Deep Learning-Based Wave Digital Modeling of Rate-Dependent Hysteretic Nonlinearities for Virtual Analog Applications

Electromagnetic components greatly contribute to the peculiar timbre of analog audio gear. Indeed, distortion effects due to the nonlinear behavior of magnetic materials are known to play an important role in enriching the harmonic content of an audio signal. However, despite the abundant research that has been devoted to the characterization of nonlinearities in the context of virtual analog modeling over the years, the discrete-time simulation of circuits exhibiting rate-dependent hysteretic phenomena remains an open challenge. In this article, we present a novel data-driven approach for the wave digital modeling of rate-dependent hysteresis using recurrent neural networks (RNNs). Thanks to the modularity of wave digital filters, we are able to locally characterize the wave scattering relations of a hysteretic reluctance by encapsulating an RNN-based model into a single one-port wave digital block. Hence, we successfully apply the proposed methodology to the emulation of the output stage of a vacuum-tube guitar amplifier featuring a nonlinear transformer

Wave digital modeling of the diode-based ring modulator

The ring modulator is a strongly nonlinear circuit common in audio gear, especially as part of electronic musical instruments. In this paper, an accurate model based on Wave Digital (WD) principles is developed for implementing the ring modulator as a digital audio effect. The reference circuit is constituted of four diodes and two multi-winding transformers. The proposed WD implementation is based on the Scattering Iterative Method (SIM), recently developed for the static analysis of large nonlinear photovoltaic arrays. In this paper, SIM is shown to be suitable for implementing also audio circuits for Virtual Analog applications, such as the ring modulator, since it is stable, robust and comparable to or more efficient than state-of-the-art strategies in terms of computational cost

Wave-Based Analysis of Large Nonlinear Photovoltaic Arrays

In this paper, a novel analysis method based on wave digital (WD) principles is presented. The method is employed for modeling and efficiently simulating large photovoltaic (PV) arrays under partial shading conditions. The WD method allows rapid exploration of the current-voltage curve at the load of the PV array, given: the irradiation pattern, the nonlinear PV unit model (e.g., exponential junction model with bypass diode) and the corresponding parameters. The maximum power point can therefore easily be deduced. The main features of the proposed method are the use of a scattering matrix that is able to incorporate any PV array topology and the adoption of independent 1-D nonlinear solvers to handle the constitutive equations of PV units. It is shown that the WD method can be considered as an iterative relaxation method that always converges to the PV array solution. Rigorous proof of convergence and results about the speed of convergence are provided. Compared with standard spice-like simulators, the WD method results to be 35 times faster for PV arrays made of some thousands elements. This paves the way to possible implementations of the method in specialized hardware/software for the real time control and optimization of complex PV plants

Modeling nonlinear wave digital elements using the Lambert function

A large class of transcendental equations involving exponentials can be made explicit using the Lambert W function. In the last fifteen years, this powerful mathematical tool has been extensively used to find closed-form expressions for currents or voltages in circuits containing diodes. Until now almost all the studies about the W function in circuit analysis concern the Kirchhoff (K) domain, while only few works in the literature describe explicit models for diode circuits in the Wave Digital (WD) domain. However explicit models of NonLinear Elements (NLEs) in the WD domain are particularly desirable, especially in order to avoid the use of iterative algorithms. This paper explores the range of action of the W function in the WD domain; it describes a procedure to search for explicit wave mappings, for both one-port and multi-port NLEs containing diodes. WD models, describing an arbitrary number of different parallel and anti-parallel diodes, a transformerless ring modulator and some BJT amplifier configurations, are derived. In particular, an extended version of the BJT Ebers-Moll model, suitable for implementing feedback between terminals, is introduced