Power-Balanced Modelling Of Circuits As Skew Gradient Systems

Rémy Muller (1) , Thomas Hélie (2)

1 S3AM - Systèmes et Signaux Sonores : Audio/Acoustique, instruMents
2 S3AM - Sound Systems and Signals: Audio/Acoustics, InstruMents

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.

Domaines: Systèmes dynamiques [math.DS]

Rémy Muller, Thomas Hélie. Power-Balanced Modelling Of Circuits As Skew Gradient Systems. 21 st International Conference on Digital Audio Effects (DAFx-18), Sep 2018, Aveiro, Portugal. ⟨hal-01871464⟩