An Eigenanalysis-based technique is presented for the study and design of large complicated closed cavities and particularly Reverberation Chambers, including conductor and dielectric material losses. Two different numerical approaches are exploited, while a Perturbation technique is employed to acquire an approximate reference solution. First, a straightforward approach is adopted where the finite walls conductivity is incorporated into the Finite Element Method (FEM) formulation through the Leontovich Impedance boundary conditions. The resulting eigenproblem is linearized through an eigenvalue transformation and solved using the Arnoldi algorithm. To address the excessive computational requirements of this approach and to achieve a fine mesh ensuring convergence, a novel approach is adopted. Within this, a linear eigenvalue problem is formulated and solved assuming all metallic structures as perfect electric conductors (PEC). In turn, the resulting eigenfunctions are post-processed within the Leontovich boundary condition for the calculation of the metals finite conductivity losses. Mode stirrer design guidelines are setup based on the eigenfunction characteristics. Both numerical eigenanalysis techniques are validated against an analytical solution for the empty cavity and a reverberation chamber simulated by a commercial FEM simulator. A series of classical mode stirrers are studied to verify the design guidelines, and an improved mode stirrer is developed.
Constantinos L. Zekios,
Peter C. Allilomes,
Michael T. Chryssomallis,
"Finite Element Based Eigenanalysis for the Study of Electrically Large Lossy Cavities and Reverberation Chambers," Progress In Electromagnetics Research B,
Vol. 61, 269-296, 2014. doi:10.2528/PIERB14071804
1. IEC 61000-4-21-Electromagnetic Compatibility (EMC) --- Port 4-21, "Testing and measurement techniques-reverberation chamber test methods, international electrotechnical commission (IEC),", Int. Std., CISPR/A and IEC SC 77B, IEC, Geneva, Switzerland, Apr. 2011. doi:10.1109/MCOM.2004.1367562
2. Project for 2010–2013, "Institute of electronics, microelectronics and nanotechnology,", http://www.iemn.univ-lille1.fr/en/home.html, 1992. doi:10.1002/mop.1323
3. Kildal, P. S. and K. Rosengren, "Correlation and capacity of MIMO systems and mutual coupling radiation efficiency and diversity gain of their antennas: Simulation and measurements in reverberation chamber," IEEE Communications Magazine, Vol. 42, No. 12, 104-122, Dec. 2004. doi:10.1109/TEMC.2005.860561
4. Rosengren, K. and P. S. Kildal, "Study of distributions of modes and plane waves in reverberation chambers for the characterization of antennas in a multipath environment," Microwave and Optical Technology Letters, Vol. 30, No. 6, 386-391, Sep. 2001.
5. Clegg, J., A. C. Marvin, J. F. Dawson, and S. J. Porter, "Optimization of stirrer designs in a reverberation chamber," IEEE Trans. on Electromagnetic Compatibility, Vol. 47, No. 4, 824-832, Nov. 2005. doi:10.1109/TEMC.2005.850677
6. Bruns, C., "Three-dimensional simulation and experimental verification of a reverberation chamber,", Ph.D., University of Fridericiana Karlsruhe, Germany, 2005. doi:10.1109/TAP.2006.883995
7. Bruns, C. and R. Vahldieck, "A closer look at reverberation chambers 3-D simulation and experimental verification," IEEE Trans. on Electromagnetic Compatibility, Vol. 47, 612-626, Aug. 2005.
8. Karlsson, K., J. Carlsson, and P.-S. Kildal, "Reverberation chamber for antenna measurements: Modeling using method of moments, spectral domain techniques, and asymptote extraction," IEEE Trans. on Antennas and Propagation, Vol. 54, No. 11, 3106-3113, Nov. 2006. doi:10.1109/TEMC.2010.2041005
9. Laermans, E., L. Knockaert, and D. De Zutter, "Two-dimensional method of moments modelling of lossless overmoded transverse magnetic cavities," Journal of Computational Physics, Vol. 198, 326-348, Elsevier, 2004. doi:10.1109/TAP.2012.2194677
10. Zhao, H. and Z. Shen, "Hybrid discrete singular convolution --- Method of moments analysis of a 2-D transverse magnetic reverberation chamber," IEEE Trans. on Electromagnetic Compatibility, Vol. 52, No. 3, 612-619, Aug. 2010.
11. Zhao, H. and Z. Shen, "Memory-efficient modeling of reverberation chambers using hybrid recursive update discrete singular convolution-method of moments," IEEE Trans. on Antennas and Propagation, Vol. 60, No. 6, 2781-2789, Jun. 2012. doi:10.1109/TMTT.2014.2335176
12. Gruber, M. E., S. B. Adrian, and T. F. Eibert, "A finite element boundary integral formulation using cavity Green’s function and spectral domain factorization for simulation of reverberation chambers," International Conference on Electromagnetics in Advanced Applications (ICEAA), 460-463, Sep. 9-13, 2013. doi:10.1109/MAP.2013.6735541
13. Yang, K. and A. E. Yilmaz, "An FFT-accelerated integral-equation solver for analyzing scattering in rectangular cavities," IEEE Trans. on Microwave Theory and Techniques, Vol. 62, No. 9, 1930-1942, Sep. 2014. doi:10.1109/TEMC.2008.2011818
14. Zhao, H., "MLFMM-accelerated integral-equation modeling of reverberation chambers [open problems in CEM]," IEEE Trans. on Antennas and Propagation, Vol. 55, No. 5, 299-308, Oct. 2013.
