Explicit Neural Network-Based Modeling of Time-Varying Circuits with a Single BJT in the Wave Digital Domain

Time-varying circuits, either due to inherent physical phenomena or due to external user interactions, are ubiquitous, especially in audio processing gear. Examples of such circuits include amplification stages based on a single Bipolar Junction Transistor (BJT) with time-varying controls that adjust, for example, the transistor biasing point. In this manuscript, we extend a previously proposed Wave Digital (WD) methodology for the fully explicit simulation of circuits incorporating a single nonlinear two-port element to accommodate time-varying circuits. To this end, we introduce a novel definition for the explicit BJT WD model, using a nonlinear vector wave scattering equation implemented through a neural network architecture. The proposed approach is validated through the discrete-time simulation of a fuzz guitar pedal with two potentiometers, achieving accuracy levels comparable to standard circuit simulation software.