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 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 toward the real-time multiphysics emulation of nonlinear audio circuits that is essential in Virtual Analog applications.
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