Transformers have been playing a fundamental role in the audio industry since the birth of audio electronics. The subtle flaws, caused by the strongly nonlinear characteristic of their magnetic materials, lead to an enrichment of the signal harmonic content, thus contributing to that peculiar analog timbre well-liked by many musicians. In order to digitally emulate the unique shades of this analog gear, in this paper, a new methodology based on Wave Digital principles is presented. The method is highly flexible and able to accurately simulate the geometry/nonlinear behavior of magnetic cores, while implementing the reference system physical domains (electric and magnetic) in a modular fashion. The nonlinear reluctances are modeled with Canonical Piecewise-Linear functions, which can be arbitrarily tuned to improve the accuracy of the representation. The algorithm presents itself as a hierarchical generalization of the so-called Scattering Iterative Method (SIM), i.e., a fixed-point method that has demonstrated outstanding performance for the simulation of large photovoltaic arrays and the emulation of audio circuits. The proposed multiphysics approach is thus characterized by some SIM features, such as the remarkable efficiency, and it paves the way towards the real-time multiphysics emulation of nonlinear audio circuits that is essential in Virtual Analog applications.

Accurate models of electromagnetic systems can be derived by coupling electric and magnetic equivalent circuits together. The different nature of such physical domains constitutes a big challenge that puts a continuous strain on software simulators. To face this problem, a simulation approach based on Wave Digital Filters (WDFs) is proposed in this manuscript. The method is employed to solve nonlinear electromagnetic systems containing complex magnetic equivalent circuits while maintaining the modularity of the electric and magnetic subsystems. The nonlinearities can be locally handled, enabling the possibility to choose a dedicated model for each one of them. The proposed algorithm is a hierarchical generalization of the Scattering Iterative Method, which has shown, over the past few years, promising performance for the simulation of large nonlinear circuits. In addition, the method constitutes a further step towards the development of novel general-purpose circuit simulators based on WDF principles. In a comparison with mainstream circuit simulation software, the proposed approach turns out to be considerably faster and thus particularly promising for parametric analyses of electromagnetic systems.

Modern audio systems and musical effects feature multi-core processing units. The development of parallel audio processing algorithms capable of exploiting the architecture of such hardware is thus in order. In this paper, we present a parallel version of the Hierarchical Scattering Iterative Method (HSIM), a technique based on Wave Digital Filter principles recently proposed for the emulation of multiphysics audio circuits containing multiple nonlinear oneports and nonlinear transformers. HSIM operates in a modular fashion, and it is characterized by a high number of embarrassingly parallelizable operations, making it a good candidate for parallel execution. After analyzing HSIM from the parallel computing perspective, we propose three different strategies for the distribution of HSIM workload among threads of execution, and we show how to compute the maximum achievable speedup. The emulation of a possible output stage of a vacuum-tube guitar amplifier is considered, and a performance comparison between parallel and serial implementations of HSIM is presented, pointing out a speedup of nearly 30%. The proposed method proves thus to be promising for Virtual Analog modeling applications, leading the way towards the parallel digital emulation of increasingly complex audio circuits.

No abstract

No abstract