Evaluation of the Inductive Coupling between Coplanar Concentric Coils in the Presence of the Ground

IF 1.2 4区 计算机科学 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC International Journal of Antennas and Propagation Pub Date : 2024-03-08 DOI:10.1155/2024/6640727
Mauro Parise
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Abstract

An analytical approach is presented that allows deriving an exact series-form representation for the flux linkage between two physically large concentric circular coils located on a lossy soil. The expression comes from a three-step analytical procedure. First, the integral expression for the flux linkage is converted into a double integral consisting of a finite and a semi-infinite integral. Next, the semi-infinite integral is recognized to be a well-known tabulated Sommerfeld integral, which may be analytically evaluated straightforwardly. Finally, applying Lommel’s expansion allows rewriting the remaining finite integral as a sum of elementary integrals amenable to analytical evaluation. As a result, the flux linkage between the two coils is given as a sum of spherical Hankel functions of the wavenumber in the air and in the ground, multiplied by a coefficient depending on the geometrical dimensions of the coils. The accuracy and robustness of the proposed formulation is tested by comparing its outcomes with those generated by numerical integration of the complete integral representation for the flux linkage and with the results provided by previous analytical approaches to the same problem. It is found that the use of the derived expression for the inductance makes it possible to obtain significant time savings as compared to numerical quadrature schemes.
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评估共面同心线圈在有地面存在时的感应耦合情况
本文提出了一种分析方法,可以推导出位于有损土壤上的两个物理上大型同心圆线圈之间磁通量联系的精确序列形式表示。该表达式来自三步分析程序。首先,将磁通量联系的积分表达式转换为由有限积分和半无限积分组成的双积分。接着,半无限积分被认为是著名的表格式索默费尔德积分,可以直接进行分析评估。最后,应用洛梅尔展开法,可以将剩余的有限积分改写为可进行分析评估的基本积分之和。因此,两个线圈之间的磁通量联系可以用空气中和地面上波长的球形汉克尔函数之和,乘以一个取决于线圈几何尺寸的系数来表示。通过将拟议公式的结果与磁通量联系的完整积分表示法数值积分结果以及以前对同一问题的分析方法所提供的结果进行比较,检验了拟议公式的准确性和稳健性。结果发现,与数值正交方案相比,使用导出的电感表达式可以大大节省时间。
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来源期刊
International Journal of Antennas and Propagation
International Journal of Antennas and Propagation ENGINEERING, ELECTRICAL & ELECTRONIC-TELECOMMUNICATIONS
CiteScore
3.10
自引率
13.30%
发文量
158
审稿时长
3.8 months
期刊介绍: International Journal of Antennas and Propagation publishes papers on the design, analysis, and applications of antennas, along with theoretical and practical studies relating the propagation of electromagnetic waves at all relevant frequencies, through space, air, and other media. As well as original research, the International Journal of Antennas and Propagation also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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