Geometrical interpretation of jump phenomena in nonlinear dynamical circuits

Abstract

There is a special class of nonlinear electronic circuits containing a fold in their state space which results in a jump behaviour in the system characteristic. This can lead to difficulties during the simulation of these systems with common circuit simulators. For this reason usually suitably located parasitic inductors L's and capacitors C's were added to regularize the electronic circuit. We for our purpose describe these circuits in a differential geometric setting to detect jump points ahead. Having the jump points and defining the jump direction with physical constraints, one can overcome the problems of jumps without adding regularization L's or C's. In this paper differential geometric methods were applied to two example circuits and numerical results were presented.