Modeling Piecewise-Linear Systems by Topological Techniques

Flowgraph techniques are extended to systems with piecewise-linear characteristics by developing criteria for construction of an optimum model from related subregions in which linearity holds. This requires the synthesis of several known techniques and results in a wide range of useful applications including: 1) devices with nonlinear characteristics which may be considered as linear over certain subregions; 2) networks whose response to changes in applied signal frequency or magnitude may be approximated by piecewise-linear asymptotes; 3) systems processing two or more signals simultaneously with different transfer or immitance characteristics for each signal; 4) circuits approximated by different equivalent circuits depending on the numerical values of critical parameters. Representative examples will illustrate these and similar applications. Procedures are presented to provide a logical, orderly, and effective approach to construct a model, to determine figures of merit, and to optimize the model for a prescribed region of operation or for a desired range of parameters.