Geometrical interpretation of jump phenomena in nonlinear dynamical circuits

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.