Radar Range Equation

Power density at the target is

(watt/m²)

Multiplying this by the target effective aperture A_tgt, the power received by the target is

Here, A_tgt is called the radar cross section of the target.

If we assume that the target radiates this power isotropically in every direction, the power density at the receiving antenna (which is the same antenna as the transmitting antenna) is

(watt/m²)

The power received by the receiving antenna is then (A_r = the receiving antenna cross section)

(watt)

Substituting previous equations in Eq. 4, the total power received by the antenna can be written as

Antenna gain (G_p) and effective antenna aperture (A_r) are related to the wavelength through

We can set this power received by the antenna to be equal to the minimum power, P_min that can be detected by the receiver system

The distance in this equation now becomes the maximum distance that can be detected by the receiving antenna. Identifying this distance as the Range of the radar and solving for the range R_max, we obtain

Here R_max is the maximum distance that the radar can detect an object with the radar cross section of A_tgt.

Equation 8 is called the Radar range equation. We can identify this maximum distance as range of the radar: R_ran.