Vol. 136

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On the Efficiency and Gain of Antennas

By Anders Karlsson
Progress In Electromagnetics Research, Vol. 136, 479-494, 2013


The fundamental limits of the gain and efficiency of an antenna are explored. These are very important quantities for e.g., superdirective arrays. The antenna is in this paper confined in a sphere and all of the currents are assumed to run in a material with a given conductivity. It is shown that one can find the current distribution in the sphere that optimizes the gain, given the frequency and the radius of the sphere. The results indicate the distribution of antenna elements in an antenna array in order to maximize gain, or efficiency. The analysis is based on the expansion of the electromagnetic fields in terms of vector spherical harmonics. Explicit expressions for the limits of gain and efficiency, and the corresponding current densities, are derived for different types of antennas.


Anders Karlsson, "On the Efficiency and Gain of Antennas," Progress In Electromagnetics Research, Vol. 136, 479-494, 2013.


    1. Hansen, R. C., "Fundamental limitations in antennas," Proc. IEEE, Vol. 69, No. 2, 170-182, 1981.

    2. Chu, L. J., "Physical limitations of omni-directional antennas," Appl. Phys., Vol. 19, 1163-1175, 1948.

    3. Harrington, R. F., Time Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961.

    4. Collin, R. E., "Minimum Q of small antennas," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 10, 1369-1393, 1998.

    5. Sohl, C. and M. Gustafsson, "A priori estimates on the partial realized gain of ultra-wideband (UWB) antennas," Quart. J. Mech. Appl. Math., Vol. 61, No. 3, 415-430, 2008.

    6. Gustafsson, M., C. Sohl, and G. Kristensson, "Illustrations of new physical bounds on linearly polarized antennas," IEEE Trans. on Antennas and Propagat., Vol. 57, No. 5, 1319-1327, May 2009.

    7. Gustafsson, M. and S. Nordebo, "On the spectral efficiency of a sphere," Progress In Electromagnetics Research, Vol. 67, 275-296, 2007.

    8. Karlsson, A., "Physical limitations of antennas in a lossy medium," IEEE Trans. on Antennas and Propagat., Vol. 52, 2027-2033, 2004.

    9. Hansen, J. E., Spherical Near-Field Antenna Measurements, IEE Electromagnetic Waves Series, No. 26, Peter Peregrinus Ltd., Stevenage, UK, 1988, ISBN: 0-86341-110-X.

    10. Arfken, G., Mathematical Methods for Physicists, 3rd Ed., Academic Press, Orlando, 1985.