Evaluation of Modal Velocities and Impedance of Transmission Lines using Cotangent Hyperbolic Transformation

The paper presents the method of derivations of the elements of the capacitance matrix of a dielectric coated twin cylinder transmission line with two semiinfinite grounded-plates with a gap, located at the plane of symmetry between the cylinders. The cotangent hyperbolic transformation transforms the cylinders to parallel plates and the grounded semiinfinite plates with a gap to a grounded strip between the plates. The transformation of the dielectric boundaries coincident with equipotential contours and concentric with individual conductors are obtained as straight and curved contours respectively in the transformed plane. The characteristic parameters of the eigenmodes are found from the solution of the eigenvalue equation. It is shown that for a symmetrical structure the eigenvalues are identical when the dielectric boundaries coincide with equipotential contour but are different when they are concentric with conductor boundaries, Numerical data are pressented.