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

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

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

Trefftz Difference Schemes on Irregular Stencils

The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions -- local solutions of the underlying differential equation. This paper advances and casts in a general form a significant modification of FLAME proposed recently by Pinheiro & Webb: a least-squares fit instead of the exact match of the approximate solution at the stencil nodes. As a consequence of that, FLAME schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions. The accuracy of the method is preserved but its robustness is improved. For demonstration, the paper presents a number of numerical examples in 2D and 3D: electrostatic (magnetostatic) particle interactions, scattering of electromagnetic (acoustic) waves, and wave propagation in a photonic crystal. The examples explore the role of the grid and stencil size, of the number of approximating functions, and of the irregularity of the stencils.Comment: 28 pages, 12 figures; to be published in J Comp Phy

Time domain edge finite elements

Diplomová práce se zabývá metodou hybridních (hranových a uzlových) konečných prvků ve frekvenční i časové oblasti. Tato metoda je použita pro analýzu vlnovodu parallel-plate, v kterém jsou umístěny dvě dielektrické vrstvy. Jako ukončení vlnovodu je implementována dokonale přizpůsobená vrstva označována PML. Projekt řeší možný výběr PML vrstvy v časové oblasti. Metoda je programována v programu MATLAB a výsledky jsou porovnány s programem COMSOL Multiphysics.This paper presents hybrid (edge and nodal) finite elements in frequency and time domain. The method is used for the numerical analysis of a parallel-plate waveguide loaded by two dielectric obstacles. A perfectly matched layer (PML) is implemented as the output port of this parallel-plate waveguide. In the project, the PLM layer for the exploitation in the time domain is developed. The method is programmed in MATLAB and is compared with results produced by COMSOL Multiphysics.

Iron Loss Computation in a Synchronous Machine from a Static Field Solution

Owing to the increasing energy demand, a highly efficient synchronous machine can play a crucial role in energy saving by reducing energy consumption. An optimum machine design requires a good estimation of the power losses, particularly the iron loss due to the complexity involved with the accurate loss prediction. The prediction of iron loss in the synchronous machine has drawn massive attraction due to the extensive use in the power stations and other industrial applications. The conventional time-stepping method for iron loss calculation is computationally highly expensive and can be productive as long as the number of computations remains in a respectable range. However, the situation is different when an excessive number of computations are required, such as for machine optimization, which turns this method into unprofitable. The development of fast and computationally efficient static analysis in case of synchronous machine induce a thought of computing the iron loss using this method which can minimize the computation cost and substitute the time consuming traditional loss computation method. Based on this notion, an effective iron loss computation technique was developed from a single static field simulation which is much faster than the conventional time-stepping method and provide a fair accuracy. A two-dimensional Finite Element Method was used, and the model was integrated with the static FEM analysis program in the in-house software FCSMEK. The model was applied to a 12.5 MW salient pole synchronous machine, and the computational accuracy was validated with the conventional time-stepping simulation

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 1

This research program has dealt with the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements; (2) finite element modeling of the electromagnetic problem; (3) coupling of thermal and mechanical effects; and (4) computer implementation and solution of the superconductivity transition problem. The research was carried out over the period September 1988 through March 1993. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles; (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements; and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects; and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The grant has fully supported the thesis work of one doctoral student (James Schuler, who started on January 1989 and completed on January 1993), and partly supported another thesis (Carmelo Militello, who started graduate work on January 1988 completing on August 1991). Twenty-three publications have acknowledged full or part support from this grant, with 16 having appeared in archival journals and 3 in edited books or proceedings