Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects

Abstract—This paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index Terms—Finite difference methods, time-domain analysis, transmission lines, wavelet transforms. I

Aplicação do método de Galerkin descontínuo para a análise de guias fotônicos

Orientador: Hugo Enrique Hernández FigueroaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Um novo método de onda completo para realizar a análise modal em guias de onda é introduzido nesta dissertação. A ideia central por trás do método é baseada na discretização da equação de onda vetorial com o Método de Galerkin Descontínuo com Penalidade Interior (IPDG, do inglês Interior Penalty Discontinuous Galerkin). Com uma função de penalidade apropriada, um método de alta precisão e sem modos espúrios é obtido. A eficiência do método proposto é provada em vários guias de onda, incluindo complicados guias de ondas ópticos com modos vazantes e também em guias de onda plasmônicos. Os resultados foram comparados com os métodos do estado-da-arte descritos na literatura. Também é discutida a importância dessa nova abordagem. Além disso, os resultados indicam que o método é mais preciso do que abordagens anteriores baseadas em Elementos Finitos. As principais contribuições deste trabalho são: foi desenvolvido um novo método robusto e de alta precisão para a análise de guias de ondas arbitrários, uma nova função de penalidade para o IPDG foi proposta e aplicações práticas do método proposto são apresentadas. Adicionalmente, no apêndice é apresentado uma aplicação da análise modal em simulação eletromagnética 3D com um método de Galerkin DescontínuoAbstract: A novel full-wave method to perform mode analysis on waveguides is introduced in this dissertation. The core of the method is based on an Interior Penalty Discontinuous Galerkin (IPDG) discretization of the vector wave equation. With an appropriate penalty function a spurious-free and high accuracy method is achieved. The efficiency of the proposed method was proved in several waveguides, including intricate optical waveguides with leaky modes and also on plasmonic waveguides. The obtained results were compared with the state-of-the-art mode solvers described in the literature. Also, a discussion on the importance of this new approach is presented. Moreover, the results indicate that the proposed method is more accurate than the previous approaches based on Finite Elements Methods. The main contributions of this work are: the development of a novel robust and accurate method for the analysis of arbitrary waveguides, a new penalty function for the IPDG was proposed and practical applications of the methods are discussed. In addition, in the appendix an application of modal analysis on 3D electromagnetic simulations with a Discontinuous Galerkin method is detailedMestradoTelecomunicações e TelemáticaMestre em Engenharia ElétricaCAPE

Application of state-of-the-art FEM techniques to magnetostatic NDE

A typical example of the complexities involved in the numerical modeling of electromagnetic phenomena is that of modeling the magnetic flux leakage inspection of gas transmission pipelines. The problem calls for three-dimensional modeling of motionally induced currents (using transient analysis), modeling nonlinearity of the ferromagnetic parts, and accurate modeling of the permanent magnet used in the magnetizer. Researchers, have thus far simplified the problem using several assumptions, including that of axisymmetry, and modeling velocity effects using steady-state analysis. However, there has been no attempt to quantify the errors introduced by these assumptions. Also, due to the unavailability of commercial codes to solve three-dimensional motion-related problems using transient analysis, a detailed study of the true nature of velocity effects has not been possible;This dissertation implements and evaluates state-of-the-art finite element modeling techniques applied to the specific problem of modeling magnetic flux leakage inspection of gas pipelines. This provides the basis from which conclusions can be drawn on the general problem of modeling magnetostatic phenomena. Axisymmetric and three-dimensional models are developed capable of modeling velocity effects. A detailed analysis of the differences between axisymmetric and three-dimensional geometries, based on a study of permeability variations in the vicinity of defects is presented. Also, the need for transient analysis is argued based on results generated. As part of this study, serious problems (including spurious solutions and corner singularities) associated with the traditional node-based finite-element techniques, when applied to the three-dimensional modeling, are discussed. In this work, new and efficient numerical modeling concepts, using the edge-based finite-element technique are employed to overcome these problems;This study demonstrates the need for accurate modeling of the full three-dimensional geometry, incorporating velocity effects and nonlinear permeability, for realistic predictions of flux leakage inspection tools. Major contributions of this work include: (1) detailed analysis of the physical processes associated with the magnetic flux leakage tool, (2) design ideas to improve the performance of the tool, and (3) development of an edge-based finite element code for modeling magnetostatic nondestructive testing applications in three-dimensions incorporating velocity effects. This is the first study of this nature, applied to pipeline inspection, and, many of the conclusions presented can be applied to nondestructive testing techniques in general

