volume | PIER Journals

Abstract

The Chu circuit model provides the basis for analyzing the minimum radiation quality factor, Q, of a given spherical mode. However, examples of electrically large spherical radiators readily demonstrate that this Q limit has limitations in predicting bandwidth. Spherical mode radiation is reexamined, and an equivalent 1D transmission line model is derived that exactly models the fields. This model leads to a precise cutoff frequency of the spherical waveguide, which provides a clear boundary between propagating and evanescent fields. A new delineation of `stored' and `radiated' electromagnetic energy is postulated, which leads to a new definition of spherical mode Q. Next, attention is turned to the Harrington bound on the directivity-bandwidth tradeoff of an antenna with an arbitrary size. Harrington derived the maximum directivity for a specified number of spherical harmonics such that the Q is not `large'. Here, the method of Lagrange multipliers is used to quantify the maximum directivity for a given bandwidth. It is shown that optimally exciting all spherical harmonics (including n>ka) enables both larger directivity and bandwidth than Harrington's previous limit. While Chu and Harrington's analyses are generally good approximations for most situations, the new self-consistent theory that defines fundamental antenna limits leads to updated results.

1. Pfeiffer, Carl, "Fundamental efficiency limits for small metallic antennas," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 4, 1642-1650, 2017. Google Scholar

2. Gustafsson, Mats and Miloslav Capek, "Maximum gain, effective area, and directivity," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 8, 5282-5293, 2019. Google Scholar

3. Thal, Herbert L., "Radiation efficiency limits for elementary antenna shapes," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 5, 2179-2187, 2018. Google Scholar

4. Losenicky, Vit, Lukas Jelinek, Miloslav Capek, and Mats Gustafsson, "Dissipation factors of spherical current modes on multiple spherical layers," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 9, 4948-4952, 2018. Google Scholar

5. Capek, Miloslav and Lukas Jelinek, "The upper bound on antenna gain and its feasibility as a sum of characteristic gains," IEEE Transactions on Antennas and Propagation, Vol. 72, No. 1, 277-289, 2024. Google Scholar

6. Bode, H. W., Network Analysis and Feedback Amplifier Design, New York: Van Nostrand, 1945.

7. Fano, R. M., "Theoretical limitations on the broadband matching of arbitrary impedances," Journal of the Franklin Institute, Vol. 249, No. 1, 57-83, 1950. Google Scholar

8. Chu, L. J., "Physical limitations of omnidirectional antennas," Journal of Applied Physics, Vol. 19, No. 12, 1163-1175, 1948. Google Scholar

9. Collin, R. and S. Rothschild, "Evaluation of antenna Q," IEEE Transactions on Antennas and Propagation, Vol. 12, No. 1, 23-27, 1964. Google Scholar

10. Murray, Alexander B. and Ashwin K. Iyer, "Analytical expressions for spherical wire antenna quality factor demonstrating exact agreement between circuit-based and field integration techniques," IEEE Transactions on Antennas and Propagation, Vol. 72, No. 2, 1636-1647, 2024. Google Scholar

11. Thal, H. L., "New radiation Q limits for spherical wire antennas," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 10, 2757-2763, 2006. Google Scholar

12. 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. Google Scholar

13. Thal, Herbert L., "Q bounds for arbitrary small antennas: A circuit approach," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 7, 3120-3128, 2012. Google Scholar

14. Geyi, W., "A method for the evaluation of small antenna Q," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 8, 2124-2129, 2003. Google Scholar

15. Vandenbosch, Guy A. E., "Reactive energies, impedance, and Q factor of radiating structures," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 4, 1112-1127, 2010. Google Scholar

16. Gustafsson, Mats and B. Jonsson, "Stored electromagnetic energy and antenna Q," Progress In Electromagnetics Research, Vol. 150, 13-27, 2015. Google Scholar

