Oscillations of Coupled Windings [includes discussion]

The oscillations of a single winding have been extensively investigated, but actually the most important practical case, the oscillations of coupled windings, has received but scant attention. The wave shapes and natural frequencies are determined in this paper for two coupled windings of any turn ratio and with the same or opposite winding direction, in air or on an iron core. The integral equation and the equivalent circuit methods, previously developed for single windings, are extended to introduce the effect of the secondary on the primary, and then to investigate various winding combinations of turns ratio varying from 1 to 1 to 1 to 9. Good agreement is found between computed and measured values of the natural frequencies and wave shapes.