Recasting modified nodal analysis to improve reliability in numerical circuit Simulation

Modified nodal analysis (MNA) can be considered as the most adopted method in circuit simulation programs. Once node equations were written and complemented with those from the current controlled branches, a nonlinear system of algebraic and/or differential equations is obtained. In general, by using linear multistep integration methods, differential equations are recast as nonlinear algebraic ones, which are solved through the Newton method at each integration time step. While computer precision is not an issue in most situations, some specific but frequent cases yield ill-conditioned or singular matrices even in originally well posed circuits. This drawback can occur in different situations namely in presence of strongly nonlinear elements and/or when very small integration time steps are used. In the second case, very large conductances in the companion model of capacitors can introduce roundoff errors. In this paper, a transformation of the MNA that overcomes these problems is proposed. It is based on a suitable recombination of equations and electrical variables of the conventional MNA and it can be easily implemented in a circuit simulator.