Natural Frequencies of Coils and Windings Determined by Equivalent Circuit [includes discussion]

Knowledge of the natural frequencies of air-core and iron-core coils and of transformer and generator windings is of essential theoretical and practical importance. In this paper an equivalent circuit method is derived for the computation of all the natural frequencies of interest of both air-core and iron-core coils. This method takes into account all mutual inductance linkages, which usually have been neglected in the literature. Neglect of mutual inductance linkages leads to computed frequencies which do not agree with the measured frequencies. It is therefore necessary to consider the mutual inductance linkages in the computation of the natural frequencies of coils and windings. The equivalent circuit with all mutual inductance linkages may be solved by punch-card equipment, or by setting up an appropriate circuit on the a-c network analyzer. Both methods of solution are accurate; either one may be preferable in practice, depending upon the circumstances. The natural frequencies of a coil with air and iron core and different capacitive parameters, computed in this manner, are compared with the measured frequencies. Agreement between computed and measured values is excellent for the first seven harmonics of the air-core coil, and for the first three harmonics of the iron-core coil.