2023-11-13
An Addition to Binomial Array Antenna Theory
By
Progress In Electromagnetics Research Letters, Vol. 113, 113-117, 2023
Abstract
This research extends the theory of binomial array antennas. A closed-form expression for the half-power beamwidth of the array factor of an array antenna is presented. The expression is correct for the ratios of element spacing to wavelength greater than or equal to one quarter. Also, exact equations for determining the half-power beamwidth for main-beam steering are derived. A comparison with an approximate formula for the half-power beamwidth of binomial array antennas is carried out.
Citation
Peter Apostolov, "An Addition to Binomial Array Antenna Theory," Progress In Electromagnetics Research Letters, Vol. 113, 113-117, 2023.
doi:10.2528/PIERL23080104
References

1. Josefsson, L. and P. Persson, Conformal Array Antenna Theory and Design, IEEE Press, 2006.
doi:10.1002/047178012X

2. Balanis, C. A., Antenna Theory Analysis and Design, 3rd Ed., 329, Wiley, 2005.

3. Van Trees, H. L., Optimum Array Processing Part IV of Detection, Estimation, and Modulation Theory, Wiley, 2002.
doi:10.1002/0471221104

4. Orfanidis, S. J., Electromagnetic Waves and Antennas, 1141-1144, Sophocles J. Orfanidis, 2016.

5. Stutzman, W. L. and G. A. Thiele, “Arrays,” Antenna Theory and Design, 2nd Edition, Ch. 3, Wiley, New York, NY, USA, 1998.

6. Nikolova, N. K., "Lecture notes on antenna engineering,", 308, McMaster University, Canada, 2018.        Google Scholar

7. Hansen, R. C., "Array pattern control and synthesis," Proceedings of the IEEE, Vol. 80, No. 1, 141-151, Jan. 1992.
doi:10.1109/5.119573        Google Scholar

8. Mailloux, R. J., Phased Array Antenna Handbook, 2nd Ed., Artech House Antennas and Propagation Library, 2005.

9. Apostolov, P., A. Stefanov, and S. Andonova, "Application of Hausdorff window for array antennas design," 2019 27th National Conference with International Participation (TELECOM), 4-7, 2019.
doi:10.1109/TELECOM48729.2019.8994898        Google Scholar

10. Mistialustina, H., Chairunnisa, and A. Munir, "Performance analysis of power weighted linear array antennas based on Blackman function," 2019 PhotonIcs & Electromagnetics Research Symposium — Spring (PIERS-Spring), 4132-4137, Rome, Italy, Jun. 17–20, 2019.        Google Scholar

11. Haupt, R. L., "Phase-only adaptive nulling with a genetic algorithm," IEEE Transactions on Antennas and Propagation, Vol. 45, No. 6, 1009-1015, Jun. 1997.
doi:10.1109/8.585749        Google Scholar

12. Han, J.-H., S.-H. Lim, and N.-H. Myung, "Array antenna TRM failure compensation using adaptively weighted beam pattern mask based on genetic algorithm," IEEE Antennas and Wireless Propagation Letters, Vol. 11, 18-21, 2012.
doi:10.1109/LAWP.2011.2181475        Google Scholar

13. Toso, G. and R. Mailloux, "Guest editorial for the special issue on innovative phased array antennas based on non-regular lattices and overlapped subarrays," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 4, 1546-1548, Apr. 2014.
doi:10.1109/TAP.2014.2311312        Google Scholar

14. Lee, Y., J. Seo, J. Ha, and D. Park, "Null steering of linear phased array antenna using genetic algorithm," 2009 Asia Pacific Microwave Conference, 2726-2729, 2009.
doi:10.1109/APMC.2009.5385356        Google Scholar

15. Miller, E. K., "Synthesizing linear-array patterns via matrix computation of element currents," IEEE Antennas and Propagation Magazine, Vol. 55, No. 5, 85-96, Oct. 2013, doi: 10.1109/MAP.2013.6735478.
doi:10.1109/MAP.2013.6735478        Google Scholar

16. Kyurkchiev, N., Some Intrinsic Properties of Adaptive Functions to Piecewise Smooth Data, Plovdiv University Press, 2021, ISBN 978-619-202-670-7.

17. Kyurkchiev, N., A. Iliev, V. Arnaudova, and A. Rahnev, "Investigations on some new cumulative distributions via cosine and sine functions," International Journal of Differential Equations and Applications, Vol. 20, No. 1, 75-88, 2021.        Google Scholar

18. Sendov, B., Hausdorff Approximations, Springer, 1990, ISBN: 978-94-009-0673-0.
doi:10.1007/978-94-009-0673-0

19. Kedar, A., Sparse Phased Array Antennas: Theory and Applications, Artech, 2022.

20. Morabito, A. F., A. Di Carlo, L. Di Donato, T. Isernia, and G. Sorbello, "Extending spectral factorization to array pattern synthesis including sparseness, mutual coupling, and mounting-platform effects," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 7, 4548-4559, Jul. 2019, doi: 10.1109/TAP.2019.2905977.
doi:10.1109/TAP.2019.2905977        Google Scholar

21. Morabito, A. F., A. Massa, P. Rocca, and T. Isernia, "An effective approach to the synthesis of phase-only reconfigurable linear arrays," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 8, 3622-3631, Aug. 2012, doi: 10.1109/TAP.2012.2201099.
doi:10.1109/TAP.2012.2201099        Google Scholar

22. Apostolov, P., "Efficient two-element array antenna," 12th National Conference with International Participation (ELECTRONICA), 1-4, 2021.        Google Scholar

23. Apostolov, P., B. Yurukov, and A. Stefanov, "Efficient threeelement binomial array antenna," 2019 PhotonIcs & Electromagnetics Research Symposium — Spring (PIERS-Spring), 4127-4131, Rome, Italy, Jun. 17–20, 2019.        Google Scholar

24. Apostolov, P. and D. G. Valchev, "Steering of two-element array antenna with arbitrary narrow beam array factor," 2023 Photonics & Electromagnetics Research Symposium (PIERS), 89-95, Prague, Czech Republic, 2023.        Google Scholar

25. Apostolov, P., "Antenna array synthesis, using method of compressed cosines," PIERS Proceedings, 1816-1820, Stockholm, Aug. 2013.        Google Scholar

26. Apostolov, P. S., "Linear equidistant antenna array with improved selectivity," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 10, 3940-3943.
doi:10.1109/TAP.2011.2163743        Google Scholar

27. Stone, S., United States Patents No. 1,643,323 and No. 1,715,433.

28. Ricardi, L. J., "Radiation properties of the binomial array," Microw. J., Vol. 15, No. 12, 20-21, Dec. 1972.        Google Scholar

29. Jangi Golezani, J., S. Paker, and C. A. Balanis, "Compact expression for the directivity of binomial array with no restriction in element spacing," IEEE Antennas and Wireless Propagation Letters, Vol. 16, 653-656, 2017.
doi:10.1109/LAWP.2016.2595107        Google Scholar

30. Mahmood, A. S. and D. A. Ibrahim, "Study of the binomial excitation of a linear broadside 10-element dipole antenna array," International Journal of Electronics Communication and Computer Engineering, Vol. 7, No. 3, 2016.        Google Scholar