Electrical length

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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

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

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 lightwave with the materials of which the fiber is made, and fiber geometry, affect the velocity of propagation of the signal.

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 antennae 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 artificially shortened with a capacitive load.

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