Jump behavior of circuits and systems

Abstract

Some circuits exhibit jump behavior. for example, this occurs when the velocity field specified by the\dot{i}_Land\dot{\upsilon}_cof the inductor and capacitor characteristics cannot be "lifted" on to the resistive constraint manifold. The (jump) behavior is viewed as the limit as\epsilon \rightarrow 0of the solutions of a regularized system of equations obtained by introducing suitably located\epsilon-parasiticL's andC's: this leads to a consistent way of defining discontinuous solutions. In particular, the behavior near a fold and cusp is examined. The concept of physically measurable operating point is defined and is related to that of strict local dissipativeness (which generalizes that of strict local passivity). Two examples are included.