Impedance calculation of a single-layer air-core coil by means of resonant modal theory

A method for calculating the impedance of a single-layer air-core coil is developed. The coil is expressed by a pair of multiphase distributed-parameter lines. The nodal voltages within the coil are transformed into a modal domain by applying an eigen theory. The transformation diagonalises the nodal equation expressed by Y-parameters of the distributed-parameter lines. The method permits composition of an equivalent circuit of the air-core coil. The accuracy of the model is easily tuned by adjusting the number of eigenvalues taken into account. The choice of the eigenvalues is carried out by the voltage distribution along the wire of the coil. The dominant mode is obtained by an assumption that the voltage distribution is uniform. This mode gives the lowest antiresonant frequency of the coil. The other distribution patterns are assumed to be sinusoidal. The second dominant mode corresponds to the lowest space frequency among the distribution patterns. In general, there is no relation between the order of the calculated eigenvectors and the voltage distribution. Its order is sorted according to the voltage distribution using an initial eigenvector matrix. The accuracy of the impedance increases with the number of eigenvalues, which are taken into account according to the sorted order. A simplified lumped-parameter equivalent circuit of the coil is derived for the major modes. The simplified model is able to represent not only antiresonances but also resonances of an air-core coil. The accuracy of the proposed model is confirmed by comparisons with measured and theoretical results.