1. ENE 429 Antenna and Transmission lines Theory Lecture 10 Antennas DATE: 18/09/06 22/09/06

2. Review (1) 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

3. Review (2) 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

4. Review (3) Radiation characteristics Hertzian dipole

5. Ex1 Let a Hertzian dipole of the length /100 be given the current A, find a)P max at r = 100 m

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

7. The small loop antenna (magnetic dipole) Assume a << A complicate derivation brings to If the loop contains N-loop coil then S = N  a 2

8. Dipole antennas Longer than Hertizian dipole therefore they can generate higher radiation resistance and efficiency. Divide the dipole into small elements of Hertzian dipole. Then find and.

9. Field derivations (Far field) (1) The current on the two halves are Symmetrical and go to zero at the ends. We can write Where Assume  = 0 for simplicity.

10. Field derivations (Far field) (2) From In far field but since small differences can be critical.

11. Field derivations (Far field) (3) We can write

12. From In our case Field derivations (Far field) (3)

13. Field derivations (Far field) (4) where

14. Antenna properties 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

15. Half-wave dipole (most popular antenna) (1)

16. Using Matlab, we get Half-wave dipole (most popular antenna) (2)  p = 7.658 D max = 1.64 R rad = 73.2  This is much higher than that of the Hertzian dipole.

17. Antenna arrays A group of several antenna elements in various configurations (straight lines, circles, triangles, etc.) with proper amplitude and phase relations, main beam direction can be controlled. Improvement of the radiation characteristic can be done over a single-element antenna (broad beam, low directivity)

18. Two-element arrays (1) To simplify, 1. All antennas are identical. 2. Current amplitude is the same. 3. The radiation pattern lies in x-y plane From Consider,

19. Two-element arrays (2) Let I 1 = I 0, I 2 = I 0 e j , since r 1 and r 2 >> d/2 for far field, we can assume  1   2   and r 1  r 2  r.

20. Two-element arrays (3) But the exponential terms cannot be approximated, then

21. Principle of pattern multiplication We can write this as F unit = a unit factor or the maximum time-averaged power density for an individual element at F array = array factor = where This depends only on distance d and relative current phase, . We can conclude that the pattern function of an array of identical elements is described by the product of the element factor and the array factor.

22. N-element linear arrays We will simplify assumptions as follows: 1. The array is linear, evenly spaced along the line. 2. The array is uniform, driven by the same magnitude current source with constant phase difference between adjacent elements. (F array ) max = N 2

23. Parasitic arrays Yagiuda (rooftop antenna) Parasitic elements are indirectly driven by current induced in them from the driven element.

24. Friis transmission equation (1) Consider power transmission relation between transmitting and receiving antennas where particular antennas are aligned with same polarization. Let P rad1 be P total radiated by antenna 1 have a directivity D max1, With reciprocal property, Therefore, we have

25. Friis transmission equation (2) Each variable is independent of one another, so each term has to be constant, we found that

26. Friis transmission equation (3) Effective area (A e ) is much larger than the physical cross section. More general expressions We can also write

27. Friis transmission equation (4) Finally, consider P rad = e t P in, P out = e r P rec, and G t = e t D t, G r = e r D r Friis transmission equation Note: Assume - matched impedance condition between the transmitter circuitry/antenna and receiver - antenna polarizations are the same.

28. Receiver matching (1) Additional impedance matching network improves receiver performances

29. Receiver matching (2) Since the receiver is matched, half the received power is dissipated in the load, therefore Without the matching network,