a similar frequency dependence, an m = 1 mode with some ideal characteristics is observed. Stability calculations show that ideal modes that are either destabilised by a resistive shell or whose growth rates are reduced by a resistive liner would have the same radial structure and timescales as this mode.