Properties of Sub-Wavelength Spherical Antennas With Arbitrarily Lossy Magnetodielectric Cores Approaching the Chu Lower Bound

Troels Vejle Hansen, Oleksiy S. Kim, Olav Breinbjerg

Research output: Contribution to journalJournal articleResearchpeer-review


For a spherical antenna exciting any arbitrary spherical mode, we derive exact closed-form expressions for the dissipated power and stored energy inside (and outside) the lossy magneto-dielectric spherical core, as well as the radiated power, radiation efficiency, and thus the
radiation quality factor. These expressions are valid for the entire range from zero to infinite material loss tangents, with any dispersion of the
real parts and an inverse frequency variation of the imaginary parts of permittivity and permeability. For the dipole modes of a sub-wavelength
antenna, we demonstrate how an increasing magnetic loss tangent initially leads to a decreasing radiation quality factor, but in the limit of a perfect magnetic conductor (PMC) core the dissipated power tends to zero and the radiation quality factor reaches the fundamental Chu lower bound.
Original languageEnglish
JournalIEEE Transactions on Antennas and Propagation
Issue number3
Pages (from-to)1456-1460
Publication statusPublished - 2014


  • Electrically small antennas
  • Energy storage
  • Magnetic losses
  • Quality factor
  • Spherical antennas

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