15. Carlberg, U., P.-S. Kildal, and J. Carlsson, "Numerical study of position stirring and frequency stirring in a loaded reverberation chamber," IEEE Trans. on Electromagnetic Compatibility, Vol. 51, No. 1, 12-17, Feb. 2009.
16. Adardour, A., G. Andrieu, and A. Reineix, "Influence of a stirrer on the cavity modes within a reverberation chamber," International Symposium on Electromagnetic Compatibility (EMC EUROPE), 1-4, Sep. 17-21, 2012.
17. Moglie, F., "Finite difference, time domain analysis convergence of reverberation chambers," Proc. 15th Int. Zurich Symp. and Technical Exhibition on Electromagnetic Compatibility, 223-228, Swiss Federal Inst. Technol. Zurich, Zurich, Switzerland, 2003.
18. Moglie, F. and V. M. Primiani, "Reverberation chambers: Full 3D FDTD simulations and measurements of independent positions of the stirrers," IEEE International Symposium on Electromagnetic Compatibility (EMC), 226-230, Aug. 14-19, 2011.
19. Primiani, V. M. and F. Moglie, "Numerical determination of reverberation chamber field uniformity by a 3-D simulation," International Symposium on Electromagnetic Compatibility (EMC EUROPE), 829-832, Sep. 26-30, 2011. doi:10.1109/TEMC.2006.888187
20. Lallechere, S., S. Girard, R. Vernet, P. Bonnet, and F. Paladian, "FDTD/FVTD methods and hybrid schemes applied to Reverberation chambers studies," First European Conference on Antennas and Propagation, EuCAP, 1-6, Nov. 6-10, 2006. doi:10.1109/TEMC.2007.908266
21. Orjubin, G., E. Richalot, S. Mengue, M.-F. Wong, and O. S. Picon, "On the FEM modal approach for a reverberation chamber analysis," IEEE Trans. on Electromagnetic Compatibility, Vol. 49, No. 1, 76-85, Feb. 2007. doi:10.1049/ip-map:19952261
22. Orjubin, G., E. Richalot, O. S. Picon, and O. Legrand, "Chaoticity of a reverberation chamber assessed from the analysis of modal distributions obtained by FEM," IEEE Trans. on Electromagnetic Compatibility, Vol. 49, No. 4, 762-771, Nov. 2007.
23. Golias, N. A., T. V. Yioultsis, and T. D. Tsiboukis, "Vector complex eigenmode analysis of microwave cavities," IEEE Proc. --- Microw. Antennas Propag., Vol. 142, 457-461, Dec. 1995.
24. Zekios, C. L., P. C. Allilomes, C. S. Lavranos, and G. A. Kyriacou, "A three dimensional finite element eigenanalysis of reverberation chambers," EMC Europe Workshop 2009 — Materials in EMC Applications, 129-132, Athens, Greece, Jun. 11-12, 2009.
25. Zekios, C. L., P. C. Allilomes, and G. A. Kyriacou, "A finite element eigenanalysis of arbitrary loaded cavities including conductor losses," 32nd ESA Antenna Workshop on Antennas for Space Applications, Noordwijk, The Netherlands, Oct. 5-8, 2010. doi:10.1049/el.2012.1852
26. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing, Cambridge University Press, 1992. doi:10.1002/0471786381
27. Zekios, C. L., P. C. Allilomes, and G. A. Kyriacou, "On the evaluation of eigenmodes quality factor of large complex cavities based on a PEC linear finite element formulation," Electronics Letters, Vol. 48, No. 22, 1399-1401, Oct. 2012.
28. Zhu, Y. and A. C. Cangellaris, Multigrid Finite Element Methods for Electromagnetic Field Modeling, Wiley Interscience, 605 Third Avenue, New York, 2006.
29. Reddy, C. J., M. D. Deshpande, C. R. Cockrell, and F. B. Beck, "Finite element method for eigenvalue problems in electromagnetics,", NASA Technical Paper 3485, Dec. 1994. doi:10.1109/9780470546710
30. Lehman, T. H., "A statistical theory of electromagnetic fields in complex cavities,", Interaction Note 494, Sandia Labs, May 1993.
31. Harrington, R. F., Time-harmonic Electromagnetic Fields, IEEE Press, John Wiley and Sons, Inc., 605 Third Avenue, New York , 2001.
32. Jackson, J. D., Classical Electrodynamics, 3rd edition, Wiley, New York, 1999.
33. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley and Sons, Inc., 605 Third Avenue, New York, 1989.
34. Saad, Y., Iterative Methods for Sparse Linear Systems, 2nd Edition, Society for Industrial and Applied Mathematics , 2000.
37. The HDF group, http://www.hdfgroup.org/, , 2013.
38. Extensible Markup Language (XML), http://en.wikipedia.org/wiki/XML, , 2014.
39. Godfrey, E. A., "Effects of corrugated walls on the field uniformity of reverberation chambers at low frequencies," IEEE International Symposium on Electromagnetic Compatibility (EMC), Vol. 1, 23-28, 1999.