三维柱坐标系下近场-远场转换及其验证

Study on Near-Far Field Transformation and Its Validation in Three-Dimensional Cylindrical Coordinates

在三维扩展圆柱坐标系下推导了麦克斯韦方程在完全匹配层吸收边界条件下的时域有限差分表达式(PML FDTD),并用Mur边界条件对PML有关参数的设置进行了修正。利用线性插值法和等效原理完成了柱坐标系下的近场 远场转换,从而把PML拓展到三维柱坐标系。提出了利用等效激励源法、等距离线法及方向图法等对算法进行验证的方法,这些验证方法也同样适用于其它坐标系及边界条件下的FDTD方法验证。最后利用FDTD方法计算分析了同轴电缆的孔缝电磁辐射效应。

In this paper, the finitedifference timedomain (FDTD) equations of perfectly matched layer (PML) are deduced in 3D cylindrical stretched coordinates, and the related parameter of PML is modified using Mur's boundary conditions. Then, the nearfar field transformation is completed with linear interpolation method and equivalence theory, so that PMLFDTD is extended to 3D cylindrical coordinates. In order to verify the validity of the algorithm given here, the testing methods such as equivalent source excitation method, equidistance method and radiation pattern method are proposed and used. These testing methods can also be used in the verification of FDTD in other coordinates and boundary conditions. At last, the effect of the electromagnetic radiation from the aperture on coaxial cables are studied by using FDTD method.