volume | PIER Journals

Abstract

This paper proposes a novel design criterion for optimal pyramidal horns. According to it, the optimal aperture phase error parameters of a pyramidal horn are determined from the minimization of the horn's lateral surface area. We present two families of curves that illustrate the optimal aperture phase error parameters for frequency and directivity values in the area of practical interest. We also discuss two simple approximate design methods for the calculation of the optimal horn parameters. Comparisons with well-known design methods demonstrate the efficacy of our approach. The proposed criterion produces the lightest horn for a given directivity; as a result its fabrication requires less material compared to other structures. Moreover, the designed horns have smaller aperture area and occupy less space. The present approach is a useful design tool when the size and weight of a pyramidal horn or its manufacturing cost are of concern.

1. Balanis, C. A., Antenna Theory: Analysis and Design, 3 Ed., John Wiley & Sons, Inc., Hoboken, 2005.

2. Milligan, T. A., Modern Antenna Design,, John Wiley & Sons, Inc., Hoboken, 2005.
doi:10.1002/0471720615

3. Dehdasht-Heydari, R., H. R. Hassani, and A. R. Mallahzadeh, "Quad ridged horn antenna for UWB applications," Progress In Electromagnetics Research, Vol. 79, 23-38, 2008.
doi:10.2528/PIER07091602

4. Mallahzadeh, A. R., A. A. Dastranj, and H. R. Hassani, "A novel dual-polarized double-ridged horn antenna for wideband applications," Progress In Electromagnetics Research B, Vol. 1, 67-80, 2008.
doi:10.2528/PIERB07101602

5. Green, H. E., "The phase centre of a pure mode, smooth wall, conical horn," Progress In Electromagnetics Research B, Vol. 4, 285-298, 2008.
doi:10.2528/PIERB08010705

6. Fazaelifar, M. and M. R. Fatorehchy, "Design, fabrication and test of parabolic cylinder reflector and horn for increasing the gain of vlasov antenna," Progress In Electromagnetics Research Letters, Vol. 4, 191-203, 2008.
doi:10.2528/PIERL08102403

7. Amineh, R. K., A. Trehan, and N. K. Nikolova, "TEM horn antenna for ultra-wide band microwave breast imaging," Progress In Electromagnetics Research B, Vol. 13, 59-74, 2009.
doi:10.2528/PIERB08122213

8. Mallahzadeh, A. R. and F. Karshenas, "Modified TEM horn antenna for broadband applications," Progress In Electromagnetics Research, Vol. 90, 105-119, 2009.
doi:10.2528/PIER08123106

9. Liu, Y. and S. Gong, "Design of a compact broadband double-ridged horn antenna," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5/6, 765-774, 2010.
doi:10.1163/156939310791036449

10. Jacobs, B., J. W. Odendaal, and J. Joubert, "The effect of manufacturing and assembling tolerances on the performance of double-ridged horn antennas," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 10, 1279-1290, 2010.
doi:10.1163/156939310791958761

11. Güney, K., "Simple design method for optimum gain pyramidal horns," AEU --- International Journal of Electronics and Communications, Vol. 55, 205-208, 2001.
doi:10.1078/1434-8411-00031

12. Güney, K. and D. Karaboga, "New narrow aperture dimension expressions obtained by using a differential evolution algorithm for optimum gain pyramidal horns," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 3, 321-339, 2004.
doi:10.1163/156939304323085694

13. Güney, K. and N. Sarikaya, "Neural computation of wide aperture dimension of optimum gain pyramidal horn," International Journal of Infrared and Millimeter Waves, Vol. 26, 1043-1057, 2005.
doi:10.1007/s10762-005-6175-y

14. Odendaal, J. W., J. Joubert, and M. J. Prinsloo, "Extended edge wave diffraction model for near-field directivity calculations of horn antennas," IEEE Transactions on Instrumentation and Measurement, Vol. 54, 2469-2473, 2005.
doi:10.1109/TIM.2005.858141

