PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 150 > pp. 13-27

STORED ELECTROMAGNETIC ENERGY AND ANTENNA Q (Invited Paper)

By M. Gustafsson and L. Jonsson

Full Article PDF (240 KB)

Abstract:
Decomposition of the electromagnetic energy into its stored and radiated parts is instrumental in the evaluation of antenna Q and the corresponding fundamental limitations on antennas. This decomposition is not unique and there are several proposals in the literature. Here, it is shown that stored energy defined from the difference between the energy density and the far field energy equals the energy expressions proposed by Vandenbosch for many but not all cases. This also explains the observed cases with negative stored energy and suggests a possible remedy to them. The results are compared with the classical explicit expressions for spherical regions where the results only differ by the electrical size ka that is interpreted as the far-field energy in the interior of the sphere. Q

Citation:
M. Gustafsson and L. Jonsson, "Stored Electromagnetic Energy and Antenna Q (Invited Paper)," Progress In Electromagnetics Research, Vol. 150, 13-27, 2015.
doi:10.2528/PIER14111502
http://www.jpier.org/PIER/pier.php?paper=14111502

References:
1. Bostrom, A., G. Kristensson, and S. Strom, "Transformation properties of plane, spherical and cylindrical scalar and vector wave functions," Field Representations and Introduction to Scattering; Acoustic, Electromagnetic and Elastic Wave Scattering, V. V. Varadan, A. Lakhtakia, and V. K. Varadan, (eds.), Chapter 4, 165–210, Elsevier Science Publishers, Amsterdam, 1991.

2. Capek, M., P. Hazdra, and J. Eichler, "A method for the evaluation of radiation Q based on modal approach," IEEE Trans. Antennas Propagat., Vol. 60, No. 10, 4556-4567, 2012.
doi:10.1109/TAP.2012.2207329

3. Capek, M., L. Jelinek, P. Hazdra, and J. Eichler, "The measurable Q factor and observable energies of radiating structures," IEEE Trans. Antennas Propagat., Vol. 62, No. 1, 311-318, Jan. 2014.
doi:10.1109/TAP.2013.2287519

4. Carpenter, C. J., "Electromagnetic energy and power in terms of charges and potentials instead of fields," IEE Proc. A, Vol. 136, No. 2, 55-65, 1989.

5. Chu, L. J., "Physical limitations of omnidirectional antennas," J. Appl. Phys., Vol. 19, 1163-1175, 1948.
doi:10.1063/1.1715038

6. Cismasu, M. and M. Gustafsson, "Antenna bandwidth optimization with single frequency simulation," IEEE Trans. Antennas Propagat., Vol. 62, No. 3, 1304-1311, 2014.
doi:10.1109/TAP.2013.2295426

7. Collin, R. E., "Minimum Q of small antennas," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 10, 1369-1393, 1998.
doi:10.1163/156939398X01457

8. Collin, R. E. and S. Rothschild, "Evaluation of antenna Q," IEEE Trans. Antennas Propagat., Vol. 12, 23-27, Jan. 1964.
doi:10.1109/TAP.1964.1138151

9. Endean, V. G. and C. J. Carpenter, "Electromagnetic energy and power in terms of charges and potentials instead of fields (comments with reply)," IEE Proc. A, Vol. 139, No. 6, 338-342, 1992.

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

11. Feynman, R. P., R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Addison-Wesley, Reading, MA, USA, 1965.

12. Foltz, H. D. and J. S. McLean, "Limits on the radiation Q of electrically small antennas restricted to oblong bounding regions," IEEE Antennas and Propagation Society International Symposium, Vol. 4, 2702-2705, 1999.

13. Geyi, W., "A method for the evaluation of small antenna Q," IEEE Trans. Antennas Propagat., Vol. 51, No. 8, 2124-2129, 2003.
doi:10.1109/TAP.2003.814755

14. Geyi, W., Foundations of Applied Electrodynamics, John Wiley & Sons, 2011.

15. Gustafsson, M., "Sum rules for lossless antennas," IET Microwaves, Antennas & Propagation, Vol. 4, No. 4, 501-511, 2010.
doi:10.1049/iet-map.2009.0083

16. Gustafsson, M., M. Cismasu, and S. Nordebo, "Absorption efficiency and physical bounds on antennas," International Journal of Antennas and Propagation, Vol. 2010, Article ID 946746, 1-7, 2010.

