Fundamental Oscillations of Coils and Windings [includes discussion]

Knowledge of the wave shapes and frequencies of the normal functions (or standing waves) of air and iron-core coils, transformer windings, and generator windings is of fundamental importance for the study of the response of these structures to impulse voltages and switching surges. In this paper the normal functions are determined for the cases of grounded and isolated neutral for the fundamental oscillations only. The mutual inductance between all turns of the winding is taken into account, by solving an integral equation, wherein the kernel depends upon the mutual inductance function. Examples are given for air and iron-core coils, and transformer windings, both uniform and non-uniform. Computed wave shapes and frequencies compare satisfactorily with measurements.