The Smith chart is, fundamentally, a graphical representation of the interrelationships between electrical parameters of a uniform waveguide. Accordingly, its design and many of its applications can best be described in accordance with principles of guided wave propagation. The qualitative descriptions of the electrical behavior of a waveguide, as presented in this chapter, will provide a background for better understanding the significance of various interrelated electrical parameters which are more quantitatively described in the following chapter. As will be seen, many of these parameters are represented directly by the coordinates and associated scales of a Smith chart, and their relationships are basic to its construction.

This chapter describes the construction of the basic coordinates of the SMITH CHART and then discusses some of the more important waveguide electrical parameters related thereto. All of these related parameters may be graphically portrayed as either radial or peripheral scales. The construction of the basic series impedance or parallel admittance coordinates of the SMITH CHART is shown.

In this chapter some fundamental waveguide phase conventions will first be reviewed. Following this, more generalized uses of the peripheral scale labeled 'angle of reflection coefficient' will be presented. Next, a discussion of the voltage, current, and power transmission coefficient, with generalized SMITH CHART overlays therefore, will be given. Finally, some additional waveguide voltage and waveguide current phase relationships will be discussed and presented in the form of general-purpose overlays for the SMITH CHART. These latter phase relationships are of fundamental importance in the design of waveguide components and antennas employing phased radiating elements excited through waveguide feed systems.

In this chapter, enlargements of the more frequently used regions of the SMITH CHART will be presented and discussed, and special applications for these will be given. The graphical representation of the properties of stub sections of waveguide which are operated near their resonant or antiresonant frequency, as may be readily portrayed on two of these expanded charts, will be discussed in some detail.

Several commonly used devices for obtaining a match at the load end of a transmission line will be described in this chapter. These include the single and the dual matching stub, and the single and the dual matching slug transformers. Matching stubs or building-out sections, as they are sometimes called, are sections of transmission line, frequently of the same characteristic impedance (or characteristic admittance) as that of the main line, and either open or short-circuited at their far end, connected in shunt with the main line at any one of several permissible positions in the general location where it is desired to provide the match. Slug transformers, on the other hand, are sections of line of appropriate characteristic impedance (or characteristic admittance) and length connected in series with, and forming a continuation of, the main line. These devices are described in some detail herein since it is through its terminations alone that the transmission characteristics of waves along any given waveguide can be controlled. Furthermore, the SMITH CHART provides the ideal medium for visualization of the principle of operation of such transformers and for quantitatively determining their specific design constants.

At radio frequencies where slotted waveguide or transmission line sections would be excessively long, probe measurements of the relative current (or relative voltage) amplitudes at discrete sampling points along the waveguide provide a convenient and practical technique for measuring the complex impedance and related parameters. The SMITH CHART is useful for interpreting and evaluating data obtained from such measurements as will be described herein. The principle is made use of in the SMITH CHART plotting board shown.

The many uses of the Smith chart may conveniently be classified as 'basic,' 'specific,' and 'special.' The more common uses in the first two categories, in which procedures for solving problems will be evident from the material which has been presented in previous chapters, are listed below. These lists are followed by descriptions of some of the more important 'special' uses of this chart.

This chapter demonstrate the use of winSmith. winSmith is a computer program which operates under Microsoft Windows 3.1, Windows 95, 98, 2000 and NT. winSmith automates the graphical solution of transmission line and simple matching problems and serves as an excellent training aid. This chapter uses the program to illustrate key SMITH CHART concepts with examples that illustrate common matching problems. Because the pertinent screen displays are included in this chapter, a copy of winSmith is not required to learn from these examples.

A conformal transformation can be applied to the curves on the rectangular transmission line chart in Fig. 1.2 in order to obtain the more convenient circular form shown in Fig. 1.3.