A radar for tracking aircraft broadcasts at 12 GHz microwave beam from a 2.0-m-diameter circular...

Katherine Walls

Answered question

2022-01-17

A radar for tracking aircraft broadcasts at 12 GHz microwave beam from a 2.0-m-diameter circular radar antenna. From a wave perspective the antenna is a circular aperture through which the microwaves diffracts. A. what is the diameter of the radar beam at a distance of 30 km? B. if the antenna emits 100 kW of power what is the average microwave intensity at 30 km?

Answer & Explanation

ramirezhereva

Beginner2022-01-16Added 28 answers

b) The average microwave intensity is,
$I=\frac{P}{A}$ $=\frac{P}{\pi {r}^{2}}$ $=\frac{4P}{\pi {d}^{2}}$ $=\frac{4(100\times {10}^{3}\text{}W)}{\pi {\left(915\text{}m\right)}^{2}}$ $=0.152\text{}\frac{W}{{m}^{2}}$

RizerMix

Skilled2022-01-19Added 437 answers

a) The wavelength of the wave is,
$\lambda =\frac{c}{f}$$=\frac{3\times {10}^{8}\text{}m/s}{12\times {10}^{9}\text{}Hz}$$=0.025\text{}m$$=25\text{}mm$
The angular resolution of the system is,
$\mathrm{sin}\theta =1.22(\frac{\lambda}{D})$$=1.22(\frac{25\text{}mm}{2\text{}m})$$\theta ={\mathrm{sin}}^{-1}(0.01525)$$=15.25\text{}mrad$
The diameter of the radar beam from the half angle is,
$d=2(15.25\text{}mrad)(30\text{}km(\frac{1000\text{}m}{1\text{}km}))$$=915\text{}m$