Mathematic analysis of omnidirectional wireless power transfer part-II 3-dimensional systems

Part-II of this paper focuses on the mathematical analysis of the 3-D omnidirectional wireless power transfer (WPT) and also addresses the general principle of load detection. It provides the mathematical forms of distributions of the input power vector and output power vector, and demonstrates that the geometry of such 3-D distributed space follows the revolution of the Lemniscate of Bernoulli along its longitudinal axis. It provides the mathematical proof that the direction of energy transfer for the maximum energy efficiency is always in line with that of the maximum load power path in the 3-D space. Experimental verification is included to confirm the 3-D omnidirectional WPT theory.