Problem 22.60 Part A A radar for tracking aircraft broadcasts a 12 GHz microwave

Question

Problem 22.60 Part A 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. What is the diameter of the radar beam at a distance of 30 km? Express your answer with the appropriate units. Value UUnits Submit My Answers Give Up Part B If the antenna emits 100 kW of power, what is the average microwave intensity at 30 km? Express your answer with the appropriate units IA IValue Units Submit My Answers Give Up

Explanation / Answer

The angular resolution of the system can be calculated with this formula:

Sin theta = 1.22 lambda / D

Where theta is the angular resolution, lambda is wavelength and D is the aperture diameter.

Lambda = c / 12 GHz = 25mm

Sin Theta = Theta = 1.22 x 25mm / 2m = 15.25 mrad

30km x 15.25 mrad x 2 = 915 m (multiply by 2 because theta is half angle)

Part B:
Take the total power and divide it by area
a = pi x r^2 = 3.14159 x 457.5^2 = 658 x 10^3 m^2
Power = 100kW
Intensity = 100kW / 658 x 10^3 m^2 = 152mW/m^2

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