Question

A radar operates at a power source that can provide the maximal amount of 150kW, and has a frequency of 12.1 GHz. It needs to detect an object in which the object has reflects radar waves as though it only has a cross-sectional area of 0.2 m^2

Make reasonable assumptions, determines the intensity and the maximum value of the electric field vector of the reflected radar signal

Answer 1

Assumptions:

1. The antenna used for transmission of signal is parabolic dish antenna with a nominal gain G=30 dB =1000(linear sale)

2. Signal loss due to rain is neglected

3. Range of Radar, R = 1 Km

Parameters given:

Target cross section area $\sigma =$ 0.2 sq.m

Frequency f0= 12.1 GHz; Wavelength,

$\lambda _{0}= \frac{c}{f}= \frac{3*10^{8}}{12.1*10^{9}} =0.025 m$

Transmitted power Pt=150 KW

Intrinsic impedance of air , $\eta =377 \Omega$

According to Radar range equation,

Recieved Power ,

$P{_{r}}= \frac{P{_{t}} G^{2}\lambda ^{2}\sigma }{(4\Pi) ^{3}R^{4}}=\frac{150*10^{3}*10^{6}*.025^{2}*0.2}{(4\Pi) ^{3}*(100*10^{3})^{4}}$$P{_{r}}= \frac{P{_{t}} G^{2}\lambda ^{2}\sigma }{(4\Pi) ^{3}R^{4}}=\frac{150*10^{3}*10^{6}*.025^{2}*0.2}{(4\Pi) ^{3}*(1*10^{3})^{4}}$

Solving We get Pr= 9.45 nW. But

$P_{r}= \frac{E_{max}^{2}}{2\eta }$

Solving we get Maximum Electric field intensity Emax= 2.67 mV/m.