Practical_Antenna_Handbook_0071639586
CHAPTER 26 The Smith Chart The mathematics of transmission lines can become cumbersome at times, especially when dealing with complex impedances and nonstandard situations. In 1939, Phillip H. Smith published a graphical device for solving these problems, and an improved version of the chart followed in 1945. That graphic aid, somewhat modified over time, is still in constant use in microwave electronics and other fields where complex impedances and transmission line problems are found. The Smith chart is indeed a powerful tool for the RF designer. Smith Chart Components The modern Smith chart is shown in Fig. 26.1. It consists of a series of overlapping orthogonal circles (i.e., circles that intersect each other at right angles). This chapter will dissect the Smith chart, so that the origin and use of these circles is apparent. You may find it useful in going through the tutorial and examples of this chapter to download and print out any of the free Smith chart templates and document files that can be found on the Internet. Simply search on the phrase “smith chart”. Pure Resistance Line Figure 26.2 highlights (in bold) the horizontal axis that bisects the Smith chart outer circle. This line is called the pure resistance line, and it forms the reference for measurements made on the chart. Recall that a complex impedance contains both resistance and reactance, and can be expressed in the form: where Z = complex impedance R = resistive component of impedance X = reactive component of impedance* Z = R ± jX (26.1) Points along the pure resistance line represent all possible impedances where X = 0. To make the Smith chart universal, the printed values of impedance along the pure resistance line are normalized with respect to a system impedance (usually chosen to be equal to the Z 0 of the predominant transmission line or the output impedance of the transmitter). For most microwave RF systems the system impedance is standardized at 50 W; for *According to convention, inductive reactance (X L ) is positive (+) and capacitive reactance (X C ) is negative (−). The term X in Eq. (26.1) is the difference between the two reactances (X = X L − X C ). 559
560 Figure 26.1 Smith chart. (Courtesy of Kay Elementrics)
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Figure 26.1 Smith chart. (Courtesy of Kay Elementrics)
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