Katherine Walls

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?

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

Expert2022-01-19Added 656 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,
$d=2(15.25\text{}mrad)(30\text{}km(\frac{1000\text{}m}{1\text{}km}))$
$=915\text{}m$

alenahelenash

Expert2022-01-23Added 556 answers

Refer to this one, they're both correct!

22+64

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