Radar Equation for point Target 雷達氣象學講義-台大周 …

1、Chapter 3:Principle of Radar Observation雷達系統與觀測原理Radar system: Transmitter, Receiver, Antenna, and Display of dataScattering theory, Mie scatteringThe stabilized local oscillator (STALO) generates a continuous wave (cw) signal of nearly perfect sinusoid form (coherent signal ) which is modulated (pu

2、lse on and off 脈衝觸發器 ) and amplified by a klystron to produce intense microwave power.Klystron (調速管) amplifier is phase coherent and Magnetron (磁控管) amplifier is phase incoherent oscillator. Radar pulses are phase coherent from pulse to pulse if the phase angle for each pulse is fixed.MOPA: master o

3、scillator and power amplifier: TransmitterBlock diagram of a coherent pulse radarThe choice of the transmitted frequency f0 results from a compromise, taking into account the conditions of propagation in the atmosphere and the technological requirements involved in implementing the equipment. The em

4、itted wave: S(t) = At cos0tThe received signal: Pr(t) = a cos (0t + t) , t= 2(2r/)(PRF)Transmitted frequencyW-band, 90-100GHz, 0.33-0.3 cm, for example: a 94GHz cloud radar, 3.2mm wavelength, by Lhermitte (1987)K-band, 18-26.5GHz, 1.6-1.13 cm (H2O absorption band 22.3GHZ sits in the center, thus was

5、 abolished, then use above and under K bands), Ka-band, 26.5-40GHz, 1.13-0.75 cm (US air force for cloud observations) , Ku-band, 12.5-18GHz, 2.4-1.6 cmX-band, 8-12.5GHz, 3.7-2.4 cm (installed on board B-17 bomber) after WW2 donated to meteorological institutions in the world (wavelength 3.2cm, APQ1

6、3 and APS15)C-band, 4-8GHz, 7.5-3.7 cm S-band, 2-4GHz, 15-10 cmL-band, 1-2GHz, 30-15 cmUHF, 0.3-1 GHz, 1 to 0.3 m (clear air backscattering motion)VHF, 0.1-0.3GHz, 3 to 1 mBlock diagram of a coherent pulse radarI (t) = A0 cos (d t)Q (t) = A0 sin (d t)Or E (t) = A0 exp id tFor the pulse n, En = A0 ex

7、p i r,n with r = tan-1Q/IFor two samples n and n-1 corresponding to two successive pulses, we haver/t = r,n - r,n-1/ PRT = d (PRF)The electron gun produces a flow of electrons.The bunching cavities regulate the speed of the electrons so that they arrive in bunches at the output cavity. The bunches o

8、f electrons excite microwaves in the output cavity of the klystron. The microwaves flow into the waveguide, which transports them to the accelerator. The electrons are absorbed in the beam stop. In a klystronKlystron gallery in Stanford U.Stanford University-Klystron galleryIn a magnetronThe nucleus

9、 of the high-voltage system is the magnetron tube . The magnetron is a diode-type electron tube which is used to produce the required 2450 MHz of microwave energy. It is classed as a diode because it has no grid as does an ordinary electron tube. A magnetic field imposed on the space between the ano

10、de (plate) and the cathode serves as the grid. While the external configurations of different magnetrons will vary, the basic internal structures are the same. These include the anode, the filament/cathode, the antenna, and the magnetsSolid state transmitterSolid State FM Exiter/Amplifier/Transimitt

11、ers from 500 w to 20 kw Tube(Zero Bias triode) type, long life economical FM Transmitter from 1 kw to 32.5 kw STL systems (Composite Studio Transmitter Links) Solid State AM Transimitter from 250 watts to100 kw Spectral purity: the absence of power at frequencies other than the intended ones. 發射訊號頻率

12、純度對地面雜波去除以及大範圍強回波區內偵測弱回波訊號龍捲都非常重要。Ground clutter cancellation: suppressing echoes from stationary objects on the ground.Microwave pulsesPulse repetition time (frequency): PRT (PRF) Ts (fs)Pulse duration (pulse width) 1 s (defined as the time between instances when the power is one-quarter of the pea

13、k).Listening period: Ts- , receiving signal, Power density of an idealized pulse S(r, , ) U(t-r/c) ，where U(t-r/c) = 1, r/c t (r/c+ ) and U(t-r/c) = 0, otherwise. Antenna 天線天線由輻射器 (radiator) 與反射器 (reflector) 組合而成輻射器是由波導管 (wave-guide) 以及波導管擴展而成之喇叭口 (horn feed) 組合而成經放大之高能微波脈衝經由波導管引至喇叭口放射至反射器上反射器為一拋物面之

