The energy intercepted by the target will be:
where s is the back scattering cross section of the target. NOTE: s is not necessarily equal to the geometrical cross section.
The amount of energy which gets back to the antenna is:
The amount of power that is collected by the antenna is:
where [Pr] = watts
Ae = effective area of the antenna
What are typical values of these quantities?
Pt ~ 105 W
r ~ 100 km
G ~ 40 dB
s ~ 1 m2
Inserting these numbers into the above equation gives
The gain can be express in terms of the effective area of the antenna and the wavelength of the radar by:
so substituting (4) into (3) gives:
This is the radar equation for a point target.