volume | PIER Journals

Abstract

Pattern synthesis usually involves determining the strengths of the current sources in a given array that yield a specified pattern. Demonstrating that this pattern can be produced by an actual array of physical elements is a step that is rarely included in the discussion. The purpose of this article is to examine how well a numerical model of these sources will match the desired pattern when mutual interactions between the array elements are taken into account. An investigation of this process is described here using NEC (the Numerical Electromagnetics Code), although any wire-antenna computer code could be used. Modeling wire antennas in codes like NEC typically involves specifying the input or exciting voltage of the antenna to find the induced current from which the far field can be obtained. The pattern-synthesis problem for a specified array geometry, by contrast, requires instead finding the exciting voltages that will induce the synthesized currents needed to produce the pattern of interest. The radiation pattern that results can then be compared with the desired pattern to determine how well the physical array performs. Several examples of this approach are included here to demonstrate the process.

1. Schelkunoff, S. A., "A mathematical theory of linear arrays," Bell System Technical Journal, Vol. 22, 80-107, 1943.
doi:10.1002/j.1538-7305.1943.tb01306.x Google Scholar

2. Dolph, C. L., "A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level," Proceedings of the IRE, Vol. 34, No. 7, 335-348, 1946.
doi:10.1109/JRPROC.1946.225956 Google Scholar

3. Woodward, P. M., "A method of calculating the field over a plane aperture required to produce a given polar diagram," Journal Institute of Electrical Engineering, Pt. IIIA, Vol. 93, 1554-1558, 1946. Google Scholar

4. Taylor, T. T., "Design of line-source antennas for narrow beamwidth and low sidelobes," IRE Transactions on Antennas and Propagation, Vol. 7, 16-28, 1955. Google Scholar

5. Elliott, R. S., "On discretizing continuous aperture distributions," IEEE Transactions on Antennas and Propagation, Vol. 25, No. 5, 617-621, September 1977.
doi:10.1109/TAP.1977.1141658 Google Scholar

6. Elliott, R. S., Antenna Theory and Design, Prentice-Hall, Englewood Cliffs, NJ, 1981.

7. Balanis, C. A., Antenna Theory: Analysis and Design, Harper & Row, Publishers, New York, 1982.

8. Kummer, W. H., "Basic array theory," Proceedings of the IEEE, Vol. 80, No. 1, 127-140, January 1992.
doi:10.1109/5.119572 Google Scholar

9. Chang, H.-P., T. K. Sarkar, and O. M. C. Pereira-Filho, "Antenna pattern synthesis utilizing spherical bessel functions," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 6, 853-859, June 2000.
doi:10.1109/8.865216 Google Scholar

10. Durr, M., A. Trastoy, and F. Ares, "Multiple-pattern linear antenna arrays with single pre-fixed amplitude distributions: Modified Woodward-Lawson synthesis," Electronics Letters, Vol. 36, No. 16, 1345-1346, 2000.
doi:10.1049/el:20000980 Google Scholar

11. Marcano, D. and F. Duran, "Synthesis of antenna arrays using genetic algorithms," IEEE Antennas and Propagation Magazine, Vol. 42, No. 3, 12-20, June 2000.
doi:10.1109/74.848944 Google Scholar

12. Virga, K. L. and M. L. Taylor, "Transmit patterns for active linear arrays with peak amplitude and radiated voltage distribution constraints," IEEE Transactions on Antennas and Propagation, Vol. 49, No. 5, 732-730, May 2001.
doi:10.1109/8.929627 Google Scholar

13. Bucci, O. M., M. D'Urso, and T. Isernia, "Optimal synthesis of difference patterns subject to arbitrary sidelobe bounds by using arbitrary array antennas," IEE Proceedings on Microwaves, Antennas and Propagation, Vol. 152, No. 3, 129-137, 2005.
doi:10.1049/ip-map:20045073 Google Scholar

14. Vescovo, R., "Consistency of constraints on nulls and on dynamic range ratio in pattern synthesis for antenna arrays," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 10, 2662-2670, October 2007.
doi:10.1109/TAP.2007.905828 Google Scholar

15. Liu, Y., Z. Nie, and Q. H. Liu, "Reducing the number of elements in a linear antenna array by the matrix pencil method," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 9, 2955-2962, September 2008.
doi:10.1109/TAP.2008.928801 Google Scholar

16. Gomez, N. G., J. J. Rodriguez, K. L. Melde, and K. M. McNeill, "Design of low-sidelobe linear arrays with high aperture efficiency and interference nulls," IEEE Antennas and Wireless Propagation Letters, Vol. 8, 607-610, 2009.
doi:10.1109/LAWP.2009.2018126 Google Scholar

17. Comisso, M. and R. Vescovo, "Fast iterative method of power synthesis for antenna arrays," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 7, 1952-1962, July 2009.
doi:10.1109/TAP.2009.2021894 Google Scholar

18. Wong, A. M. H. and G. V. Eleftheriades, "Adaptation of Schelkunoff's superdirective antenna theory for the realization of superoscillatory antenna arrays," IEEE Antennas and Wireless Propagation Letters, Vol. 9, 315-318, 2010.
doi:10.1109/LAWP.2010.2047710 Google Scholar

19. Apostolov, P. S., "Linear equidistant antenna array with improved selectivity," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 10, 3940-3943, October 2011.
doi:10.1109/TAP.2011.2163743 Google Scholar

20. Zhang, T. and W. Ser, "Robust beampattern synthesis for antenna arrays with mutual coupling effect," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 8, 2889-2895, 2011.
doi:10.1109/TAP.2011.2152329 Google Scholar

21. Singh, H., H. L. Sneha, and R. M. Jha, "Mutual coupling in phased arrays: A review," International Journal of Antennas and Propagation, 23 pages, 2013. Google Scholar

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

23. Miller, E. K., "Using Prony's Method to synthesize discrete arrays for prescribed source distributions and exponentiated patterns," IEEE Antennas and Propagation Society Magazine, Vol. 57, No. 1, 147-163, February 2015.
doi:10.1109/MAP.2015.2397111 Google Scholar

Dr. Edmund K. Miller