17. Gustafsson, M. and B. L. G. Jonsson, "Antenna Q and stored energy expressed in the fields, currents, and input impedance," IEEE Trans. Antennas Propagat., Vol. 63, No. 1, 2015, DOI: 10.1109/TAP.2014.2368111.
doi:10.1109/TAP.2014.2368111

18. Gustafsson, M. and S. Nordebo, "Optimal antenna currents for Q, superdirectivity, and radiation patterns using convex optimization," IEEE Trans. Antennas Propagat., Vol. 61, No. 3, 1109-1118, 2013.
doi:10.1109/TAP.2012.2227656

19. Gustafsson, M., C. Sohl, and G. Kristensson, "Physical limitations on antennas of arbitrary shape," Proc. R. Soc. A, Vol. 463, 2589-2607, 2007.
doi:10.1098/rspa.2007.1893

20. Gustafsson, M., C. Sohl, and G. Kristensson, "Illustrations of new physical bounds on linearly polarized antennas," IEEE Trans. Antennas Propagat., Vol. 57, No. 5, 1319-1327, May 2009.
doi:10.1109/TAP.2009.2016683

21. Gustafsson, M., M. Cismasu, and B. L. G. Jonsson, "Physical bounds and optimal currents on antennas," IEEE Trans. Antennas Propagat., Vol. 60, No. 6, 2672-2681, 2012.
doi:10.1109/TAP.2012.2194658

22. Gustafsson, M. and B. L. G. Jonsson, "Stored electromagnetic energy and antenna Q,", Technical Report LUTEDX/(TEAT-7222)/1-25/(2012), Lund University, Department of Electrical and Information Technology, P. O. Box 118, S-221 00 Lund, Sweden, 2012, http://www.eit.lth.se.
doi:10.1109/TAP.2012.2194658

23. Gustafsson, M. and S. Nordebo, "Bandwidth, Q factor, and resonance models of antennas," Progress In Electromagnetics Research, Vol. 62, 1-20, 2006.
doi:10.2528/PIER06033003

24. Gustafsson, M., D. Tayli, and M. Cismasu, "Q factors for antennas in dispersive media,", Technical Report LUTEDX/(TEAT-7232)/1-24/(2014), Department of Electrical and Information Technology, Lund University, P. O. Box 118, S-221 00 Lund, Sweden, 2014, http://www.eit.lth.se.

25. Hansen, J. E. (ed.), "Spherical near-field antenna measurements," IEE Electromagnetic Waves Series, Vol. 26, Peter Peregrinus Ltd., Stevenage, UK, 1988.

26. Hansen, R. C. and R. E. Collin, "A new Chu formula for Q," IEEE Antennas and Propagation Magazine, Vol. 51, No. 5, 38-41, 2009.
doi:10.1109/MAP.2009.5432037

27. Hansen, T. V., O. S. Kim, and O. Breinbjerg, "Stored energy and quality factor of spherical wave functions — In relation to spherical antennas with material cores," IEEE Trans. Antennas Propagat., Vol. 60, No. 3, 1281-1290, 2012.
doi:10.1109/TAP.2011.2180330

28. Harrington, R. F., Time Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961.

29. Harrington, R., "Characteristic modes for antennas and scatterers," Numerical and Asymptotic Techniques in Electromagnetics, Topics in Applied Physics, Vol. 3, 51-87, R. Mittra (ed.), Springer Berlin Heidelberg, 1975.

