An electrically small antenna is defined as an antenna with a volume smaller than a radian sphere defined by H. A. Wheeler.
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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 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:
History
The theoretical limitation of an electrically small antenna and its bandwidth was first investigated by L. J. Chu.
Examples
Near-electrically small antennas include the Goubau antenna, Foltz antenna and Rogers cone antenna.
Fundamental limitations of antennas
Electrically small antennas belong to one of the four fundamental limitations 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.
Measurement
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.