Practical_Antenna_Handbook_0071639586
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Practical_Antenna_Handbook_0071639586

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Figure 26.2 Normalized impedance line. (Courtesy of Kay Elementrics) 561

562 P a r t V I I : T u n i n g , T r o u b l e s h o o t i n g , a n d D e s i g n A i d CATV systems, it is 75 W. Most amateur applications use one of those impedances, but open-Âwire lines provide additional choices—most frequently 300 W, 450 W, or 600 W. To normalize any impedance, divide it by the system impedance. For example, if the load impedance of a transmission line is Z L, and the characteristic impedance of the line is Z 0 , then Z′ = Z L /Z 0 . In other words, Z R ± ′ = jX Z 0 (26.2) The pure resistance line is structured such that the system impedance is in the center of the chart and has a normalized value of 1.0 (see point A in Fig. 26.2). This value results from the fact that Z′ = Z 0 /Z 0 = 1.0. To the left of the 1.0 point on the pure resistance line are decimal fractional values used to denote impedances less than the system impedance. For example, in a 50-ÂW transmission line system with a 25-ÂW load impedance, the normalized value of the load impedance is 25 W/50 W, or 0.50 (point B in Fig. 26.2). Similarly, points to the right of 1.0 are greater than 1 and denote impedances that are higher than the system impedance. For example, in a 50-ÂW system connected to a 100-ÂW resistive load, the normalized impedance at the load end of the transmission line is 100 W/50 W, or 2.0; this value is shown as point C in Fig. 26.2. By employing normalized impedances, you can use the Smith chart for virtually any practical combination of system, load and source, and impedances, whether resistive, reactive, or complex. Conversion of the normalized impedance to actual impedance values is done by multiplying the normalized impedance by the system impedance. For example, if the resistive component of a normalized impedance in a 50-ÂW system is 0.45, then the actual impedance is Z = ( Z′ ) ( Z ) (26.3) = (0.45) (50 Ω) = 22.5 Ω 0 Constant Resistance Circles An isoresistance circle, also called a constant resistance circle, represents all possible chart locations of a specific value of resistance, corresponding to the family of complex impedances that include all possible values of reactance in combination with that single resistance value. Several of these circles are shown highlighted in Fig. 26.3. These circles are all tangent to the point R = ∞ at the right-Âhand extreme of the pure resistance line and are bisected by that line. When you construct complex impedances (for which X is nonzero) on the Smith chart, all points on any one of these circles will have an identical resistive component. Circle A, for example, passes through the center of the chart, so it has a normalized constant resistance of 1.0. Note that impedances that are pure resistances (i.e., Z′ = R′ + j0) will fall at the intersection of a constant resistance circle and the pure resistance line, and complex impedances (i.e., X ≠ 0) will appear at any other points on that same constant resistance circle. In Fig. 26.3, circle A passes through the

Figure 26.2<br />

Normalized impedance line. (Courtesy of Kay Elementrics)<br />

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