Indexreduktion in der Schaltungssimulation

Simulation is widely used to test electrical circuits of microchips before a prototype is built. However a quick and reliable simulation of modern microchip circuits is very difficult because of their complexity and high number of elements.

The main methods of simulation used today generate systems of equations containing differential and algebraic relations, the DAE system. The problem is that the generated DAEs contain so called hidden constrains, that can only be revealed by differentiating certain equations. The order of these differentiations and thus complexity of the whole DAE system is closely related to the tractability index of a DAE. DAEs having an index higher than 1 are costly to solve while accuracy suffers as well. The aim of our new method is to obtain DAEs of index 1. Therefore the hidden con-strains are derived from the information contained in the circuit, through a topological index analysis, without algebraic transformations of the circuit equations. They are directly embedded into the circuit model by replacing “critical” elements. The resulting DAE is of index 1 and can easily be implemented into existing solvers.

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