Resonances of Characteristic Modes for Perfectly Conducting Objects

Joni Lappalainen, Pasi Yla-Oijala, Dimitrios C. Tzarouchis, Ari Sihvola

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)


Resonances, i.e., extrema of the eigenvalues of characteristic modes for closed perfectly conducting objects are investigated. The characteristic modal solutions based on the electric, magnetic, and combined field integral operators (EFIO, MFIO, and CFIO) are studied and compared with analytical solutions for a sphere. All these formulations are found to capture both external (radiating) and internal (cavity) resonances predicted by the analytical expressions. At the internal resonances the eigenvalues obtained with the EFIO and MFIO-based approaches are not correct and the corresponding modes are non-unique. These solutions exhibit also a strong duality between the electric (TM) and magnetic (TE) type modes. A connection is found between the external and internal resonances and the condition numbers of the matrices. The modal expansion of the CFIObased solution is correct, even though it also experiences the non-uniqueness of the EFIO and MFIO-based solutions.

Original languageEnglish
Pages (from-to)5332-5339
Number of pages8
JournalIEEE Transactions on Antennas and Propagation
Issue number10
Publication statusPublished - Oct 2017
MoE publication typeA1 Journal article-refereed


  • Antennas
  • Cavity resonators
  • Eigenvalues and eigenfunctions
  • Electric field integral operator
  • external resonance
  • Integral equations
  • internal resonance
  • magnetic field integral operator
  • Magnetic resonance imaging
  • perfect electric conductor
  • Resonant frequency
  • theory of characteristic modes


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