FEA-Based Model of Elliptic Coils of Rectangular Cross Section

We present a 3-D finite element analysis (FEA)-based model of elliptic coils. The type of elliptic coil addressed in this paper is the constant-turn density coil, which corresponds to practical implementations of flat or solenoid-type coils wound on an ellipse-shaped bobbin. We assume a coil model consisting of constant current density perpendicular to the cross section along the current trajectory. This model covers the dc operation and the ac applications with multistranded litz wires. The perpendicular current condition of the elliptic coil is implemented in the FEA tool by the gradient of the winding function and the vector trajectory of the currents. In addition, a frequency-dependent calculation of the resistance of the litz wire is included. Hence, electric parameters as the self-inductance or resistance of the elliptic coil can be extracted from the FEA tool as a function of the geometrical parameters. The model is applied to obtain the mutual inductance between two elliptic coils for different misalignments. Finally, a comparison between the self-inductance and winding resistance measurements obtained from a flat coil prototype in several scenarios and the simulation results is presented.