The inductance of planar structures

A method for calculating the inductance of planar-spiral structures in the presence, and in the absence, of magnetic core material is presented. In this method, the current is assumed to flow in the exact center of the planar conductor. Simplified expressions for the self inductance of each turn comprising the inductor, and the mutual inductance between turns on the same layer of the inductor are developed. An expression for the leakage flux between turns on adjacent layers is presented. The effect of a magnetic core on the inductance is considered, and an equivalent magnetic circuit for the core is developed. At the measurement frequency of 100 kHz, the new expressions exhibit better agreement with measurements than do existing ones presented in the literature.>