General expressions for the quality factor (Q) of antennas are minimized to obtain lower-bound formulas for the Q of electrically small, lossy or lossless, combined electric and magnetic dipole antennas confined to an arbitrarily shaped volume. The lower-bound formulas for Q are derived for the dipole antennas excited by both electric and magnetic surface currents as well as by electric surface currents alone. With either excitation, separate formulas are found for the dipole antennas containing only lossless or nondispersive-conductivity material and for the dipole antennas containing highly dispersiveconductivity material. The formulas involve the quasi-static electric and magnetic polarizabilities of the associated perfectly conducting volume of the antenna, the ratio of the powers radiated by the electric and magnetic dipoles, and the efficiency of the antenna.
Arthur D. Yaghjian,
"Minimum Q for Lossy and Lossless Electrically Small Dipole Antennas (Invited Paper)," Progress In Electromagnetics Research,
Vol. 143, 641-673, 2013. doi:10.2528/PIER13103107
10. Fante, R. L., "Quality factor of general ideal antennas," IEEE Trans. on Antennas and Propagat., Vol. 17, No. 2, 151-155, 1969. doi:10.1109/TAP.1969.1139411
11. Yaghjian, A. D. and S. R. Best, "Impedance, bandwidth, and Q of antennas," IEEE Trans. on Antennas and Propagat., Vol. 53, No. 4, 1298-1324, 2005. doi:10.1109/TAP.2005.844443
12. Gustafsson, M., C. Sohl, and G. Kristensson, "Physical limitations on antennas of arbitrary shape," Proc. Roy. Soc. A, Vol. 463, 2589-2607, 2007. doi:10.1098/rspa.2007.1893
13. Yaghjian, A. D. and H. R. Stuart, "Lower bounds on the Q of electrically small dipole antennas," IEEE Trans. on Antennas and Propagat., Vol. 58, No. 10, 3114-3121, 2010. doi:10.1109/TAP.2010.2055790
14. Yaghjian, A. D., "Internal energy, Q-energy, Poynting's theorem and the stress dyadic in dispersive material," IEEE Trans. on Antennas and Propagat., Vol. 55, No. 6, 1495-1505, 2007. doi:10.1109/TAP.2007.897350
15. Jonsson, B. L. G. and M. Gustafsson, "Stored energies for electric and magnetic currents with applications to Q for small antennas," Proc. of the Intn'l Symp. on Electromagnetic Theory, 1050-1053, 2013.
16. Gustafsson, M., C. Sohl, and G. Kristensson, "Illustrations of new physical bounds on linearly polarized antennas," IEEE Trans. on Antennas and Propagat., Vol. 57, No. 5, 1319-1327, 2009. doi:10.1109/TAP.2009.2016683
17. Gustafsson, M. and S. Nordebo, "Optimal antenna currents for Q, superdirectivity, and radiation patterns using convex optimization ," IEEE Trans. on Antennas and Propagat., Vol. 61, No. 3, 1109-1118, 2013. doi:10.1109/TAP.2012.2227656
18. Vandenbosch, G. A. E., "Vandenbosch, G. A. E., \Reactive energy, impedance, and Q factor of radiating structures," IEEE Trans. on Antennas and Propagat., Vol. 58, No. 4, 1112-1127, 2010. doi:10.1109/TAP.2010.2041166
19. Fano, R. M., "Theoretical limitations on the broadband matching of arbitrary impedances," J. Franklin Inst., Vol. 249, 57-54, 1950. doi:10.1016/0016-0032(50)90006-8
20. Hujanen, A., J. Holmberg, and J. C.-E. Sten, "Bandwidth limitations of impedance matched ideal dipoles," IEEE Trans. on Antennas and Propagat., Vol. 53, No. 10, 3236-3239, 2005. doi:10.1109/TAP.2005.856352
21. Stuart, H. R. and Limitations in, "Limitations in relating quality factor to bandwidth in a double resonance small antenna ," IEEE Antennas Wireless Propagat. Letts., Vol. 6, 460-463, 2007. doi:10.1109/LAWP.2007.905018
22. Hrabar, S., Z. Sipus, and I. Malcic, "Broadening of cloaking bandwidth by passive and active techniques," Transformation Electromagnetics and Metamaterials, 2014.