15. Akdagli, A. and K. Güney, "New wide-aperture-dimension formula obtained by using a particle swarm optimization for optimum gain pyramidal horns," Microwave and Optical Technology Letters, Vol. 48, 1201-1205, 2006.
doi:10.1002/mop.21580

16. Teo, J. L. and K. T. Selvan, "On the optimum pyramidal-horn design methods," International Journal of RF and Microwave Computer-Aided Engineering, Vol. 16, 561-564, 2006.
doi:10.1002/mmce.20177

17. Najjar, Y., M. Moneer, and N. Dib, "Design of optimum gain pyramidal horn with improved formulas using particle swarm optimization," International Journal of RF and Microwave Computer-Aided Engineering, Vol. 17, 505-511, 2007.
doi:10.1002/mmce.20245

18. Ikram, S. and G. Ahmad, "Design & implementation of a standard gain horn antenna for optimized gain and radiation pattern using MathCAD & HFSS," Second International Conference on Electrical Engineering (ICEE 2008), Lahore, Pakistan, 2008, doi:10.1109/ICEE.2008.4553906.

19. Harima, K., M. Sakasai, and K. Fujii, "Determination of gain for pyramidal-horn antenna on basis of phase center location," 2008 IEEE International Symposium on Electromagnetic Compatibility, Detroit, USA, 2008, doi:10.1109/ISEMC.2008.4652010.

20. Baltzis, K. B., "Calculation of the half-power beamwidths of pyramidal horns with arbitrary gain and typical aperture phase error," IEEE Antennas and Wireless Propagation Letters, Vol. 9, 612-614, 2010.
doi:10.1109/LAWP.2010.2055031

21. Foged, L. J., A. Giacomini, L. Scialacqua, R. Morbidini, and N. Isman, "Comparative investigation of SGH performance prediction formulas, measurements and numerical modelling," Fourth European Conference on Antennas and Propagation (EuCAP), 1-4, paper ID 924, Barcelona, Spain, 2010.

22. Milligan, T., "Scales for rectangular horns," IEEE Antennas and Propagation Magazine, Vol. 42, 79-83, 2000.

23. Kordas, G., K. B. Baltzis, G. S. Miaris, and J. N. Sahalos, "Pyramidal-horn design under constraints on half-power beamwidth," IEEE Antennas and Propagation Magazine, Vol. 44, 102-108, 2002.
doi:10.1109/74.997920

24. Schelkunoff, S. A., Electromagnetic Waves, D. Van Nostrand Company, Inc., New York, 1943.

25. Aurand, J. F., "Pyramidal horns, Part II: a novel design method for horns of any desired gain and aperture phase error," 1989 IEEE Antennas Propagation Society International Symposium, Vol. 3, 1439-1442, San Jose, USA, 1989.

26. Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, 2 Ed., Chapman & Hall/CRC, Boca Raton, 2002.
doi:10.1201/9781420035223

27. Slayton, W. T., Design and calibration of microwave antenna gain standards, Rep. 4433, US Naval Research Laboratory, Washington DC, USA, 1954.

28. Baltzis, K. B. and K. Natsiouli, "A genetic algorithm based resource allocation scheme for throughput optimization of WCDMA networks," International Review of Automatic Control, Vol. 1, 125-131, 2008.

29. Stanković, Z., B. Milovanović, and N. Donćov, "Hybrid empirical-neural model of loaded microwave cylindrical cavity," Progress In Electromagnetics Research, Vol. 83, 257-277, 2008.
doi:10.2528/PIER08051503

30. Agastra, E., et al., "Genetic algorithm optimization of high-efficiency wide-band multimodal square horns for discrete lenses," Progress In Electromagnetics Research, Vol. 83, 335-352, 2008.
doi:10.2528/PIER08061806

