Radar

:This article is about the device. For the fictional character in M*A*S*H (movie) and M*A*S*H (TV series), see Corporal Walter (Radar) O'Reilly.

Radar equation

The amount of power Pr returning to the receiving antenna is given by the radar equation:

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:P_r = {{P_t G_t A_r sigma}over{{(4pi)}^2 R_t^2R_r^2}}

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where

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• P_t = transmitter power,
• G_t = gain of transmitting antenna,
• A_r = effective aperture (area) of receiving antenna,
• σ = Radar Cross Section, or scattering coefficient of target,
• R_t = distance from transmitter to target,
• R_r = distance from target to receiver.

In the common case where the transmitter and receiver are at the same location, Rt = Rr and the term Rt² Rr² can be replaced by R4, where R is the range.

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This yields:

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:P_r = {{P_t G_t A_r sigma}over{{(4pi)}^2 R^4}}

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This shows that the received power declines as the fourth power of the range, which means that the reflected power from distant targets is very, very small.

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Note that the equation above is a simplification for vacuum without interference. In a real-world situation, pathloss effects should be considered, as well as other factors of the transmission medium.

Related Topics:
Vacuum - Pathloss

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Other mathematical developments in radar signal processing include time-frequency analysis (Weyl Heisenberg or wavelet), as well as the chirplet transform which makes use of the fact that radar returns from moving targets typically "chirp" (change their frequency as a function of time, as does the sound of a bird or bat).

Related Topics:
Wavelet - Chirplet transform

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