填充多层介质的共焦椭圆同轴线传播特性

Propagation characteristics of confocal elliptical coaxial line filled with multilayer dielectrics

采用在椭圆柱坐标系中分离变量的方法,得到了填充多层介质共焦椭圆同轴线模式特征方程．研究表明,当椭圆退化为圆时,利用角向和径向马修函数的渐进关系,可得到填充多层介质的圆形同轴线的模式特征方程,由此可见,圆形同轴线可看作椭圆形同轴线的特例;当椭圆同轴线内导体半长轴大小为零时,则椭圆同轴线就变成椭圆波导,同样的方法,可得到填充多层介质的椭圆波导模式特征方程．当填充一层介质时,得到了椭圆同轴线和椭圆波导的模式特征方程,结果和相关文献所得结果相同．作为示例,对填充一层介质和两层介质的椭圆同轴线中一些模式色散特性进行了数值计算,分析了椭圆同轴线中介质参数的变化以及椭圆同轴结构的变化等对其传播特性的影响．

By using the method of separation of variables in the elliptical-cylindrical coordinate system, the mode eigenequation for a confocal elliptical coaxial line filled with multilayer dielectrics is presented. When the elliptical coaxial line becomes a circular coaxial line, the mode eigenequation of the circular coaxial line can be obtained from the mode eigenequation of the elliptical coaxial line using the asymptotic formulae of angular and radial Mathieu functions. The results show that the mode eigenequation of a circular coaxial line filled with multilayer dielectrics can be treated as a special case of an elliptical coaxial line. When the major semi-axis value of the interior conductor of an elliptical coaxial line equals zero, the elliptical coaxial line becomes an elliptical waveguide. In the same way, the mode eigenequation of the elliptical waveguide filled with multilayer dielectrics is derived. When the elliptical coaxial line or elliptical waveguide is only filled by one layer dielectric, the mode eigenequations for them are obtained from the general mode eigenequations. These results are consistent with other scientific literatures. Finally, numerical results for some modes are presented to analyze the propagation characteristics influenced by the dielectrics filled in the confocal elliptical coaxial lines and influenced by their structures, etc.