ECE 480 Wireless Systems Lecture 4 Propagation and Modulation of RF Waves

1. ECE 480 Wireless Systems Lecture 4 Propagation and Modulation of RF Waves

2. Antenna Radiation Characteristics • Antenna pattern: • Describes the far – field directional properties of an antenna when measured at a fixed distance from the antenna • 3 – d plot that displays the strength of the radiated field (or power density) as a function of direction (spherical coordinates) specified by the zenith angle  and the azimuth angle  • From reciprocity, a receiving antenna has the same directional antenna pattern as the pattern that it exhibits when operated in the transmission mode

3. The differential power through an elemental area dA is always in the radial direction in the far – field region

4. Define: Solid angle,  for a spherical surface

5. The total power radiated by an antenna is given by

6. is the normalized radiation intensity

7. 3 – D Pattern of a Narrow – Beam Antenna

8. Antenna Pattern It is convenient to characterize the variation of F ( , ) in two dimensions Two principle planes of the spherical coordinate system Elevation Plane ( - plane) Corresponds to a single value of  ( = 0 x –z plane) ( = 90 y –z plane) Azimuth Plane ( - plane) Corresponds to  = 90 o (x – y plane)

9. Clearer to express F in db for highly directive patterns  = 0 plane

10. Side lobes are undesirable • Wasted energy • Possible interference

11. Beam Dimensions Define: Pattern solid angle  p  p = Equivalent width of the main lobe For an isotropic antenna with F ( , ) = 1 in all directions:

12. Defines an equivalent cone over which all the radiation of the actual antenna is concentrated with equal intensity signal equal to the maximum of the actual pattern

13. The half – power (3 dB) beamwidth, , is defined as the angular width of the main lobe between the two angles at which the magnitude of F ( , ) is equal to half its peak value

14. F () is max at  = 90 o ,  2 = 135 0 ,  1 = 45 o ,  = 135 o – 45 o = 90 o

15. Null Beamwidth,  null Beamwidth between the first nulls on either side of the peak

16. Antenna Directivity  p = Pattern solid angle For an isotropic antenna,  p = 4  D = 1

17. D can also be expressed as S iso = power density radiated by an isotropic antenna D = ratio of the maximum power density radiated by the antenna to the power density radiated by an isotropic antenna

18. For an antenna with a single main lobe pointing in the z direction:

19. Example – Antenna Radiation Properties • Determine: • The direction of maximum radiation • Pattern solid angle • directivity • half – power beamwidth • in the y-z plane for an antenna that radiates into only the upper hemisphere and its normalized radiation intensity is given by

20. Solution The statement in the upper hemisphere can be written mathematically as

21. a. The function is maximum when  = 0 b. The pattern solid angle is given by Polar plot of

22. c. d. The half – power by setting Polar plot of

23. Example – Directivity of a Hertzian Dipole For a Hertzian dipole:

24. Antenna Gain P t = Transmitter power sent to the antenna P rad = Power radiated into space P loss = Power loss due to heat in the antenna = P t – P rad Define: Radiation Efficiency,   = 1 for a lossless antenna

25. Define: Antenna Gain, G Accounts for the losses in the antenna

26. Radiation Resistance P loss = Power loss due to heat in the antenna = P t – P rad

27. To find the radiation resistance: • Find the far – field power by integrating the far – field power density over a sphere • Equate to

28. Example – Radiation Resistance and Efficiency of a Hertzian Dipole A 4 – cm long center – fed dipole is used as an antenna at 75 MHz. The antenna wire is made of copper and has a radius a = 0.4 mm. The loss resistance of a circular wire is given by Calculate the radiation resistance and the radiation efficiency of the dipole antenna

29. Solution The parameters of copper are

30. At 75 MHz:  This is a short dipole From before,

32. Half – Wave Dipole Antenna In phasor form:

33. For a short dipole Expand these expressions to obtain similar expressions for the half – wave dipole

34. Consider an infinitesimal dipole segment of length dz excited by a current and located a distance from the observation point

35. The far field due to radiation by the entire antenna is given by Two assumptions: (length factor)

36. Note that "s" appears in the equation twice – once for the distance away and once for the phase factor is not valid for the length factor If Q is located at the top of the dipole, the phase factor is which is not acceptable

39. is max when

40. Directivity of Half – Wave Dipole Need P rad and S (R , )

41. Radiation Resistance of Half – Wave Dipole Recall: for the short dipole (l = 4 cm) at 75 MHz R rad = 0.08  R loss = 0.036  For the half – wave dipole (l = 4 m) at 75 MHz R loss = 1.8 

42. Effective Area of a Receiving Antenna Assume an incident wave with a power density of S i The effective area of the antenna, A e , is P int = Power intercepted by the antenna It can be shown: = Magnitude of the open – circuit voltage developed across the antenna

43. The power density carried by the wave is For the short dipole

44. In terms of D: Valid for any antenna Example: Antenna Area The effective area of an antenna is 9 m 2. What is its directivity in db at 3 GHz?

45. Friis Transmission Formula • Assumptions: • Each antenna is in the far – field region of the other • Peak of the radiation pattern of each antenna is aligned with the other • Transmission is lossless

46. For an isotropic antenna: (ideal) In the practical case, In terms of the effective area A t of the transmitting antenna

47. On the receiving side, Friis transmission formula

48. When the antennas are not aligned (More general expression)

49. Homework 1. Determine the following: a. The direction of maximum radiation b. Directivity c. Beam solid angle d. Half – power beamwidth in the x – z plane for an antenna whose normalized radiation intensity is given by: Hint: Sketch the pattern first

50. 2. An antenna with a pattern solid angle of 1.5 (sr) radiates 30 W of power. At a range of 1 km, what is the maximum power density radiated by the antenna? 3. The radiation pattern of a circular parabolic – reflector antenna consists of a circular major lobe with a half – power beamwidth of 2 o and a few minor lobes. Ignoring the minor lobes, obtain an estimate for the antenna directivity in dB.