非对称共面带线保角变换解及Landen变换

Conformal transformation solution of asymmetrical coplanar stripline and landen transformation

非对称共面带线 (ACPS)和与其成互补结构的非对称共面波导 (ACPW )的分布电容与特性阻抗是表征它们特性的两个重要参量。通过线性分式映射、镜象原理以及保角变换方法实现了从ACPS向对称共面带线 (SCPS)的转换 ,简便求出了它的分布电容和特性阻抗严格解的明晰表达式 ,同时给出了不同模数下椭圆积分比的精确表达式及其正确反演式 ,并以之为基础很简洁地证明了Landen变换。

The distributed capacitance and characteristic impedance of asymmetrical coplanar stripline (ACPS) and its complementary structure asymmetrical coplanar waveguide (ACPW) are important parameters to characterize their properties. By using linear fraction mapping, image theory and conformal transformation, ACPS is transformed to symmetrical coplanar stripline (SCPS), and the exact solutions of its distributed capacitance and characteristic impedance are obtained. Simultaneously, accurate expressions and inverse ones for the ratio of elliptical integral with different moduli are shown as well. Based on these results, famous Landen transformation is proved easily.