倾斜轴空心矩形截面圆柱线圈互感计算

Mutual Inductance Calculations of Inclined Axial Air-Core Circular Coils with Rectangular Cross-Sections

运用等效圆环回路法与任意方位的两圆环之间的互感公式得到了倾斜轴空心矩形截面圆柱线圈的互感公式。由于任意方位圆环互感公式保持了简洁的单重积分形状,本文的公式亦具有简洁的单重积分形状。除了线圈间距很近的情况外,任意方位的矩形截面圆柱线圈的互感可以被足够精确地算出。本文公式在同轴与平行轴的情形与已有文献数据进行了比较以验证本文公式的精度;在线圈轴倾斜的情形与精确公式进行了比较以验证本文公式计算一般情形互感时的精度。比较结果表明这些公式具有足够高的精度,可以用于一般方位矩形截面圆柱线圈互感的计算。同时,两任意线圈的解耦位置也可以运用本文公式求得。

In this work, the formulas for mutual inductance calculations of the coils mentioned in the title were derived by using method of equivalent circular loops and formula for mutual inductance between two arbitrarily located circular loops. Owing to the brevity of one-dimensional integral expression of the circular loops, the concise form of derived formulas is maintained. The mutual inductance of circular coils with rectangular cross-sections arbitrarily positioned can be calculated with sufficient accuracy, except the case of too short distance between coils. The derived formulas for the cases of coaxial and parallel axial coils were compared with the existing literatures, and those of inclined axial case were compared with exact formula to confirm the sufficient accuracy of derived formulas. The obtained formulas can be applied to calculate the mutual inductance of generally positioned coils with rectangular cross-sections and the decoupling position can be also determined by these formulas.