30. Hazdra, P., M. Capek, and J. Eichler, "Radiation Q-factors of thin-wire dipole arrangements," IEEE Antennas and Wireless Propagation Letters, Vol. 10, 556-560, 2011.
doi:10.1109/LAWP.2011.2158050

31. Jackson, J. D., Classical Electrodynamics, 3rd edition, John Wiley & Sons, New York, 1999.

32. Jin, J. M., Theory and Computation of Electromagnetic Fields, Wiley Online Library, 2010.
doi:10.1002/9780470874257

33. Jonsson, B. L. G. and M. Gustafsson, "Stored energies in electric and magnetic current densities for small antennas," Classical Physics, arXiv: 1410.8704, 2014.

34. Landau, L. D., E. M. Lifshitz, and L. P. Pitaevskiı, Electrodynamics of Continuous Media, 2nd edition, Pergamon, Oxford, 1984.

35. McLean, J. S., "A re-examination of the fundamental limits on the radiation Q of electrically small antennas," IEEE Trans. Antennas Propagat., Vol. 44, No. 5, 672-676, May 1996.
doi:10.1109/8.496253

36. Sten, J. C.-E., P. K. Koivisto, and A. Hujanen, "Limitations for the radiation Q of a small antenna enclosed in a spheroidal volume: Axial polarisation," AE¨U Int. J. Electron. Commun., Vol. 55, No. 3, 198-204, 2001.
doi:10.1078/1434-8411-00030

37. Thal, H. L., "Exact circuit analysis of spherical waves," IEEE Trans. Antennas Propagat., Vol. 26, No. 2, 282-287, Mar. 1978.
doi:10.1109/TAP.1978.1141822

38. Thal, H. L., "New radiation Q limits for spherical wire antennas," IEEE Trans. Antennas Propagat., Vol. 54, No. 10, 2757-2763, Oct. 2006.
doi:10.1109/TAP.2006.882184

39. Uehara, M., J. E. Allen, and C. J. Carpenter, "Electromagnetic energy and power in terms of charges and potentials instead of fields (comments with reply)," IEE Proc. A, Vol. 139, No. 1, 42-44, 1992.

40. Van Bladel, J. G., Electromagnetic Fields, 2nd edition, IEEE Press, Piscataway, NJ, 2007.
doi:10.1002/047012458X

41. Vandenbosch, G. A. E., "Reactive energies, impedance, and Q factor of radiating structures," IEEE Trans. Antennas Propagat., Vol. 58, No. 4, 1112-1127, 2010.
doi:10.1109/TAP.2010.2041166

42. Vandenbosch, G. A. E., "Simple procedure to derive lower bounds for radiation Q of electrically small devices of arbitrary topology," IEEE Trans. Antennas Propagat., Vol. 59, No. 6, 2217-2225, 2011.
doi:10.1109/TAP.2011.2143657

43. Vandenbosch, G. A. E., "Radiators in time domain, Part I: Electric, magnetic, and radiated energies," IEEE Trans. Antennas Propagat., Vol. 61, No. 8, 3995-4003, 2013.
doi:10.1109/TAP.2013.2261044

44. Vandenbosch, G. A. E., "Radiators in time domain, Part II: Finite pulses, sinusoidal regime and Q factor," IEEE Trans. Antennas Propagat., Vol. 61, No. 8, 4004-4012, 2013.
doi:10.1109/TAP.2013.2261045

45. Volakis, J., C. C. Chen, and K. Fujimoto, Small Antennas: Miniaturization Techniques & Applications, McGraw-Hill, New York, 2010.

46. Yaghjian, A. D., M. Gustafsson, and B. L. G. Jonsson, "Minimum Q for lossy and lossless electrically small dipole antennas," Progress In Electromagnetics Research, Vol. 143, 641-673, 2013.
doi:10.2528/PIER13103107

47. Yaghjian, A. D. and H. R. Stuart, "Lower bounds on the Q of electrically small dipole antennas," IEEE Trans. Antennas Propagat., Vol. 58, No. 10, 3114-3121, 2010.
doi:10.1109/TAP.2010.2055790

48. Yaghjian, A. D. and S. R. Best, "Impedance, bandwidth, and Q of antennas," IEEE Trans. Antennas Propagat., Vol. 53, No. 4, 1298-1324, 2005.
doi:10.1109/TAP.2005.844443


© Copyright 2014 EMW Publishing. All Rights Reserved