In the moment method solution of the integral equations for currents of a rectangular microstrip patch reflectarray, the Leontovich boundary condition is employed to determine the conductor loss. If the basis functions contain edge conditions that approach infinity, the moment matrix elements will have diverging integrals in the Galerkin technique. In this paper, we present a criterion to stop the evaluation of these integrals at a distance before the edge, thereby avoiding the divergence problem. The stopping distance derived here is found to work for a range of values of permittivity, loss tangent, and thickness of the substrate, polarization, angles of incidence of the plane wave source, and also for superstrates. Our computed results are in good agreement with measured results and those computed by HFSS.
1. Pozar, D. M., S. D. Targonski, and H. D. Syrigos, "Design of millimeter wave microstrip reflectarray," IEEE Trans. Antennas Propag., Vol. 45, No. 2, 287-296, Feb. 1997. doi:10.1109/8.560348
2. Rengarajan, S. R., "Choice of basis functions for accurate characterization of infinite array of microstrip reflectarray elements," IEEE Antennas Wireless Propag. Lett., Vol. 4, 47-50, 2005. doi:10.1109/LAWP.2005.844127
3. Mosig, J., "Arbitrary shaped microstrip structures and their analysis with a mixed potential integral equation," IEEE Trans. Antennas Propag., Vol. 36, No. 2, 314-323, Feb. 1988.
4. Van Deventer, T. E., L. P. B. Katehi, and A. C. Cangellaris, "Analysis of conductor losses in high-speed interconnects," IEEE Trans. Microw. Theory Techn., Vol. 42, No. 1, 78-83, Jan. 1994. doi:10.1109/22.265532
5. Lewin, L., "A method of avoiding edge current divergence in perturbation loss calculations," IEEE Trans. Microw. Theory Techn., Vol. 32, No. 7, 717-719, Jul. 1984. doi:10.1109/TMTT.1984.1132762
6. Barsotti, E. L., E. F. Kuester, and J. M. Dunn, "A simple method to account for edge in the conductor loss in microstrip," IEEE Trans. Microw. Theory Techn., Vol. 39, No. 1, 98-106, Jan. 1991. doi:10.1109/22.64611
7. Theron, I. P. and J. H. Cloete, "On the surface impedance used to model the conductor losses of microstrip structures," IEE Proceedings on Microwaves Antennas and Propag., Vol. 142, No. 1, 35-40, Feb. 1995. doi:10.1049/ip-map:19951652
8. Rajagopalan, H. and Y. Rahmat-Samii, "Dielectric and conductor loss quantification for microstrip reflectarray: simulation and measurements," IEEE Trans. Antennas and Propag., Vol. 56, No. 4, 1192-1196, Apr. 2008. doi:10.1109/TAP.2008.919225
10. Richards, W. F., Y. T. Lo, and D. D. Harrison, "An improved theory for microstrip antennas and applications," IEEE Trans. Antennas Propag., Vol. 39, No. 1, 38-46, Jan. 1991. doi:10.1109/TAP.1981.1142524