Effect of dielectric support on the inner conductor of eccentric coaxial line

This paper presents a method for the evaluation of the effect of the dielectric support between the inner and the outer conductors of eccentric coaxial line. Two different conformal mappings are used to obtain two different approximate formulas for the evaluation of the capacitance of this structure. First, a cotangent hyperbolic transformation is used, which transforms the conductor boundaries to parallel straight lines, and the circle surrounding the dielectric support to a curved contour. The same structure is also analyzed using a bilinear transformation expressed in terms of mutually inverse points followed by a logarithmic transformation. In each case, an expression for the capacitance is found by replacing the continuous curve representing the dielectric boundary by a number of infinitesimally small discrete steps. A comparison of numerical data obtained by the two methods is presented