基于增强型截断域本征函数展开法的磁屏圆筒铁心线圈电感的解析计算

doi:10.19595/j.cnki.1000-6753.tces.250121

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Abstract The size of air-core coils does not meet the demands of modern electrical devices, which require both compactness and strong anti-interference capabilities. Additionally, air-core coils require a large amount of material due to their high number of turns, and are often susceptible to external interference, leading to instability. To overcome the defects, the air-cored coil is replaced by a tubular iron-core coil with a magnetic shield, where the tubular iron-core can reduce material cost of an iron core without remarkably affecting the inductance values. However, the complex structure makes it challenging to determine the parameters such as self and mutual- inductance. In previous studies, the inductance problems of iron-core coils were typically solved using boundary value problem (BVP) methods. Recently, a novel approach was provided that can solve problem of coil’s inductance with magnetic core effectively. Building on this approach, this paper proposes formulas for calculating self and mutual-inductance of a tubular iron-core coil with a magnetic shield by the enhanced truncated region eigenfunction expansion (ETREE) method.
In Section 1, we firstly address the inductance calculation problem of a tubular iron-core coil with an infinite permeability of the magnetic shield, which consists of three sub-domains in the vertical direction. However, when the permeability of the magnetic shield is not sufficiently large, this assumption may introduce an error. To overcome this limitation, the Section 2 considers the precise permeability and thickness of the magnetic shield. In this case, the coil system has seven sub-domains in vertical direction, requiring more computational steps than in Section 1. By employing the ETREE technique, the resulting equations are simpler and more streamlined than those derived from the traditional TREE method. Matrix operations and the energy method are then applied to efficiently and accurately calculate both self-inductance and mutual inductance.
Simulations by COMSOL Multiphysics^® are carried out in this paper to verify the accuracy of the proposed formulas. For the simulation verification of self-inductance, the different positions of coils 1 and 2 are verified respectively. The simulation verification of mutual inductance is carried out by moving coil 2 with fixed coil 1. The results show that the analytical solutions by ETREE technology has high computational efficiency and computational accuracy. In addition, the inductance calculated by an infinite magnetic permeability shield shows a small error (<2%) compared to the results obtained from an accurate magnetic permeability model when the ratio γ between permeability of magnetic wall and magnetic core is larger than 30%. In terms of time cost, the method in section 1 consumes around 0.7 seconds whereas the method in section 2 costs averagely 1.2 seconds. For comparison, the corresponding time for the finite elements method is 6~7 seconds.
The following conclusions can be drawn:
(1) The formulas presented in this paper can be used to calculate the inductance of coil systems with varying geometric parameters, magnetic permeabilities, and coil positions, including those for coils, cores, and shields.
(2) The formulas developed in this work exhibit both high accuracy and efficiency. This improvement can be applied to related electrical devices, such as passive filters and iron-core reactors.
(3) Assuming the shield has infinite permeability enhances computational efficiency while maintaining accuracy. However, when the difference between the magnetic permeabilities of the iron core and the shield becomes too large, this assumption introduces significant error. In such cases, the method outlined in Section 2 is recommended.

Key words： Magnetic shield inductance of iron-core coils enhanced truncated region eigenfunction expansion inductance calculation

Received: 16 January 2025

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TM153+.2

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	Yu Dongze
	Chen Baichao
	Luo Yao
	Xiang Yike

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Yu Dongze,Chen Baichao,Luo Yao等. The Analytical Calculation of the Inductance of Magnetic Shielded Tubular Core Coils Based on the Enhanced Truncated Region Eigenfunction Expansion Method[J]. Transactions of China Electrotechnical Society, 2026, 41(3): 749-759.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.250121 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I3/749

