Electrically small antenna

Technically, an electrically short antenna has length 2h, such that ${\displaystyle {\frac {2\pi h}{\lambda }}\ll 1}$, where λ is the free space wavelength.[1][2][3]

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

${\displaystyle Q\propto {\frac {1}{k^{3}r^{3}}}}$, ${\displaystyle k=2\pi /\lambda }$[4]

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.

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[5] in 1948.

Near-electrically small antennas include the Goubau antenna,[6] Foltz antenna[7] and Rogers cone antenna.[8]

Principal new type of electrically small antennas are nanomechanical magnetoelectric (ME) antennas. [9] ME antennas have sizes as small as one-thousandth of a wavelength.[9] 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.[9]

Electrically small antennas belong to one of the four fundamental limitations of antennas[10] addressed by R. C. Hansen.[11] 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.

• Electrical length - the concept of a conductor's electrical length, in particular, for transmission line and antennas.