17. Gustafsson, Mats, Marius Cismasu, and B. L. G. Jonsson, "Physical bounds and optimal currents on antennas," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 6, 2672-2681, 2012. Google Scholar

18. Capek, Miloslav, Lukas Jelinek, and Guy A. E. Vandenbosch, "Stored electromagnetic energy and quality factor of radiating structures," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 472, No. 2188, 20150870, 2016. Google Scholar

19. Vandenbosch, Guy A. E., "Radiators in time domain --- Part I: Electric, magnetic, and radiated energies," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 8, 3995-4003, 2013. Google Scholar

20. Vandenbosch, Guy A. E., "Radiators in time domain --- Part II: Finite pulses, sinusoidal regime and Q factor," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 8, 4004-4012, 2013. Google Scholar

21. Schab, Kurt, Lukas Jelinek, Miloslav Capek, Casimir Ehrenborg, Doruk Tayli, Guy A. E. Vandenbosch, and Mats Gustafsson, "Energy stored by radiating systems," IEEE Access, Vol. 6, 10553-10568, 2018. Google Scholar

22. Neto, Andrea, Nuria Llombart, and Angelo Freni, "The observable field for antennas in reception," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 4, 1736-1746, 2018. Google Scholar

23. Doane, Jonathan P., Kubilay Sertel, and John L. Volakis, "Matching bandwidth limits for arrays backed by a conducting ground plane," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 5, 2511-2518, 2013. Google Scholar

24. Kwon, Do-Hoon and David M. Pozar, "Optimal characteristics of an arbitrary receive antenna," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 12, 3720-3727, 2009. Google Scholar

25. Harrington, Roger F., "Effect of antenna size on gain, bandwidth, and efficiency," Journal of Research of the National Bureau of Standards --- D. Radio Propagation, Vol. 64, No. 1, 1-12, 1960. Google Scholar

26. Fante, Ronald L., "Maximum possible gain for an arbitrary ideal antenna with specified quality factor," IEEE Transactions on Antennas and Propagation, Vol. 40, No. 12, 1586-1588, 1992. Google Scholar

27. Geyi, Wen, "Physical limitations of antenna," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 8, 2116-2123, 2003. Google Scholar

28. Passalacqua, Laura, Cristina Yepes, Enrica Martini, and Stefano Maci, "Q-bounded maximum directivity of self-resonant antennas," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 12, 9549-9558, 2023. Google Scholar

29. Passalacqua, Laura, Cristina Yepes, Alejandro Murillo Barrera, Bruno Biscontini, Enrica Martini, and Stefano Maci, "Maximum gain of lossy antennas without and with Q-bounds," IEEE Transactions on Antennas and Propagation, Vol. 72, No. 4, 3033-3043, 2024. Google Scholar

30. Yaghjian, A. D. and S. R. Best, "Impedance, bandwidth, and Q of antennas," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 4, 1298-1324, 2005. Google Scholar

31. Fante, R., "Quality factor of general ideal antennas," IEEE Transactions on Antennas and Propagation, Vol. 17, No. 2, 151-155, 1969. Google Scholar

32. McLean, J. S., "A re-examination of the fundamental limits on the radiation Q of electrically small antennas," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 5, 672, 1996. Google Scholar

33. Levis, Curt A., "A reactance theorem for antennas," Proceedings of the IRE, Vol. 45, No. 8, 1128-1134, 1957. Google Scholar

34. Rhodes, Donald R., "Observable stored energies of electromagnetic systems," Journal of the Franklin Institute, Vol. 302, No. 3, 225-237, 1976. Google Scholar

35. Davis, W. A., T. Yang, E. D. Caswell, and W. L. Stutzman, "Fundamental limits on antenna size: A new limit," IET Microwaves, Antennas & Propagation, Vol. 5, No. 11, 1297-1302, 2011. Google Scholar