14、圓形天線, 喇叭口位於此反射器之焦點上, 產生窄波束之波鋒Antenna There are several critical parameters that affect an antennas performance and can be adjusted during the design process. These are resonant frequency, impedance, gain, aperture or radiation pattern, polarization, efficiency and bandwidth. Transmit antennas may al

15、so have a maximum power rating, and receive antennas differ in their noise rejection properties.Resonant frequencyThe resonant frequency is related to the electrical length of the antenna. This is usually the physical length of the wire multiplied by the ratio of the speed of wave propagation in the

16、 wire. Typically an antenna is tuned for a specific frequency, and is effective for a range of frequencies usually centered on that resonant frequency. Impedance and SWRImpedance is similar to refractive index in optics. As the electric wave travels through the different parts of the antenna system

17、(radio, feed line, antenna, free space) it may encounter differences in impedance. At each interface, some fraction of the waves energy will reflect back to the source, forming a standing wave in the feed line. The ratio of maximum power to minimum power in the wave can be measured and is called the

18、 standing wave ratio (SWR). A SWR of 1:1 is ideal. A SWR of 1.5:1 is considered to be marginally acceptable in low power applications where power loss is more critical, although an SWR as high as 6:1 may still be usable with the right equipment. Minimizing impedance differences at each interface (im

19、pedance matching) will reduce SWR and maximize power transfer through each part of the antenna system.Antenna gain: dBi or dBd. It is important to note that antenna gain is different than amplifier gain. Antennas do not have a power source that allows the antenna to create additional energy to boost

20、 the signal. An antenna is similar to a reflective lens in principle - it takes the energy available from the source and focuses it over a wider or narrower area. Antenna gain is then a measure of the amount of focus that an antenna can apply to the incoming signal relative to one of two reference d

21、ispersion patterns. MaxStream specifies all antenna gains in dBi.dBi is the amount of focus applied by an antenna with respect to an Isotropic Radiator (a dispersion pattern that radiates the energy equally in all directions onto an imaginary sphere surrounding a point source). Thus an antenna with

22、2.1 dBi of gain focuses the energy so that some areas on an imaginary sphere surrounding the antenna will have 2.1 dB more signal strength than the strength of the strongest spot on the sphere around an Isotropic Radiator.dBd refers to the antenna gain with respect to a reference dipole antenna. A r

23、eference dipole antenna is defined to have 2.15 dBi of gain. So converting between dBi and dBd is as simple as adding or subtracting 2.15 according to these formulas:dBi = dBd + 2.15 dBd = dBi - 2.15Specifying antenna gain in dBd means that the antenna in question has the ability to focus the energy

24、 x dB more than a dipole.Isotropic and dipole antennaThe isotropic radiator is a purely theoretical antenna that radiates equally in all directions. It is considered to be a point in space with no dimensions and no mass. This antenna cannot physically exist, but is useful as a theoretical model for

25、comparison with all other antennas. Most antennas gains are measured with reference to an isotropic radiator, and are rated in dBi (decibels with respect to an isotropic radiator). The dipole antenna is simply two wires pointed in opposite directions arranged either horizontally or vertically, with

26、one end of each wire connected to the radio and the other end hanging free in space. Since this is the simplest practical antenna, it is also used as reference model for other antennas; gain with respect to a dipole is labeled as dBd. Generally, the dipole is considered to be omnidirectional in the

27、plane perpendicular to the axis of the antenna, but it has deep nulls in the directions of the axis. Variations of the dipole include the folded dipole, the half wave antenna, the groundplane antenna, the whip, and the J-pole. Beam WidthBecause higher gain antennas achieve the extra power by focusin

28、g in on a smaller area it is important to remember that the greater the gain, the smaller the area covered as measured in degrees of beam width (think of an adjustable beam flashlight). In many cases a high gain antenna is a detriment to the system performance because the system needs to have recept

29、ion over a large area.Dipole antenna radiation patternIsotropic antenna (dBi), half -wavelength dipole antenna (actually no gain antenna, dBd), omni vs directional antenna, parabolic antenna The vast majority of antennas are simple vertical rods a quarter of a wavelength long. Such antennas are simp

30、le in construction, usually inexpensive, and both radiate in and receive from all horizontal directions (omnidirectional). One limitation of this antenna is that it does not radiate or receive in the direction in which the rod points. This region is called the antenna blind cone or null.Aperture is

31、the shape of the beam cross section in the direction of highest gain, and is two-dimensional. (Sometimes aperture is expressed as the radius of the circle that approximates this cross section or the angle of the cone.) and radiation patternBandwidth and polarizationThe bandwidth of an antenna is the

