Abstract In the wide field of contactless energy transfer over a large distance, e.g. for charging electric vehicles or for supplying energy to implanted medical devices in the human body, different types of coils are used. For being able to determine the properties of the path of energy transfer, the spatial distribution of the generated magnetic field is very important. An analytic expression has several advantages for determining the spatial distribution of the magnetic field in an efficient way. In this paper, an analytic approximation for the vector potential and the magnetic flux density of a filamentary circular current loop is proposed. The derivation of the fundamental equations and the concept of the approximation is presented and the range of parameters, in which an analytic solution with sufficient precision is obtained, is determined and evaluated dependent on the parameters of the design and the approximation. The results of the analytic approximation for the magnetic flux density are presented based on an exemplary filamentary circular current loop. Finally, the results are verified by a FEM simulation. The analytic approximation shows a sufficient accuracy at large distances as well as in the close vicinity of the current loop and turns out to be a fast and efficient option to evaluate the magnetic field of one or more circular coils.

中文翻译：

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丝状环形电流回路磁场的解析多泰勒近似 (MTA)

摘要 在长距离非接触式能量传输的广泛领域中，例如为电动汽车充电或为人体植入的医疗设备提供能量，使用了不同类型的线圈。为了能够确定能量传递路径的特性，所产生磁场的空间分布非常重要。解析表达式在以有效方式确定磁场的空间分布方面具有多个优点。在本文中，提出了丝状圆形电流回路的矢量电势和磁通密度的解析近似。介绍了基本方程的推导和近似的概念，以及参数的范围，其中获得了具有足够精度的解析解，取决于设计参数和近似值来确定和评估。磁通密度的解析近似结果基于示例性丝状圆形电流回路呈现。最后，通过有限元模拟验证结果。解析近似在远距离以及在电流回路附近显示出足够的精度，结果证明是评估一个或多个圆形线圈的磁场的一种快速有效的选择。