Fano Resonance Among Magnetic Coils for Midrange Position Sensing Capability

A magnetically coupled three-coil system to have one transmitting and two receiving coils is considered. We show that the position of the transmitting coil can be estimated from the ratio of received wave amplitudes and its angular derivative when the two receiving coils are strongly coupled to each other and each of the receiving coils is weakly coupled to the transmitting coil, i.e., a Fano resonance phenomenon. A coupled mode theory is developed to elucidate the midrange position sensing mechanism, where the ratio of received wave amplitudes is inversely proportional to the ratio of the coupling strengths of each receiving coil to the transmitting coil at the intrinsic resonance frequency of the receiving coils.