1. 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)

2. 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….

3. Dolph-Chebyshev Linear Array
The Chebyshev polynomials:
Property used:

4. Chebyshev Polyminals

5. 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,

6. Chebyshev Polynomial Example

7. Synthesis Standards SLL=-20log R (dB) so Optimum spacing, Endfire:
Broadside:
Endfire:
, where

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

9. Example No.1 Five element array (P=5), -20dB Side-Lobe,
Half-Wavelength Spaced Dolph-Chebyshev Array

10. Synthesized Array Factor

11. Example No.2 Optimum Spaced 10-Element, -30dB Side Lobe,
Dolph-Chebyshev Endfire Array

12. Taylor Line Source Method
Transform:
where a is a constant and,
So the pattern maximum is,
For the side-lobe region:
Main beam region:

13. Transformed Chebyshev Polynomial

14. 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,

15. 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,

16. Ideal Pattern Factor Normalizing the pattern to unity at x=0,
(side lobes)
(main beam)

17. Realistic Pattern Factor
where
In format of w,

18. Woodward-Lawson Equivalent
for
The source current is

19. Beamwidth and Directivity
(ideal Taylor)
(realistic Taylor)

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

21. Pattern and Current Source