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Published byVincent Reeves Modified about 1 year ago

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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, Broadside: Endfire:, where

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Beamwidth and Directivity In general, (broadside) (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 where a is a constant and, So the pattern maximum is, Transform: 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, For large N, and

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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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