Multiphysics Modeling of Audio Circuits With Nonlinear Transformers

Abstract

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.

A better SPQR‐tree decomposition of electrical circuits containing multiports and its application to wave digital emulation

“…Specifically, an advanced procedure, called the hierarchical scattering iterative method (HSIM), has been recently developed, leveraging the SPQR-tree representation for efficient evaluation of wave digital structures. 1,10,26 This method has even been extended to evaluate wave digital algorithms with multiple nonlinearities and complex topologies. 26 Notably, HSIM outperforms standard circuit simulation software in terms of simulation runtime.…”

“…Systematic analysis and simulation methods for electrical circuitry are of paramount importance for both the design and the development of novel technologies in the electrical engineering community. Some application examples can be found in energy technology, 1,2 oscillator‐based technology, 3–6 and audio circuitry 7–10 …”

“…Some examples of utilizing SPQR-trees to represent electrical circuits can be found in previous studies. 1,10,19,20,[24][25][26] What makes SPQR-trees especially interesting is the fact that they can be used to emulate electrical circuits in an autonomous manner. In fact, an algorithmic procedure for the wave digital emulation of general electrical circuits, whether linear or nonlinear, has been recently developed (cf.…”

Pruning Deep Neural Network Models of Guitar Distortion Effects

“…Approaches to VA modeling of distortion circuits can broadly be classified as white-box, black-box, or gray-box [2]. In white-box modeling [4]- [7], the circuitry is analyzed and simulated using time-stepping methods. Additionally, these models can then be further optimized using data recorded from the target device [8], [9].…”

A Template-Based SPQR-Tree Decomposition of Electrical Circuits

“…Systematic analysis and simulation methods for electrical circuitry are of paramount importance for both the design as well as the development of novel technologies in the electrical engineering community. Some application examples can be found in energy technology [1]- [3], bio-inspired technology [4]- [8], physics-inspired optimization [9]- [12], audio circuitry [13]- [16], robust numerical integration [17]- [20], modeling and solution of partial differential equations [21]- [24], etc.…”