Time- and frequency-domain modeling of passive interconnection structures in field and circuit analysis

Die vorliegende Arbeit widmet sich den theoretischen Grundlagen und numerischen Verfahren zur Analyse passiver Verbindungsstrukturen auf der Basis der elektromagnetischen Feld- und Netzwerktheorie. Die Simulation elektromagnetischer Phänomene gewinnt eine immer stärkere Bedeutung sowohl im Entwicklungsprozess elektronischer Komponenten und Systeme als auch bei der EMV-Analyse. Ständig steigende Operationsfrequenzen erfordern die Einbeziehung der passiven Verbindungsstrukturen in die Analyse sowohl im Frequenz- als auch im Zeitbereich. Dabei wächst insbesondere die Bedeutung von Zeitbereichsmethoden bei der Behandlung elektrodynamischer Probleme infolge zunehmender Schaltfrequenzen und immer steilerer Anstiegsflanken. Frequenzbereichsmethoden in Kombination mit der Fourierrücktransformation erfordern bei extrem breiten Frequenzspektren einen hohen Rechenaufwand, um Zeitbereichslösungen mit hinreichender Genauigkeit zu erhalten. Im Falle von Nichtlinearitäten sind Zeitbereichsmethoden sogar die einzige Möglichkeit. Aus diesem Grunde wird in der vorliegenden Arbeit ein besonderer Schwerpunkt auf die Zeitbereichsmodellierung der Verbindungsstrukturen einschließlich der Schaltungsumgebung sowie die Behandlung mittels Netzwerksimulatoren gelegt.  Throughout the first period of electrical-engineering history, passive interconnections, i.e., conductors serving as the connection of electronic devices or system components, were typically not considered in the system modeling, except for some special cases and "electrically long" structures, which were successfully described via the transmission-line theory. This changed dramatically after the wide-spread introduction of digital, radio-frequency, and microwave technologies, which required transmission via the passive interconnection structures of high-frequency (HF) signals. The parasitic effects introduced by passive interconnections at high frequencies have motivated modern digital-system designers to consider such interconnections more precisely. &nbsp

The Partial Elements Equivalent Circuit Method: The State Of The Art

This year marks about half a century since the birth of the technique known as the partial element equivalent circuit modeling approach. This method was initially conceived to model the behavior of interconnect-type problems for computer-integrated circuits. An important industrial requirement was the computation of general inductances in integrated circuits and packages. Since then, the advances in methods and applications made it suitable for modeling a large class of electromagnetic problems, especially in the electromagnetic compatibility (EMC)/signal and power integrity (SI/PI) areas. The purpose of this article is to present an overview of all aspects of the method, from its beginning to the present day, with special attention to the developments that have made it suitable for EMC/SI/PI problems

Libre culture: meditations on free culture

Libre Culture is the essential expression of the free culture/copyleft movement. This anthology, brought together here for the first time, represents the early groundwork of Libre Society thought. Referring to the development of creativity and ideas, capital works to hoard and privatize the knowledge and meaning of what is created. Expression becomes monopolized, secured within an artificial market-scarcity enclave and finally presented as a novelty on the culture industry in order to benefit cloistered profit motives. In the way that physical resources such as forests or public services are free, Libre Culture argues for the freeing up of human ideas and expression from copyright bulwarks in all forms

Analogue filter networks: developments in theory, design and analyses

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