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Solved Problems-1

Problem-1
Determine the directivity of the following antennas:
  1. Infinitesimal dipole or Hertzian dipole antenna
  2. Half-wave dipole antenna
  3. Quarter-wave monopole antenna
  4. Hertzian monopole
Solution
(a) For an infinitesimal dipole antenna, Description: Description: 30509.png
 
The radiation intensity is given as,
 
Description: Description: 30501.png
 
The power radiated by the antenna is,
 
Description: Description: 30488.png
 
Average radiation intensity is,
 
Description: Description: 30480.png
 
The directive gain is given as,
 
Description: Description: 30472.png
 
The directivity is given as,
Description: Description: 30465.png
 
Description: Description: 30458.png
 
(b) For a half-wave dipole antenna, Description: Description: 30450.png
 
The radiation intensity is given as,
 
Description: Description: 30439.png
 
The power radiated by the antenna is,
 
Description: Description: 30432.png
 
As obtained earlier, the integral is 1.2188. Hence,
 
Description: Description: 30423.png
 
Average radiation intensity is,
 
Description: Description: 30414.png
 
The directive gain is given as,
 
Description: Description: 30405.png
 
The directivity is given as,
 
Description: Description: 30392.png
 
Description: Description: 30384.png
 
(c) For a quarter-wave monopole antenna, Description: Description: 30377.png
 
The radiation intensity is given as,
 
Description: Description: 30370.png
 
The power radiated by the antenna is,
Description: Description: 30363.png
 
As obtained earlier, the integral is Description: Description: 30355.png.
 
Hence, Description: Description: 30345.png
 
Average radiation intensity is,
 
Description: Description: 30338.png
 
The directive gain is given as,
 
Description: Description: 30329.png
 
The directivity is given as,
 
Description: Description: 30321.png
 
Description: Description: 30312.png
 
(d) For a Hertzian monopole antenna, Description: Description: 30300.png
 
The radiation intensity is given as,
 
Description: Description: 30293.png
 
The power radiated by the antenna is,
 
Description: Description: 30286.png
 
Average radiation intensity is,
 
Description: Description: 30279.png
 
The directive gain is given as,
 
Description: Description: 30272.png
 
The directivity is given as,
Description: Description: 30264.png
 
Description: Description: 30255.png
 





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