圆盘线圈自、互感的闭式解及其自感最优值

doi:10.11930/j.issn.1004-9649.201804035

中国电力 ›› 2019, Vol. 52 ›› Issue (8): 71-77.DOI: 10.11930/j.issn.1004-9649.201804035

圆盘线圈自、互感的闭式解及其自感最优值

朱润杭, 赵雅婷

武汉大学电气与自动化学院, 湖北武汉 430072

收稿日期:2018-04-13 修回日期:2018-09-24 发布日期:2019-08-14
通讯作者: 朱润杭(1995-),男,通信作者,硕士研究生,从事电磁场的解析计算研究,E-mail:zrh1041353994@outlook.com
作者简介:赵雅婷(1998-),女,本科,从事无源电力滤波器的设计及研究,E-mail:1292098313@qq.com
基金资助:
国家自然科学基金资助项目（互感耦合多调谐无源电力滤波器技术原理与设计方法研究，51507115）。

Closed Form Expressions of Self and Mutual Inductance of Disk Coils and the Optimal Value of Self-Inductance

ZHU Runhang, ZHAO Yating

School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

Received:2018-04-13 Revised:2018-09-24 Published:2019-08-14
Supported by:
This work is supported by National Natural Science Foundation of China (Research on technology principle and design method of mutual inductance coupled multi-tuned passive power filter, No.51507115).

摘要/Abstract

摘要： 圆盘线圈是近年来兴起的无线能量传输系统中能量耦合的核心元件。通过引入广义超几何函数_pF_q将圆盘线圈的自感积分表达式化为闭式。类似地，通过建立完全椭圆积分与广义超几何函数之间的联系将同轴共面圆盘线圈的互感化为闭式。这些闭式解使上述电感计算问题不再需要数值积分。进一步，基于所得闭式解，分析了圆盘线圈的GPW（given piece of wire）优化问题，得到了给定导线所能绕制的圆盘线圈自感最大值，且达到最大值的圆盘线圈外半径与内半径之比是一个与导线几何参数无关的常数。数值计算表明所得公式与已有方法所得结果一致性较好。

关键词: 圆盘线圈, 自/互感, 广义超几何函数, 完全椭圆积分, GPW优化问题

Abstract: The disk coils are the core element of energy coupling of the wireless power transmission system blooming in recent years. By introducing generalized hypergeometric functions _pF_q, the integral expression of self-inductance of disk coils is transformed into a closed form. Similarly, the closed form expression of mutual inductance of coaxial coplanar disk coils is obtained by establishing a relationship between the complete elliptic integrals and generalized hypergeometric functions. These closed form solutions can bypass the numerical integration of traditional methods for the inductance calculations. Furthermore, based on the obtained closed form solution the GPW (given piece of wire) optimization problem is analyzed and the maximum value of self-inductance is found for disk coils which are wound by a piece of given wire. It is also revealed that the ratio of the outer and inner radii of the optimal disk coils is independent of the geometric parameters of winding wires. Numerical results show the high consistency between existing methods and methods proposed in this paper.

Key words: disk coils, self and mutual inductance, generalized hypergeometric functions, complete elliptic integrals, GPW optimization problem

中图分类号:

TM12
TM153

朱润杭, 赵雅婷. 圆盘线圈自、互感的闭式解及其自感最优值[J]. 中国电力, 2019, 52(8): 71-77.

ZHU Runhang, ZHAO Yating. Closed Form Expressions of Self and Mutual Inductance of Disk Coils and the Optimal Value of Self-Inductance[J]. Electric Power, 2019, 52(8): 71-77.

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圆盘线圈自、互感的闭式解及其自感最优值

Closed Form Expressions of Self and Mutual Inductance of Disk Coils and the Optimal Value of Self-Inductance

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