Electrically short
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An electrically small or electrically short antenna is an
antenna Antenna ( antennas or antennae) may refer to: Science and engineering * Antenna (radio), also known as an aerial, a transducer designed to transmit or receive electromagnetic (e.g., TV or radio) waves * Antennae Galaxies, the name of two collid ...
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.


Definition

Technically, an electrically short antenna has length 2h, such that \frac \ll 1, where λ is the free space wavelength. Chapter 3, The antenna as an aperture, pp 49. The far-field radiation pattern of an antenna is the sum of its near-field spherical modes, expressed using Legendre functions and
spherical Bessel function Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary ...
s. 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 Evanescent may refer to: * Evanescent (dermatology), a class of skin lesions * "Evanescent" (song), a song by Vamps * Evanescent wave, a term applied to electromagnetic waves that decay exponentially See also * Evanescence (disambiguation) Ev ...
modes with high
Q factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy los ...
, where :Q \propto \frac,\quad k = \fracSlyusar 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

/ref> In short, the maximum bandwidth of an electrically small antenna is regulated by its maximum dimension enclosed within a sphere of radius r. The difficulties of designing an electrically small antenna includes: * impedance matching, * a small
radiation resistance Radiation resistance, \ R_\mathsf\ or \ R_\mathsf\ , is proportional to the part of an antenna's feedpoint electrical resistance that is caused by power loss from the emission of radio waves from the antenna. Radiation resistance is an ''effecti ...
therefore requiring a large current and resulting ohmic losses, thus poor
radiation efficiency In antenna theory, radiation efficiency is a measure of how well a radio antenna converts the radio-frequency power accepted at its terminals into radiated power. Likewise, in a receiving antenna it describes the proportion of the radio wave's ...
.


History

Harold A. Wheeler Harold Alden Wheeler (May 10, 1903 - April 25, 1996) was a noted American electrical engineer. Biography Wheeler was born in Saint Paul, Minnesota, to William Archibald Wheeler and Harriet Marie Alden Wheeler (a descendant of John and Prisci ...
began the study of the limits of small antennas with a seminal paper in 1947, "The Fundamental Limitations of Small Antennas". Wheeler demonstrated the relationship between the radiation power factor and the geometrical parameters of electrically small cylindrical inductors and cylindrical capacitors in a circuit analysis. Shortly after, L. J. Chu derived the theoretical minimum
Q factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy los ...
for an electrically small antenna via an expansion of spherical modes. Much later, in 1964, Collin and
Rothschild Rothschild () is a name derived from the German ''zum rothen Schild'' (with the old spelling "th"), meaning "with the red sign", in reference to the houses where these family members lived or had lived. At the time, houses were designated by signs ...
found an expression for the minimum Q for the lowest order spherical wave in the form Q = \frac + \frac, which has become a common reference standard used in later evaluations of small antenna performance.


Examples

In addition to the lumped-element capacitor and inductor antennas, there are various types of electrically small antennas that include the Goubau antenna, Foltz antenna and Rogers cone antenna. The lumped-element capacitor and inductor antenna is typically made of a combination of the capacitor and inductor lumped element antenna and self-resonating distributed element antennas. Principal new type of electrically small antennas are nanomechanical magnetoelectric (ME) antennas.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

/ref> 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 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 Waveguide flange, RF choke or
ferrite bead A ferrite bead at the end of a Mini USB cable A ferrite bead (also known as a ferrite block, ferrite core, ferrite ring, EMI filter, or ferrite choke) is a type of choke that suppresses high-frequency electronic noise in electronic circuits. F ...
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.


See also

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


References

{{reflist Antennas (radio) Electromagnetic radiation Radio frequency antenna types Radio electronics