Mutual Inductance Calculation between Misalignment Coils for Wireless Power Transfer of Energy

In this paper we present a detailed theoretical analysis of lateral and angular misalignment effects in RF coils. Radio-frequency (RF) coils are used extensively in the design of implantable devices for transdermal power and data transmission. A design procedure is established to maximize coil coupling for a given configuration to reduce the effects of misalignment on transmission efficiency. Formulas are derived for the mutual inductance between all possible coil configurations including the coils of cross section, thin solenoids, pancakes and filamentary circular coils whose axes are laterally and angularly displaced. Coils are in air. In this approach we used the filament method and the mutual inductance between filamentary circular coils placed in any desired position. We completely describe all mathematical procedures to define coil positions that lead to relatively easy method for calculating the mutual inductance between previously mentioned coils. The practical coils in implantable devices fall into two categories: disk coils (pancakes) and solenoid coils. From the general approach for calculating the mutual inductance between coils of rectangular cross section with lateral and angular misalignments the mutual inductance between misalignment solenoids and disks will be calculated easily and accurately.