The analysis of non-linear resonant circuits

The paper describes two graphical methods of calculating the instantaneous voltages and currents which result from feeding a sinusoidal current to a resonant circuit which employs a non-linear inductor. The voltage-integral method uses a step-by-step approximation to the actual inductor characteristic, including hysteresis. Knowledge of the detailed waveforms facilitates the determination of the optimum magnitude and timing of a pulse to trigger a ferroresonant circuit from the dissonant to the resonant state. Calculated waveforms are satisfactorily confirmed experimentally. Alternatively, the phase-plane method allows the use of a piecewise linear approximation to the magnetization characteristic of the core of the inductor (e.g. three straight lines), but at the cost of ignoring hysteresis.