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- Gustafsson, Stefan
(författare)
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Electromagnetic Dispersion Modeling and Analysis for Power Cables
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis addresses electromagnetic wave propagation in power cables. It consists of five papers, where the three first papers are based on one and the same model, and the last two papers are based on a similar but slightly different model. The first model considers electromagnetic modeling in connection with basic transmission line theory with a mismatch calibration of the scattering parameters, while the second model is based on a magnetic frill generator with calibration on the input current.The two models describe the dispersion characteristics of an 82 km long High Voltage Direct Current (HVDC) power cable, and the results are validated with Time Domain Reflectometry (TDR) measurements. In both models the relevant bandwidth is 100 kHz, with the result that the fields inside the metallic layers must be calculated due to a large skin-depth. The present study is concerned with Transversal Magnetic (TM) modes of order zero. Higher order TM modes, including the Transversal Electric (TE) modes, will essentially be cut-off in this low-frequency regime.An asymptotic analysis regarding the low-frequency dispersion characteristics is provided in Paper I. Comparing the result with a numerical solution shows that the low-frequency characteristics of the power cable is complicated, and an asymptotic solution is only valid at frequencies below 1 Hz.Paper II presents a sensitivity analysis of the propagation constant. It is concluded that some of the electrical parameters of the metallic layers, and of the insulating layer, have a large impact on the model, while other parameters do not perturb the model in any substantial way.In Paper III a general framework for the electromagnetic modeling is provided. The paper addresses sensitivity analysis, computation, and measurements regarding wave propagation characteristics in power cables.The asymptotic behavior of the non-discrete radiating mode, the branch-cut, is presented in Paper IV. The result is compared with the first and second propagating Transversal Magnetic (TM) mode.Finally, Paper V addresses the numerical problems associated with large arguments in the Bessel functions, which are due to the large conductivity parameters of the metallic layers. The introduction of a perfect electric conductor (PEC) and a short illustration of an inverse problem are also discussed in the paper. At the end an analysis is presented regarding uncertainties in the model parameters, which shows that temperature is an important parameter to consider.
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| 3. |
- Ivanenko, Yevhen
(författare)
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Optimization and Physical Bounds for Passive and Non-passive Systems
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Physical bounds in electromagnetic field theory have been of interest for more than a decade. Considering electromagnetic structures from the system theory perspective, as systems satisfying linearity, time-invariance, causality and passivity, it is possible to characterize their transfer functions via Herglotz functions. Herglotz functions are useful in modeling of passive systems with applications in mathematical physics, engineering, and modeling of wave phenomena in materials and scattering. Physical bounds on passive systems can be derived in the form of sum rules, which are based on low- and high-frequency asymptotics of the corresponding Herglotz functions. These bounds provide an insight into factors limiting the performance of a given system, as well as the knowledge about possibilities to improve a desired system from a design point of view. However, the asymptotics of the Herglotz functions do not always exist for a given system, and thus a new method for determination of physical bounds is required. In Papers I–II of this thesis, a rigorous mathematical framework for a convex optimization approach based on general weighted Lp-norms, 1≤p≤∞, is introduced. The developed framework is used to approximate a desired system response, and to determine an optimal performance in realization of a system satisfying the target requirement. The approximation is carried out using Herglotz functions, B-splines, and convex optimization. Papers III–IV of this thesis concern modeling and determination of optimal performance bounds for causal, but not passive systems. To model them, a new class of functions, the quasi-Herglotz functions, is introduced. The new functions are defined as differences of two Herglotz functions and preserve the majority of the properties of Herglotz functions useful for the mathematical framework based on convex optimization. We consider modeling of gain media with desired properties as a causal system, which can be active over certain frequencies or frequency intervals. Here, sum rules can also be used under certain assumptions.In Papers V–VII of this thesis, the optical theorem for scatterers immersed in lossy media is revisited. Two versions of the optical theorem are derived: one based on internal equivalent currents and the other based on external fields in terms of a T-matrix formalism, respectively. The theorems are exploited to derive fundamental bounds on absorption by using elementary optimization techniques. The theory has a potential impact in applications where the surrounding losses cannot be neglected, e.g., in medicine, plasmonic photothermal therapy, radio frequency absorption of gold nanoparticle suspensions, etc. In addition to this, a new method for detection of electrophoretic resonances in a material with Drude-type of dispersion, which is placed in a straight waveguide, is proposed.
