A modified Schwarz-Christoffel transformation (SCT) is used to obtain guided- and radiated-wave characteristics of a singly-curved rectangular patch antenna. The method is to map a straight channel into an arbitrarily-curved channel. This simplifies the problem to that of a planar rectangular patch antenna. Applying conventional SCT to the problem confronts two difficulties: The region under investigation is elongated, and it has curved boundaries. Therefore, SCT is modified to handle the problem. Input impedance, VSWR and radiation patterns of a conformal patch antenna on a parabolic surface are obtained utilizing the proposed SCT and either numerical or analytical treatment of a planar patch antenna, and the results are verified. Effect of parabolic curvature on the above-mentioned characteristics is investigated.
"Guided- and Radiated-Wave Characteristics of a Rectangular Patch Antenna Located on a Singly-Curved Surface," Progress In Electromagnetics Research C,
Vol. 38, 205-216, 2013. doi:10.2528/PIERC12111705
1. He, , M. and X. Xu, "Closed-form solutions for analysis of cylindrically conformal microstrip antennas with arbitrary radii," IEEE Trans. Antennas Propag., Vol. 53, No. 1, 518-525, Jan. 2005. doi:10.1109/TAP.2004.838772
2. Amendola, G., "Application of Mathieu functions to the analysis of radiators conformal to elliptic cylindrical surfaces," Journal of Electromagnetic Waves and Applications, Vol. 13, No. 8, 1103-1120, 1999. doi:10.1163/156939399X01267
3. Yuan, N., X. C. Nie, Y. B. Gan, T. S. Yeo, and L. W. Li, "Accurate analysis of conformal antenna arrays with finite and curved frequency selective surfaces," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1745-1760, 2012.
4. Dib, N. and T. Weller, "Finite difference time domain analysis of cylindrical coplanar waveguide circuits," Journal of Electromagnetic Waves and Applications, Vol. 87, No. 9, 1083-1094, 2000.
5. Revuelto, I. G., L. E. G. Castillo, F. S. Adana, M. S. Palma, and T. K. Sarkar, "A novel hybrid FEM high-frequency technique for the analysis of scattering and radiation problems," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 7, 939-956, 2004. doi:10.1163/156939304323105763
6. Arakaki, D. Y., D. H. Werner, and R. Mittra, "A technique for analyzing radiation from conformal antennas mounted on arbitrarily-shaped conducting bodies," Proc. IEEE International Symp. on Antennas and Propag., Vol. 1, 10-13, 2000.
7. Macon, C. A., K. D. Trott, and L. C. Kempel, "A practical approach to modeling doubly curved conformal microstrip antennas," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 8, 1161-1163, 2003. doi:10.1163/156939303322519793
8. Hosseini, K. and Z. Atlasbaf, "Design of a cylindrical CRLH leaky-wave antenna using conformal mapping," IEEE International Symp. on Telecommun. (IST2012), Tehran, 2012.
9. Kadi, Z. and A. Rockwood, "Conformal maps defined about polynomial curves," Computer Aided Geometric Design, Vol. 15, 323-337, 1998. doi:10.1016/S0167-8396(97)00035-6
10. Driscoll, T. A., "A non-overlapping domain decomposition method for Symm's equation for conformal mapping," Society for Industrial and Applied Mathematics, Vol. 36, No. 3, 922-934, 1999.
11. Howell, L. H., "Computation of conformal maps by modified Schwarz-Christoffel transformation,", Ph.D. Dissertation, Dept. Math., Massachussets Inst. of Technology, MA, 1990.
12. Davis, R. T., "Numerical methods for coordinate generation based on Schwarz-Christoffel transformation," AIAA Computational Fluid Dynamics Conference, Vol. A79-45251, 180-194, 1979.
13. Akan, V. and E. Yazgan, "Quasi-static solutions of multilayer elliptical, cylindrical coplanar striplines and multilayer coplanar striplines with finite dielectric dimensions-asymmetrical case," IEEE Trans. Antennas Propag., Vol. 53, No. 12, 3681-3686, Dec. 2005.
14. Nguyen, C., Analysis Methods for RF, Microwave, and Millimeter-wave Planar Transmission-line Structures, Chapter 5, John Wiley & Sons, New York, 2000. doi:10.1002/0471200670
15. Brown, J. W. and R. V. Churchill, Complex Variables and Applications, 8th Ed., Chapter 11, Mc-Graw Hill, New York, 2004.
16. Balanis, C. A., Antenna Theory, Analysis and Design, 3rd Ed., Chapter 14, John Wiley, New Jersey, 2005.