Simulation of nonlinear circuits with period doubling and chaotic behavior by wave digital filter principles

For the simulation of linear and nonlinear circuits it is important that the unavoidable errors which are caused by the discretization in time and by the quantization of signals do not change the properties of the circuit in an inadmissible manner. Especially, this is valid for the errors which may result from the applied numerical methods, e.g. for the integration. The effects of various numerical methods can easily be studied at a simple circuit. In particular, nonlinear circuits are well suited because they are very sensitive to small changes of their element parameters. In this paper, a simple RLC circuit containing a nonlinear capacitance is simulated. The circuit exhibits a chaotic dynamic and, if driven by a sinusoidal input, produces subharmonic oscillations. The simulation is based on the well-known wave digital (WD) filter principles, i.e., as signal parameters wave quantities are used and the integration is performed according to the trapezoidal rule. The advantages of WD simulation are demonstrated by showing that the results are not very much affected if the sample rate is changed within certain limits