SOLVED Numerical's - Antenna Theory - Page 5.


13) A 1-m-long car radio antenna operates in the AM frequency of 1.5 MHz. How much current is required to transmit 4 W of power?

SOLUTION:

This is a monopole antenna

λ = c / f = (3 x 108) / (1.5 x 106) = 200 m

In this case, it’s pretty clear that l << λ




14) An antenna located on the surface of a flat earth transmits an average power of 200 kW. Assuming that all the power is radiated uniformly over the surface of a hemisphere with the antenna at the center, calculate
(a) The time-average Poynting vector at 50 km, and
(b) The maximum electric field at that location.

SOLUTION:

a)

     Prad = ∫ Prad . ∂s = Pave . 2πr2 (hemisphere)

     Pave = Prad / 2πr2 = (200 x 103) / (2π 50 x 106)2

            =12.73 µW / m2

                                             Pave = 12.73 ar µW / m2


b)

      Pave = (Emax)2 / 2η

      (Emax)2 = 240π x 12.73 x 10-6

       Emax = 0.098 V/m



 15) A 100-turn loop antenna of radius 20 cm operating at 10 MHz in air is to give a 50 mV/m field strength at a distance 3 m from the loop. Determine
(a) The current that must be fed to the antenna
(b) The average power radiated by the antenna
SOLUTION:

a)

            λ = c / f = (3 x 108) / (100 x 106) = 3 m



                       Prad = 1/2 (Io2 Rrad) = 0.25mW



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