Simulation of the Diode Limiter in Guitar Distortion Circuits by Numerical Solution of Ordinary Differential Equations

The diode clipper circuit with an embedded low-pass filter lies at the heart of both diode clipping “Distortion” and “Overdrive” or “Tube Screamer” effects pedals. An accurate simulation of this circuit requires the solution of a nonlinear ordinary differential equation (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 methods such as Forward Euler and fourth order Runge-Kutta, which require very high sampling rates for stability. This paper surveys 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 implicit or semiimplicit solvers are preferred and that the filter/static nonlinearity approximation is often perceptually adequate.