Decomposition of Impedance Loci in WPT Systems Under Mutual Interference of Magnetic Flux Conductivity Using Möbius Transform

In automotive application, wireless power transfer (WPT) systems are desired to operate in a wide range of coupled coils and system topology combinations. The operating range of a single primary side is therefore subject to alternating load conditions and resonant tank detuning. This is caused by parameter uncertainties due to relative coil positioning, different vehicle types and numerous degrees of freedom during interoperable design. In terms of running WPT systems with diverse charging entities, this paper introduces the Mobius transform as a valuable tool to decompose and visualize the inherent shifting of a systems operational range due to mutual interference of magnetic flux conductivity and varying inductive coupling condition. By its rigorous formalism and yet intuitive geometry, the image of locus trajectories can be classified into four characteristic categories. In this context, this paper demonstrates the application of cascaded Möbius Transforms in double-sided LCC-compensated systems to decompose its input impedance.