A radar for tracking aircraft broadcasts a 12 GHz microwave

Mary Hammonds 2021-12-13 Answered
A radar for tracking aircraft broadcasts a 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 diffract. 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.
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Expert Answer

Donald Cheek
Answered 2021-12-14 Author has 41 answers
For a circular aperture with diameter D, the diameter of the central maximum w is:
w=2.44λLD
λ is the wavelength and L is a distance to the screen
Given: the frequency of the wave f=12GHz, the diameter of the aperture D=2m, The distance to the screen L=30km, the antenna emits P=100kW
λ=cf=3×10812×109m=25mm
Now, find the diameter of the radar bean:
w=2.44λLD=2.44×25×103×30×1032m=915m
The intensity of radiation I at L=30km is given by:
I=P(w2)2π=100×103×4(915)2×3.14Wm2=0.152Wm2
Thus, the answers are: (a) 915m; (b) 0.152Wm2

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