Models for nonlinear transmission lines

Nonlinear wave equations can be investigated either by numerical simulations with the aid of a model of computation or by building an equivalent electrical circuit with concentrated network elements. In both cases it is of great importance to find a model being close to the physical reality. Since the model is an approximation only some properties of the wave equation can be preserved by the model. A spatial discretization by an integration method reduces the nonlinear partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). This ODE can be interpreted as an electrical circuit. A variety of integration methods is available. Regions of validity for the circuit model have to be derived from stability conditions of the associated integration method. Hence the modelling involves physical and mathematical aspects. In this papers several circuit models for both linear and nonlinear lossless wave equations are presented. The quality in the linear case is evaluated by a comparison of network properties like reciprocity, symmetry, losslessness and non-minimum-phase property with the analytic solution.