Using the Smith Chart in an E-Learning Approach

Abstract

Prior to the advent of digital computers and calculators, engineers developed all sorts of aids (tables, charts, graphs) to facilitate their calculations for design and analysis in different areas in particular for line transmission problems. To reduce the tedious manipulations involved in calculating the characteristics of transmission lines, graphical tools have been developed. The Smith chart is the most commonly used of these graphical techniques. It is basically a graphical indication of the impedance change along a transmission line as one moves along it. It becomes easy to use after a small amount of experience. We will first explain how the Smith chart is constructed and then how to use it to calculate transmission line characteristics such as: the reflection coefficient (), the Voltage Standing Wave Ratio (VSWR), the impedance along the line (Z(d)), the maximum and minimum voltage localization and impedance matching. For the majority of these Smith chart applications lossless lines will be assumed, although this is not absolutely required. Since the main topic of this book is concerned with e-learning, the aim of this chapter is to help the reader understand and learn how to use the Smith chart, following step by step procedure based on MATLAB scripts that will be available for download and should be used when reading this chapter. This approach should teach the students how to solve several kinds of transmission line problems by themselves, in a paper chart using a pencil, a ruler and a compass. MATLAB scripts are a good tool to help students better understand the Smith chart and explain, step by step, several procedures related to transmission line problems, (Mak & Sundaram, 2008), (Pereira & Pinho, 2010). The goals of the chapter are to explain the reasons why using and understanding the Smith chart is still important nowadays, despite the present generalization of personal computers and powerful calculators. It is easy to plug a few numbers into a program and have it spit out solutions. When the solutions are complex and multifaceted, having a computer to do the grunt work is especially handy. However, knowing the underlying theory and principles that have been ported to computer platforms, and where they came from, makes the engineer or designer a more well-rounded and confident professional, and makes the results more reliable. Moreover it is interesting to note that these kinds of graphical tools are still useful nowadays. For example some types of modern laboratory equipment, such as