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Antenna Fundamentals

Antenna Fundamentals 4
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Published Date:13-07-2017
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NUS/ECE EE5308 Antenna Fundamentals 1 Introduction Antennas are device designed to radiate electromagnetic energy efficiently in a prescribed manner. It is the current distributions on the antennas that produce the radiation. Usually these current distributions are excited by transmission lines or waveguides. Transmission line Current distributions Antenna Hon Tat Hui Antenna Fundamentals 1NUS/ECE EE5308 2 Antenna Parameters 2.1 Poynting Vector and Power Density Instantaneous Poynting vector: pE xy,,z,tH xy, ,z,t  jt jt 2  ReEH xy , ,z e Re xy , ,z e (W/m )    Time expressions: Note: Average Poynting vector: E(x,y,z,t) H(x,y,z,t) 1 2 Phasor expressions: PE Re xy ,,zH x,, y z (W/m )    av E(x,y,z) 2 H(x,y,z) Note that Poynting vector is a real vector. Its magnitude gives the instantaneous or average power density of the electromagnetic wave. Its direction gives the direction of the power flow at that particular point. Hon Tat Hui Antenna Fundamentals 2NUS/ECE EE5308 2.2 Power Intensity Note that U is a function of direction (θ,) only and 2 not distance (r). Ur P W/sr  av sr = steradian, unit for measuring the solid angle. Solid angle  is the ratio of that part of a spherical surface area S subtended at the centre of a sphere to the square of the radius of the sphere. S Spherical S  sr  surface 2 r  The solid angle subtended o by a whole spherical r surface is therefore: 2 4r  4 (sr) 2 r Hon Tat Hui Antenna Fundamentals 3NUS/ECE EE5308 2.3 Radiated Power 1 P Pds ReEH ds (W) rad av    2 ss 2 ˆ ds r sindd n  P av  Antenna r Note that the integration is over a closed surface with the antenna inside and the surface is sufficiently far from the antenna (far field conditions). Hon Tat Hui Antenna Fundamentals 4NUS/ECE EE5308 Example 1 Find the total average radiated power of a Hertzian dipole. Solution 11  PE  ReH ReEHa   av  r 22 2   E 1 EE    Re aa  rr 22   2 2  kId sin 2  a (W/m ) r 2 24 r Hon Tat Hui Antenna Fundamentals 5NUS/ECE EE5308 P Pds rad av  s 2  2 2  kId sin 2 aa rd sin d rr 2  24 r 00 2  Id  (W) 3 Hon Tat Hui Antenna Fundamentals 6NUS/ECE EE5308 Example 2 Find the total average radiated power of a half-wave dipole. Solution For a half-wave dipole:  jkr cos 2 cos eE θ Ej 60I , H θ m  r sin  2 E  Pa av r 2 2 2 15I cos( / 2)cos 2 m  a (W/m ) r 2   r sin Hon Tat Hui Antenna Fundamentals 7NUS/ECE EE5308 P Pds rad av   s 2  2 2 15I cos( / 2)cos 2 m aa rd sin d rr 2   r sin 00  2 cos ( / 2)cos 2  30Id (W) m  sin 0 The above remaining integral can be evaluated numerically to give: 2 PI 36.54 (W) rad m Hon Tat Hui Antenna Fundamentals 8NUS/ECE EE5308 Hence for a /4 monopole over a ground plane with a maximum current at its base = I , the radiated power is m half that of a /2 dipole, i.e., 2 PI 18.27 (W) rad m Why?? Think about it Hon Tat Hui Antenna Fundamentals 9NUS/ECE EE5308 2.4 Radiation Pattern A radiation pattern (or field pattern) is a graph that describes the relative far field value, E or H, with direction at a fixed distance from the antenna. A field pattern includes an magnitude pattern E or H and a phase pattern ∠E or ∠H. A power pattern is a graph that describes the relative (average) radiated power density P of the far-field av with direction at a fixed distance from the antenna. By the reciprocity theorem, the radiation patterns of an antenna in the transmitting mode is same as the those for the antenna in the receiving mode. Hon Tat Hui Antenna Fundamentals 10NUS/ECE EE5308 A radiation pattern shows only the relative values but not the absolute values of the field or power quantity. Hence the values are usually normalized (i.e., divided) by the maximum value. Hon Tat Hui Antenna Fundamentals 11NUS/ECE EE5308 Hon Tat Hui Antenna Fundamentals 12NUS/ECE EE5308 For example, the radiation pattern of the Hertzian dipole can be plotted using the following steps. (1) Far field: 0   jkr kId e  Ej sinθ, 0 2  θ  4 r   r fixed  (2) Far field magnitude: 0  kId  E sinθ , 0 2  θ 4 r  r fixed  Hon Tat Hui Antenna Fundamentals 13NUS/ECE EE5308 (3) Normalization: kId 0  sinθ  4 r E sinθ , 0 2  θ n kId  r fixed  4 r (4) Plot –plane pattern (fix  at a chosen value, for example  = 0°) E with  at = 0° & 180°  n Hon Tat Hui Antenna Fundamentals 14NUS/ECE EE5308 (5) Plot –plane pattern (fix  at a chosen value, for example  = 90°) E with  at = 90°  n See animation “Field Behaviour and Radiation Pattern” Hon Tat Hui Antenna Fundamentals 15NUS/ECE EE5308 2.5 Polarization The polarization of an antenna in a given direction is defined as the polarization of the plane wave transmitted by the antenna in that direction. The polarization of a plane wave is the figure the tip of the instantaneous electric-field vector E traces out with time at a fixed observation point. There are three types of typical antenna polarizations: the linear, circular, and elliptical polarizations, corresponding to the same three types of typical plane wave polarizations. Hon Tat Hui Antenna Fundamentals 16NUS/ECE EE5308 E E E y y y E E E x x x Eectric-field vector Eectric-field vector Eectric-field vector Linearly polarized Circularly polarized Elliptically polarized See animation “Polarization of a Plane Wave - 2D View” See animation “Polarization of a Plane Wave - 3D View” Hon Tat Hui Antenna Fundamentals 17NUS/ECE EE5308 2.5.1 Polarization of Plane Waves (a) Linear polarization A plane wave is linearly polarized at a fixed observation point if the tip of the electric-field vector at that point moves along the same straight line at every instant of time. (b) Circular Polarization A plane wave is circularly polarized at a a fixed observation point if the tip of the electric-field vector at that point traces out a circle as a function of time. Hon Tat Hui Antenna Fundamentals 18NUS/ECE EE5308 Circular polarization can be either right-handed or left-handed corresponding to the electric-field vector rotating clockwise (right-handed) or anti- clockwise (left-handed). (c) Elliptical Polarization A plane wave is elliptically polarized at a a fixed observation point if the tip of the electric-field vector at that point traces out an ellipse as a function of time. Elliptically polarization can be either right-handed or left-handed corresponding to the electric-field vector rotating clockwise (right-handed) or anti-clockwise (left-handed). Hon Tat Hui Antenna Fundamentals 19NUS/ECE EE5308 E and E are x0 y0 For example, consider a plane wave: both real numbers  jkz E E e ˆ ˆ E xE yE x x0 x y  jkz  jkz jkz E jE e ˆ ˆ  xE e yjE e y y0 x0 y0 Note that the phase difference between E and E is 90º. x y The instantaneous expression for E is: j t jkz j t jkz  ˆ ˆ E z,t RexE e yjE e x0 y0 ˆ ˆ  xE cost kz yE sint kz x0 y0 Let: X E =c E os tkz , YEE sin tk z  xx00 y y Hon Tat Hui Antenna Fundamentals 20