This is the second part of a two-part paper that presents a procedural approach to derive nonlinear filters from schematics of audio circuits for the purpose of digitally emulating musical effects circuits in real-time. This work presents the results of applying this physics-based technique to two audio preamplifier circuits. The approach extends a thread of research that uses variable transformation and offline solution of the global nonlinear system. The solution is approximated with multidimensional linear interpolation during runtime to avoid uncertainties in convergence. The methods are evaluated here experimentally against a reference SPICE circuit simulation. The circuits studied here are the bipolar junction transistor (BJT) common emitter amplifier, and the triode preamplifier. The results suggest the use of function approximation to represent the solved system nonlinearity of the K-method and invite future work along these lines.

This paper presents a procedural approach to derive nonlinear filters from schematics of audio circuits for the purpose of digitally emulating analog musical effects circuits in real time. This work, the first in a two-part series, extends a well-known efficient nonlinear continuous-time state-space formulation for physical modeling of musical acoustics to real-time modeling of nonlinear circuits. Rules for applying the formulation are given, as well as a procedure to derive simulation parameters automatically from circuit netlists. Furthermore, a related nonlinear discrete-time state-space algorithm is proposed to alleviate problems in solving particular circuit configurations. These methods were devised to solve non-convergence problems in the simulation of strongly saturated, nonparametric guitar distortion circuits such as the saturating diode clipper, which is presented as an example derivation. Experimental considerations and sonic performance on various other circuits will be presented in a subsequent paper.