SOLVED Numerical's - Antenna Theory - Page 3.

6) An antenna in air radiates a total power of 100 kW so that maximum radiated electric field strength of 12 mV/m is measured 20 km from the antenna. 
Find its:
(a) Directivity in dB
(b) Maximum power gain if η_r = 98%.


SOLUTION:

a)

G = 10 log ₁₀ G_d = 10 log ₁₀ (2.16) = 3.34 dB

b) G = η_r G_d = 0.98 x 2.16 = 2.117



7) A C-band radar with an antenna 1.8 m in radius transmits 60 kW at a frequency of 6000 MHz. If the minimum detectable power is 0.26 mW, for a target cross section of 5 m², calculate the maximum range in nautical miles and the signal power density at half this range. Assume unity efficiency and that the effective area of the antenna is 70% of the actual area.


SOLUTION:

8) The magnetic vector potential at point P(r, θ, φ) due to a small antenna located at the origin is given by

where r² = x² + y² + z². Find E(r, θ, φ, t) and H(r, θ, φ, t) at the far field.

SOLUTION:

Using Vector transformation,

         A_rs = A_xs sinθ cosφ

         A_θs = A_xs cosθ cosφ

         A_φs = A_xs sinφ

At far field only 1/r term remains. Hence