State-Space Generation via Modified MNA for Numerical Integration Applications

Abstract This article derives a state-space (SS) model directly from an admittance-based MNA model using linear transformations and the Schur complement. The resulting system has dimension equal to the number of independent inductors and capacitors, takes the form $$E_j\dot{x}_{ss}+G_jx_{ss}+P_ju_{ss}=0$$ E j x ˙ ss + G j x ss + P j u ss = 0 and is graph-theory-free, as are the method’s two exceptions: circuits with more $$x_{ss}$$ x ss candidates than nodes, and parallel LL/LC combinations. When the formulation requires separating resistive elements from energy-storage elements, graph theory is employed to obtain $$E_{ss}\dot{x}_{ss}+G_{ss}x_{ss}+P_{ss}u_{ss}=0$$ E ss x ˙ ss + G ss x ss + P ss u ss = 0 . In this formulation, $$E_{ss}$$ E ss includes only capacitors and inductors (through addition and subtraction), while $$G_{ss}$$ G ss contains only resistive elements and couplings. The method is validated on ideal circuits, circuits with parasitic elements, circuits with nonlinear models, and degenerate circuits (capacitor delta). In comparisons, the SS system agreed with MNA simulation, for both fixed and variable step sizes. Flop counting shows an advantage of state-space for low state space quantities systems. It is concluded that the relative computational cost depends not only on the reduced system dimension but also on the sparsity preserved by the MNA structure.