36. Manteghi, Majid, "Fundamental limits, bandwidth, and information rate of electrically small antennas: Increasing the throughput of an antenna without violating the thermodynamic Q-factor," IEEE Antennas and Propagation Magazine, Vol. 61, No. 3, 14-26, 2019. Google Scholar

37. Stuart, Howard R., Steven R. Best, and Arthur D. Yaghjian, "Limitations in relating quality factor to bandwidth in a double resonance small antenna," IEEE Antennas and Wireless Propagation Letters, Vol. 6, 460-463, 2007. Google Scholar

38. Gustafsson, Mats and Sven Nordebo, "Bandwidth, Q factor, and resonance models of antennas," Progress In Electromagnetics Research, Vol. 62, 1-20, 2006. Google Scholar

39. Thal, Herbert L., "Gain and Q bounds for coupled TM-TE modes," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 7, 1879-1885, 2009. Google Scholar

40. Gustafsson, Mats and Sven Nordebo, "Optimal antenna currents for Q, superdirectivity, and radiation patterns using convex optimization," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 3, 1109-1118, 2013. Google Scholar

41. Ehrenborg, Casimir and Mats Gustafsson, "Fundamental bounds on MIMO antennas," IEEE Antennas and Wireless Propagation Letters, Vol. 17, No. 1, 21-24, 2018. Google Scholar

42. Capek, Miloslav, Mats Gustafsson, and Kurt Schab, "Minimization of antenna quality factor," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 8, 4115-4123, 2017. Google Scholar

43. Gustafsson, Mats, Miloslav Capek, and Kurt Schab, "Tradeoff between antenna efficiency and Q-factor," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 4, 2482-2493, 2019. Google Scholar

44. Vandenbosch, Guy A. E., "Reply to" Comments on'Reactive energies, impedance, and Q factor of radiating structures'"," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 12, 6268-6268, 2013. Google Scholar

45. Kildal, Per-Simon, Enrica Martini, and Stefano Maci, "Degrees of freedom and maximum directivity of antennas: A bound on maximum directivity of nonsuperreactive antennas," IEEE Antennas and Propagation Magazine, Vol. 59, No. 4, 16-25, 2017. Google Scholar

46. Kildal, Per-Simon and Steven R. Best, "Further investigations of fundamental directivity limitations of small antennas with and without ground planes," 2008 IEEE Antennas and Propagation Society International Symposium, 1-4, San Diego, CA, USA, 2008.

47. Harrington, R. F., Time-Harmonic Electromagnetic Fields, Wiley, New York, NY, USA, 2001.

48. Marks, Roger B. and Dylan F. Williams, "A general waveguide circuit theory," Journal of Research of the National Institute of Standards and Technology, Vol. 97, No. 5, 533-562, 1992. Google Scholar

49. Pozar, D. M., Microwave Engineering, John Wiley & Sons, 2011.

50. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, American Association of Physics Teachers, 1988.

51. Huting, W. A. and K. J. Webb, "Comparison of mode-matching and differential equation techniques in the analysis of waveguide transitions," IEEE Transactions on Microwave Theory and Techniques, Vol. 39, No. 2, 280-286, 1991. Google Scholar

52. Vandenbosch, Guy A. E., "Recoverable energy of radiating structures," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 7, 3575-3588, 2017. Google Scholar

53. Vandenbosch, Guy A. E., "Impedance-based closed-form expressions to calculate recoverable energy and corresponding Q of single-port radiators," IEEE Transactions on Antennas and Propagation, Vol. 68, No. 7, 5442-5452, 2020. Google Scholar

54. Schantz, Hans G., "Energy velocity and reactive fields," Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, No. 2134, 20170453, 2018. Google Scholar

55. Kaspar, Peter, Roman Kappeler, Daniel Erni, and Heinz Jäckel, "Average light velocities in periodic media," Journal of the Optical Society of America B, Vol. 30, No. 11, 2849-2854, 2013. Google Scholar

Dr. Carl Pfeiffer

Dr. Bae-Ian Wu