Electrical length

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

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 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.

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.

The electrical length of an antenna element is, in general, different from the physical length. This is especially true of elements on a printed board, which will be affected by the dielectric medium on which they are printed. The electrical length required for antenna elements is often λ/2 or λ/4. At lower frequencies, this can mean an impractically large antenna. This problem is frequently solved by loading the antenna with an inductance to artificially lengthen the electrical length. Elements can also be electrically shortened with a capacitive load.[1]

Contents

Lengthening antennas

Electrical lengthening is the modification of an aerial which is shorter than a whole-number 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 whole-number multiple of a quarter of the used wavelength. A lengthening is only possible to the next whole-number 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.

Advantages

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.

Disadvantages

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

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)

Application

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 then a quarter of the radiated wavelength.

See also

References

  1. ^ US Federal Standard 1037C

Further reading