32、 range of frequencies over which it is effective, usually centered around the resonant frequency. The bandwidth of an antenna may be increased by several techniques, including using thicker wires, replacing wires with cages to simulate a thicker wire, tapering antenna components (like in a feed horn

33、), and combining multiple antennas into a single assembly and allowing the natural impedance to select the correct antenna. Small antennas are usually preferred for convenience, but there is a fundamental limit relating bandwidth, size and efficiency.The polarization of an antenna or orientation of

34、the radio wave is determined by the electric field or E-plane. The ionosphere changes the polarization of signals unpredictably, so for signals which will be reflected by the ionosphere, polarization is not crucial. However, for line-of-sight communications, it can make a tremendous difference in si

35、gnal quality to have the transmitter and receiver using the same polarization. Polarizations commonly considered are linear, such as vertical and horizontal, and circular, which is divided into right-hand and left-hand circular.Antenna efficiencyEfficiencyEfficiency is the ratio of power actually ra

36、diated to the power put into the antenna terminals. A dummy load may have a SWR of 1:1 but an efficiency of 0, as it absorbs all power and radiates heat but not RF energy, showing that SWR alone is not an effective measure of an antennas efficiency. Radiation in an antenna is caused by radiation res

37、istance which can only be measured as part of total resistance including loss resistance. Loss resistance usually results in heat generation rather than radiation, and therefore, reduces efficency.Overview of antenna parametersOf the parameters above, SWR is most easily measured. Impedance can be me

38、asured with specialized equipment, as it relates to the complex SWR. Measuring radiation pattern requires a sophisticated setup including significant clear space (enough to get into the antennas far field) or an anechoic chamber designed for antenna measurements, careful study of experiment geometry

39、, and specialised measurement equipment that rotates the antenna during the measurements. Bandwidth depends on the overall effectiveness of the antenna, so all of these parameters must be understood to understand bandwidth. However, typically bandwidth is measured by only looking at SWR, i.e., by fi

40、nding the frequency range over which the SWR is less than a given value. Bandwidth over which an antenna exhibits a particular radiation pattern might also be considered.Transmission and receptionAll of these parameters are expressed in terms of a transmission antenna, but are identically applicable

41、 to a receiving antenna, due to reciprocity. Impedance, however, is not applied in an obvious way; for impedance, the impedance at the load (where the power is consumed) is most critical. For a transmitting antenna, this is the antenna itself. For a receiving antenna, this is at the (radio) receiver

42、 rather than at the antenna.Antennas used for transmission have a maximum power rating, beyond which heating, arcing or sparking may occur in the components, which may cause them to be damaged or destroyed. Raising this maximum power rating usually requires larger and heavier components, which may r

43、equire larger and heavier supporting structures. Of course, this is only a concern for transmitting antennas; the power received by an antenna rarely exceeds the microwatt range.Antennas designed specificially for reception might be optimized for noise rejection capabilities. This can be done by sel

44、ecting a narrow bandwidth so that noise from other frequencies is rejected, or selecting a specific radiation pattern to reject noise from a specific direction, or by selecting a polarization different from the noise polarization, or by selecting an antenna that favors either the electric or magneti

45、c field.For instance, an antenna to be used for reception of low frequencies (below about ten megahertz) will be subject to both man made noise from motors and other machinery, and from natural sources such as lightning. Successfully rejecting these forms of noise is an important antenna feature. A

46、small coil of wire with many turns is more able to reject such noise than a vertical antenna. However, the vertical will radiate much more effectively on transmit, where extraneous signals are not a concern.Parabolic antennaRadar scan modeElevation angleeAzimuth angleRange rHorizontal distance dHeig

47、ht hZenith zVarious typical antenna reflectors and associated beamsMost weather radars use symmetrical beams with widths of 1 to 3 degrees.Narrow vertical and wider horizontal beams is used to measure heights and vertical dimensions of small targets.Search radar for detecting aircraft generally use

48、wide vertical beams.The precision of the measurements of azimuthal and elevation angles to a target is largely a function of the shape of the beam produced by the antenna.The shape of the beam is governed by the shape and size of the antenna reflector and the wavelength of the radar set. Reflector a

49、nd horn feed3-dB beam width當脈衝離開天線以天線直徑大小平行電磁波束行進。由於繞射緣故，此一平行電磁波束在到達第一個繞射零點 (距離為 r = Da2/ )後開始發散成圓錐狀。雷達波束的束寬( beam width )定義為能流密度不小於最大值的一半之波束寬，或稱之為3-dB束寬。由於雷達天線發射出之雷達束的能流密度可以 S(r, , )表示。天線無法將能量完全集中在一個窄束中，因此脈衝能流密度分佈呈現主瓣 (main lobe) 和幾個副瓣 (side lobe) 現象。現有一般雷達設計，副瓣的能流密度沒有大於主瓣百分之一的。事實上，所有副瓣能流密度的總和僅佔主瓣的

