Analytical Modeling of Self- and Mutual Inductances of DD Coils in Wireless Power Transfer Applications

Abstract

Self- and mutual inductances are major design parameters for wireless power transfer (WPT) systems. To optimize a WPT system and estimate its performance in terms of received power and efficiency, it is essential to obtain a simple, fast, and accurate calculation of these two parameters. The polarized double-D (DD) coils were selected due to their simplicity of structure, high efficiency, and low sensitivity to misalignment conditions. This paper presents analytical calculations of self- and mutual inductance using the Biot-Savart law for DD coils. The results of the analytical calculations of mutual inductance in different distances between coils were investigated, and the results of the calculations were verified using experimental and finite element method (FEM) simulation results. This paper also presents analytical and FEM-based optimization guidelines for the coupling coefficient of the transmitter coil.

Fast Analytic‐Numerical Algorithms for Calculating Self and Mutual Inductances of Air Coils

“…The magnetic field distribution in the configuration analyzed above is shown in Figure 3a (both coils are powered by the current having the same value and direction), while the field distributions when powering single coils are shown in Figure 3b,c, respectively. The values of self-inductances calculated using the FEM from formula ( 5) is equal to The papers [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] discuss, among other things, many configurations of cylindrical coaxial coils and determine their mutual inductances. These results were also confirmed using the computational algorithm described herein.…”

“…The problem of determining self-and mutual inductances, as well as the field distribution of such coils, is thus reduced to determining the interactions between elementary thin coaxial coils. A similar approach to this issue was also discussed in articles [23,24].…”

“…Methods for calculating the self and mutual inductances of different air coils have been presented in many articles [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Fast Analytic–Numerical Algorithms for Calculating Mutual and Self-Inductances of Air Coils

“…The problem of determining mutual and self-inductances, as well as the field distribution of such coils, is thus reduced to determining the interactions between elementary thin coaxial coils. A similar approach to this issue was also discussed in articles [30,31].…”

“…The mutual inductance between both coils can finally be calculated as in Equation (20). Similar methods using the magnetic flux linking other rectangular coils were used, among others, in [30,31].…”