椭圆外导体-矩形内导体同轴线的特性阻抗

本文提出用图形逼近和取尺寸上、下限值的几何平均值的方法,计算椭圆外导体-矩形内导体同轴线特性阻抗。矩形截面内导体的内切共焦椭圆和外接共焦椭圆,通过保角变换,变成同心圆。矩形变成近于矩形的闭合曲线,二同心圆分别为它的最小值和最大值,取二者的几何平均值,与同轴椭圆截面外导体同时变成的同心圆,构成一个标准同轴线,得到了特性阻抗公式。并由此推导出椭圆外导体-微带内导体、圆形外导体-方形内导体、圆形外导体-矩形内导体及圆形外导体-微带内导体等各种同轴线的特性阻抗的初等函数表示式。给出了上述几种同轴线的特性阻抗准确数值。关键词：

ON THE CHARACTERISTIC IMPEDANCE OF A COAXIAL LINE WITH ELLIPTIC OUTER CONDUCTOR AND RECTANGULAR INNER CONDUCTOR

In this paper, the methods using the graphical approximation and taking the geo-metrical average of the upper and lower bounds to the size of the line are put forward, to calculate the characteristic impedance of a coaxial line with elliptic outer conductor and rectangular inner conductor. The boundary of rectangular inner conductor is con-formally mapped into a closed curve which is nearly a rectangle, and its inscribed con-focal ellipse and outer connected confocal ellipse are conformally mapped into two con-centric circles, the geometrical average of the both is taken as its equivalent value. At the same time, the boundary of elliptic outer conductor is conformally mapped into a concentric circle. So they constitute a standard coaxial line, and the formula for calculating its characteristic impedance is obtained.The calculating formulae of the characteristic impedance of some eoaxial lines (i. e. elliptic outer and microstrip inner conductors, circular outer and square inner conduc-tors, circular outer and rectangular inner conductors) in elementary functional forms are derived, so that the lengthy and complicated integral calculation involving elliptical functions are avoided. The characteristic impedances of some coaxical lines as mention-ed above are given in accurate values for references.