A universal analytic model for planar coils with circular windings close to conductive-permeable foils

For many applications the dimensions of the circuit are important design parameters especially for consumer electronics. In many cases the height of the whole circuit is fixed by the passive components like capacitors, transformers and inductors. So ultra thin planar coils are one of the possibilities for a height reduction. In this paper a universal analytical model for investigating the influence of conductive, permeable foils on the inductance of ultra thin planar coils for power electronics is introduced and explained in detail. First of all the equations for the magnetic vector potential in the whole circuit are derived. Based on that the final determination of the inductance is easily possible. Finally the equations are verified by measurements