Cheng-Chi Yu

1. 2012/8/13 Cheng-Chi Yu 1 Cheng-Chi Yu

2. Cheng-Chi Yu 2 2012/8/13 Contents Basic parameter Patterns Beam area Beam efficiency Directivity and gain Physical and effective apertures Scattering aperture and radar cross section The radio link (Friis formula)

3. Cheng-Chi Yu 3 2012/8/13 Contents Apertures of dipoles and ?/2 antennas Radiation resistance Antenna impedance Antenna duality Sources of radiation Field zones Shape-impedance considerations polarization

4. Cheng-Chi Yu 4 2012/8/13 Basic Antenna Parameters

5. Cheng-Chi Yu 5 2012/8/13 How to produce radiation A radio antenna nay be defined as the structure associated with the region of transition between a guided wave and a free-space wave. The antenna is a device which interfaces a circuit and space. Radiation is produced by accelerated charge. AC current flowing on metal radiates electromagnetic wave. So, time-changing current radiates and accelerated charge radiates.

6. Cheng-Chi Yu 6 2012/8/13 Basic radiation equation

7. Cheng-Chi Yu 7 2012/8/13 The currents on the transmission line flow out on the antenna and end there, but the fields associated with them keep on going. An antenna is a transition device, or transducer, between a guided wave and a free-space wave, or vice-versa.

8. Cheng-Chi Yu 8 2012/8/13

9. Cheng-Chi Yu 9 2012/8/13 ??:Practical Antenna Handbook (eBook) by Carr, Joseph J.Publication: New York McGraw-Hill Professional, 2001.

10. Cheng-Chi Yu 10 2012/8/13 Radiation resistance Rr is not related to any resistance in the antenna itself but is a resistance coupled from space to the antenna terminals. (That is a view point from circuit and may be thought of as a virtual resistance.) A receiving antenna may be regarded as a remote-sensing temperature –measuring device. The radiation resistance, the antenna temperature, and the radiation patterns are functions of the frequency.

11. Cheng-Chi Yu 11 2012/8/13 Patterns

12. Cheng-Chi Yu 12 2012/8/13 Coordinates System Rectangular coordinates Cylinder coordinates Sphere coordinates

13. Cheng-Chi Yu 13 2012/8/13 Patterns The radiation patterns are three dimensional quantities involving the variation of field or power (proportional to the field squared) as a function of the spherical coordinates ? and ?.

14. Cheng-Chi Yu 14 2012/8/13 Patterns To completely specify the radiation pattern with respect to field intensity and polarization requires three patterns: The ? component of the electric field as a function of the angles ? and ? or E?(?, ?). (Figure 2-3 and 2-4) The ? component of the electric field as a function of the angles ? and ? or E?(?, ?). The phase of these fields as a function of the angles ? and ? or ? ?(?, ?) and ??(?, ?). Principal plane patterns (as in the xz and yz planes in Fig. 2-3)

15. Cheng-Chi Yu 15 2012/8/13 HPBW: the angular beamwidth at the half-power level FNBW: the beamwidth between first nulls

16. Cheng-Chi Yu 16 2012/8/13 Normalized field pattern Normalized field pattern is dimensionless The half-power level occurs at E?(?, ?)n=1/(2)0.5=0.707

17. Cheng-Chi Yu 17 2012/8/13 Far-field condition Far-field: at distances that are large compared to the wavelength, the shape of the field pattern is independent of distance.

18. Cheng-Chi Yu 18 2012/8/13 Normalized power pattern Expressed in terms of the power per unit area (Poynting vector)

19. Cheng-Chi Yu 19 2012/8/13

20. Cheng-Chi Yu 20 2012/8/13 ???:

21. Cheng-Chi Yu 21 2012/8/13 BEAM AREA ?A (BEAM SOLID ANGLE)

22. Cheng-Chi Yu 22 2012/8/13 Solid angle

23. Cheng-Chi Yu 23 2012/8/13

24. Cheng-Chi Yu 24 2012/8/13

25. Cheng-Chi Yu 25 2012/8/13

26. Cheng-Chi Yu 26 2012/8/13

27. Cheng-Chi Yu 27 2012/8/13 Radiation intensity Radiation intensity U: The power radiated from an antenna per unit solid angle (W/sr ; W/deg2) The normalized power pattern can be expressed in terms of U:

