On wireless power transfer between coils in the presence of radiation

Wireless power transfer (WPT) between magnetically coupled coils is necessarily accompanied by radiation that may hamper efficient power transfer and may cause harmful electromagnetic pollution. Hence careful control of the ratio between WPT and radiation is required. We have a formulation that allows the simultaneous determination of both the transferred and the radiated power by relying on both field and circuit theory and introducing the concept of a complex mutual inductance. Emphasis is placed on the visualisation of a radiative WPT system by using the streamlines of the Poynting vector. We perform several optimisations. We can find the parameters, coil radius, coil separation and load resistance, that maximise the ratio of load power to radiated power and at the same time minimise the radiated power. We identify the location of the singularities of the Poynting vector streamlines, the so-called P-points, and of the boundaries of a 'power bubble' surrounding the wireless two-coil system and forming an impenetrable barrier between the wireless power flow to the load and the power radiated out. A relationship between the size of the power bubble and the ratio between the useful load power and the harmful radiated power is established in a series of parametric studies. Field theory of Poynting vector streamlines is shown to quantitatively agree with the predictions of the circuit model. The new physical picture emerging for the power moving in space is expected to aid the design of complex practical WPT systems when radiation needs to be closely watched and for which a simple circuit model would fail to describe power distribution around the structure.