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

Abstract

Abstract-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.

2d Disturbance Map of Low-Power Front-End Circuits in Low Frequency Band

“…To determine the mutual inductance, the method presented by Soma et al [14] and used by [2,15,16] in the analysis of the efficiency of inductive energy transfer was applied. The works of [17,18] are its extension, introducing the possibility of a more precise analysis of multi-winding coils based on replacing the integral from Equation (6) with its development into the Taylor series. In accordance with [14], the mutual inductance M of two magnetically coupled coils that are separated from each other by (x, y, 0) can be determined as…”

“…where K(r) and E(r) are complete elliptic integrals of the first and second type, respectively. The mutual inductance M is associated with the coupling factor k by formula (12) [16][17][18][19], which makes it possible to refer it to the inductance values of the Tx and Rx coils.…”

“…Formula (17) indicates that there is a significant increase in the error for decreasing values of k, i.e., for the most distant positions (x, y). The position x = 35 mm, y = 25 mm was assumed as the measurement limit in which repeatable k values were obtained, despite its main determination by L short (L open was almost constant).…”

“…It is not necessary to search for the analytical form of Equation 18 12and (13), taking into account the uncertainties in Eqs. (17) and (18). For the coaxial direction, i.e., along the X(5, 0) → (35, 0) axis, a precise mapping of the theoretical course is visible.…”

Near Field Shielding of a Wireless Power Transfer (Wpt) Current Coil

“…Nowadays, growing interest is directed to EMF safety concerns about magnetic fields in applications related to the emerging technology of the Wireless Power Transfer (WPT) based on magnetic resonant coils [13][14][15][16][17][18][19][20]. WPT for battery recharging is spreading in a number of applications such as automotive, biomedical devices, and consumer electronics.…”