# Electrically small antenna

An electrically small antenna is defined as an antenna with a volume smaller than a radian sphere defined by H. A. Wheeler.[1][2]

${\displaystyle {2\pi r \over \lambda }}$${\displaystyle \scriptstyle \ll 1}$

where r is the radius of a sphere, and λ is the free space wavelength.

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, where

${\displaystyle Q\propto {\frac {1}{r^{3}}}}$

In short, the maximum bandwidth of an electrically small antenna is regulated by its maximum dimension enclosed within a sphere of radius ${\displaystyle r}$.

The difficulties of designing an electrically small antenna includes:

• impedance matching,
• insertion loss from high current density flowing on a non-perfect conductor, resulting in joule heating, and
• a small radiation aperture with low radiation efficiency.

## History

The theoretical limitation of an electrically small antenna and its bandwidth was first investigated by L. J. Chu.[3]

## Examples

Near-electrically small antennas include the Goubau antenna,[4] Foltz antenna[5] and Rogers cone antenna.[6]

## Fundamental limitations of antennas

Electrically small antennas belong to one of the four fundamental limitations of antennas[7] addressed by R. C. Hansen.[8] The four fundamental limitations of antennas are, electrically small antennas, superdirective antennas, superresolution antennas, and high-gain antennas.

## Measurement

Passive measurement of an electrically small antenna requires a quarter-wavelength RF choke or ferrite bead to be add 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.

## References

1. H. A. Wheeler, "Fundamental Limitations of Small Antennas," Proceedings of the IRE, vol. 35, pp. 1479-1484, 1947.
2. H. A. Wheeler, "The Radiansphere around a Small Antenna," Proceedings of the IRE, vol. 47, pp. 1325-1331, 1959.
3. L. J. Chu, "Physical Limitations on Omni-Directional Antennas," J. Appl. Phys., Vol. 9, pp. 1163-1175, 1948.
4. G. Goubau, "Multi-element Monopole Antennas," Proc. Workshop on Electrically Small Antennas, ECOM, Ft. Monmouth, NJ, pp. 63-67, May 1976.
5. 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.
6. J. A. Dobbins and R. L. Rogers, “Folded Conical Helix Antenna,” IEEE Trans. Antennas Propagation, vol. 49, No. 12, pp. 1777- 1781, December 2001.
7. R. C. Hansen. Fundamental limitations in antennas. Proceedings of the IEEE, 69(2):170–182, February 1981.
8. http://www.ieeeghn.org/wiki/index.php/Robert_C._Hansen