23. Hansen, T. V., O. S. Kim, and O. Breinbjerg, "Quality factor and radiation e±ciency of dual mode self-resonant spherical antennas with lossy magnetodielectric cores," IEEE Trans. on Antennas and Propagat., No. 99, 1, 2013. doi:DOI 10.1109/TAP.2013.2287290
24. Yaghjian, A. D., "Improved formulas for the Q of antennas with highly lossy dispersive materials," IEEE Antennas Wireless Propagat. Lett., Vol. 5, No. 1, 365-369, 2006. doi:10.1109/LAWP.2006.881913
25. Loudon, R., "The propagation of electromagnetic energy through an absorbing dielectric," J. Phys. A, Vol. 3, 233-245, 1970. doi:10.1088/0305-4470/3/3/008
27. Tretyakov, S. A., "Electromagnetic field energy density in artificial microwave materials with strong dispersion and loss," Phys. Letts. A, Vol. 343, 231-237, 2005. doi:10.1016/j.physleta.2005.06.023
28. Boardman, A. D., "Electromagnetic energy in a dispersive metamaterial," Phys. Rev. B, Vol. 73, 165110-1-165110-7, 1987.
29. Landau, L. D. and Electrodynamics of Continuous Media, "Electrodynam-,", 1984.
30. Yaghjian, A. D. and S. Maci, "Alternative derivation of electromagnetic cloaks and concentrators," New Journal of Physics, Vol. 10, 115022, 2008. doi:10.1088/1367-2630/10/11/115022
31. Yaghjian, A. D., A. Alµu, and M. G. Silveirinha, "Anisotropic representation for spatially dispersive periodic metamaterial arrays ," Transformation Electromagnetics and Metamaterials , 2014.
33. Stratton, J. A., "Electromagnetic Theory," McGraw-Hill, 1941.
34. Sohl, C., M. Gustafsson, and G. Kristensson, "Physical limitations on broadband scattering by heterogeneous obstacles," J. Phys. A: Math. Theor., Vol. 40, 1165-1182, 2007.
35. Lee, K. S. H., "Relations between electric and magnetic polarizabilities and other related quantities," Radio Science, Vol. 22, 1235-1238, 2004.
36. Sihvola, A., P. Yla-Oijala, S. Jarvenpaa, and J. Avelin, "Polarizabilities of platonic solids," IEEE Trans. on Antennas and Propagat., Vol. 52, No. 9, 2226-2233, 2004. doi:10.1109/TAP.2004.834081
37. McLean, J. S., "A re-examination of the fundamental limits on the radiation Q of electrically small antennas," IEEE Trans. on Antennas and Propagat., Vol. 44, No. 5, 672-676, 1996. doi:10.1109/8.496253
38. Stuart, H. R. and A. D. Yaghjian, "Approaching the lower bounds on Q for electrically small electric-dipole antennas using high permeability shells," IEEE Trans. on Antennas and Propagat., Vol. 58, No. 12, 3865-3872, 2010. doi:10.1109/TAP.2010.2078466
39. Kim, O. S., O. Breinbjerg, and A. D. Yaghjian, "Electrically small magnetic-dipole antennas with quality factors approaching the Chu lower bound ," IEEE Trans. on Antennas and Propagat., Vol. 58, No. 6, 1898-1906, 2010. doi:10.1109/TAP.2010.2046864
40. Hansen, R. C. and R. E. Collin, "A new Chu formula for Q," IEEE Antennas Propagat. Mag., Vol. 51, No. 5, 38-41, 2009. doi:10.1109/MAP.2009.5432037