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Linear & Planar Array Synthesis

This document discusses linear and planar array pattern synthesis with separable distributions. It compares the Chebyshev pattern synthesis method to the Taylor line source synthesis method. The Chebyshev method results in maximum directivity for small arrays but directivity decreases for large arrays due to forced constant sidelobes. The Taylor method overcomes this issue by allowing sidelobes to vary for large angles, maintaining high directivity even for large arrays.

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100 views1 page

Linear & Planar Array Synthesis

This document discusses linear and planar array pattern synthesis with separable distributions. It compares the Chebyshev pattern synthesis method to the Taylor line source synthesis method. The Chebyshev method results in maximum directivity for small arrays but directivity decreases for large arrays due to forced constant sidelobes. The Taylor method overcomes this issue by allowing sidelobes to vary for large angles, maintaining high directivity even for large arrays.

Uploaded by

anjali9myneni
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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3.

1 Linear Arrays and Planar Arrays with Separable Distributions 121 120 Pattern Synthesis for Linear and Planar Arrays

.6 1000 1 1 1
40 dB
20 50 60
.5 30
30 40
NT = 256
60

20
100
1
a
15

i
SLdB -

Figure 3.5 (Continued.)


10 -

for isotropic elements. The figure shows a linear increase in directivity with array
length for relatively small arrays, but each curve reaches a maximum directivity
related to its sidelobe level. This effect is due to the forced constant sidelobes that '//
take a progressively large part of the power as the array size increases and
beam-width narrows. 100
Figure 3.5(c) shows the Chebyshev beamwidth as computed from (3.20) and
10
the exact value, and Figure 3.5(d) shows the normalized directivity D/Nj or taper /1 I ! 1 1 1 1 I I I

efficiency ej as defined in Chapter 1 as a function of sidelobe level SLjg, computed 1000


from (3.19). The general trend of the curves (for SLJB > 40) is a result of beam LJ}.
broadening and is almost independent of array size once the array is large enough. (b)

For higher sidelobe levels at the left of the figure, the lowered efficiency ratio is a
result of the saturation effect mentioned earlier. The larger arrays need lower
sidelobes to be efficient.
Although the Chebyshev pattern is a classic synthesis procedure and is well
documented and conveniently tabulated, it is not useful for large arrays because of
the gain limitation mentioned earlier. The stipulation that the sidelobes remain 20
I i(instant for large angles leads to a maximum in the directivity and then reduced
10
directivity with further increases in array length, as shown in Figure 3.5(a, b, d). In CO

addition, for increasingly large arrays, this requires a nonmonotonic aperture


illumination with peaks at the array edges and cannot be excited efficiently. These
details of aperture illumination are discussed in the next section, since they pertain KI
It 1
Taylor pattern synthesis. |
.04
•• R = 100
i. 1.5 Taylor Line Source Synthesis Approximate x
Elliott — Exact
In .i landmark paper, Taylor [6] analyzed the deficiencies of the Chebyshev pattern
i n J formulated a pattern function that has good efficiency for large arrays. Taylor R= 10
5
10

Relative length (LA) (c)

Figure 3.5 (Continued.)

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