A New Numerical Design Method for Log-periodic Eleven Feed – The Partial Array Method

1. A New Numerical Design Method for Log-periodic Eleven Feed – The Partial Array Method JianYang, Associate Professor Chalmers University of Technology Sweden

2. Outline • Introduction • New Method: the partial array method • Optimization Procedure • Result of Optimization • Simulations and Measurements • Conclusions

3. Introduction - The Eleven Feed dipoles • Two unique characteristics over decade bandwidth • Constant beam width; • Fixed phase center location Phase center Ground plane

4. Introduction - The Eleven Feed • Simple geometry, small volume • Can be located in cryostat; • -10 dB reflection coefficient • Low cross pol. level

5. Introduction - challenge • Minimizing reflection coefficient is needed. • Challenge: Eleven feed is very large at highest frequency. • New method for global optimization scheme. Photo of the 2-13 GHz Eleven feed

6. New Method - Partial array method Scaled S-parameters due to scaled geometry • If the log-periodic array is infinite, we have the frequency scaling on s-parameters as: jdipole+n idipole+n jdipole idipole

7. D6 D5 D4 D3 D2 D1 2 1 2 1 2 1 2 1 1 2 1 1 2 2 Partial Array Method: Scaled S-parameters • example:

8. D6 D5 D4 D3 D2 D1 2 1 2 1 2 1 2 1 1 2 1 1 2 2 Partial Array Method: far separated mutual couplings very low

9. Partial Array Method • We can predict the S matrix for the whole array using S parameters in a small part of the array by • Scaling S parameters; • Ignoring mutual coupling between far separated elements.

10. Partial Array MethodImplementation Port definition port1 port2 S1(3)2(4) dipole4 dipole3

11. Partial Array Method 0 S= 0

12. Partial Array Method • Formula

13. Partial Array Methodfor details J. Yang and P.-S. Kildal, “Optimizing large log-periodic array by computing a small part of it”, appears in IEEE Trans. on Antennas Propag. Special Issue on Antennas for Next Generation Radio Telescopes, vol. 59, no. 3, March 2011.

14. Example Reflection coefficient of a 14-element log-periodic Eleven antenna array based on simulation of a 6-element array

15. Optimization ProcedureGenetic Algorithm • Six parameters are optimized: • scaling factor k, • dipole length L, • arm width w, • arm spacing da, • transmission line gap dc, • height above ground plane h.

16. Optimization • GA is used for minimizing S11 in a 6-element folded dipole array. • Elite crossover, Roulette wheel selection, crossover and mutation are used in GA. • population size: 50; • 5 generations; • Simulation tool is CST MS and the optimization is done by in-house Matlab program. • Computation Time • Each case 1 hours; • Fully optimized 1 week.

17. Result of Optimization • 14 pairs of folded dipoles with scaling factor 1 .24.

18. Result of Optimization • The port impedance is 200 Ohms.

19. Simulated and Measured ResultsReflection coefficient including centre puck

20. φ : 0-360o with step 1o. θ : 0-180o with step 1o. Frequency: 2–15 GHz with step 0.1 GHz. Spherical near field measurement Radiation Measurement at Technical University of Denmark

21. Efficiencies based on measured patterns in reflector with subtended semi-angle of 60 deg

22. Efficiencies based on Simulated patterns in reflector with subtended semi-angle of 60 deg

23. Radiation Patterns of BOR1 component Simulated Measured

24. Directivity

25. Conclusions • The reflection coefficient is below -10 dB for 2 – 13 GHz. • The radiation pattern is constant for 2 – 13 GHz. • BOR1 efficiency is • > -0.5 dB for most part of 2 – 13 GHz, • > -1.5 for 2 –13 GHz. • Directivity is about 11 dBi. • Aperture efficiency is better than – 3 dB for 2 – 13 GHz.

26. Questions?