Título

Modified method of hyperspheres: tracing homotopic bounded paths in nonlinear circuits

Autor

DELIA TORRES MUÑOZ

Colaborador

LUIS HERNANDEZ MARTINEZ (Asesor de tesis)

HECTOR VAZQUEZ LEAL (Asesor de tesis)

Nivel de Acceso

Acceso Abierto

Licencia

http://creativecommons.org/licenses/by-nc-nd/4.0

Materias

Homotopy method - (MÉTODO HOMOTOPY) Nonlinear - (NO LINEAL) Equation nonlinear - (ECUACIÓN NO LINEAL) Continuation algorithm - (ALGORITMO DE CONTINUACIÓN) CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA - (CTI) FÍSICA - (CTI) ELECTRÓNICA - (CTI)

Resumen o descripción

The equations describing the behavior of a electronic circuit are nonlinear due to nonlinear

elements and the DC analysis is the first step for analyzing a nonlinear circuit and also to

find the solution, or solutions, of the system of equations. Methods like Newton Raphson

algorithm present disadvantages to solve nonlinear problems besides are not capable to

find multiple solutions. To overcome above problems the homotopy methods can locate

multiple solutions for a system of equations; however homotopy methods convergence

depends of the starting point, the continuous methods and nonlinearities. The homotopy

formulation require suitable path tracking techniques to accurately trace the homotopy

curve, the algorithm to path-tracking used in this work is the spherical algorithm because

it is geometrically clear and this characteristic can facilitate its programming. However

during programming hyperspheres method there were some problems as reversion of the

path on the curve and slow for tracing. In this thesis, two proposed methodologies are used

to solve the above problems, the first proposed methodology is based in calculating the

normal vector to the curve for detecting the problem of reversion then the methodology

is used to avoid the problem of reversion. The second methodology is achieved during the

tracing of the homotopy curve to reduce the number of iterations and the computational

time. Both strategies are implemented and programmed for the hyperspheres method;

also several case studies are solved, and we found satisfactory results for the path tracking

problem.

Editor

Instituto, Nacional de Astrofísica, Óptica y Electrónica

Fecha de publicación

agosto de 2015

Tipo de publicación

Tesis de doctorado

Recurso de información

http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/131

Formato

application/pdf

Idioma

Inglés

Audiencia

Público en general

Sugerencia de citación

Torres-Muñoz D.

Repositorio Orígen

Repositorio Institucional del INAOE

Descargas

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