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

Abstract

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 presented.

Indexing terms:

• Modal velocities and impedances
• Conformal transformation
• Capacitance matrix
• Dielectric coated cylinder pair
• Presence of a third conductor

Additional information

Notes on contributors

B N Das

B N Das obtained MSc (Tech) degree of the Institute of Radio Physics & Electronics, from University of Calcutta in 1956, and PhD in Electronics & Communication Engineering in 1967. He joined Department of Electronics & Electrical Communication Engineering, IIT, Kharagpur as a lecturer in 1958, and retired as Professor from the same in 1990. He was UNIDO expert in SAMEER, Taramoni, Chennai from July 1991 to July 1992. He was CSIR Emeritus Scientist, Emeritus Professor and INSA Senior Scientist from July 1992 to February 2001 in Department of Electronics & Electrical Communication Engineering, IIT, Kharagpur.

At present he is INSA Honorary Scientist, Department of Electronics & Electrical Communication Engineering, IIT, Kharagpur. He published a large number of papers in reputed Journals of USA, UK, USSR (at present Russia) and India.

Professor Das is Fellow of INSA, INAE, IE and IETE.

D Parida

Debashis Parida was born in Baripada, India, in 1974. He received the BSc degree in Physics (Hons) from Utkal University, Bhubaneswar, India in 1994 and the MCA degree from Regional Engineering College, Rourkela, India in 1997. He is carrying out research work in the Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur, India as Junior Project Assistant since November, 1997 and is also working for PhD degree.