volume | PIER Journals

Abstract

A novel implementation of aggressive space mapping (ASM) for the automatic layout synthesis of planar metamaterial structures is outlined in this article. Specifically, we employ a model-trust region optimisation approach to significantly reduce the computational burden associated with the direct optimisation of high-fidelity models. A Visual Basic for application (VBA) link to a commercial full-wave electromagnetic (EM) solver is created, to ensure that the automated Matlab-based platform has complete control of the design and analysis of the entire ASM process. The validity and efficiency of our approach is demonstrated with examples of complementary split-ring resonator (CSRR)-loaded transmission lines, comparing both modified and unmodified version of the quasi-Newton iteration within the ASM framework.

1. Bandler, J. W., R. M. Biernacki, S. H. Chen, P. A. Grobelny, and R. H. Hemmers, "Space mapping technique for electromagnetic optimization," IEEE Transactions on Microwave Theory and Techniques, Vol. 42, No. 12, 2536-2544, Dec. 1994.
doi:10.1109/22.339794

2. Koziel, S., Q. S. Cheng, and J. W. Bandler, "Rapid design optimisation of microwave structures through automated tuning space mapping," IET Microwaves, Antennas Propagation, Vol. 4, No. 11, 1892-1902, Nov. 2010.
doi:10.1049/iet-map.2009.0618

3. Koziel, S., J. W. Bandler, and Q. S. Cheng, "Robust trust-region space-mapping algorithms for microwave design optimization," IEEE Transactions on Microwave Theory and Techniques, Vol. 58, No. 8, 2166-2174, Aug. 2010.
doi:10.1109/TMTT.2010.2052666

4. Bandler, J. W., R. M. Biernacki, S. H. Chen, R. H. Hemmers, and K. Madsen, "Electromagnetic optimization exploiting aggressive space mapping," IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 12, 2874-2882, Dec. 1995.
doi:10.1109/22.475649

5. Nocedal, J. and J. Wright, Numerical Optimization, Springer, Aug. 2000.

6. Pawlowski, R. P., J. P. Simonis, H. F. Walker, and J. N. Shadid, "Inexact newton dogleg methods," SIAM J. Numer. Anal., Vol. 46, No. 4, 2112-2132, May 2008.
doi:10.1137/050632166

7. Bakr, M. H., J. W. Bandler, R. Biernacki, S. Chen, and K. Madsen, "A trust region aggressive space mapping algorithm for em optimization," IEEE Transactions on Microwave Theory and Techniques, Vol. 46, 2412-2425, 1998.
doi:10.1109/22.739229

8. Selga, J., A. Rodriguez, M. Gil, J. Carbonell, V. E. Boria, and F. Martin, "Towards the automatic layout synthesis in resonanttype metamaterial transmission lines," IET Microwaves, Antennas Propagation, Vol. 4, No. 8, 1007-1015, Aug. 2010.
doi:10.1049/iet-map.2009.0551

9. Bonache, J., M. Gil, I. Gil, J. Garcia-Garcia, and F. Martin, "On the electrical characteristics of complementary metamaterial resonators," IEEE Microwave and Wireless Components Letters, Vol. 16, No. 10, 543-545, Oct. 2006.
doi:10.1109/LMWC.2006.882400

10. Gil, I., J. Bonache, M. Gil, J. García-García, F. Martín, and R. Marquées, "Accurate circuit analysis of resonant-type left handed transmission lines with inter-resonator coupling," Journal of Applied Physics, Vol. 100, No. 7, 074908, 2008.
doi:10.1063/1.2353174

11. Hu, X., Q. Zhang, Z. Lin, and S. He, "Equivalent circuit of complementary split-ring resonator loaded transmission line," Microwave and Optical Technology Letters, Vol. 51, No. 10, 2432-2434, 2009.
doi:10.1002/mop.24625

12. Caloz, C. and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, Wiley, 2005.

13. Pozar, D. M., Microwave Engineering, 3rd Ed., Wiley, 2005.

14. Baena, J. D., J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, and M. Sorolla, "Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines ," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 4, 1451-1461, Apr. 2005.
doi:10.1109/TMTT.2005.845211

15. Bahl, I. J. and P. Bhartia, Microwave Solid State Circuit Design, Wiley-Interscience, 2003.

16. Vicente, L. N., "Space mapping: Models, sensitivities, and trustregions methods," Optimization and Engineering, Vol. 4, 159-175, 2003.
doi:10.1023/A:1023968629245

17. Dennis, Jr., J. E. and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics), Vol. 16, Society for Industrial & Applied Mathematics, 1996.

18. Powell, M. J. D., A hybrid method for nonlinear equations, Numerical Methods for Nonlinear Algebraic Equations, Philip Rabinowitz, Ed., 87-114, Gordon & Breach, 1970.

19. Dennis, J. E. and H. H. W. Mei, "Two new unconstrained optimization algorithms which use function and gradient values," Journal of Optimization Theory and Applications, Vol. 28, 453-482, 1979.
doi:10.1007/BF00932218

20. Bonache, J., M. Gil, O. Garca-Abad, and F. Martn, "Parametric analysis of microstrip lines loaded with complementary split ring resonators," Microwave and Optical Technology Letters, Vol. 50, No. 8, 2093-2096, Aug. 2008.
doi:10.1002/mop.23571

Dr. Patrick J. Bradley