Innovative Systems Design and Engineering www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol.5, No.12, 2014 80 Modelling of the Behavior of Lossless Transmission Lines Bourdillon.O.Omijeh 1 , Stanislaus.K.Ogboukebe 2 , Temitope .J. Alake 3 1,2. Department of Electronic and Computer Engineering, University of Port Harcourt, Rivers state, Nigeria 3. Department of Electrical & Electronic Engineering, Federal Polytechnic, Ado-Ekiti, Ekiti State. E-mail: omijehb@yahoo.com, bourdillon.omijeh@uniport.edu.ng ABSTRACT The behavior of a lossless transmission line is investigated and modeled in this paper. Lossless transmission lines as the name implies are lines with little or no signal loss during signal flow. Certain factors are responsible for this condition and they are discussed in this paper. These factors which are applied to coaxial and two-wire transmission lines were modeled using MATLAB in this work; a Graphical User Interface was then incorporated to provide an interactive way of analyzing the effect they have on signal flow efficiency. The modeling results show why lossless transmission lines are the best choice for optimum transmission efficiency. Keywords: Behavior, lossless transmission lines, modeling, Matlab 1. Introduction A transmission line is any device designed to guide electrical energy from one point to another. Transmission lines are used for a variety of purposes such as connecting radio transmitters and receivers with their antennas, distributing cable television signals and connections in a computer network. For a transmission line to be efficient, there must be little or no attenuation (distortion) in the line during signal flow. Itshould not also radiate any of its signals as radio energy. Lines which radiate some of its signals are called lossy lines. Certain transmission line parameters such as reflection coefficient, attenuation and voltage standing wave ratio affects transmission line performance and are major determinants of the best type of line for optimal signal flow. The objective of this paper is to model and investigate the responses of a lossless transmission line under three circuit conditions: short circuit, open circuit and matched load circuits. Javan and Newman (2005), describes some of the important parameters of different transmission media, such as twisted pair, co-axial cables and fiber optics. Important line parameters such as characteristics impedance of the line, frequency dependent losses, radiation, and interference were identified and presented as tabulated results to assist communication system designers’ select appropriate media for their applications. Luyan and Zhengyu (2012) analyzed transmission line parameters of Coaxial cables, such as propagation delay, reflection coefficient, attenuation incoaxial cablesby simulationand verification of different types of coaxial cables, including lossless cables using MATLAB and MODELICA. 2. Theoretical Background Generally, a transmission line has these four parameters: Resistance, Inductance, Capacitance and Conductance ( McCammon, Roy, 2010) as seen in Figures 1 and 2. The lossless transmission line model is made up of the series inductance and shunt capacitance only, while represent the distance and time components of current and voltage (Naredo, 1995). Applying Kirchhoff’s voltage and current laws, we get; (1) (2) Also, to obtain the second order Telegraphers’ equation for voltage and current, we differentiate equations ( 1) and (2) respectively, with respect to distance (x) and time (t), we get;