Fully-Implicit Algebro-Differential Parametrization of Circuits
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.