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精确有效计算Sommerfeld型广义积分是分析导电媒质半空间电磁波辐射和散射问题的关键。基于精确镜像理论,详细推导了导电媒质平面上方垂直磁偶极子激励的磁场垂直分量。该表达式快速收敛,易于数值计算,适用于源点与场点为任意位置、导电媒质参数任意的情形。首先利用源点与场点均位于分界面处特殊情形下磁场垂直分量的精确解析表达式,验证了精确镜像理论退化至特殊条件下给出的磁场表达式。然后计算了源与场点位于某一高度的场强。文中结果在可以等效为磁偶极子的小电流圆环场强计算中具有重要的应用价值。
Accurate and efficient calculation of Sommerfeld type generalized integral is the key to analyze the problem of electromagnetic radiation and scattering in half-space of conductive medium. Based on the accurate mirror theory, the perpendicular magnetic field components excited by perpendicular magnetic dipoles above the plane of the conductive medium are deduced in detail. The expression converges quickly and is easy to be calculated numerically. It is suitable for any situation where the source and field points are arbitrary and the parameters of conductive medium are arbitrary. First of all, by using the exact analytical expression of the vertical component of the magnetic field in the special case where the source point and the field point are located at the interface, the magnetic field expression given by the exact mirror image theory degenerated to a special condition is verified. Then the source and field points are calculated at a certain field strength. The results in this paper have an important application value in the field strength calculation of small current circle which can be equivalent to a dipole.