Current Distribution and Radiation Characteristics of Thin, PEC Loops and Rings

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


The current flowing around the circumference of a loop is symmetric in mode number n in a closed loop, but asymmetric in an impedance loaded loop. In other words for symmetric current, the Fourier coefficients \(I_{-n} = I_n\), while for asymmetric current, this is not the case. Characterising this asymmetry is a recent advance in the theory. We set up this study in symmetry in this chapter and give the analytical formulae for the radiation from a closed loop. The radiation patterns at the fundamental resonance radiates directly along the \(\pm z\) axis; the second harmonic shows an expected quadrupole behaviour. “Small” loops are defined as those with circumference less than \(0.10 \lambda \), for decidedly good reasons and the radiation patterns for such loops are strongly azimuthal.


  1. 1.
    C.A. Balanis, Antenna Theory, Analysis and Design, 4th edn. (Wiley, New York, 2016)Google Scholar
  2. 2.
    E.J. Martin, IRE Trans. Antennas Propag. 106–107 (1960)Google Scholar
  3. 3.
    D.H. Werner, IEEE Trans. Antennas Propag. 44(2), 157 (1996)MathSciNetCrossRefGoogle Scholar
  4. 4.
    D.H. Werner, in Lommel Expansions in Electromagnetics, Chapter in Frontiers in Electromagnetics, ed. by D.H. Werner, R. Mittra (IEEE Press, 2000), pp. 474–522Google Scholar
  5. 5.
    L.W. Li, M.S. Leong, P.S. Kooi, T.S. Yeo, IEEE Trans. Antennas Propag. 45(12), 1741 (1997)CrossRefGoogle Scholar
  6. 6.
    S. Savov, IEEE Antennas Propag. Mag. 44(5), 98 (2002),
  7. 7.
    B.Q. Lu, J. Nagar, T. Yue, M.F. Pantoja, D.H. Werner, IEEE Trans. Antennas Propag. 65(1), 121 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.University College LondonLondonUK

Personalised recommendations