Chapter 5. Polarization 第五章 極化 亞洲大學 資訊工程學系碩士班 呂克明教授 二○○六年十月十六日 11/20/2018

Chapter 5. Polarization (第五章極化) Introduction (緒言) Antenna Polarization (天線極化角) Polarization of Satellite Signals (衛星訊號的極化) Cross-Polarization Discrimination (交叉極化的區隔) Depolarization (去極化) Homework problems (習題) 11/20/2018

Introduction (緒言) In the far field zone of a transmitting antenna, the radiated wave takes on the characteristics of a transverse electromagnetic wave (TEM, 橫向電磁波). Far field zone: At distances greater than 2*D^2/ λ from the antenna, where D is the larger linear dimension of the antenna and λ is the wavelength. For a parabolic antenna of 3 m diameter transmitting a 6 GHz wave (λ = 5 cm), the far field zone begins at approximately 360 m. Transverse electromagnetic wave (TEM): Both the magnetic field H and the electric field E are transverse to the direction of propagation. TEM wave is a plane at great distance from the transmitting antenna. 11/20/2018

Introduction (緒言)(continued) The direction of the line traced out by the tip of the electric field vector determine the polarization of the wave. Electric and magnetic fields are varying as functions of time. The magnetic field varies exactly in phase with the electric field, and its amplitude is proportional to the electric field in this discussion. Polarization: Linear, elliptical, and circular polarization (線性極化,橢圓極化,與圓形極化). Linear polarization: The tip of the E vector may be trace out a straight line, in which case the polarization is referred to as linear. Vertical polarization: the electric field was perpendicular to the earth’s surface or parallel to the earth’s polar axis. Horizontal polarization: the electric field was parallel to the earth’s surface. 11/20/2018

Introduction (緒言)(continued) Circular Polarization (圓形極化): The tip of the resultant electric field vector traces out a circle and resultant wave is said to be circularly polarized. Right-hand circular polarization (右旋圓形極化): The IEEE defines right-hand circular polarization (RHC) as a rotation in the clockwise direction when viewed from behind. Left-hand circular polarization (左旋圓形極化): The IEEE defines left-hand circular polarization (LHC) as a rotation in the counterclockwise direction when viewed from behind. IEEE definitions versus Classical optics definitions: they are just opposite. The IEEE definition will be used throughout this text. 11/20/2018

Antenna Polarization (天線極化角) Transmitting antenna polarization: A horizontal dipole would produce a horizontally polarized wave. Two dipoles mounted close together symmetrically and at right angles to each other would produce a circularly polarized wave if fed current equal in magnitude but differing in phase by 90 degree. Receiving antenna polarization: The polarization of a receiving antenna has to be aligned to that of the wave for maximum power transfer. A single dipole will always receive a signal from a circularly wave, but at a loss of 3 dB. This is so because the single dipole will respond only to one of the linear components, and hence the received power will be half that of the cross dipoles. 11/20/2018

Polarization of Satellite Signals (衛星訊號的極化) Satellite linear polarization (衛星線性極化): The horizontal polarization (水平極化) is where the electric field vector is parallel to the equatorial plane (赤道面), The vertical polarization (垂直極化) is where the electric field vector is parallel to the earth’s polar axis (地極軸面). 11/20/2018

Cross-Polarization Discrimination (交叉極化的區隔) The propagation path between a satellite and earth station passes through the ionosphere, and possibly through layers of ice crystals in the upper atmosphere and rain, all of which are capable of altering the polarization of the wave being transmitted. Depolarization: An orthogonal component may be generated from the transmitted polarization, an effect referred to as depolarization. This can cause interference where orthogonal polarization is used to provided isolation between signals, as in the case of frequency reuse (頻率重複使用). 11/20/2018

Cross-Polarization Discrimination (交叉極化的區隔)(continued) Two measures are in use to quantify the effects of polarization interference: Cross-Polarization Discrimination (交叉極化區隔度): The most widely used measure is called Cross-Polarization Discrimination (XPD). Co-polar component of E1 = E11 and cross-polar component of E1 = E12 XPD = 20 log (E11/E12) Polarization Isolation (極化隔離度): The second measure is polarization isolation (I) that is defined by the ratio of received co-polar power to received cross-polar power and thus takes into account any additional depolarization introduced by the receiving system. Co-polar component of E2 = E22 and cross-polar component of E2 = E21 I = 20 log (E11/E21) When the transmitted signals have the same magnitudes and where the receiving system introduces negligible depolarization, then I and XPD give identical results. 11/20/2018

Depolarization (去極化) Ionospheric Depolarization (電離層之去極化): One of the effects of the ionoshpere is to produce a rotation of the polarization of a signal, an effect known as Faraday rotation. (法拉第旋轉, Michael Faraday, 1791-1867, 英國物理學家,化學家) Faraday rotation is inversely proportional to frequency squared (跟頻率的平方成反比) and is not considered to be a serious problem for frequency above about 10 GHz. Maximum values for Faraday rotation are 9 degree at 4 GHz and 4 degree at 6 GHz. In order to counter the depolarizing effects of Faraday rotation, circular polarization may be used. When a linear polarization is used, a 15 dB amount added to the XPD, where is only 0.13 dB as with circular polarization. 11/20/2018

Depolarization (去極化) (continued) Rain Depolarization (雨滴之去極化): The shape of small raindrops is close to spherical, but large drops are better modeled as oblate spheroids (扁圓球體). There will be a difference therefore in the attenuation, termed differential attenuation (衰減損耗差), and phase shift, termed differential phase shift. (相位偏移差) Ice Depolarization (冰之去極化): Value of 2 dB added to the XPD are suggested for North America and 4 to 5 dB for maritime regions. 11/20/2018

Homework Problems (習題) 5.1 Explain what is meant by a plane TEM wave. 5.15 Explain what is meant by vertical polarization of a satellite signal. 5.16 Explain what is meant by horizontal polarization of a satellite signal. 5.19 Explain what is meant by cross-polarization discrimination. 5.20 Explain the difference between cross-polarization discrimination and polarization isolation. 5.22 Why is Faraday rotation of no concern with circular polarized wave? 5.23 Explain how depolarization is caused by rain. 11/20/2018