1. 1

2.  Antenna is a structure designed for radiating and receiving EM energy in a prescribed manner  Far field region ( the distance where the receiving antenna is located far enough for the transmitter to appear as a point source)  The shape or pattern of the radiated field is independent of r in the far field.  Normalized power function or normalized radiation intensity 2

3.  Directivity is the overall ability of an antenna to direct radiated power in a given direction.  An antenna’s pattern solid angle:  Total radiated power can be written as  Antenna efficiency e is measured as 3

4.  If the current distribution of a radiating element is known, we can calculate radiated fields.  In general, the analysis of the radiation characteristics of an antenna follows the three steps below: 1. Determine the vector magnetic potential from known of assumed current on the antenna. 2. Find the magnetic field intensity from. 3. Find the electric field intensity from. 4

5. From the point form of Gauss’s law for magnetic field, Define therefore we can express as where J d = current density at the point source (driving point) R = distance from the point source to the observation point (m) 5

6.  From here we can determine, then find in free space.  We can then find the electric field from  The time-averaged radiated power is The subscript “0” represents the observation point. W/m 2. 6

7. 1. Hertzian dipole (electric dipole) 2. Small loop antenna (magnetic dipole) 3. Dipole antenna 7

8.  A short line of current that is short compared to the operating wavelength. This thin, conducting wire of a length dl carries a time-harmonic current A and in a phasor form A. 8

9. The current density at the source seen by the observation point is A differential volume of this current element is dV = Sdz. 9

10. Therefore Then Where at the observation point. For short dipole, R  r, thus we can write Conversion into the spherical coordinate gives 10

11. Therefore We can then calculate for 11

12. Multiply  2 to both nominator and denominator, so we have We are interested in the fields at distances very far from the antenna, which is in the region where or 12

13. Under a far-field condition, we could neglect and Then and Finally, W/m 2. 13

14. Since the current along the short Hertzian dipole is uniform, we refer the power dissipated in the radial distance R rad to I, or m. 14

15. 15

16. 16 a)P max at r = 100 m

17. b) What is the time-averaged power density at P (100,  /4,  /2)? c) Radiation resistance 17

18. Assume a << A complicate derivation brings to 18 If the loop contains N-loop coil then S = N  a 2

19.  Longer than Hertizian dipole therefore they can generate higher radiation resistance and efficiency. 19 Divide the dipole into small elements of Hertzian dipole. Then find and. Figure of dipole

20. 20

21. The current on the two halves are Symmetrical and go to zero at the ends. We can write Where Assume  = 0 for simplicity. 21

22. From 22 In far field but since small differences can be critical.

23. We can write 23

24. From In our case 24

25. where 25

26. 1. Find P n (  ), calculate F(  ) over the full range of  for length L in terms of wavelength then find F max (this step requires Matlab) 2. Find  p 3. D max (Directivity) 4. R rad 26

27.  Link to Matlab file Link to Matlab file 27

28. 28

29. Using Matlab, we get 29  p = 7.658 D max = 1.64 R rad = 73.2  This is much higher than that of the Hertzian dipole.