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### Antenna Theory - Solved Numerical's / Problems - ElectroMagnetic Theory...

1) An electric field strength of 10 µV/m is to be measured at an observation point θ = π/2, 500 km from a λ/4 monopole antenna operating in air at 50 MHz.
• (a) What is the length of the dipole?
• (b) Calculate the current that must be fed to the antenna.
• (c) Find the average power radiated by the antenna.
• (d) If a transmission line with Zo = 75 Ω is connected to the antenna, determine the standing wave ratio. --- For Solution  CLICK HERE.

2) Calculate the directivity of
• The Hertzian Monopole.

3) A certain antenna with an efficiency of 95% has maximum radiation intensity of 0.5 W/sr. Calculate its directivity when
(a) The input power is 0.4 W
(b) The radiated power is 0.3 W

4) Evaluate the directivity of an antenna with normalized radiation intensity

5) Determine the maximum effective area of a Hertzian dipole of length 10 cm operating at 10 MHz. If the antenna receives 3 µW of power, what is the power density of the incident wave?   --- For Solution  CLICK HERE.

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 ηr = 98%.

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.        --- For Solution  CLICK HERE.

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.       --- For Solution  CLICK HERE.

9) A Hertzian dipole at the origin in free space has dl = 20 cm and I = 10 cos2π107t A, find |Eθs| at the distant point (100, 0, 0).          --- For Solution  CLICK HERE.

10) A 2-A source operating at 300 MHz feeds a Hertzian dipole of length 5 mm situated at the origin. Find Es and Hs at (10, 30°, 90°).          --- For Solution  CLICK HERE.

11) An antenna can be modeled as an electric dipole of length 5 m at 3 MHz. Find the radiation resistance of the antenna assuming a uniform current over its length.           --- For Solution  CLICK HERE.

12) A half-wave dipole fed by a 50 Ω transmission line, calculate the reflection coefficient and the standing wave ratio.          --- For Solution  CLICK HERE.

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?            --- For Solution  CLICK HERE.

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.

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

16) Sketch the normalized E-field and H-field patterns for
a. A half-wave dipole
b. A quarter-wave monopole.

17) In free space, an antenna has a far zone field given by

18) At the far field, the electric field produced by antenna is

Sketch the vertical pattern of the antenna. Your plot should include as many points as possible.

19) At the far field, an antenna produces

Calculate the directive gain and the directivity of the antenna?