Discontinuous transition time between stable states in ferroresonant circuits

The nonlinear differential equations for series and parallel ferroresonant circuits are solved to give the discontinuous transition time between stable states. This time agrees with experiment. Such things as the dependence of ¿jump time¿ on lamination thickness and a discussion of some general negative-resistance factors are given. The mathematical solution is accomplished by assuming the saturation curve of the inductor to be a series of odd-powered functions and the investigation is limited to the cubic term. First, a single sinusoidal solution is assumed and then a second term, third-harmonic correction, is included. The static results are compared with the actual observed circuit characteristic as well as with a simple graphical solution. Transient analysis is carried out using a variational approach which allows the perturbed differential equations to be reduced to canonical form. This results in a damping-time constant and oscillation frequency both of which are nonlinear. Hysteresis and eddy-current losses are found to have a significant effect and are included in the study.