Advertisement

Thin-Wire Perfectly Conducting Loops and Rings

  • Arnold McKinleyEmail author
Chapter
Part of the Signals and Communication Technology book series (SCT)

Abstract

This chapter covers the analytical theory of thin-wire, perfectly conducting loop antennas and nano-scaled rings. It relies on the thin-wire approximation and assumes no energy loss in the material. The chapter covers the early history of the development of the theory and points out the difficulties and how they were handled. The governing equations that need to be solved and Storer’s 1956 solution for the Fourier coefficients are shown. Difficulties with the derivation are indicated and Wu’s 1962 fix is examined. A new elliptical solution that has not appeared in the literature to date is then derived and yields a result similar to Storer’s. The difficulties Storer and Wu encountered with regard to the convergence of the Fourier series are described. Wu’s solution solves the convergence problem. Much of the problem involves the non-solvability of the governing equation when certain mathematical models of the driving generator are used. These difficulties are summarised. The Storer and Wu solutions are summarised with the elliptical solution.

References

  1. 1.
    C.W. Oseen, Ark. Mat. Astr. Fys. 9, 1 (1913)Google Scholar
  2. 2.
    E. Hallen, Nova Actae Regiae Soc. Sci. Ups. Ser. IV 11(4), 1 (1938)Google Scholar
  3. 3.
    J.E. Storer, Trans. AIEE 75, 606 (1956)Google Scholar
  4. 4.
    T.T. Wu, J. Math. Phys. 3(6), 1301 (1962)CrossRefGoogle Scholar
  5. 5.
    R.W.P. King, in Antenna Theory, part 1, Inter-University Electronic Series, vol. 7, ed. by R.E. Collin, F.J. Zucker, 1st edn. (McGraw-Hill, New York, 1969), Chap. 11, pp. 458–482Google Scholar
  6. 6.
    A.F. McKinley, T.P. White, K.R. Catchpole, J. Appl. Phys. 114(4), 044317 (2013).  https://doi.org/10.1063/1.4816619, http://scitation.aip.org/content/aip/journal/jap/114/4/10.1063/1.4816619
  7. 7.
    T. Wu, R.W.P. King, J. Appl. Phys. 30, 76 (1959)CrossRefGoogle Scholar
  8. 8.
    T.T. Wu, in Antenna Theory Part 1, ed. by R.E. Collin, F.J. Zucker (McGraw-Hill, 1969), Chap. 8, pp. 306–351Google Scholar
  9. 9.
    G. Fikioris, T.T. Wu, I.E.E.E. Trans, Antennas Propag. 49(3), 383 (2001)CrossRefGoogle Scholar
  10. 10.
    G. Fikioris, J. Lionas, C. Lioutas, IEEE Trans, Antennas Propag. 51(8), 1847 (2003).  https://doi.org/10.1109/TAP.2003.815412
  11. 11.
    H. Anastassiu, I.E.E.E. Trans, Antennas Propag. 54(3), 860 (2006).  https://doi.org/10.1109/TAP.2006.869929CrossRefGoogle Scholar
  12. 12.
    P.J. Papakanellos, G. Fikioris, Prog. Electromagn. Res. 69, 77 (2007)CrossRefGoogle Scholar
  13. 13.
    G. Fikioris, P. Papakanellos, H. Anastassiu, IEEE Trans, Antennas Propag. 56(1), 151 (2008).  https://doi.org/10.1109/TAP.2007.913076
  14. 14.
    P. Papakanellos, G. Fikioris, A. Michalopoulou, IEEE Trans, Antennas Propag. 58(5), 1635 (2010).  https://doi.org/10.1109/TAP.2010.2044319
  15. 15.
    G. Fikioris, P.J. Papakanellos, T.K. Mavrogordatos, N. Lafkas, D. Koulikas, SIAM, J. Appl. Math. 71(2), 559 (2011).  https://doi.org/10.1137/100785727
  16. 16.
    I. Tastsoglou, G. Fikioris, I.E.E.E. Trans, Antennas Propag. 61(11), 5517 (2013).  https://doi.org/10.1109/TAP.2013.2279423CrossRefGoogle Scholar
  17. 17.
    E. Janke, F. Emde, F. Loesch, Tafeln Hoherer Funktionen (B. G. Verlagsgesellschaft, Stuttgart, 6th edition, 1960)Google Scholar
  18. 18.
    I. Stegun, M. Abramowitz, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Applied Mathematics Series 55 (US. Government Printing Office, WDC, 1964)Google Scholar
  19. 19.
    G.N. Watson, Theory of Bessel Functions (The MacMillan Company, New York, 1945)Google Scholar
  20. 20.
    T. Do-Nhat, R.H. Macphie, IEEE Trans, Antennas Propag. 37(12), 1545 (1989).  https://doi.org/10.1109/8.45096
  21. 21.
    I. Tastsoglou, G. Fikioris, IEEE Trans, Antennas Propag. 61(11), 5527 (2013).  https://doi.org/10.1109/TAP.2013.2279426
  22. 22.
    G. Fikioris, P. Papakanellos, H. Anastassiu, IEEE Trans, Antennas Propag. 58(10), 3436 (2010).  https://doi.org/10.1109/TAP.2010.2055816
  23. 23.
    M. Kanda, IEEE Trans. Electromagn. Compat. EMC-26(3), 102 (1984)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.University College LondonLondonUK

Personalised recommendations