Index characterization of differential-algebraic equations in hybrid analysis for circuit simulation

Modern modeling approaches in circuit simulation naturally lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. The modified nodal analysis (MNA) is known to yield a DAE with index at most two in a wide class of nonlinear time-varying electric circuits. In this paper, we consider a broader class of analysis method called the hybrid analysis. For linear time-invariant RLC circuits, we prove that the index of the DAE arising from the hybrid analysis is at most one, and give a structural characterization for the index of a DAE in the hybrid analysis. This yields an efficient algorithm for finding an hybrid analysis in which the index of the DAE to be solved attains zero. Finally, for linear time-invariant electric circuits which may contain dependent sources, we prove that the optimal hybrid analysis by no means results in a higher index DAE than MNA.

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