Characteristic impedance of a cylindrical-rectangular coaxial line with offset inner circular conductor

In this paper, characteristic impedance of a Cylindrical-Rectangular (C-R) coaxial line is found for a line with a circular inner conductor of any arbitrary position inside an outer rectangular conductor. Results are given in the form of families of curves of characteristic impedance of the line vs. the diameter of the inner conductor and its orientation inside the rectangle. For symmetrical cases they are very close to the exact solutions