Fully-Implicit Algebro-Differential Parametrization of Circuits

Rémy Müller; Thomas Hélie
DAFx-2020 - Vienna (virtual)
This paper is concerned with the conception of methods tailored for the numerical simulation of power-balanced systems that are well-posed but implicitly described. The motivation is threefold: some electronic components (such as the ideal diode) can only be implicitly described, arbitrary connection of components can lead to implicit topological constraints, finally stable discretization schemes also lead to implicit algebraic equations. In this paper we start from the representation of circuits using a power-balanced Kirchhoff-Dirac structure, electronic components are described by a local state that is observed through a pair of power-conjugated algebro-differential operators (V, I) to yield the branch voltages and currents, the arc length is used to parametrize switching and non-Lipschitz components, and a power balanced functional time-discretization is proposed. Finally, the method is illustrated on two simple but non-trivial examples.