50、百分之幾而已。 天線-反射器經常成拋物圓形, 能流密度(輻射強度)與離束軸(beam axis)距離 () 成 1-4(/Da)2 2的關係。在此情形下, 常態化能流密度形狀(或稱為輻射形狀函數radiation pattern)與偏角的關係可寫成： 2() = S()/S(0) = 8J2(Dasin)/ / (Dasin)/22 其中為離束軸之偏角大小, 為雷達發射電磁波波長, Da為天線直徑, J2 是Bessel function of second order。 雷達發射之微波脈衝可視為厚度為c (脈衝寬) 的球形殼以光速往外傳播並擴張。因此, 在一封閉球體內所發射之脈衝能量Pt)為

51、常數, 但是散射物所接收到的能流密度大小與距離平方成反比。此外由於天線本身,傳輸線,天線罩等造成的電磁波能量減損, 進入天線之脈衝能量 Pt 要大於實際發射出的 Pt 。Antenna beam patternBeam pattern 束形天線(雷達發射之微波脈衝)束形, 脈衝之主瓣以及多個副瓣清楚可見。Beam patternWith a parabolic reflector and Gaussian illumination(氣象常用) Width of the beam at 3 dB, 1/2 = 70 / DaWidth of the main lobe (between null

52、s) null = 170 / DaLevel of first side lobe: -23dB below the value on the axis天線增益 Antenna GainThe maximum directional gain of the antenna gt Sp / Pt/4r2 Pt is difficult to measure, so usually Pt (the power delivered to the antennas input port)is measured. Sp is the peak power and measured at distanc

53、e far ( r 2Da2/) from the antenna.Thus, the computed gain gt accounts for losses of energy associated with the antenna system (radome and waveguide).The incident radiation power density at range r without considering attenuation is given by Si(, ) = Pt gt 2(, ) / 4r22(, ) is the normalized i. e., (,

54、 ) = 1 at 0, 0 power gain pattern and gt is the antenna power gain along the beam axis.Signal processor (receiver)Separating clutter signal and weather signal: an exampleThe (back) -scattering cross section (反) 散射截面The cross section of a scatterer (hydrometeor) is an apparent area that intercepts a

55、power Si which, if radiated isotropically, produces at the receiver a power density Sr = Si /4r2 equal to that scattered by the actual hydrometeor.注意: 目標物的散射截面並不等於目標物的幾何截面The backscattering cross section b of a spherical water drop of diameter D small compared to (I.e., Rayleigh scattering or small

56、drop scattering approximation, D /16) is well approximated by b ( 5/4 )Km2 D6，Where Km = (m2-1)/(m2+2) and m = n-jn is the complex refractive index of water, n is refractive index, is the attenuation index. Some authors define the absorption coefficient k = n.The scattering phase function P()= (2 /8

57、2) ( D/)6Km2 (1+cos2)Fois the angle between the incident beam and the scattered beam. Mie and Rayleigh Scattering 米散射和雷利散射Complex refractive index: ice and water = 10 cm and longer,For water, n = 9 (independent of T), k = 0.63 1.47 for 200For ice, n = 1.78 (also independent of T), k = 2.4x10-35.5x10

58、-4 for 0-20 For water drops, Km2 = 0.910.93, =1-10cm, indep. of TFor ice spheres, Km2 = 018, =0.917gcm-3, indep. of T and Note, when D , b / D2/4 = (m-1)2/(m+1)2 If D b (ice) = 0.20 b (water) (-6.989dB)If D b (ice) = 0.12 b (water) (-9.2dB)米散射 Mie scattering懸浮粒子散射的相函數型態, 硫酸氨粒子, 相對溼度80%, 入射電磁波 (由圖左方)

59、 波長為550nm.University of North Dakota radarThe radar is a modified Enterprise Electronics Corporation C-band (5cm wavelength) Doppler radar. In June 1989, a new Sigmet Model PPP-02 pulse-pair signal processor was added to the system, replacing the older Doppler signal processor. The pulse-pair proces

60、sor provides high quality reflectivity, Doppler radial velocity, and velocity spectrum-width measurements at as many as 1024 range gates. The system is capable of recording these data digitally as wel l as displaying them in real-time on a number of color displays. The radar electronics and computer