统一保角映射和三线传输线电容

Unified conformal mapping and the three-wire transmission line capacitor

镜像法、电轴法和复保角映射法是求解电磁位场的典型方法.由于镜像法仅用于求解分布在导体附近电荷产生的场,而电轴法仅用于求解平行无限长圆柱导体间的电位函数,因此这两种方法都存在局限性.为此,采用统一保角映射法取代传统的电轴法,将偏心同轴线问题和平行双圆柱问题统一起来,研究了三线传输线电容的复杂实例.统一保角映射法可以取代镜像法和电轴法,使电磁位场的求解得以简化.

The mirror method, the electric axis method and the complex conformal mapping method are the typical methods to solve electromagnetic-field problems. The image method is used only to solve the field distribution of charges near the conductor. The electrical axis method is used merely to solve the potential function between two infinite long parallel cylindrical conductors. Therefore, the conventional electric axis method is relaced by the uniform conformal mapping method in this paper, and the issues of eccentric coaxial lines and parallel pairs of cylinders are unified. This paper also presents the complex examples of the three-wire transmission line capacitor. Therefore, the unified conformal mapping method can replace the image method and electrical axis method and simplify the solution of the electromagnetic-field problem.