28. Cheng-Chi Yu 28 2012/8/13 Beam efficiency The (total) beam area consists of the main beam area plus the minor-lobe area Beam efficiency: The ratio of the main beam area to the total beam area Stray factor: The ratio of the minor-lobe area to the total beam area

29. Cheng-Chi Yu 29 2012/8/13 Directivity D and Gain G Directivity D: the ratio of the maximum power density P(?, ?)max (W/m2) to its average value over a sphere as observed in the far field of an antenna. D ? 1

30. Cheng-Chi Yu 30 2012/8/13 Directivity D

31. Cheng-Chi Yu 31 2012/8/13 Directivity D For an antenna that radiates over only half a sphere the beam area ?A = 2? sr, the D is :

32. Cheng-Chi Yu 32 2012/8/13 Directivity D The idealized isotropic antenna (?A = 4? sr) has the lowest possible D=1. All actual antennas have directivities greater than 1 (D>1) The simple short dipole has a beam area ?A = 2.67? sr and D=1.5 (=1.76dBi)

33. Cheng-Chi Yu 33 2012/8/13 Directivity D If the HPBW of an antenna are known, then For example:

34. Cheng-Chi Yu 34 2012/8/13 Directivity D Since the upper equation neglects minor lobes, a better approximation: For example:

35. Cheng-Chi Yu 35 2012/8/13 Gain G The gain of an antenna is an actual or realized quantity which is less than the directivity D due to ohmic losses or mismatching in feeding the antenna . Gain G of an antenna: K may be close to unity in many well-designed antennas. G ? D Gain can be measured by comparing with a reference antenna of known gain.

36. Cheng-Chi Yu 36 2012/8/13

37. Cheng-Chi Yu 37 2012/8/13

38. Cheng-Chi Yu 38 2012/8/13 Directivity and resolution The resolution of an antenna may be defined as equal to half the beamwidth between first nulls (FNBW)/2 The number N of radio transmitters or point sources of radiation distributed uniformly over the sky which an antenna can resolve is given approximately by : so, D = N, the directivity is equal to the number of point sources in the sky that the antenna can resolve

39. Cheng-Chi Yu 39 2012/8/13

40. Cheng-Chi Yu 40 2012/8/13 Antenna apertures Physical aperture Ap Suppose the horn extracts all the power from the wave over entire physical aperture, then the total power P absorbed from the wave is:

41. Cheng-Chi Yu 41 2012/8/13 Antenna apertures The effective aperture Ae is less than the physical aperture Ap Aperture efficiency: Aperture-beam-area relation: All antennas have an effective aperture which can be calculated or measured. For example: an idealized isotropic antenna

42. Cheng-Chi Yu 42 2012/8/13 Expressions for directivity D

43. Cheng-Chi Yu 43 2012/8/13 The condition of maximum power transfer The condition of maximum power transfer (antenna assumed lossless): RL = Rr

44. Cheng-Chi Yu 44 2012/8/13 Effective height The effective height may be defined as the ratio of the induced voltage to the incident field h = V/E (m)

45. Cheng-Chi Yu 45 2012/8/13 If the current distribution of the dipole were uniform, its effective height would be l. The actual current distribution is nearly sinusodial with an average value 2/? = 0.64 of the maximum, so that its effective height h = 0.64 l. (assumed the antenna is oriented for maximum response)

46. Cheng-Chi Yu 46 2012/8/13 The average current is ½ of the maximum so that so that its effective height h = 0.5 l. (assumed the antenna is oriented for maximum response)

47. Cheng-Chi Yu 47 2012/8/13 Effective height Another definition of The effective height (consider the transmitting case)

48. Cheng-Chi Yu 48 2012/8/13 Effective aperture ?? effective height where Zo = intrinsic impedance of space (= 377?) The parameter effective height is useful for some types of antennas, such as tower-type antennas, small antennas. The parameter effective aperture has more general application to all types of antennas.

