Electrically small antenna
An electrically small or electrically short antenna is an antenna much shorter than the wavelength of the signal it is intended to transmit or receive. Electrically short antennas are generally less efficient and more challenging to design than longer antennas such as quarter- and half-wave antennas, but are nonetheless common due to their compact size and low cost.
The far-field radiation pattern of an antenna is the sum of its near-field spherical modes, expressed using Legendre functions and spherical Bessel functions. In its simplest form, it is an omnidirectional radiation pattern with no variation in the azimuth plane. When the antenna becomes electrically small, the propagating modes are replaced by evanescent modes with high Q factor, where
- , 
In short, the maximum bandwidth of an electrically small antenna is regulated by its maximum dimension enclosed within a sphere of radius .
The difficulties of designing an electrically small antenna includes:
Harold A. Wheeler first published "The Fundamental Limitations of Small Antennas" (1947). The theoretical limitation of an electrically small antenna and its bandwidth was first investigated by L. J. Chu in 1948.
Principal new type of electrically small antennas are nanomechanical magnetoelectric (ME) antennas.  ME antennas have sizes as small as one-thousandth of a wavelength. For example, the length and width of the FeGaB/AlN active resonant body of this antenna for 60,7 MHz of electromagnetic waves are 200 and 50 µm, respectively.
Fundamental limitations of antennasEdit
Electrically small antennas belong to one of the four fundamental limitations[clarification needed] of antennas addressed by R. C. Hansen. The four fundamental limitations of antennas are, electrically small antennas, superdirective antennas, superresolution antennas, and high-gain antennas.
Passive measurement of an electrically small antenna requires a quarter-wavelength RF choke or ferrite bead to be added to the end of the feeding coaxial cable to limit or prevent the current from flowing onto the surface of the cable. Current flowing on the exterior of the feeding cable increases the electrical size and radiation aperture of the antenna, resulting in erroneous measurement result. The quarter-wavelength choke are narrow-band and the ferrite beads are lossy at higher frequency greater than 1 GHz. These techniques are not without problems; the quarter-wavelength choke technique allows currents to travel up to 0.25 wavelengths from the antenna and increases the effective size, whereas the lossy choke (e.g. ferrite bead) technique introduces losses that should be considered.
- Kraus, John D. (1950). Antennas. McGraw-Hill. Chapter 3, The antenna as an aperture, pp 49.
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- H. A. Wheeler, "The Radiansphere around a Small Antenna," Proceedings of the IRE, vol. 47, pp. 1325-1331, 1959.
- Slyusar V. I. 60 Years of Electrically Small Antennas Theory.//Proceedings of the 6-th International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine. - Pp. 116 - 118. 
- L. J. Chu, "Physical Limitations on Omni-Directional Antennas," J. Appl. Phys., Vol. 9, pp. 1163-1175, 1948.
- G. Goubau, "Multi-element Monopole Antennas," Proc. Workshop on Electrically Small Antennas, ECOM, Ft. Monmouth, NJ, pp. 63-67, May 1976.
- H. Foltz, J. McLean, G. Crook, "Disk-Loaded Monopoles with Parallel Strip Elements," IEEE Transactions on Antennas and Propagation, vol. 46, no.12, December 1998, pp. 1894-1896.
- J. A. Dobbins and R. L. Rogers, “Folded Conical Helix Antenna,” IEEE Trans. Antennas Propagation, vol. 49, No. 12, pp. 1777- 1781, December 2001.
- Tianxiang Nan, Hwaider Lin, Yuan Gao, Alexei Matyushov, Guoliang Yu, Huaihao Chen, Neville Sun, Shengjun Wei, Zhiguang Wang, Menghui Li, Xinjun Wang, Amine Belkessam, Rongdi Guo, Brian Chen, James Zhou, Zhenyun Qian, Yu Hui, Matteo Rinaldi, Michael E. McConney, Brandon M. Howe, Zhongqiang Hu, John G. Jones, Gail J. Brown & Nian Xiang Sun, "Acoustically actuated ultra-compact NEMS magnetoelectric antennas", Nature Communications, 8, 296, pp. 1 - 8, 22 August 2017. 
- R. C. Hansen. Fundamental limitations in antennas. Proceedings of the IEEE, 69(2):170–182, February 1981.