Wave Digital Modeling and Implementation of Nonlinear Audio Circuits with Nullors

The nullor is a theoretical two-port element suitable to model several multi-port devices common in audio circuitry, such as ideal operational amplifiers, operational transconductance amplifiers, and transistors operating in linear regime. In this manuscript, we present an approach for the Wave Digital (WD) modeling and implementation of circuits with multiple nullors. In particular, we propose an approach to compute scattering matrices of WD topological junctions absorbing nullors that is less computationally demanding than the techniques available in the literature on WD Filters. We show that the proposed approach turns out to be particularly useful when simulating nonlinear circuits through the Scattering Iterative Method (SIM), a WD fixed-point method recently developed for the solution of circuits with multiple nonlinearities, because it requires a frequent update of the scattering matrices. We also provide a novel convergence analysis of SIM applied to WD structures composed of multiple one-port nonlinear elements and a topological junction absorbing nullors. In order to verify the effectiveness of the proposed methodology, we discuss some WD implementations of analog audio circuits with multiple diodes and opamps, including a precision half-wave rectifier and a wave folder circuit.