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**Chapter 4. Antenna Synthesis**

4.1 Basic principle for antenna synthesis 4.2 Line source synthesis (Fourier transform, woodward-lanson sampling) 4.3 Linear array synthesis (Fourier series, woodward-lanson sampling) 4.4 Low sidelobe synthesis (Dolph-Chebyshev, Taylor)

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**Synthesis Problems Given affordable SLL, No. of elements,**

how to synthesize? Ideal case: narrow beam, constant side-lobe envelope Approaches: Dolph-Chebyshev, Taylor Line Source…. Secret behind: to synthesize a polynomial like pattern….

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**Dolph-Chebyshev Linear Array**

The Chebyshev polynomials: Property used:

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Chebyshev Polyminals

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**Symmetrically Excited Array**

, P odd , P even Property: is P-1 th polynomial of Let Choose appropriate to match the coefficients to those in Chebyshev polynomial, we obtain,

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**Chebyshev Polynomial Example**

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**Synthesis Standards SLL=-20log R (dB) so Optimum spacing, Endfire:**

Broadside: Endfire: , where

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**Beamwidth and Directivity**

(broadside) In general, (endfire) , where An approximation for the broadside: Beambroadening factor: Directivity:

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**Example No.1 Five element array (P=5), -20dB Side-Lobe,**

Half-Wavelength Spaced Dolph-Chebyshev Array

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**Synthesized Array Factor**

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**Example No.2 Optimum Spaced 10-Element, -30dB Side Lobe,**

Dolph-Chebyshev Endfire Array

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**Taylor Line Source Method**

Transform: where a is a constant and, So the pattern maximum is, For the side-lobe region: Main beam region:

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**Transformed Chebyshev Polynomial**

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**Basic Properties of Zeros**

Zeros of the transformed function in the side-lobes are given by: For the main beam, Introduce A so that, and For large N,

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**Selection of Constant a**

a is selected so that the first zero location remains fixed as N increases, Then The pattern should have the following format,

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**Ideal Pattern Factor Normalizing the pattern to unity at x=0,**

(side lobes) (main beam)

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**Realistic Pattern Factor**

where In format of w,

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**Woodward-Lawson Equivalent**

for The source current is

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**Beamwidth and Directivity**

(ideal Taylor) (realistic Taylor)

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Example A 10-Wavelength Taylor Line Source with –25 dB side lobes and

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**Pattern and Current Source**

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