Abstract
We present a method that generates passive-guaranteed stable simulations of analog audio circuits from electronic schematics for real-time issues. On one hand, this method is based on a continuous-time power-balanced state-space representation structured into its energy-storing parts, dissipative parts, and external sources. On the other hand, a numerical scheme is especially designed to preserve this structure and the power balance. These state-space structures define the class of port-Hamiltonian systems. The derivation of this structured system associated with the electronic circuit is achieved by an automated analysis of the interconnection network combined with a dictionary of models for each elementary component. The numerical scheme is based on the combination of finite differences applied on the state (with respect to the time variable) and on the total energy (with respect to the state). This combination provides a discrete-time version of the power balance. This set of algorithms is valid for both the linear and nonlinear case. Finally, three applications of increasing complexities are given: a diode clipper, a common-emitter bipolar-junction transistor amplifier, and a wah pedal. The results are compared to offline simulations obtained from a popular circuit simulator.
Highlights
The characteristic input-to-output behavior of analog audio circuits rests on the possibly highly nonlinear components appearing in such systems
First and foremost, we provide an introduction to the port-Hamiltonian systems (PHS) formalism
In step 2, we propose an algorithm that analyzes if Formulation (2) is available and delivers the matrix J in this case
Summary
The characteristic input-to-output behavior of analog audio circuits (timbre, transitory) rests on the possibly highly nonlinear components appearing in such systems. PHS are extensions of classical Hamiltonian systems [24], defined to address open dynamical systems made of energy storage components, dissipative components, and some connection ports through which energy can transit This approach leads to a state-space representation of physical systems structured according to energy flow, encoding the passivity property, even for nonlinear cases.
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