Konstantinos B. Baltzis

Abstract: The aperture phase taper due to quadratic phase errors in the principal planes of a rectangular horn imposes signifi-cant constraints on the on-axis far-field gain of the horn. The precise calculation of gain reduction involves Fresnel integrals; therefore, exact results are obtained only from numerical methods. However, in horns’ analysis and design, simple closed-form expressions are often required for the description of horn-gain. This paper provides a set of simple polynomial approximations that adequately describe the gain reduction factors of pyramidal and sectoral horns. The proposed formulas are derived using least-squares polynomial regression analysis and they are valid for a broad range of quadratic phase error values. Numerical results verify the accuracy of the derived expressions. Application examples and comparisons with methods in the literature demonstrate the efficacy of the approach.

Keywords: Microwave Antennas, Rectangular Horn, Gain, Quadratic Phase Error, Linear Regression

Cite this paper: nullK. Baltzis, "Polynomial-Based Evaluation of the Impact of Aperture Phase Taper on the Gain of Rectangular Horns," Journal of Electromagnetic Analysis and Applications, Vol. 2 No. 7, 2010, pp. 424-430. doi: 10.4236/jemaa.2010.27055.

References

[1]   C. A. Balanis, “Antenna Theory: Analysis and Design,” 3rd Edition, John Wiley & Sons, Inc., Hoboken, 2005.

[2]   S. A. Schelkunoff, “Electromagnetic Waves,” David Van Nostrand Company, Inc., New York, 1943.

[3]   J. L. Teo and K. T. Selvan, “On the Optimum Pyramidal- Horn Design Methods,” International Journal of RF and Computer-Aided Engineering, Vol. 16, No. 6, November 2006, pp. 561-564.

[4]   E. Jull, “Errors in the Predicted Gain of Pyramidal Horns,” IEEE Transactions on Antennas and Propagation, Vol. 21, No. 1, January 1973, pp. 25-31.

[5]   K. T. Selvan, “An Approximate Generalization of Schel- kunoff’s Horn-Gain Formulas,” IEEE Transactions on Antennas and Propagation, Vol. 47, No. 6, June 1999, pp. 1001-1004.

[6]   G. Kordas, K. B. Baltzis, G. S. Miaris and J. N. Sahalos, “Pyramidal-Horn Design under Constraints on Half-Power Beamwidth,” IEEE Transactions on Antennas and Propa- gation, Vol. 44, No. 1, February 2002, pp. 102-108.

[7]   K. T. Selvan, R. Sivaramakrishnan, K. R. Kini and D. R. Poddar, “Experimental Verification of the Generalized Schelkunoff’s Horn-Gain Formulas for Sectoral Horns,” IEEE Transactions on Antennas and Propagation, Vol. 50, No. 6, June 2002, pp. 875-877.

[8]   K. Guney and N. Sarikaya, “Neural Computation of Wide Aperture Dimension of Optimum Gain Pyramidal Horn,” International Journal of Infrared and Millimeter Waves, Vol. 26, No. 7, July 2005, pp. 1043-1057.

[9]   A. Akdagli and K. Guney, “New Wide-Aperture-Dimension Formula Obtained by Using a Particle Swarm Optimization for Optimum Gain Pyramidal Horns,” Microwave and Optical Technology Letters, Vol. 48, No. 6, June 2006, pp. 1201-1205.

[10]   Y. Najjar, M. Moneer and N. Dib, “Design of Optimum Gain Pyramidal Horn with Improved Formulas Using Particle Swarm Optimization,” International Journal of RF and Computer-Aided Engineering, Vol. 17, No. 5, Sep-tember 2007, pp. 505-511.

[11]   K. T. Selvan, “Accurate Design Method for Pyramidal Horns of Any Desired Gain and Aperture Phase Error,” IEEE Antennas Wireless Propagation Letters, Vol. 7, 2008, pp. 31-32.

[12]   W. T. Slayton, “Design and Calibration of Microwave Antenna Gain Standards,” Report 0594740, US Naval Research Laboratory, Washington, 1954.

