SIMULATION OF THE DIODE LIMITER IN GUITAR DISTORTION CIRCUI TS BY NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

The diode clipper circuit with an embedded low-pass filter li es at the heart of both diode clipping "Distortion" and "Overdrive" or "Tube Screamer" effects pedals. An accurate simulation of this cir- cuit requires the solution of a nonlinear ordinary differen tial equa- tion (ODE). Numerical methods with stiff stability - Backward Euler, Trapezoidal Rule, and second-order Backward Difference Formula - allow the use of relatively low sampling rates at the cost of accuracy and aliasing. However, these methods require iteration at each time step to solve a nonlinear equation, and the tradeoff for this complexity must be evaluated against simple explicit meth- ods such as Forward Euler and fourth order Runge-Kutta, which require very high sampling rates for stability. This paper s urveys and compares the basic ODE solvers as they apply to simulating circuits for audio processing. These methods are compared to a static nonlinearity with a pre-filter. It is found that impli cit or semi- implicit solvers are preferred and that the filter/static no nlinearity approximation is often perceptually adequate.