<p> This thesis addresses recent trends and developments of the adjoint-variable method (AVM) for microwave structures with the time-domain transmission-line modeling (TD-TLM) method. </p> <p> Design sensitivity analysis of high-frequency (HF) structures is concerned with estimating the sensitivity of the response with respect to the design parameters. This information is essential at different stages of the design cycle such as the optimization, tolerance analysis, and yield analysis. </p> <p> Traditional approaches of sensitivity calculations involve estimating the sensitivities thought fmite-difference approximations. They suffer from formidable simulation time, as the full-wave analysis of practical HF structure requires extensive computational time. For a structure with N design parameters, at least N+l system analyses are required to extract the design response and its sensitivities. The adjoint variable method, on the other hand, supplies the sensitivity information in a very efficient way. Using at most two system analysis, the algorithm provides the design responses and its sensitivities, regardless of the number of the design parameters. </p> <p> In this thesis two contributions have been achieved which aims at enhancing the efficiency of the TLM-A VM framework. The first contribution is a reformulation of the AVM. This reformulation results in casting both the original and the adjoint systems in mathematically identical forms. It is shown that both systems can thus be modeled using a single TLM simulator with the only difference in the excitation. The second contribution focuses on generalizing the A VM algorithm by employing it for more advanced TLM nodes. The compatibility of the symmetrical condensed node (SCN) with the AVM algorithm has been verified in previous work for a general 3-D problem. Here, this is extended to include the hybrid symmetrical condensed node (HSCN), which is more efficient in terms of memory saving and simulation time. The new approaches are all illustrated through sensitivity estimation of different waveguide structures. </p> / Thesis / Master of Applied Science (MASc)

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This thesis covers recent advances in the adjoint variable method for the sensitivity estimations through time-domain electromagnetic simulations. It considers both frequency-independent and frequency-dependent response functions, and at the same time, provides a novel adjoint treatment for addressing dispersive sensitivity parameters in the material constitutive relation. With this proposed adjoint technique, response sensitivities with respect to all N sensitivity parameters can be computed through at most one extra simulations regardless of the value of N. This thesis also extends the existing adjoint technique to estimate all N^2 second-order sensitivity entries in the response Hessian matrix through N additional simulations. All adjoint sensitivity techniques presented in this thesis are numerically validated through various practical examples. Comparison shows that our produced adjoint results agree with those produced through central finite-difference approximations or through exact analytical approaches. / Dissertation / Doctor of Engineering (DEng)

We propose an efficient wideband theory for adjoint variable sensitivity analysis of problems with general anisotropic materials. The method is formulated based on the transmission line numerical modeling technique. The anisotropic material properties of potential interest are the full tensors of permittivity, permeability, electrical conductivity, magnetic resistivity, magnetoelectric coupling, and electromagnetic coupling. The tensors may contain non-diagonal elements. Our method estimates the gradients of the desired response with respect to all designable parameters using at most one extra simulation, regardless of their number. In contrast, in the conventional sensitivity analysis method using central finite differences, the number of the required simulations scales linearly with the number of designable parameters. The theory has been implemented for sensitivity analysis of the two and three-dimensional structures. The available adjoint variable method (AVM) sensitivities enable the optimization-based design of anisotropic and dispersive anisotropic structures. We apply our AVM technique to optimization-based wideband invisibility cloak design of arbitrary-shape objects. Our method optimizes the voxel-by-voxel constitutive parameters of an anisotropic cloak. This results in a large number of optimizable parameters. The associated sensitivities of a wideband cloaking objective function are efficiently estimated using our anisotropic adjoint variable method technique. A gradient-based optimization algorithm utilizes the available sensitivity information to iteratively minimize the visibility objective function and to determine the constitutive parameters of the optimal cloak. / Thesis / Doctor of Philosophy (PhD)

