Electromagnetic induction of planar windings with cylindrical symmetry between two half-spaces

A closed-form solution is derived for the equivalent impedance of a planar winding with cylindrical symmetry placed between two half-spaces. This is basically the structure of a domestic induction heating appliance comprised of a planar winding, a metallic vessel, and a lossless magnetic substrate. The first matter addressed is the impedance of a sandwiched single-turn coil, obtained by using the vector potential Helmholtz equation solution, and the result is generalized to n-turn coils. The real part of this impedance represents power dissipated in the form of heat. The proposed model includes geometry dependence, frequency of excitation currents, and electromagnetic properties of both top and bottom media. Enhancement of power dissipation in the conducting media as a result of the inclusion of a magnetic substrate is also explored. Experimental results are presented in order to validate the theoretical model.