49. Cheng-Chi Yu 49 2012/8/13

50. Cheng-Chi Yu 50 2012/8/13

51. Cheng-Chi Yu 51 2012/8/13

52. Cheng-Chi Yu 52 2012/8/13

53. Cheng-Chi Yu 53 2012/8/13

54. Cheng-Chi Yu 54 2012/8/13 Radio communication link Assuming lossless, matched antennas:

55. Cheng-Chi Yu 55 2012/8/13 Friis transmission formula

56. Cheng-Chi Yu 56 2012/8/13

57. Cheng-Chi Yu 57 2012/8/13 Fields from oscillating dipole

58. Cheng-Chi Yu 58 2012/8/13 Fields from oscillating dipole

59. Cheng-Chi Yu 59 2012/8/13 Antenna field zones The fields around an antenna may be divided into two principal regions: Near field (Fresnel zone) Far field (Fraunhofer zone) The boundary between the two zone may be arbitrarily taken to be at a radius:

60. Cheng-Chi Yu 60 2012/8/13 Antenna field zones In the far field, the shape of the field pattern is independent of the distance. In the near field, the shape of the field pattern depends, in general, on the distance.

61. Cheng-Chi Yu 61 2012/8/13 The region near the poles of the sphere acts as a reflector. The reciprocating energy represents reactive power that is trapped near the antenna like in a resonator.

62. Cheng-Chi Yu 62 2012/8/13 Shape-impedance considerations omnidirectional

63. Cheng-Chi Yu 63 2012/8/13 Shape-impedance considerations

64. Cheng-Chi Yu 64 2012/8/13 Polarization The polarization of an electromagnetic wave is defined by the direction in which its electric field vector is oriented over at least one cycle of oscillation. Classification Linear polarization Horizontal polarization Vertical polarization Circular polarization Left circular polarization Right circular polarization Elliptical polarization

65. Cheng-Chi Yu 65 2012/8/13 Polarization

66. Cheng-Chi Yu 66 2012/8/13 Linear polarization The E field at all times in the y-direction, this wave is said to be linearly polarized (in the y direction)

67. Cheng-Chi Yu 67 2012/8/13 Elliptical polarization The electric field of a wave traveling in the z direction have both a y component and an x component ,with a phase difference ? between the components, the wave is said to be elliptically polarized. At a fixed value of z the electric vector E rotates as a function of time, the tip of the vector describing an ellipse called the polarization ellipse. The ratio of the major to minor axes of the polarization ellipse is called the Axial Ratio (AR)

68. Cheng-Chi Yu 68 2012/8/13 Elliptical polarization and circular polarization AR = E2 / E1 For E1 = E2 ( AR = 1 ) ? circular polarization For E1 = 0 ( AR = ? ) ? linear polarization

69. Cheng-Chi Yu 69 2012/8/13 Polarization ellipse equation If the wave is traveling in the positive z direction, the electric components in the x and y directions are:

70. Cheng-Chi Yu 70 2012/8/13 Polarization ellipse equation

71. Cheng-Chi Yu 71 2012/8/13 Polarization ellipse equation If E1 = 0, the wave is linearly polarized in the y direction. If E2 = 0, the wave is linearly polarized in the x direction. If ? = 0 and E1 = E2 , the wave is linearly polarized but in a plane at an angle of 45o with respect to the x axis (? = 45o).

72. Cheng-Chi Yu 72 2012/8/13 circular polarization If E1 = E2 and ? = ?90o , the wave is circularly polarized. When ? = +90o, the wave is left circularly polarized. When ? = -90o, the wave is right circularly polarized. ??: The IEEE definition is opposite to the classical optics definition which had been in use for centuries. A left-handed helical antenna radiates ( or receives) left circular (IEEE) polarization.

73. Cheng-Chi Yu 73 2012/8/13 Poynting vector for elliptically and circularly polarized waves

74. Cheng-Chi Yu 74 2012/8/13

75. Cheng-Chi Yu 75 2012/8/13