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Abstract A method for calculating the mutual inductance of circular coils with parallel axes is presented by using the modified Bessel and modified Struve functions, which is obtained by the expansion expressions of the reciprocal distance in the cylindrical coordinates. The obtained expressions are further coped with the asymptotic expansions to facilitate the numerical calculations. The monotonicity of the modified Bessel and Struve functions is beneficial to the numerical evaluations of the improper integral, especially in the case of short thick coils or disk coils with large radial distance and small axial distance. The proposed method is several tens to hundreds times faster than the existing method using the oscillatory Bessel and Struve functions, with the same accuracy. Additionally, a closed-form solution of the mutual inductance for coplanar circular loops is given using the Gauss hypergeometric functions, and it is verified by numerical calculations.
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Received: 03 January 2014
Published: 03 March 2016
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[1] Raju S, Wu R, Chan M, et al. Modeling of mutual coupling between planar inductors in wireless power applications[J]. IEEE Transactions on Power Electro- nics, 2014, 29(1): 481-490.
[2] Acero J, Carretero C, Lope I, et al. Analysis of the mutual inductance of planar-lumped inductive power transfer systems[J]. IEEE Transactions on Industrial Electronics, 2013, 60(1): 410-419.
[3] Low Z N, Chinga R A, Tseng R, et al. Design and test of a high-power high-efficiency loosely coupled planar wireless power transfer system[J]. IEEE Transactions on Industrial Electronics, 2009, 56(5): 1801-1812.
[4] 卡兰塔罗夫П Л, 采伊特林Л А. 电感计算手册[M]. 北京: 机械工业出版社, 1992.
[5] Conway J T. Inductance calculations for circular coils of rectangular cross section and parallel axes using Bessel and Struve functions[J]. IEEE Transactions on Magnetics, 2010, 46(1): 75-81.
[6] Buchholz H. Elektrische und magnetische Potential- felder[M]. Gottingen: Springer, 1957.
[7] Hannakam L. Berechnung der Gegeninduktivitat achsenparalleler Zylinderspulen[J]. Archiv für Elek- trotechnik, 1967, 51(5): 141-154.
[8] Hannakam L. Praktische Berechnung der gegenin- duktivitat zweier kreisförmigen Leiterschleifen in allgemeiner Lage[J]. Archiv für Elektrotechnik, 1980, 62(1): 351-357.
[9] Abramowitz M, Stegun I. Handbook of mathematical functions with formulas, graphs, and mathematical tables[M]. Washington D C: National Bureau of Standards, 1972.
[10] Conway J T. Analytical solutions for the self-and mutual inductances of concentric coplanar disk coils[J]. IEEE Transactions on Magnetics, 2013, 49(3): 1135-1142.
[11] Yao Luo, Chen Baicao. Improvement of self- inductance calculations for circular coils of rectan- gular cross section[J]. IEEE Transactions on Magnetics, 2013, 49(3): 1249-1255.
[12] Babic S, Sheppard S, Akyel C. The mutual induc- tance of two thin coaxial disk coils in air[J]. IEEE Transactions on Magnetics, 2004, 40(2): 822-825.
[13] Conway J T. Inductance calculations for noncoaxial coils using Bessel functions[J]. IEEE Transactions on Magnetics, 2007, 43(3): 1023-1034.
[14] 罗垚, 陈柏超, 袁佳歆,等. 倾斜轴空心矩形截面圆柱线圈互感计算[J]. 电工技术学报, 2012, 27(5): 132-136.
Luo Yao, Chen Baichao, Yuan Jiaxin,et al. Mutual inductance calculations of inclined axial air-core circular coils with rectangular cross-sections[J]. Trans- actions of China Electrotechnical Sosiety, 2012, 27(5): 132-136.
[15] 罗垚, 陈柏超. 空心矩形截面圆柱线圈自感计算的新方法[J]. 电工技术学报, 2012, 27(6): 1-5.
Luo Yao, Chen Baichao. New method for self- inductance calculations of air-core circular coils with rectangular cross-sections[J]. Transactions of China Electrotechnical Sosiety, 2012, 27(6): 1-5.
[16] Haas H. Ein Beitrag zur Berechnung der Gegenin- duktivität koaxialer Zylinderspulen[J]. Archiv für Elektrotechnik, 1975, 57(1): 21-26.
[17] Babic S, Sirois F, Akyel C, et al. Mutual inductance calculation between circular filaments arbitrarily posi- tioned in space: alternative to Grover’s formula[J]. IEEE Transactions on Magnetics, 2010, 46(9): 3591-3600.
[18] Watson G N. A Treatise on the theory of bessel functions[M]. Cambridge, U. K.: Univ. Press, 1944.
[19] Prudnikov A P, Brychkov Y A, Marichev O I. Inte- grals and series[M]. New York: Gordon and Breach, 1992. |
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2016, Vol. 31 
