Download Power-balanced Modelling Of Circuits As Skew Gradient Systems This article is concerned with the power-balanced simulation of analog audio circuits, governed by nonlinear differential algebraic equations (DAE). The proposed approach is to combine principles from the port-Hamiltonian and Brayton-Moser formalisms to yield a skew-symmetric gradient system. The practical interest is to provide a solver, using an average discrete gradient, that handles differential and algebraic relations in a unified way, and avoids having to pre-solve the algebraic part. This leads to a structure-preserving method that conserves the power balance and total energy. The proposed formulation is then applied on typical nonlinear audio circuits to study the effectiveness of the method.
Download 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.
Download Lyapunov Stability Analysis of the Moog Ladder Filter and Dissipativity Aspects in Numerical Solutions This paper investigates the passivity of the Moog Ladder Filter and its simulation. First, the linearized system is analyzed. Results based on the energy stored in the capacitors lead to a stability domain which is available for time-varying control parameters meanwhile it is sub-optimal for time-invariant ones. A second storage function is proposed, from which the largest stability domain is recovered for a time-invariant Q-parameter. Sufficient conditions for stability are given. Second, the study is adapted to the nonlinear case by introducing a third storage function. Then, a simulation based on the standard bilinear transform is derived and the dissipativity of this numerical version is examined. Simulations show that passivity is not unconditionally guaranteed, but mostly fulfilled, and that typical behaviours of the Moog filter, including self-oscillations, are properly reproduced.