**1. Introduction**

98 E-Learning – Organizational Infrastructure and Tools for Specific Areas

student via an emotionally expressive agent tutor "Alice" through facial expression and synthetic emotional speech. Tutoring actions are guided by a case-based method that recommends a set of tutor actions and expressions for adapting to student states. The data that this case-based program uses were generated from questionnaires presented to human

In future work, it is necessary that the accuracy of emotion recognition and classification algorithm should be improved. Meanwhile, the MITS will be extended to integrate information from other sources including posture recognition and physiological channels such as pressure. We hope to evaluate the effectiveness of our system in a range of learning situations including more both young and adult learners. The test will provide more

This work is supported by the National Nature Science Foundation of China (No.60873269)

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teachers.

**8. Acknowledgment**

**9. References** 

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

Using the Smith Chart in an E-Learning Approach 101

could show all values of impedance and is essentially the Smith chart used today. Smith approached a number of technical magazines for publications of his transmission line diagram, however acceptance was slow. Finally, after two years Smith's article describing his chart was published in January 1939 issue of Electronics magazine. In a second article, published in the January 1944 issue of Electronics, Smith incorporated further improvements into his chart, including its usage as an impedance chart or an admittance

An interesting historical and theoretical background of the Smith chart can be found in the

The Smith chart is constructed based on the voltage reflection coefficient and can be considered as parameterized plot, on polar coordinates, of the generalized voltage reflection

It is well known from transmission line theory, that the voltage reflection coefficient at the

*L*

*L Z Z Z Z*

where *ZL* is the load impedance and *Z*0 is the characteristics impedance of the line. According to the transmission line theory, *Z*0 is a real value but in general *ZL* is a complex

*LL r i*

Instead of having separate Smith chart for transmission lines with different characteristics impedances, it is preferable to have just one that can be used for any line. This is achieved using a normalized chart in which all impedances are normalized to the characteristic impedance *Z*0 of the particular line under consideration. For example, for the load

> 0 *L*

where *r* and *x* are respectively the real and imaginary parts of the normalized impedance.

*<sup>z</sup> <sup>j</sup> z*

 1 1

*<sup>j</sup> r jx <sup>j</sup>* 

*r i*

 

*L*

0 0

> 

*<sup>i</sup>* are respectively the real and imaginary parts of the reflection coefficient.

1 1 *L*

*L*

*r i r i*

1 .

(1)

*j* (2)

*<sup>Z</sup> z r jx <sup>Z</sup>* (3)

(5)

(4)

, within a circle of unit radius

*L*

 

impedance *ZL* , the normalized impedance *Lz* is given by,

Substituting equations 2 and 3 into equation 1 gives,

article written by Aleksandar Marinčić, (Marinčić, 1997).

**3. Construction of the Smith chart** 

 

value. Equation 1 can be written as:

chart, (Inan, 2005).

coefficient , *<sup>j</sup> e*

 

load is given by:

where

or

*<sup>r</sup>* and 

network analyzers still have displays that imitate the Smith chart. Another example is the use of Smith charts in a lot of commercial software about antennas and microwave devices, to display the simulation results. The importance of the chart is enhanced by the global information that is possible to obtain simultaneously.

The authors believe that the use of the Smith chart by undergraduate students and engineers is an important pedagogical tool, since many aspects of the voltage, current, impedance, Voltage Standing Wave Ratio (VSWR), referred commonly as SWR, reflection coefficient and matching design problems can be easily interpreted and well visualized using the Smith chart.

The chapter will be organized as follows:


Throughout the chapter, when explaining the step by step procedure, several displays will be shown to illustrate the use of the Smith chart.
