volume | PIER Journals

Abstract

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.

1. Wheeler, H. A., "Fundamental limitations of antennas," Proc. IRE, Vol. 35, 1479-1484, Dec. 1947.
doi:10.1109/JRPROC.1947.226199 Google Scholar

2. Wheeler, H. A., "The spherical coil as an inductor, shield or antenna," Proc. IRE, Vol. 46, 1595-1602, Sep. 1958.
doi:10.1109/JRPROC.1958.286978 Google Scholar

3. Wheeler, H. A., "Small antennas," Antenna Engineering Handbook, 1993. Google Scholar

4. Chu, L. J., "Physical limitations of omni-directional antennas," J. Appl. Phys., Vol. 19, 1163-1175, Dec. 1948.
doi:10.1063/1.1715038 Google Scholar

5. Harrington, R. F., "Effect of antenna size on gain, bandwidth, and effciency," J. Res. Nat. Bur. Stand., Vol. 64D, 1-12, Jan. 1960. Google Scholar

6. Thal, H. L., "New radiation Q limits for spherical wire antennas," IEEE Trans. on Antennas and Propagat., Vol. 54, No. 10, 2557-2761, Oct. 2006. Google Scholar

7. Thal, H. L., "Gain and Q bounds for coupled TM-TE modes," IEEE Trans. on Antennas and Propagat., Vol. 57, No. 7, 1879-1885, Jul. 2009.
doi:10.1109/TAP.2009.2021930 Google Scholar

8. Collin, R. E. and S. Rothschild, "Evaluation of antenna Q," IEEE Trans. on Antennas and Propagat., Vol. 12, No. 1, 23-27, Jan. 1964.
doi:10.1109/TAP.1964.1138151 Google Scholar

9. Levis, C. A., "A reactance theorem for antennas," Proc. IRE, Vol. 45, 1128-1134, Aug. 1957.
doi:10.1109/JRPROC.1957.278271 Google Scholar

10. Fante, R. L., "Quality factor of general ideal antennas," IEEE Trans. on Antennas and Propagat., Vol. 17, No. 2, 151-155, Mar. 1969.
doi:10.1109/TAP.1969.1139411 Google Scholar

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, Apr. 2005.
doi:10.1109/TAP.2005.844443 Google Scholar

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 Google Scholar

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 Google Scholar

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, Jun. 2007.
doi:10.1109/TAP.2007.897350 Google Scholar

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. Google Scholar

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, May 2009.
doi:10.1109/TAP.2009.2016683 Google Scholar

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, Mar. 2013.
doi:10.1109/TAP.2012.2227656 Google Scholar

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 Google Scholar

19. Fano, R. M., "Theoretical limitations on the broadband matching of arbitrary impedances," J. Franklin Inst., Vol. 249, 57-54, Jan. 1950.
doi:10.1016/0016-0032(50)90006-8 Google Scholar

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, Oct. 2005.
doi:10.1109/TAP.2005.856352 Google Scholar

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 Google Scholar

22. Hrabar, S., Z. Sipus, and I. Malcic, "Broadening of cloaking bandwidth by passive and active techniques," Transformation Electromagnetics and Metamaterials, 2014. Google Scholar

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 Google Scholar

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, Aug. 2006.
doi:10.1109/LAWP.2006.881913 Google Scholar

25. Loudon, R., "The propagation of electromagnetic energy through an absorbing dielectric," J. Phys. A, Vol. 3, 233-245, May 1970.
doi:10.1088/0305-4470/3/3/008 Google Scholar

26. Ruppin, R., "Electromagnetic energy density in a dispersive and absorptive material," Phys. Letts. A, Vol. 299, 309-312, Jul. 2002.
doi:10.1016/S0375-9601(01)00838-6 Google Scholar

27. Tretyakov, S. A., "Electromagnetic field energy density in artificial microwave materials with strong dispersion and loss," Phys. Letts. A, Vol. 343, 231-237, Jun. 2005.
doi:10.1016/j.physleta.2005.06.023 Google Scholar

28. Boardman, A. D., "Electromagnetic energy in a dispersive metamaterial," Phys. Rev. B, Vol. 73, 165110-1-165110-7, Dec. 1987. Google Scholar

29. Landau, L. D. and Electrodynamics of Continuous Media, "Electrodynam-,", 1984. Google Scholar

30. Yaghjian, A. D. and S. Maci, "Alternative derivation of electromagnetic cloaks and concentrators," New Journal of Physics, Vol. 10, 115022, Nov. 2008.
doi:10.1088/1367-2630/10/11/115022 Google Scholar

31. Yaghjian, A. D., A. Alµu, and M. G. Silveirinha, "Anisotropic representation for spatially dispersive periodic metamaterial arrays ," Transformation Electromagnetics and Metamaterials , 2014. Google Scholar

32. Karni, S., Network Theory: Analysis and Synthesis, Allyn and, 1966.

33. Stratton, J. A., "Electromagnetic Theory," McGraw-Hill, 1941. Google Scholar

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. Google Scholar

35. Lee, K. S. H., "Relations between electric and magnetic polarizabilities and other related quantities," Radio Science, Vol. 22, 1235-1238, Sep. 2004. Google Scholar

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, Sep. 2004.
doi:10.1109/TAP.2004.834081 Google Scholar

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, May 1996.
doi:10.1109/8.496253 Google Scholar

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, Dec. 2010.
doi:10.1109/TAP.2010.2078466 Google Scholar

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, Jun. 2010.
doi:10.1109/TAP.2010.2046864 Google Scholar

40. Hansen, R. C. and R. E. Collin, "A new Chu formula for Q," IEEE Antennas Propagat. Mag., Vol. 51, No. 5, 38-41, Oct. 2009.
doi:10.1109/MAP.2009.5432037 Google Scholar

Dr. Arthur D. Yaghjian

Dr. Mats Gustafsson

Dr. Lars Jonsson