Homepages of the Author, Hartwig Harm, DH2MIC: German: http://dh2mic.darc.de/ English: http://www.qsl.net/dh2mic/ | Infopage of Transmission Line Calculator tlc-e.htm (tlc–info–e.htm) Characteristic Impedance, Inductance/m and Capacitance/m of unusual Structures The Programm makes use of the Approximation Formula (1) which is valid only for large ratios of 2a/d and two other different formulas, which are valid for the whole range of 2a/d. They are called k-Interpolation (2) and Z-Interpolation (3) respectively. All structures are completly described by the Diameter of the center conductor, the distance a and in four cases the distance b plus a structural factor k that is specific to each arrangement. See the adjacent picture. The Approximation Formula is valid only for 2a/d>3 as indicated by the dashed lines for k=2 and k=1.4 . The other two formulas will give valid results within the whole range of input parameters. The results of Z-Interpolation will be slightly higher than those of the k-Interpolation. At least for the square outer conductor the results of Z-Interpolation agree much better with realty. The file tlc.pdf (in German) contains a detailed description of the developement of the formulas. It can be downloaded here. The translated version tlc-e.pdf is available too and can be downloaded here. Relationship (4) describes the dependence of the structural factor k w.r.t. the ratio a/b. It is based on multiple calculations of the four structures making use of the program Arbitrary Transmission Line Calculator - atlc2.exe by Kenneth L. Nist, KQ6QV. The exponent n in expression (4) differs for the four structures in question. The values are contained in the four graphics (see left). The precision acheived is a compromise but should be sufficient for practical purposes. In more critical cases a direct simulation with atlc2 should be taken into account. There is the possibility to define a specific structural k-factor together with any structure. This factor replaces temporarily the k-value computed by the program. Because the calculation of k is skipped, the value of b is disregared temporarily too. The specific k value is automatically cleared after the calculation of the new results. This feature can be used to check the sensitivity of results w.r.t. the structural factor k and to calculate results using values of k obtained by other means or estimations. Other equations - apart from those given here - are unknown to the author except for the structure with a square outer conductor. These formulas were found in the well known book Referece Data for Radio Engineers issued 1946 and 1956 respectively. As both of them do not refer to the k-factor they were included in the selection list as separate structures, especially for easy comparison purposes. Additional informations to these formulas can be found in the obove mentioned paper. Back to the program tlc-e.htm 2. July 2018