ON THE CHARACTERISTIC IMPEDANCE OF A COAXIAL LINE WITH ELLIPTIC OUTER CONDUCTOR AND RECTANGULAR INNER CONDUCTOR
椭圆外导体-矩形内导体同轴线的特性阻抗

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.