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Element‐based index reduction in electrical circuit simulation
Author(s) -
Ebert Falk,
Bächle Simone
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610346
Subject(s) - electronic circuit , computer simulation , reduction (mathematics) , algebraic number , computer science , topology (electrical circuits) , numerical analysis , differential algebraic equation , network analysis , algebraic equation , index (typography) , mathematics , differential equation , engineering , ordinary differential equation , simulation , mathematical analysis , physics , electrical engineering , nonlinear system , geometry , combinatorics , quantum mechanics , world wide web
The numerical simulation of very large scale integrated circuits is an important tool in the development of new industrial circuits. In the course of the last years, this topic has received increasing attention. Common modeling approaches for circuits lead to differential‐algebraic systems (DAEs). In circuit simulation, these DAEs are known to have index 2, given some topological properties of the network. This higher index leads to several undesirable effects in the numerical solution of the DAEs. Recent approaches try to lower the index of DAEs to improve the numerical behaviour. These methods usually involve costly algebraic transformations of the equations. Especially, for large scale circuit equations, these transformations become too costly to be efficient. We will present methods that change the topology of the network itself, while replacing certain elements in oder to obtain a network that leads to a DAE of index 1, while not altering the analytical solution of the DAE. This procedure can be performed prior to the actual numerical simulation. The decreasing of the index usually leads to significantly improved numerical behaviour. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)