[13]   J. W. Odendaal, “Predicting Directivity of Standard-Gain Pyramidal-Horn Antennas,” IEEE Antennas and Propa- gation Magazine, Vol. 46, No. 4, August 2004, pp. 93-98.

[14]   K. Harima, M. Sakasai and K. Fujii, “Determination of Gain for Pyramidal-Horn Antenna on Basis of Phase Center Location,” Proceedings of the 2008 IEEE Interna-tional Symposium on Electromagnetic Compatibility-EMC 2008, Detroit, 18-22 August 2008, pp. 1-5.

[15]   G. Mayhew-Ridgers, J. W. Odendaal and J. Joubert, “Im- proved Diffraction Model and Numerical Validation for Horn Antenna Gain Calculations,” International Journal of RF and Computer-Aided Engineering, Vol. 19, No. 6, November 2009, pp. 701-711.

[16]   M. Ali and S. Sanyal, “A Finite Edge GTD Analysis of the H-Plane Horn Radiation Pattern,” IEEE Transactions on Antennas and Propagation, Vol. 58, No. 3, March 2010, pp. 969-973.

[17]   J. F. Aurand, “Pyramidal Horns, Part I: Simple Expres-sions for Directivity as a Function of Aperture Phase Er-ror,” Proceedings of the 1989 IEEE Antennas Propagation Society International Symposium, San Jose, Vol. 3, 1989, pp. 1435-1438.

[18]   J. F. Aurand, “Pyramidal Horns, Part II: A Novel Design Method for Horns of Any Desired Gain and Aperture Phase Error,” Proceedings of the 1989 IEEE Antennas and Propagation Society International Symposium, San Jose, Vol. 3, 26-30 June 1989, pp. 1439-1442.

[19]   T. Milligan, “Scales for Rectangular Horns,” IEEE Trans- actions on Antennas and Propagation, Vol. 42, No. 5, Oc-tober 2000, pp. 79-83.

[20]   T. A. Milligan, “Modern Antenna Design,” 2nd Edition, John Wiley & Sons, Inc., Hoboken, 2005.

[21]   J. N. Sahalos, “Orthogonal Methods for Array Synthesis: Theory and the ORAMA Computer Tool,” John Wiley & Sons, Inc., Chichester, 2006.

[22]   M. J. Maybell and P. S. Simon, “Pyramidal Horn Gain Calculation with Improved Accuracy,” IEEE Transactions on Antennas and Propagation, Vol. 41, No. 7, July 1993, pp. 884-889.

[23]   E. W. Weisstein, “CRC Concise Encyclopedia of Mathe-matics,” 2nd Edition, Chapman & Hall/CRC, Boca Raton, 2002.

[24]   D. M. Pozar, “Microwave Engineering,” 3rd Edition, John Wiley & Sons, Inc., New York, 2005.

[25]   T. Hastie, R. Tibshirani and J. Friedman, “The Elements of Statistical Learning: Data Mining, Inference, and Pre- diction,” 2nd Edition, Springer, New York, 2008.

[26]   J. Fox, “Applied Regression Analysis and Generalized Linear Models,” 2nd Edition, Sage Publications, Inc., Thousand Oaks, 2008.

[27]   C. R. Rao, H. Toutenburg, S. Shalabh and C. Heumann, “Linear Models and Generalizations: Least Squares and Alternatives,” 3rd Edition, Springer, Berlin, 2009.

[28]   F. Yang, J. Han, J. Yang and Z. Li, “Some Advances in the Application of Weathering and Cold-Formed Steel in Transmission Tower,” Journal of Electromagnetic Analy-sis and Applications, Vol. 1, No. 1, March 2009, pp. 24-30.

[29]   A. Gilat and V. Subramaniam, “Numerical Methods for Engineers and Scientists: An Introduction with Applica-tions Using MATLAB?,” 2nd Edition, John Wiley & Sons, Inc., Hoboken, 2010.