Fresnel zone

1. Fresnel zone over the hilly terrain of a radio link

As a Fresnel [ fʀɛnɛl- ], named after Augustin Jean Fresnel , is called at a radio transmission specific spatial regions between the transmitting and receiving antenna. The importance of the Fresnel zones is that due to the wave character, the propagation of the electromagnetic radiation can be disturbed by obstacles, even if there is a line of sight between the transmitting and receiving antenna. The amount of additional attenuation caused by the obstacles can be calculated or estimated with the help of the Fresnel zone observation.

First zone

Attenuation of radio transmissions due to obstacles partially protruding into the first Fresnel zone

The first Fresnel zone is an imaginary ellipsoid of revolution between the antennas, which are located at the focal points of the ellipsoid. In the figure opposite, the first Fresnel zone is shown over a hilly surface of the earth. At the edge of the ellipsoid, the detour for the signal bent at obstacles is half a wavelength. Within a Fresnel zone, the path difference , i.e. the difference between two propagation paths , is less than half a wavelength .

Most of the energy is transmitted in the area of ​​the first Fresnel zone. This zone should be free of obstacles (e.g. houses, trees, mountains). If this is not the case, the transmission is attenuated . If half of the first Fresnel zone is covered, the additional attenuation at the receiving antenna is 6 dB . Reception may then be disturbed or completely interrupted. In the figure above, the 1st Fresnel zone is free of obstacles, so that a virtually undamped radio transmission is possible.

The second and the higher Fresnel zones - thicker and also a little longer - with a path difference of are only of secondary importance in practice and are usually neglected in simple calculations. ${\displaystyle n\cdot {\tfrac {\lambda }{2}}}$

radius

Attenuation-free zone (distance d and radius r )

The maximum radius (half the thickness) of the Fresnel zone is frequency-dependent: At high frequencies with short wavelengths it decreases . Due to the curvature of the earth and a large distance between the antennas, noticeable attenuation can occur even at low transmission frequencies, although there is still a direct optical line of sight between the transmitting and receiving antennas. ${\displaystyle r\,}$ ${\displaystyle r\,}$ ${\displaystyle D\,}$

The location-dependent radius of the nth Fresnel zone can be approximated by: ${\displaystyle r}$

${\displaystyle r={\sqrt {\frac {n\cdot \lambda \cdot d_{1}\cdot d_{2}}{D}}}}$

Here, n the number of the Fresnel zone, the wavelength of the signal , the radio field length of the microwave field is defined as the distance between the antennas , and respectively the distance between the plane in question and the transmitter or receiver. However, this approximation does not apply to radii near the transmitter or receiver. ${\displaystyle \lambda }$ ${\displaystyle D\,}$ ${\displaystyle d_{1}\,}$ ${\displaystyle d_{2}\,}$

In the middle between transmitter and receiver, the maximum radius of the 1st Fresnel zone results as: ${\displaystyle b_{\mathrm {max} }}$

${\displaystyle b_{\mathrm {max} }={\frac {\sqrt {\lambda \cdot D}}{2}}}$.

This maximum radius increases proportionally with the square roots of the antenna spacing and wavelength. Their geometric mean just gives the maximum diameter. ${\displaystyle D\,}$

Obstacles outside the 1st Fresnel zone can even result in a slight amplification of the signal due to diffraction and interference . Slightly because most of the energy is transferred in the 1st Fresnel zone.

literature

• Hans Lobensommer: Handbook of modern radio technology . 1st edition. Franzis Verlag GmbH, Poing 1995, ISBN 3-7723-4262-0 .
• Jürgen Detlefsen, Uwe Siart: Basics of high frequency technology . 2nd Edition. Oldenbourg Verlag, Munich Vienna 2006, ISBN 3-486-57866-9 .

Web links

Commons : Fresnel zone  - collection of images, videos and audio files

• Topographic Fresnel zone calculator