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| 5. |
- Nordebo, Sven
(författare)
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Robust broadband beamforming and digital filter design : methods and applications
- 1995
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This doctoral thesis consists of a summary and six parts corresponding to six different papers. There are two published and three submitted journal papers, and one research report. The summary will highlight the main results and emphasize the interrelationships between different parts. The thesis comprises two main themes: robust broadband beamforming and digital filter design. In most of the papers in this thesis these concepts are closely related. Some of the results on digital filter design actually concern robust filter design, and one of the main contributions of this thesis concerns the possibility of anomalous designs when using conventional methods in the FIR filter design of broadband beamformers. Part I deals with robustness of broadband adaptive beamformers in the sense that there is an uncertainty in the frequency content and spatial location of the desired target signal. The adaptive beamformer should perform well over a region in space and frequency. This is achieved by defining the Spatial Filter designed Generalized Sidelobe Canceller (SFGSC), and by using an appropriate digital filter design. The novelty of the SFGSC method is the implementation of target signal constraints by using a filter design approach. With this strategy the constraints are approximated over a given design domain, rather than exactly implemented as with the conventional Generalized Sidelobe Canceller (GSC). With this new method (in contrast to the GSC) the SFGSC is able to handle a continuum of constraints. Part II introduces a quadratic programming formulation of the weighted Chebyshev FIR filter design problem for a broadband beamformer in the near-field. This technique may be used to design the digital filters of the broadband SFGSC described in Part I. Part III reveals that the digital filters of a broadband beamformer are incompletely specified whenever the beamformer is specified only in space and frequency. Using conventional filter design criteria with such incomplete specifications may lead to excessively large filter coefficients. Robust weighted least squares and weighted Chebyshev design criteria are introduced in order to avoid this anomaly. "Robustness" in this context means insensitivity to model imperfections such as sensor element placement errors, amplifier mismatch, etc. Again, the filters designed are typically components of the SFGSC described in Part I. Part IV addresses the problem of the non-uniqueness of the Chebyshev approximation for two-dimensional linear phase digital FIR filters. It is shown that the unique Chebyshev approximation having minimum Euclidean filter weight norm can be obtained by using a wellconditioned quadratic programming formulation. This is the same quadratic program that was used to define one of the robust beamformer designs in Part III. Part V deals with robust design for one-dimensional non-linear phase FIR filters which are incompletely specified. The conventional weighted Chebyshev solution can be obtained by using a quadratic programming formulation similar to that given in Part II. A robust weighted Chebyshev design criterion is defined by a modified quadratic program, similar to one of the robust design methods given in Part III. Part VI emphasizes the robustness of adaptive beamformers with respect to channel mismatch, sensor positioning, etc. In particular, the paper addresses the difficulty of mathematically modeling a beamformer for a small enclosure such as a car compartment. A calibrating scheme is proposed which is independent of array geometry and channel matching, and which calibrates the adaptive array to the given acoustic environment and to the given electronic equipment. Results from real measurements in a car compartment are included. An international patent is applied for based on this paper.
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- Sjödén, Therese, 1977-
(författare)
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Sensitivity Analysis and Material Parameter Estimation using Electromagnetic Modelling
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Estimating parameters is the problem of finding their values from measurements and modelling. Parameters describe properties of a system; material, for instance, are defined by mechanical, electrical, and chemical parameters. Fisher information is an information measure, giving information about how changes in the parameter effect the estimation. The Fisher information includes the physical model of the problem and the statistical model of noise. The Cramér-Rao bound is the inverse of the Fisher information and gives the best possible variance for any unbiased estimator.This thesis considers aspects of sensitivity analysis in two applied material parameter estimation problems. Sensitivity analysis with the Fisher information and the Cramér-Rao bound is used as a tool for evaluation of measurement feasibilities, comparison of measurement set-ups, and as a quantitative measure of the trade-off between accuracy and resolution in inverse imaging.The first application is with estimation of the wood grain angle parameter in trees and logs. The grain angle is the angle between the direction of the wood fibres and the direction of growth; a large grain angle strongly correlates to twist in sawn timber. In the thesis, measurements with microwaves are argued as a fast and robust measurement technique and electromagnetic modelling is applied, exploiting the anisotropic properties of wood. Both two-dimensional and three-dimensional modelling is considered. Mathematical modelling is essential, lowering the complexity and speeding up the computations. According to a sensitivity analysis with the Cramér-Rao bound, estimation of the wood grain angle with microwaves is feasible.The second application is electrical impedance tomography, where the conductivity of an object is estimated from surface measurements. Electrical impedance tomography has applications in, for example, medical imaging, geological surveillance, and wood evaluation. Different configurations and noise models are evaluated with sensitivity analysis for a two-dimensional electrical impedance tomography problem. The relation between the accuracy and resolution is also analysed using the Fisher information.To conclude, sensitivity analysis is employed in this thesis, as a method to enhance material parameter estimation. The sensitivity analysis methods are general and applicable also on other parameter estimation problems.
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