High-accuracy electromagnetic design and analysis of electric machines is enhanced by the use of various numerical methods. These methods solve Maxwell’s equations to determine the distribution of the electric and magnetic fields throughout the considered machine structure. Due to the complicated architectures of the machines and the nonlinearity of the utilized magnetic materials, it is a very challenging task to obtain an analytical solution and, in most cases, only a numerical solution is possible. The finite element method (FEM) is one of the standard numerical methods for electromagnetic field analysis. The considered machine domain is divided into finite elements to which the field equations are applied. FEM solvers are utilized to develop optimization procedures to assist in achieving a design that meets the required specifications without violating the design constraints. The design process of electric machines involves adjusting the machine parameters. This is usually done through experience, intuition, and heuristic approaches using FEM software which gives results for various parameter changes. There is no guarantee that the achieved design is the optimal one. An alternative approach to the design of electric machines exploits robust gradient-based optimization algorithms that are guaranteed to converge to a locally-optimal model. The gradient-based approaches utilize the sensitivities of the performance characteristics with respect to the design parameters. These sensitivities are classically calculated using finite difference approximations which require repeated simulations with perturbed parameter values. The cost of evaluating these sensitivities can be significant for a slow finite element simulation or when the number of parameters is large. The adjoint variable method (AVM) offers an alternative approach for efficiently estimating response sensitivities. Using at most one extra not-iterative simulation, the sensitivities of the response to all parameters are estimated. Here, a MATLAB tool has been developed to automate the design process of switched reluctance motors (SRMs). The tool extracts the mesh data of an initial motor model from a commercial FEM software, JMAG. It then solves for magnetic vector potential throughout the considered SRM domain using FEM taking into consideration the nonlinearity of the magnetic material and the motor dynamic performance. The tool calculates various electromagnetic quantities such as electromagnetic torque, torque ripple, phase flux linkage, x and y components of flux density, air-region stored magnetic energy, phase voltage, and phase dynamic currents. The tool uses a structural mapping technique to parametrize various design parameters of SRMs. These parameters are back iron thickness, teeth height, pole arc angle, and pole taper angle of both stator and rotor. Moreover, it calculates the sensitivities of various electromagnetic quantities with respect to all these geometric design parameters in addition to the number of turn per phase using the AVM method. The tool applies interior point optimization algorithm to simultaneously optimize the motor geometry, number of turns per phase, and the drive-circuit control parameters (reference current, and turn-on and turn-off angles) to increase the motor average dynamic torque. It also applies the ON/OFF topology optimization algorithm to optimize the geometries of the stator teeth for proper distribution of the magnetic material to reduce the RMS torque ripple. A 6/14 SRM has been automatically designed using the developed MATLAB tool to achieve the same performance specifications as 6110E Evergreen surface-mounted PM brushless DC motor which is commercially available for an HVAC system. / Thesis / Doctor of Philosophy (PhD)

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<p>The thesis intends to explain in full detail the developed techniques and approaches for the modeling, design, and sensitivity analysis of nano-plasmoic structures. However, some examples are included for audiences of general microwave background. Although the thesis is mainly focused on simulation-based techniques, analytical and convex optimization approaches are also demonstrated. The thesis is organized into two parts. Part 1 includes Chapters 2-4, which cover the simulation-based modeling and sensitivity analysis approaches and their applications. Part 2 includes Chapters 5 and 6, which cover the analytical optimization approaches.</p> / <p>We propose novel techniques for modeling, adjoint sensitivity analysis, and optimization of photonic and nano-plasmonic devices. The scope of our work is generalized to cover microwave, terahertz and optical regimes. It contains original approaches developed for different categories of materials including dispersive and plasmonic materials. Artificial materials (metamaterials) are also investigated and modeled. The modeling technique exploits the time-domain transmission line modeling (TD-TLM) technique. Generalized adjoint variable method (AVM) techniques are developed for sensitivity analysis of the modeled devices. Although TLM-based, they can be generalized to other time-domain modeling techniques like finite difference time-domain method (FDTD) and time-domain finite element method (FEM).</p> <p>We propose to extend the application of TLM-based AVM to photonic devices. We develop memory efficient approaches that overcome the limitation of excessive memory requirement in TLM-based AVM. A memory reduction of 90% can be achieved without loss of accuracy and at a more efficient calculation procedure. The developed technique is applied to slot waveguide Bragg gratings and a challenging dielectric resonator antenna problem.</p> <p>We also introduce a novel sensitivity analysis approach for materials with dispersive constitutive parameters. To our knowledge, this is the first wide-band AVM approach that takes into consideration the dependence of material properties on the frequency. The approach can be utilized for design optimization of innovative nano-plasmonic structures. The design of engineered metamaterial is systematic and efficient. Beside working with engineered new designs, dispersive AVM can be utilized in bio-imaging applications. The sensitivity of the objective function with respect to dispersive material properties enables the exploitation of parameter and gradient based optimization for imaging in the terahertz and optical regimes. Material resonance interaction can be easily investigated by the provided sensitivity information.</p> <p>In addition to the developed techniques for simulation-based optimization, several analytical optimization algorithms are proposed to foster the parameter extraction and design optimization in terahertz and optical regimes. In terahertz time-domain spectroscopy, we have developed an efficient parameter based approach that utilizes the pre-known information about the material. The algorithm allows for the estimation of the optical properties of sample materials of unknown thicknesses. The approach has been developed based on physical analytical dispersive models. It has been applied with the Debye, Lorentz, Cole-Cole, and Drude model.</p> <p>Furthermore, we propose various algorithms for design optimization of coupled resonators. The proposed algorithms are utilized to transform a highly non-linear optimization problem into a linear one. They exploit an approximate transfer function of the coupled resonators that avoids negligible multiple reflections among them. The algorithms are successful for the optimization of very large-scale coupled microcavities (150 coupled ring resonators).</p> / Doctor of Philosophy (PhD)