Wave Digital Modeling of Circuits with a Single Variable-µ Pentode based on Neural Networks

Virtual Analog effects refer to the class of digital audio effects that recreate the sound of analog equipment. Vacuum tubes, although old-fashioned, still play a crucial role in defining the distinctive tone of certain audio gear, e.g., guitar amplifiers. Among tubes, variable-mu pentodes stand out for their peculiar nonlinear behavior but are notoriously difficult to simulate using conventional methods. In this article, we extend a method previously proposed for the simulation of circuits containing a single nonlinear two-port element to the case of circuits containing a single variable-mu pentode. We show that by combining Wave Digital Filters based on vector waves and neural networks, we are able to solve said class of circuits in a fully explicit fashion, contrary to what can be done in standard simulators. Our approach is validated through the simulation of the Dogzilla preamplifier stage, offering a promising pathway for the efficient and accurate simulation of circuits containing nonlinear elements characterized by an arbitrary number of ports.