Numerical Methods for Simulation of Guitar Distortion Circuits

Abstract

Electric guitarists prefer analog distortion effects over many digital implementations. This article suggests reasons for this and proposes that detailed study of the electrical physics of guitar distortion circuits provides insight to design more accurate emulations. This work introduces real- time emula- tion applied to guitar audio amplifi ers in the form of a tutorial about relevant numerical methods and a case study. The results here make a compelling case for simulating musical electronics using numerical methods in real time. Analog guitar distortion effect devices known as solid- state distortion boxes commonly include a diode clipper circuit with an embedded low- pass fi lter. These distortion- effect devices can be mod- eled and accurately simulated as Ordinary Differen- tial Equations (ODEs). A survey and a comparison of the basic numerical integration methods are presented as they apply to simulating circuits for audio processing, with the widely used diode clipper presented as an example. A dedicated simulator for the diode clipper has been developed to compare several numerical integration methods and their real- time feasibility. We found that implicit or semi- implicit solvers are preferred, although the prefi lter / static nonlinearity approximation comes surprisingly close to the actual solution.