Improved Formulae for the Inductance of Straight Wires
Improved Formulae for the Inductance of Straight Wires
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直导线电感的改进公式
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
B. Aebischer
中科院分区：
文献类型：
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作者：
H. Aebischer;B. Aebischer
文献中提供的圆形横截面矩形线圈自感的最佳解析公式源自直导线的部分电感公式，而直导线的部分电感公式又基于众所周知的并联电流丝互感公式，以及用于对导线横截面上的互感公式进行积分的几何平均距离（GMD）的精确值。但这样，只对互感公式的一项进行了积分，而它还包含了其他项。在文献中找到的公式中，这些其他项要么完全被忽略，要么它们的积分只是粗略地近似。我们证明，通过使用导线横截面的算术平均距离（AMD）和算术均方距离（AMSD）可以准确地积分这些其他项。我们基于 GMD、AMD 和 AMSD 的使用，提出了任何横截面和任何频率的直导线的部分电感和互感的通用公式。由于无法测量单线的部分电感，因此借助定义电感的六维积分的精确计算来计算解析近似的误差。这些是通过坐标变换获得的，将六维积分简化为三维积分，然后进行数值求解。我们给出了应用我们的分析公式来计算短路两线电感的示例。新公式显示短线精度有了显着提高。
The best analytical formulae for the self-inductance of rectangular coils of circular cross section available in the literature were derived from formulae for the partial inductance of straight wires, which, in turn, are based on the well-known formula for the mutual inductance of parallel current filaments, and on the exact value of the geometric mean distance (GMD) for integrating the mutual inductance formula over the cross section of the wire. But in this way, only one term of the mutual inductance formula is integrated, whereas it contains also other terms. In the formulae found in the literature, these other terms are either completely neglected, or their integral is only coarsely approximated. We prove that these other terms can be accurately integrated by using the arithmetic mean distance (AMD) and the arithmetic mean square distance (AMSD) of the wire cross section. We present general formulae for the partial and mutual inductance of straight wires of any cross section and for any frequency based on the use of the GMD, AMD, and AMSD. Since partial inductance of single wires cannot be measured, the errors of the analytical approximations are computed with the help of exact computations of the six-dimensional integral defining induction. These are obtained by means of a coordinate transformation that reduces the six-dimensional integral to a three-dimensional one, which is then solved numerically. We give examples of an application of our analytical formulae to the calculation of the inductance of short-circuited two-wire lines. The new formulae show a substantial improvement in accuracy for short wires.