Question

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?

Answer 1

Answer:

a) 915 m

b) 0.15 W/$m^{2}$

Explanation:

solution:

a) The wavelength of the microwaves electromagnetic wave is:

λ=$\frac{c}{f}$=$\frac{3*10^{8} }{12*10^{9}}$=0.025 m

the circular radar antenna acts like a circular aperture of diameter D will have a bright central maximum of diameter:

w=2.44λL/D

so at 30 km screen:

w=2.44λL/w

  =2.44*0.025*30*10^3/2

  =915 m

b)

The area of a beam at 30 km is:

A=$\pi r^{2}$=$\pi (\frac{w}{2} )^2$=$\pi (\frac{915}{2} )^2$=$657*10^{3} m^{2}$

the average microwave intensity is equal to the ratio of the power of the antenna and area of the beam:

I=P/A

So at 30 km:

I=100*10^3/657*10^3

=0.15 W/$m^{2}$