31. Rostami, A. and A. Yazdanpanah-Goharrizi, "Hybridization of neural networks and genetic algorithms for identification of complex Bragg gratings," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 5/6, 643-664, 2008.
doi:10.1163/156939308784159598

32. Gürel, L. and Ö. Ergül, "Design and simulation of circular arrays of trapezoidal-tooth log-periodic antennas via genetic optimization," Progress In Electromagnetics Research, Vol. 85, 243-260, 2008.
doi:10.2528/PIER08081809

33. Su, D. Y., D.-M. Fu, and D. Yu, "Genetic algorithms and method of moments for the design of pifas," Progress In Electromagnetics Research Letters, Vol. 1, 9-18, 2008.
doi:10.2528/PIERL07110603

34. Panduro, M. A., C. A. Brizuela, L. I. Balderas, and D. A. Acosta, "A comparison of genetic algorithms, particle swarm optimization and the differential evolution method for the design of scannable circular antenna arrays," Progress In Electromagnetics Research B, Vol. 13, 171-186, 2009.
doi:10.2528/PIERB09011308

35. Li, J.-Y. and J. L. Guo, "Optimization technique using differential evolution for yagi-uda antennas," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 4, 449-461, 2009.
doi:10.1163/156939309787612356

36. Pathak, N., G. K. Mahanti, S. K. Singh, J. K. Mishra, and A. Chakraborty, "Synthesis of thinned planar circular array antennas using modified particle swarm optimization," Progress In Electromagnetics Research Letters, Vol. 12, 87-97, 2009.
doi:10.2528/PIERL09090606

37. Mangoud, M. A. and H. M. Elragal, "Antenna array pattern synthesis and wide null control using enhanced particle swarm optimization," Progress In Electromagnetics Research B, Vol. 17, 1-14, 2009.
doi:10.2528/PIERB09070205

38. Li, J.-Y., "A bi-swarm optimizing strategy and its application of antenna design," Journal of Electromagnetic Waves and Applications, Vol. 23, 1877-1886, 2009.
doi:10.1163/156939309789932449

39. Tokan, F. and F. Gunes, "The multi-objective optimization of non-uniform linear phased arrays using the genetic algorithm," Progress In Electromagnetics Research B, Vol. 17, 135-151, 2009.
doi:10.2528/PIERB09072309

40. Wang, A.-N. and W.-X. Zhang, "Design and optimization of broadband circularly polarized wide-slot antenna," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 16, 2229-2236, 2009.
doi:10.1163/156939309790109289

41. Goudos, S. K., Z. Zaharis, K. B. Baltzis, C. Hilas, and J. N. Sahalos, "A comparative study of particle swarm optimization and differential evolution on radar absorbing materials for EMC applications," EMC Europe Workshop 2009 --- Materials in EMC Applications, 56-59, Athens, Greece, 2009, doi:10.1109/EMCEUROPE.2009.5189697.

42. Wang, W.-T., S.-X. Gong, Y.-J. Zhang, F.-T. Zha, J. Ling, and T. Wan, "Low RCS dipole array synthesis based on MoM-PSO hybrid algorithms," Progress In Electromagnetics Research, Vol. 94, 119-132, 2009.
doi:10.2528/PIER09060902

43. Goudos, S. K., K. B. Baltzis, C. Bachtsevanidis, and J. N. Sahalos, "Cell-to-switch assignment in cellular networks using barebones particle swarm optimization," IEICE Electronic Express, Vol. 7, 254-260, 2010.
doi:10.1587/elex.7.254

44. Vakula, D. and N. V. S. N. Sarma, "Using neural networks for fault detection in planar antenna arrays," Progress In Electromagnetics Research Letters, Vol. 14, 21-30, 2010.
doi:10.2528/PIERL10030401

45. Li, G., S. Yang, M. Huang, and Z. Nie, "Sidelobe suppression in time modulated linear arrays with unequal element spacing," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5/6, 775-783, 2010.
doi:10.1163/156939310791036368

46. Pozar, D. M., Microwave Engineering, 3 Ed., John Wiley & Sons, Inc., Hoboken, 2005.

47. Hastie, T., R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2 Ed., Springer, New York, 2008.

48. Fox, J., Applied Regression Analysis and Generalized Linear Models, 2 Ed., Sage Publications, Inc., Los Angeles, 2008.

