BROADBAND ANTENNAS 595

TABLE 10.6 Optimized Uncompensated Lengths of Parasitic Elements for Yagi-UdaAntennas of Six Different Lengths

d/λ = 0.0085 Length of Yagi-Uda (in wavelengths)

s12 = 0.2λ 0.4 0.8 1.20 2.2 3.2 4.2

LENGTH OFREFLECTOR (l1/λ) 0.482 0.482 0.482 0.482 0.482 0.475

l3 0.442 0.428 0.428 0.432 0.428 0.424

l4 0.424 0.420 0.415 0.420 0.424

l5 0.428 0.420 0.407 0.407 0.420

l6 0.428 0.398 0.398 0.407

l7 0.390 0.394 0.403

l8 0.390 0.390 0.398

l9 0.390 0.386 0.394

l10 0.390 0.386 0.390

l11 0.398 0.386 0.390

l12 0.407 0.386 0.390

LE

NG

TH

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DIR

EC

TO

RS,λ

l13 0.386 0.390

l14 0.386 0.390

l15 0.386 0.390

l16 0.386

l17 0.386

SPACING BETWEENDIRECTORS (sik/λ) 0.20 0.20 0.25 0.20 0.20 0.308

DIRECTIVITY RELATIVETO HALF-WAVEDIPOLE (dB) 7.1 9.2 10.2 12.25 13.4 14.2

DESIGN CURVE(SEE FIGURE 10.27) (A) (B) (B) (C) (B) (D)

(SOURCE: Peter P. Viezbicke, Yagi Antenna Design, NBS Technical Note 688, December 1976).

596 TRAVELING WAVE AND BROADBAND ANTENNAS

0.001 0.002 0.003 0.01 0.02 0.03 0.040.36

0.40

0.45

0.50

Element diameter d (wavelengths)

l1′ = 0.485 l1′′ = 0.482

Ele

men

t len

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0.00424 0.0085

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l3'' = l5'' = 0.428 λ

l3' = l5' = 0.442 λ

∆ l

∆ l

Figure 10.27 Design curves to determine element lengths of Yagi-Uda arrays. (SOURCE: P.P. Viezbicke, “Yagi Antenna Design,” NBS Technical Note 688, U.S. Department of Com-merce/National Bureau of Standards, December 1976).

3. Figure 10.28 which provides compensation length increase for all the parasiticelements (directors and reflectors) as a function of boom-to-wavelength ratio0.001 ≤ D/λ ≤ 0.04

The specified information is usually the center frequency, antenna directivity, d/λand D/λ ratios, and it is required to find the optimum parasitic element lengths (direc-tors and reflectors). The spacing between the directors is uniform but not the samefor all designs. However, there is only one reflector and its spacing is s = 0.2λ forall designs.

Example 10.3

Design a Yagi-Uda array with a directivity (relative to a λ/2 dipole at the same heightabove ground) of 9.2 dB at f0 = 50.1 MHz. The desired diameter of the parasitic elementsis 2.54 cm and of the metal supporting boom 5.1 cm. Find the element spacings, lengths,and total array length.

Solution:

a. At f0 = 50.1 MHz the wavelength is λ = 5.988 m = 598.8 cm. Thus d/λ =2.54/598.8 = 4.24× 10−3 and D/λ = 5.1/598.8 = 8.52× 10−3.

b. From Table 10.6, the desired array would have a total of five elements(three directors, one reflector, one feeder). For a d/λ = 0.0085 ratio theoptimum uncompensated lengths would be those shown in the second columnof Table 10.6 (l3 = l5 = 0.428λ, l4 = 0.424λ, and l1 = 0.482λ). The overall

598 TRAVELING WAVE AND BROADBAND ANTENNAS

Figure 10.28 Increase in optimum length of parasitic elements as a function of metal boomdiameter. (SOURCE: P. P. Viezbicke, “Yagi Antenna Design,” NBS Technical Note 688, U.S.Department of Commerce/National Bureau of Standards, December 1976).

Figure 10.29 Commercial Yagi-Uda dipole TV array. (Courtesy: Winegard Company,Burlington, IA).

the far-field region it has a null along its axis. As the circumference of the loopincreases, the radiation along its axis increases and reaches near maximum at aboutone wavelength [32]. Thus loops can be used as the basic elements, instead of the lineardipoles, to form a Yagi-Uda array as shown in Figure 10.30. By properly choosing thedimensions of the loops and their spacing, they can form a unidirectional beam alongthe axis of the loops and the array.

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