Tesla变压器耦合系数的静磁场解法

 为研究Tesla变压器耦合系数与各参量的关系,采用静磁场分析方法,从柱坐标系磁场Laplace方程出发,推导出磁场级数表达式的系数矩阵方程组,计算出磁芯磁场的轴向分布和间隙磁场的轴向、径向分布。引入了一种平均耦合系数概念——次级绕组每匝线圈具有独立的耦合系数,用全部单匝耦合系数的平均值作为Tesla变压器的耦合系数。重点研究了平均耦合系数与磁芯纵横比、半径比、初级绕组-磁芯长度比、磁芯材料磁导率的相对变化关系。结果表明:增大纵横比、减小半径比是提高Tesla变压器耦合系数的有效方法;增大磁芯材料的磁导率可提高耦合系数,但效果随磁导率增大而降低;初级绕组长度与磁芯长度之比约为0.7时,耦合系数达到最大值。

Magnetostatic-field solution for Tesla transformer's coupling coefficient

Based on the Laplace equation in cylindrical coordinates, coefficient matrix equations of the magnetic field series expression were derived with magnetostatic method for the Tesla transformer. Thus, we obtained the axial magnetic field distributions of the magnetic cores, and the axial and radial magnetic field distributions between the cores. The average coupling coefficient was put forward, which is the average of every single secondary coil’s coefficient. Then we studied the influences of aspect ratio, radius ratio of outer to inner magnetic cores, length ratio of primary winding to magnetic core and relative permeability on the average coefficient. It is found that increasing aspect ratio and decreasing radius ratio are two effective ways to enhance the average coupling coefficient, i