A Numerical Method For Symbolic Analysis Of Electrical Networks

In order to avoid immense time and financial effort for the production of deficiently designed prototypes of integrated circuits (ICs), industrial circuit design uses mathematical models and simulations to predict and analyse the physical behavior of analog electronical systems. The thereby generated (partial) differential-algebraic systems of equations are composed of component characteristics and Kirchhoff laws. During the last years, increasing miniaturization and integration density of components on a single chip led to systems containing several millions of equations, which have to be reduced to their dominant parts in order to handle the complexity. Besides a large number of numerical analysis and reduction methods, there also exist symbolic techniques, which indeed are costly to compute, but allow deeper analytical insights into the behavior of the system. In this book, new strategies for the analysis and reduction of systems of ever-growing size and complexity are developed by exploiting the hierarchical structure of analog electronical circuits for coupled symbolic-numerical model reduction. Thereby, the entire circuit is considered as a system of subcircuits that are interconnected by a certain topology. By using a novel concept of subsystem sensitivities, a newly developed algorithm reduces the subcircuits separately from each other. This does not only allow for a faster solving of smaller problems, it further permits the coupling of different reduction techniques. Moreover, particularly in the symbolic case, larger systems become manageable at all. Finally, the advantages and the practicability of the new techniques are demonstrated on amplifier circuit examples typically used in industrial applications.

The value of symbolic network analysis is now well recognized. In industry it has been used as an aid in the design of small linear networks. In academic institutions it has been found useful as an instructional aid. The purpose of this book is to present, in a single volume, a unified treatment of all symbolic analysis methods, using a consistent set of notation, and based on the same theoretical background (network topology, combinatorial analysis, and numerical analysis). The emphasis is on those methods which have been implemented and for which there are source codes available. The work will be of interest to all those who have the usual college-level training in circuit theory.

The only method of circuit analysis known to most engineers and students is nodal or loop analysis. Although this works well for obtaining numerical solutions, it is almost useless for obtaining analytical solutions in all but the simplest cases. In this unusual 2002 book, Vorpérian describes remarkable alternative techniques to solve, almost by inspection, complicated linear circuits in symbolic form and obtain meaningful analytical answers for any transfer function or impedance. Although not intended to replace traditional computer-based methods, these techniques provide engineers with a powerful set of tools for tackling circuit design problems. They also have great value in enhancing students' understanding of circuit operation, making this an ideal course book, and numerous problems and worked examples are included. Originally developed by Professor David Middlebrook and others at Caltech (California Institute of Technology), the techniques described here are now widely taught at institutions and companies around the world.

Neste trabalho desenvolveu-se um método para análise simbólica de redes analógicas lineares, invariantes no tempo, incluindo fontes controladas, transformadores e giradores. O algoritmo determina funções de transferência em forma simbólica analisando um modelo de grafo de fluxo de sinal (GFS) da rede. Este procedimento é baseado em método de análise de filtros digitais, anteriormente desenvolvido, enfatizando a geração de um modelo apropriado de GFS do circuito. O modelo de GFS adotado é gerado a partir de uma descrição pro equações de estado da rede. O método foi implementado, apresentando, em alguns casos, eficiência comparável à dos processos numéricos. São apresentados resultados de testes para redes típicas.

This book is an introduction to numerical analysis and intends to strike a balance between analytical rigor and the treatment of particular methods for engineering problems Emphasizes the earlier stages of numerical analysis for engineers with real-life problem-solving solutions applied to computing and engineering Includes MATLAB oriented examples An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

"Symbolic analyzers have the potential to offer knowledge to sophomores as well as practitioners of analog circuit design. Actually, they are an essential complement to numerical simulators, since they provide insight into circuit behavior which numerical "