[1] Cauer W.Die verwirklichung von wechselstrom-widerständen vorgeschriebener frequenzabhängigkeit[J]. Archiv Für Elektrotechnik, 1926, 17(4): 355-388.
[2] Humpherys D S.The analysis, design, and synthesis of electrical filters[M]. Englewood Cliffs, NJ: Prentice-Hall, 1970: 202-215.
[3] Ho S C, Hwang G J.The study of transient electromagnetic fields in a multi-turn, voltage-excited laminated core reactor[J]. IEEE Transactions on Magnetics, 1989, 25(3): 2699-2705.
[4] Kim J, Kim D H, Choi J, etal. Free-positioning wireless charging system for small electronic devices using a bowl-shaped transmitting coil[J]. IEEE Trans-actions on Microwave Theory and Techniques, 2015, 63(3): 791-800.
[5] 常雨芳, 尹帅帅, 阎晟, 等. 多方位无线电能传输耦合机构设计与分析[J]. 电源学报, 2024, 22(5): 230-241.
Chang Yufang, Yin Shuaishuai, Yan Sheng, et al.Design and analysis of multi-directional WPT coupling mechanism[J]. Journal of Power Supply, 2024, 22(5): 230-241.
[6] 李中启, 包明晗, 孔令军, 等. 无线电能传输系统多孔磁介质任意位置矩形线圈间互感计算方法[J]. 电工技术学报, 2025, 40(24): 7863-7878.
Li Zhongqi, Bao Minghan, Kong Lingjun, et al.Calculation of mutual inductance between rectangular coils at arbitrary positions of porous magnetic media for wireless energy transmission systems[J]. Trans-actions of China Electrotechnical Society, 2025, 40(24): 7863-7878.
[7] 陈彬, 姜鹏飞, 万妮娜, 等. 同轴多层筒式空心线圈自感和互感解析计算方法[J]. 电工技术学报, 2024, 39(20): 6270-6281.
Chen Bin, Jiang Pengfei, Wan Nina, et al.Analytical calculation for self and mutual inductance of coaxial multi layer cylindrical hollow coils[J]. Transactions of China Electrotechnical Society, 2024, 39(20): 6270-6281.
[8] 刘阳, 张璐, 吴德强, 等. 基于INGO-SVM的输电铁塔地脚螺栓螺母缺失无损检测方法[J]. 高压电器, 2025, 61(2): 130-140.
Liu Yang, Zhang Lu, Wu Deqiang, et al.Non-destructive detection method for nuts missing defect on anchor bolts of transmission tower based on INGO-SVM[J]. High Voltage Apparatus, 2025, 61(2): 130-140.
[9] Buchholz H.Beitragzurtheorie der reaktanzspulen mit offenem eisenkern[J]. Archiv Für Elektrotechnik, 1930, 24(3): 285-304.
[10] Buchholz H.Berechnung der reaktanzspulen mit offenem eisenkern[J]. Archiv Für Elektrotechnik, 1932, 26(4): 233-249.
[11] Timmerberg J.Kraftwirkung auf eine räumliche zylind-rische Spule infolge eines hochpermeablen Zylinders[J]. Archiv Für Elektrotechnik, 1983, 66(5): 289-293.
[12] Dodd C V, Deeds W E.Analytical solutions to eddy-current probe-coil problems[J]. Journal of Applied Physics, 1968, 39(6): 2829-2838.
[13] Lubin T, Berger K, Rezzoug A.Inductance and force calculation for axisymmetric coil systems including an iron core of finite length[J]. Progress in Electromagnetics Research B, 2012, 41: 377-396.
[14] Lu Yi, Bowler J R, Theodoulidis T P.An analytical model of a ferrite-cored inductor used as an eddy current probe[J]. Journal of Applied Physics, 2012, 111(10): 103907.
[15] LuoYao. Field and inductance calculations for coaxial circular coils with magnetic cores of finite length and constant permeability[J]. IET Electric Power Appli-cations, 2017, 11(7): 1254-1264.
[16] 陈伟华, 刘岳鹏, 闫孝姮, 等. 心脏起搏器谐振式无线供能四匹配电容无功屏蔽[J]. 电工技术学报, 2025, 40(2): 1-11.
Chen Weihua, Liu Yuepeng, Yan Xiaoheng, et al.reactive shielding of four matching capacitors for resonant wireless power transfer in cardiac pace-makers[J]. Transactions of China Electrotechnical Society, 2025, 40(14): 4382-4394.
[17] 林志远, 李中启, 胡昌轩, 等. 无线电能传输带凸字环形有界磁屏蔽任意位置圆形线圈互感计算方法[J]. 电工技术学报, 2024, 39(16): 4918-4930.
Lin Zhiyuan, Li Zhongqi, Hu Changxuan, et al.Mutual inductance calculation method of arbitrarily positioned circular coils with convex ring type finite magnetic shielding in wireless power transfer[J]. Transactions of China Electrotechnical Society, 2024, 39(16): 4918-4930.
[18] 叶宗彬, 高晨潇, 刘旭. 基于屏蔽极板全双工通信无线电能传输系统[J]. 电工技术学报, 2025, 40(12): 3770-3786.
Ye Zongbin, Gao Chenxiao, Liu Xu.Wireless power transmission system based on full-duplex commu-nication with shielded capacitor plate[J]. Transactions of China Electrotechnical Society, 2025, 40(12): 3770-3786.
[19] 张宇翔, 何为, 孔晓涵, 等. 基于硅钢片均一化的超低场磁共振抗涡流Z梯度线圈设计方法[J]. 电工技术学报, 2025, 40(4): 987-996.
Zhang Yuxiang, He Wei, Kong Xiaohan, et al.A design method for eddy current-resistant Z-gradient coil in ultra-low field magnetic resonance imaging systems based on homogeneous of silicon steel sheets[J]. Transactions of China Electrotechnical Society, 2025, 40(4): 987-996.
[20] 杨慧娜, 温珺, 丛浩熹. 大容量变压器夹件的电磁力及减振方法研究[J]. 高压电器, 2024, 60(11): 9-17.
Yang Huina, Wen Jun, Cong Haoxi.Study on electro-magnetic force and vibration reduction method of large capacity transformer clamp[J]. High Voltage Apparatus, 2024, 60(11): 9-17.
[21] Kaden H.Die Elektromagnetische Schirmung in Der Fernmelde-Und Hochfrequenztechnik[M]. Cham: Sprin-ger Berlin Heidelberg, 1950.
[22] Theodoulidis T, Bowler J R.Interaction of an eddy-current coil with a right-angled conductive wedge[J]. IEEE Transactionson Magnetics, 2010, 46(4): 1034-1042.
[23] Luo Yao, Yang Xinyi.Impedance variation in a coaxial coil encircling a metal tube adapter[J]. Sensors, 2023, 23(19): 8302.
[24] Luo Yao, Yang Xinyi, Kyrgiazoglou A.Analytical model of an I-core coil inspecting a metal disk with a borehole and an annular slot[J]. IEEE Sensors Journal, 2024, 24(7): 9765-9771.
[25] Xiang Yike, Luo Yao, Tytko G, et al.Analytical model of an I-core coil inside a metal tube of finite length[J]. Journal of Electromagnetic Waves and Applications, 2024, 38(13): 1464-1479.
[26] Jung M, Langer U.Methode der finiten Elemente für Ingenieure[M]. Wiesbaden, Germany: Springer, 2013.