Inductance calculations for air core foil wound transformers

Equations and methods for self and mutual inductance calculations of air core foil wound inductors or transformers are presented. In particular, current distribution and the related effects on inductance and coupling are analyzed and verified by experiments. The method of analysis is based on decomposing cylindrical foils into numerous loops which are characterized by self and mutual inductances. Matrix circuit analysis methods are used to solve the n-loop equations for the current distributions and to approximate a simplified equivalent circuit consisting of two coupled inductors. The effects were studied using two concentric cylinders. It was found that the effects are minimal when the lengths of the cylinders are approximately the same. When the cylinders are of significantly different lengths, large eddy currents develop in the longer cylinder which significantly affect the self and mutual inductances. In all cases the method of analysis agrees with experimental data