Powere density at a distance R from isotropic antenna

R = $\frac{P_t}{4\pi R^2} watts/(m^2)$

Powere density at a distance R from directive antenna of gain G

R = $\frac{P_t G}{4\pi R^2} watts/(m^2)$

The total power intercepted by a target having area 'A' is :

R = $\frac{P_t G}{4\pi R^2} . A$ watts where A is area seen by radar.

Power density of echo signal at radar station is

$\rho = \frac{P_t G A}{4\pi R^2} \frac{1}{4\pi R^2} $ watts

The radar antenna captures a portion of echo power. Let effective area of receiving antenna is $A_R$, the power $P_r$ received by radar is :

$P_r = \frac{P_t .G .A. A_R}{(4\pi R^2)^2}$ watts

$R_{max} = (\frac{P_t G^2 (\lambda)^2 A}{(4\pi)^3 S_{min}})^{\frac{1}{4}}$

Factors affecting radar range:

1. Transmitter Power:

In case the radar range is to be doubled, we have to increase the transmitter power 16 times since Rmax $\alpha$ (Pt)1/4

2. Minimum Detectable Signal: Rmax $\alpha$(1/Smin)1/4 ; thus redusing Smin, the receiver has to be very sensitive and gain of the Rx should be high.

But Rx is more susceptible to interference as it now amplifier weak signals rather than amplifying low power received signals.

3.Target cross sectional are: The radar cross section of a target is the area of the target as seen by a radar. The radar cross sectional area of the target is not a controller factor.