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Integral expressions of the equivalent impedance of flat-type coils for induction heating systems are derived. These expressions are obtained by integration the analytical solution of the field generated by a circular filamentary current placed between two linear and homogeneous semi-infinite media. It is considered that the windings are wound with a round wire. The model also gives the magnetic field in the cross section of the windings, which is necessary to calculate the proximity losses in the cables. The solution is given in terms of Bessel function integrals, which are calculated by means of MATLAB. Several prototypes having different turns were constructed and tested with different loads. Measurements confirm the validity of the analytical models.