How much does the radar signal decrease with distance?

MINI PROBLEM. The radar signal that comes back to the detector becomes weaker the further away the target is. But how much weaker?

(Answer further down the page)

Acronyms are words formed from the initial letters of a series of words, for example radar which stands for RAdio Detection And Rindication, i.e. radio waves used for detection and distance assessment.

Other examples from the world of technology are lasers (Light Amplification by Stimulated Emission of Radiation) and masers (Microwave Amplification by Stimulated Emission of Radiation).

Radar technology developed greatly during World War II. In Swedish it was called echo radio for a while, but soon radar became the accepted word.

In 1950 it appeared as a common noun in the ninth edition of SAOL (Swedish Academy’s dictionary). In the tenth edition, 1973, lasers were also included. When I read electrical subjects at Chalmers in 1961, the laser was something new and it was often pronounced “lejser”, but I never heard anyone say “rejdar”.

The radar signal that reaches back to the detector (which is located next to the transmitting station) naturally becomes weaker the further away the target is.

At short distances we can ignore attenuation by the interaction with the atmosphere. Then the received signal decays as a certain power of the distance to the target. What potency?

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Solution

The answer is that the detected signal decays as the distance to the target to the fourth power. It is a purely geometric effect. Compare to how the illumination from a lamp decreases. At twice the distance, the area of ​​the illuminated surface is four times as large and the illumination is reduced to a quarter, that is, with the distance squared.

Then the radar echo must go back from the target to the detector. Then it is again spread out purely geometrically, which gives a further reduction with the distance squared, in total thus as the distance raised to four.

Problem printer. Göran Grimvall is professor emeritus in theoretical physics at KTH in Stockholm, and has participated in Ny Teknik since 1979. Photo: Jörgen Appelgren

Göran Grimvall is professor emeritus in theoretical physics at KTH and has worked in Ny Teknik with mini-problems since 1979.


Source: Nyteknik – Senaste nytt by www.nyteknik.se.

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