49. Wu, B., T. Su, B. Li, and C. H. Liang, "Design of tubular filter based on curve-fitting method," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 8, 1071-1080, 2006.
doi:10.1163/156939306776930231

50. Wang, Y. G., J. Wang, Z. Q. Zhao, and J. Y. Yang, "A novel method to calculate the phase center of antennas," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2/3, 239-250, 2008.
doi:10.1163/156939308784160631

51. Li, Q., X. Lai, B. Wu, and T. Su, "Novel wideband coaxial filter with high selectivity in low rejection band," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 8/9, 1155-1163, 2009.

52. Islam, M. T., M. Moniruzzaman, N. Misran, and M. N. Shakib, "Curve fitting based particle swarm optimization for UWB patch antenna," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 17/18, 2421-2432, 2009.

53. Baltzis, K. B., "Empirical description of node-to-node distance density in non-overlapping wireless networks," Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 9, 57-68, 2010.

54. Okabe, S., T. Tsuboi, G. Ueta, J. Takami, and H. Hirose, "Basic study of fitting method for base curve extraction in lightning impulse test techniques," IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 17, 2-4, 2010.
doi:10.1109/TDEI.2010.5411995

55. Deschrijver, D. and T. Dhaene, "Rational fitting of S-parameter frequency samples with maximum absolute error control," IEEE Microwave and Wireless Components. Letters, Vol. 20, 247-249, 2010.
doi:10.1109/LMWC.2010.2045575

56. De Carlo, D. and S. Tringàli, "Automatic design of circular SIW resonators by a hybrid approach based on polynomial fitting and SVRMS," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5/6, 735-774, 2010.
doi:10.1163/156939310791036421

57. Baltzis, K. B., "Polynomial-based evaluation of the impact of aperture phase taper on the gain of rectangular horns," Journal of Electromagnetic Analysis and Applications, Vol. 2, 424-430, 2010.
doi:10.4236/jemaa.2010.27055

58. Philips, G. M., Interpolation and Approximation by Polynomials, Springer-Verlag Inc., New York, 2003.

59. Liu, X. F., Y. C. Jiao, F. S. Zhang, and Y. Wen, "Approximation method for reconstruction of 3-D antenna radiation patterns," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2351-2358, 2007.
doi:10.1163/156939307783134380

60. Yang, P., F. Yang, Z.-P. Nie, B. Li, and X. Tang, "Robust adaptive beamformer using interpolation technique for conformal antenna array," Progress In Electromagnetics Research B, Vol. 23, 215-228, 2010.
doi:10.2528/PIERB10061504

61. Sahalos, J. N., Orthogonal Methods for Array Synthesis: Theory and the ORAMA Computer Tool, John Wiley & Sons Ltd., Chichester, 2006.
doi:10.1002/0470028548

62. Selvan, K. T., "Accurate design method for pyramidal horns of any desired gain and aperture phase error," IEEE Antennas and Wireless Propagation Letters, Vol. 7, 31-32, 2008.
doi:10.1109/LAWP.2007.914119

63. Selvan, K. T., "Derivation of a condition for the normal gain behavior of pyramidal horns," IEEE Transactions on Antennas Propagation, Vol. 48, 1782-1784, 2000.
doi:10.1109/8.900237

64. Aryshev, A., et al., "Development of microwave and soft X-ray sources based on coherent radiation and Thomson scattering," Eighth International Symposium on Radiation from Relativistic Electrons in Periodic Structures, Moscow, Russian Federation, 2009, doi:10.1088/1742-6596/236/1/012009.

Dr. Konstantinos B. Baltzis