Instantaneous Switching Processes in Quasi-Linear Circuits

The paper considers instantaneous processes in electrical circuits produced by the stepwise change of the capacitance of the capacitor and the inductance of the inductor and by the switching on and switching off of the circuit. In order to determine the set of electrical circuits, for which it is possible to explicitly obtain the values of the currents and the voltages at the end of the instantaneous process, a classification of the networks with nonlinear elements is introduced in the paper. The instantaneous switching process in the moment t0 is approximated when T->t0 with a sequence of processes in the interval [t0, T]. For quasi-linear inductive and capacitive circuits; we present the type of the system satisfied by the currents and the voltages, the charges, as well as the fluxes in the interval [t0, T]. From this system, after passage to the limit T->t0, we obtain the formulas for the values of the circuits at the end of the instantaneous process. The obtained results are applied for the analysis of particular processes.