任意形状面电流磁场的半解析算法

面电流磁场的准确计算与精密电子设备的设计制造密切相关.相同宽度的任意形状面电流的磁场可采用半解析法计算:将面电流源分解为梯形面电流元和曲线面电流元,再将曲线面电流元用多个梯形面电流元进行拟合;计算梯形电流元的解析解或一重积分;利用矢量和公式将梯形面电流元和曲线面电流元的磁场合成为面电流的磁场.计算中存在如下奇异点,梯形电流元退化为直角梯形电流元或矩形电流元,场点位于梯形电流元的内部,场点位于梯形电流元的上下底边,且出现在梯形内部最大矩形的四个端点处.这些奇异点均可通过数学变换消除.

Semi-analytical Algorithm for Magnetic Field Caused by Arbitrary Surface Electric Current

It is useful to design delicate electric equipment if magnetic field distribution of surface electric current can be obtained accurately.The magnetic field caused by an arbitrary surface electric current with the same coil width can be calculated by a semi-analytic method. The method is as follows: firstly， the total surface electric current is divided into the trapezoidal and curved surface electric current segments， and then each curved surface electric current segment is further fitted by several trapezoidal segments. Numerical method is applied to give the analytical solution or one-dimensional integral for magnetic field caused by all trapezoidal segments. Finally， the magnetic field caused by the total surface electric current can be obtained by the summation of the segment vectors and solutions. However， some singularities can be arise when a trapezoidal segment turns to a right-angled trapezoidal or a rectangular one， the field point is inside the trapezoidal segment or at the top and bottom base lines of the trapezoidal segment， and the four singularities are the vertices of the largest square inside the trapezoid. Fortunately， these singularities can be eliminated by some mathematical transformation.