A planar coil of multiple loops connected in series and in parallel is proposed for wireless power transfer (WPT). The current direction in each loop is mixed in forward and in reverse. The proposed coil gives uniform mutual inductance and enables simple impedance matching for free-positioning WPT.

An effective calculation method for AC resistance and the inductance of planar rectangular spiral coils is proposed. For the calculation, a volume filament model and its equivalent circuit are provided. By using the method, AC resistance and inductance are calculated accurately in megahertz frequency range by including both skin and proximity effects. The method is verified with experiments and used to optimise rectangular spiral coils for the maximum quality factor (Qfactor) at 6.78 MHz. A small planar rectangular coil is shown to have the maximum Q-factor when the width of the innermost coil loop is about a half of that of the outermost coil loop.

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