Approach for Inductance Calculations of Coaxial Circular Coils Shielded by Cylindrical Magnetic Screen of Finite Length
Luo Yao1, Chen Baichao2, Zhou Hong1
1. School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China; 2. School of Electrical Engineering Wuhan University Wuhan 430072 China
Abstract：For the coaxial circular rings carrying currents which are placed into the cylindrical magnetic screen of finite length, a series expression of the mutual inductance is obtained. Herein, the formula of the magnetic scalar potential on the complex plane, as well as the contour deformation and the residue theorem is applied. The obtained expression is at least one hundred times faster than the traditional one. An ansatz of the magnetic scalar potential is then introduced. An alternative series expression of the mutual inductance of the coaxial circular rings is obtained, by using the spring characteristics of the magnetic scalar potential when it passing through the area surrounded by the ring. The eigenvalues of the series depend on the positive zeroes of the zero-order Bessel function. Consequently, the self and mutual inductances of the shielded coaxial circular coils with rectangular cross section are further obtained. The results of the numerical calculations are compared with those of the FEM simulations, which show good consistency.
罗垚, 陈柏超, 周洪. 有限长圆柱磁屏同轴线圈电感计算方法[J]. 电工技术学报, 2016, 31(14): 122-129.
Luo Yao, Chen Baichao, Zhou Hong. Approach for Inductance Calculations of Coaxial Circular Coils Shielded by Cylindrical Magnetic Screen of Finite Length. Transactions of China Electrotechnical Society, 2016, 31(14): 122-129.
[1] 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. [2] 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. [3] Luo Yao, Chen Baichao. Improvement of self- inductance calculations for circular coils of rectangular cross section[J]. IEEE Transactions on Magnetics, 2013, 49(3): 1249-1255. [4] Babic S, Sheppard S, Akyel C. The mutual inductance of two thin coaxial disk coils in air[J]. IEEE Transactions on Magnetics, 2004, 40(2): 822-825. [5] 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. [6] Buchholz B. Elektrische und magnetische Poten- tialfelder[M]. Göttingen: Springer, 1957. [7] Conway J T. Inductance calculations for noncoaxial coils using Bessel functions[J]. IEEE Transactions on Magnetics, 2007, 43(3): 1023-1034. [8] Hannakam L. Berechnung der gegeninduktivität achsenparalleler zylinderspulen[J]. Archiv für Elektro- technik, 1967, 51(5): 141-154. [9] Hannakam L. Praktische berechnung der Gegeni- nduktivität zweier kreisförmigen leiterschleifen in allgemeiner lage[J]. Archiv für Elektrotechnik, 1980, 62(1): 351-357. [10] 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]. Transactions of China Electrotechnical Society, 2012, 27(5): 132-136. [11] 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 Society, 2012, 27(6): 1-5. [12] Haas H. Ein beitrag zur berechnung der gegeni- nduktivität koaxialer zylinderspulen[J]. Archiv für Elektrotechnik, 1975, 57(1): 21-26. [13] 罗垚. 平行轴圆柱线圈互感计算的新方法[J]. 电工技术学报, 2016, 31(2): 31-37. Luo Yao. New approach for the mutual inductance calculations of the circular coils with parallel axes[J]. Transactions of China Electrotechnical Society, 2016, 31(2): 31-37. [14] Abramowitz M, Stegun I. Handbook of mathema- tical functions with formulas, graphs, and mathema- tical tables[M]. Washington DC: National Bureau of Standards, 1972. [15] Watson G N. A treatise on the theory of bessel functions[M]. Cambridge, UK: University Press, Mathematical Association of America, 1944. [16] Prudnikov A P, Brychkov Y A, Marichev O I. Integrals and series[J]. American Journal of Physiscs, 1988, 56(10): 957-958.
2016, Vol. 31 
