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 ).
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