# Chapter 4. Antenna Synthesis

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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)

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:

Beamwidth and 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