Electric length

In high-frequency technology and line theory , the electrical length is the length of a transmission medium on which a ( periodic ) signal propagates. ${\displaystyle l_{\mathrm {el} }}$

The absolute electrical length can be determined from the vacuum speed of light and the phase delay of the signal or - in the case of a lossless line - equivalently from the mechanical length and the relative permittivity , which describes the dielectric between the conductors : ${\displaystyle c_{0}}$ ${\displaystyle \tau _{p}}$ ${\displaystyle l_{\mathrm {mech} }}$ ${\displaystyle \varepsilon _{r}}$

${\displaystyle {\begin{aligned}l_{\mathrm {el} }&=c_{0}\cdot \tau _{p}\\&=l_{\mathrm {mech} }\cdot {\sqrt {\varepsilon _{r}}}\end{aligned}}}$

The (relative) electrical length is also often related to the multiple of the wavelength  λ of the signal and is then given in radians without dimensions .

Electromagnetic waves propagate more slowly in a medium or on a waveguide (e.g. an antenna cable ) than in a vacuum . This means that their wavelength in a medium is shorter than in a vacuum. For the mechanical dimensions of lines and resonators (e.g. antennas ) this means that they are usually mechanically smaller than they would be based on the calculation from the frequency and the vacuum speed of the light.

For example, the telescopic antennas of many portable radios are approx. 75 cm long and therefore have a relative electrical length of 1/4 in relation to the 3 m wavelength of VHF radio . Shorter rod antennas , as you often see them on cars , are electrically elongated by special measures (longitudinal induction through coiling ) and thus also have an electrical length of λ / 4. The electrical length of antennas can also be shortened by taking suitable measures.

The term shortening factor is sometimes used for waveguides such as coaxial cables . It indicates the factor by which the conductor is shorter than the calculation from the vacuum speed of light would suggest. This information is z. B. important for the calculation of stub lines .

literature

• Klaus Kark: Antennas and radiation fields - electromagnetic waves on lines, in free space and their radiation . 5th edition. Springer-Verlag, 2014, ISBN 978-3-658-03616-4 .
• Hans Fricke, Kurt Lamberts, Ernst Patzelt: Basics of electrical communication . BG Teubner Verlag, Stuttgart 1979, ISBN 3-322-94046-2 .
• Harald Schumny: Signal transmission. Textbook of communications engineering with remote data processing, 2nd revised edition, Friedrich Vieweg & Sohn Verlag, Braunschweig 1987, ISBN 3-528-14072-0 .
• H. Meinke, FW Gundlach: Pocket book of high frequency technology. Volume 3: Systems. 5th edition. Springer Verlag, Berlin / Heidelberg 1992, ISBN 3-540-54716-9 .