Electromagnetic Coupling to Transmission Lines with Symmetric Geometry Inside Rectangular Resonators

Conference paper


In this chapter, the analysis of transmission lines inside rectangular resonators is extended from one conductor with two sources/loads at the ends to many loads along the conductor and to the interaction between two conductors. To do this, the many loads are described as passive small (δ-) sources, whose corresponding electrical fields superpose with fields from other sources. The currents in the individual loads are found by imposing the boundary condition for the total electrical field on the surface of the conductor and applying a Fourier series expansion for the current. The calculation of the interaction of two lines in the resonator is based on the known description for one conductor and the two-dimensional Green’s function, which occurs in the analytical expressions for the currents. This Green’s function is used for both conductors separately. Then, with the aid of the superposition principle, the individual currents for the lines are derived. These computational procedures are illustrated by two examples.


Transmission line Cavity resonator Analytical solutions Thin wires 



This work was supported by the Bundeswehr Research Institute for Protective Technologies and NBC-Protection (WIS), Munster, Germany, under contract E/E590/CZ003/CF149 and in part by the German Research Foundation (DFG) under contract VI 207/3-1.


  1. 1.
    Tkachenko, S., Gronwald, F., Krauthäuser H.G., Nitsch, J.: High frequency electromagnetic field coupling to small antennas in rectangular resonator. In: V International Congress on Electromagnetism in Advanced Applications (ICEAA), 15–19 September 2009, pp. 74–78Google Scholar
  2. 2.
    Tkachenko, S., Nitsch, J., Al-Hamid, M.:Hochfrequente Feldeinkopplung in kleine Streuer innerhalb eines rechtwinkligen Resonators. In: Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit. 09–11. März 2010, Messe Düsseldorf, ISBN 978-3-8007-3206-7, pp. 121–128Google Scholar
  3. 3.
    Tkachenko, S., Nitsch, J., Vick, R.: HF coupling to a transmission line inside a rectangular cavity. In: Transactions of URSI International Symposium on Electromagnetic Theory, Berlin, Germany, 16–19 August 2010Google Scholar
  4. 4.
    Nitsch, J., Tkachenko, S., Potthast, S.: Transient excitation of rectangular resonators through electrically small circular holes. IEEE Trans. Electromagn. Compat. 54(6), 1252–1259 (2012)CrossRefGoogle Scholar
  5. 5.
    Tkachenko, S., Rambousky, R., Nitsch, J.: Electromagnetic field coupling to a thin wire located symmetrically inside a rectangular enclosure. IEEE Trans. Electromagn. Compat. 55(2), 334–341 (2013). doi: 10.1109/TEMC.2012.2216532 CrossRefGoogle Scholar
  6. 6.
    Markov, G.T., Chaplin, A.F.: Excitation of Electromagnetic Waves, Moscow, “Radio i Svjaz”, (1983) [In Russian] (Vozbujshdenie Elektromagnitnuh Voln)Google Scholar
  7. 7.
    Tkachenko, S., Nitsch, J., Rambousky, R.: Electromagnetic field coupling to transmission lines inside rectangular resonators. Interaction Notes, Note 623. (2011)
  8. 8.
    Nitsch, J., Tkachenko, S.: Propagation of current waves along quasi-periodical thin-wire structures: taking radiation losses into account. Radio Sci. Bull. 322, 19–40 (2007)Google Scholar
  9. 9.
    Wulf, D., Bunger, R., Ritter, J., Beyer, R.: Accelerated simulation of low frequency applications using PROTHEUS/MLFMA. In: Proceedings of the 2nd International ITG Conference on Antennas, München, Germany, March 2007, p. 240Google Scholar
  10. 10.
    Nitsch, J., Baum, C., Sturm, R.: Analytical treatment of uniform multiconductor transmission lines. IEEE Trans. Electromagn. Compat. 35(2), 1252–1259, 285–293 (1993)Google Scholar
  11. 11.
    Nitsch, J., Baum, C.: Splitting of degenerate natural frequencies in coupled two-conductor lines by distance variation. Interaction Notes, No. 477. (1989)

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Otto-von-Guericke University MagdeburgMagdeburgGermany
  2. 2.Electromagnetic Effects BranchBundeswehr Research Institute for Protective TechnologiesMunsterGermany

Personalised recommendations