Electrical length

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In telecommunications and electrical engineering, electrical length is the length of a transmission medium or antenna element[1] expressed as the number of wavelengths of the signal propagating in the medium.

Electrical wave length[edit]

Electromagnetic waves propagate more slowly in a medium than in free space, so a wave in a medium will have a larger number of waves than a wave of the same frequency propagating over the same distance in free space. Alternatively put, the distance covered in free space by the same number of waves as are in the transmission medium will be greater, hence the transmission medium is said to have an electrical length greater than its physical length. The electrical length is most commonly expressed in units of the wavelength, λ, which is related to the velocity of propagation, v, and frequency, f, by

 \lambda = \frac{v}{f}

A length may be stated as 2λ or 3λ or 0.5λ etc. It is also sometimes expressed in radians or degrees. A length of ν λ can be converted to θ radians by

 \theta = 2 \pi \nu \,

In conducting cables, distributed resistances, capacitances and inductances impede the propagation of the signal. In an optical fiber interaction of the light wave with the materials of which the fiber is made (and fiber geometry) affect the velocity of signal propagation. In both coaxial cables and optical fibers, the velocity of wave propagation is approximately two-thirds that of free space. Consequently, the wavelength will be approximately two-thirds that in free space, and the electrical length approximately 1.5 times the physical length.


Many antenna types are designed to be resonant at their intended frequency of operation; the driven element functions as a resonator with standing waves of current and voltage along it. The advantage of an antenna at resonance is that it presents an impedance to the feedline to the transmitter or receiver which is a pure resistance, while off resonance it presents a reactance, it has capacitance or inductance. The result is that the feedline works most efficiently when the antenna is resonant, transferring the maximum amount of power to the antenna. The condition for resonance in a linear dipole antenna is usually that the electrical length be equal to a multiple of a half-wavelength, λ/2, while for a monopole antenna it is a multiple of a quarter-wavelength, λ/4.

The electrical length of an antenna element is, in general, different from its physical length. For example, increasing the diameter of the conductor, or the presence of nearby metal objects, will decrease the velocity of the waves in the element, increasing the electrical length.

Antennas which are the wrong length to be resonant, or which must operate at a different frequency at which they are not resonant, are often brought into resonance by loading; adding capacitors or inductors in series with them.[2] An antenna which is shorter than its resonant length has capacitive reactance. The capacitance can be compensated by adding an equal value inductance, a loading coil in series. The coil can be thought of as electrically lengthening the antenna. Similarly, an antenna which is longer than its resonant length has inductive reactance, and can be electrically shortened by adding a loading capacitor.

Lengthening antennas[edit]

Antenna node particularly adapted for high frequency installations involving relatively small antennas, such as a small tower, or pole type antennas. The capacitance area is in the form of a sphere enclosing the coil.

Electrical lengthening is the modification of an antenna which is shorter than an integer multiple of a quarter of the radiated wavelength, by means of a suitable electronic device, without changing the physical length of the aerial, in such a way that it corresponds electrically to the next integer multiple of a quarter of the used wavelength. A lengthening is only possible to the next integer multiple of a quarter of the radiated wavelength. Thus an aerial with a length corresponding to the eighth of the radiated wavelength can be extended only to a quarter-wave radiator, but not to a half wave radiator.

Vertical antenna which may be of any desired height : less than about one-half wavelength of the frequency at which the antenna operates. These antennas may operate either as transmitting or receiving antennas


The electrical lengthening allows the construction of shorter aerials. It is applied in particular for aerials for VLF, longwave and medium-wave transmitters, because mast radiators of the necessary height cannot be realised economically. It is also used widely for whip antennas on portable devices such as walkie-talkies to allow antennas much shorter than the standard quarter-wavelength to be used. The most widely used example is the rubber ducky antenna.


The electrical lengthening reduces the bandwidth of the antenna if other phase control measures are not undertaken. An electrically extended aerial is less efficient than a non-extended antenna.

Technical realization[edit]

There are two possibilities for the realisation of the electric lengthening.

  1. switching in inductive coils in series with the aerial
  2. switching in metal surfaces, known as roof capacitance, at the aerial ends which form capacitors to earth.

Often both measures are combined. The coils switched in series must be sometimes be placed in the middle of the aerial construction. The cabin installed at a height of 150-metres on the Blosenbergturm in Beromünster is such a construction, in which a lengthening coil is installed for the supply of the upper tower part (the Blosenbergturm has in addition a ring-shaped roof capacitor on its top)


Transmission aerials of transmitters working at frequencies below the longwave broadcasting band always apply electric lengthening. Broadcasting aerials of longwave broadcasting stations apply it often. However, for transmission aerials of NDBs electrical lengthening is extensively applied, because these use antennas which are considerably less tall than a quarter of the radiated wavelength.

See also[edit]


  1. ^ Ron Schmitt, Electromagnetics explained [electronic resource]: a handbook for wireless/RF, EMC, and high-speed electronics. 8
  2. ^ US Federal Standard 1037C

Further reading[edit]