有限长圆柱磁屏同轴线圈电感计算方法  

Approach for Inductance Calculations of Coaxial Circular Coils Shielded by Cylindrical Magnetic Screen of Finite Length

作　　者：罗垚[1] 陈柏超[2] 周洪[1] 

机构地区：[1]武汉大学动力与机械学院,武汉430072 [2]武汉大学电气工程学院,武汉430072

出　　处：《电工技术学报》2016年第14期122-129,共8页Transactions of China Electrotechnical Society

摘　　要：对放置于有限长圆柱磁屏中的同轴载流圆环,借助其磁标势在复平面上的积分表达式,以围道变形和留数定理得到了一种收敛速度很快的屏蔽圆环互感级数表达式,该表达式比传统公式的运算速度快至少两个数量级。随后引入对磁标势的一种拟设,并借助磁标势在圆环所围区域上的跳跃性质求出屏蔽圆环磁标势的另一种级数表达式,其本征值依赖于零阶Bessel函数的正零点。在这种表达式基础上,求得放置于有限长圆柱磁屏中的同轴矩形截面圆柱线圈的自感和互感表达式,并将它们在数值计算中与有限元模拟的结果进行了对比,其结果显示所提出的表达式与有限元模拟结果具有很好的一致性。For the coaxial circular rings carrying currents which are placed into the cylindrical magnetic screen of finite length, a series expression of the mutual inductance is obtained. Herein, the formula of the magnetic scalar potential on the complex plane, as well as the contour deformation and the residue theorem is applied. The obtained expression is at least one hundred times faster than the traditional one. An ansatz of the magnetic scalar potential is then introduced. An alternative series expression of the mutual inductance of the coaxial circular rings is obtained, by using the spring characteristics of the magnetic scalar potential when it passing through the area surrounded by the ring. The eigenvalues of the series depend on the positive zeroes of the zero-order Bessel function. Consequently, the self and mutual inductances of the shielded coaxial circular coils with rectangular cross section are further obtained. The results of the numerical calculations are compared with those of the FEM simulations, which show good consistency.

关 键 词：电感 圆柱磁屏 留数定理 磁标势 

分 类 号：TM12[电气工程—电工理论与新技术] TM153