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)
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….
Dolph-Chebyshev Linear Array The Chebyshev polynomials: Property used:
Chebyshev Polyminals
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,
Chebyshev Polynomial Example
Synthesis Standards SLL=-20log R (dB) so Optimum spacing, Endfire: Broadside: Endfire: , where
Beamwidth and Directivity (broadside) In general, (endfire) , where An approximation for the broadside: Beambroadening factor: Directivity:
Example No.1 Five element array (P=5), -20dB Side-Lobe, Half-Wavelength Spaced Dolph-Chebyshev Array
Synthesized Array Factor
Example No.2 Optimum Spaced 10-Element, -30dB Side Lobe, Dolph-Chebyshev Endfire Array
Taylor Line Source Method Transform: where a is a constant and, So the pattern maximum is, For the side-lobe region: Main beam region:
Transformed Chebyshev Polynomial
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,
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,
Ideal Pattern Factor Normalizing the pattern to unity at x=0, (side lobes) (main beam)
Realistic Pattern Factor where In format of w,
Woodward-Lawson Equivalent for The source current is
Beamwidth and Directivity (ideal Taylor) (realistic Taylor)
Example A 10-Wavelength Taylor Line Source with –25 dB side lobes and
Pattern and Current Source