Chapter 6 Radar Antenna
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1 Chapter 6 Radar Antenna Basic Antenna Theory With the uniform amp. and phase array you will approximate sinx x sin N 2 x sin 1 2 x (discrete) (Continuous) 6-1
2 Antenna Pattern Regions Near-Field (Reactive): Fields are predominantly reactive Inter-mediate Region (Fresnel): Radiated near field angular dependence is a function of distance from the antenna (i.e., things are still changing rapidly) g r Far-Field (Fraunhofer): Radiated far field angular dependence is independent of distance R the region of interest 0.62 D 2 D 0 /2 2D 2 / reactive Near Field radiated Near Field Radiated far Field 6-2 Far-Field Approach (a) R 2 + D 2 4 D 2 D (b) R Point target 0 /2 2D 2 / reactive Near Field radiated Near Field Case: Receiving signal from point target Assume the point target radiates field e jkr R Radiated far Field The phase difference between points (a) and (b) due to signal from point target is k r 2 D r = PB PA = -----, where wave number 2 k = Assumption: r» D. 16 Using D r = r1 + D 2 8r 2 r 1 D 2 8r 2 + r = D 2 8r 2 = 16 r = 2D 2 4r
3 Point Target Approach D d 0 /2 2D 2 / reactive Near Field radiated Near Field Radiated far Field Case: Transmitting with antenna that has constant phase across aperture if we assume beam-width BW = 0.5 D. Usually BW --. L At the criteria r = 2D 2, d rbw 2D 2 = = , or D = D We select BW = 2 D, d = 4D. If the target is sufficiently small with respect to spot size d then the wave incident on the target is approximately uniform in phase and amplitude 6-4 Primary Parameters Gain, Beamwidth, Sidelobe level: These three are interdependent A number of source aperture distribution have been developed so as to optimize with respect to one or more of these parameters Uniform aperture produces the narrowest mainlobe obtainable with linear or constant phase across the aperture but at the expense of sidelobe levels (~ 13 db first sidelobe) For he Dolph Chebychev distribution, the optimum pattern is defined as the one that produce the narrowest beamwidth between first nulls (on each of main lobe) with no sidelobe higher than a stipulated level. -3 db major lobe 3 db beamwidth sidelobe (minor lobe) null back lobe 6-5
4 Rectangular Aperture (Uniform) Rectangular Aperture Antenna Pattern 6-6 Circular Aperture (Uniform) Circular Aperture Antenna Pattern 6-7
5 E-Plane v.s. H-Plane Rectangular Aperture Circular Aperture 6-8 Some Common RF Decibel Units Only one number is needed if the other is a known, standard value: dbm = db referred to 1 mw dbw = db referred to 1 W dbm = 10log P mw dbw = 10log P W dbi = db referred to an isotropic source dbd = db referred to a dipole = dbi db 6-9
6 Free-space Path Loss frequency f or wavelength P t G1 G2 distance d P r antenna 1 antenna 2 Path Gain gain P r G P 1 G t 4d 2 G 1 G c 2 = = = = 2 Path Loss = 1 / (P r /P t ) 4df G 1 G d 110 f 1 for d in km, f in MHz loss(db) = log d + 20 log f G 1 db G 2 db 6-10 Antenna Gain P o = power accepted by antenna P r = power radiated by antenna = radiation efficiency = P r P o P r = 2 0 sin 0 d d = Radiation intensity P o P r G D avg = P r 4 = average radiation intensity D = = : Directivityrelative avg P r 4 to isotropic antenna G = D = : Gain P o 4 P R R = = = G P o R 2 4R
7 Antenna Aperture A e = G : Effective Area 4 a A = ---- e : Antenna efficiency A A: Physical area of antenna s aperture A e : the peak or maximum value of A e Half-power beamwidth BW of an antenna is related to the beamwidth constant BW = BW = 2sin L --- L (Linear aperture) 2sin L --- D (Circular aperture) 4A G = a = a G o : Peak gain of antenna G o a 2 2 = A : Standard directivity = i : product of several factors i : aperture illumination efficiency, which reduce the gain of antenna. Loss in gain resulting from tapering the aperture distribution to produce sidelobs lower than those achievable from a uniform illumination 6-12 Beamwidth Const. v.s. Sidelobe Line Aperture Circular Aperture 6-13
8 Aperture Efficiency v.s. Sidelobe Line Aperture Circular Aperture 6-14 Gain Loss v.s. Sidelobe cos n aperture Gain loss: a feed in front of a reflector -> Blockage Line source of length L L b : centrally located blockage of length L b Loss (Line) > Loss (circular) Line Aperture Circular Aperture 6-15
9 Antenna Types Continuous Aperture Horn: good for short range Reflector - Gregorian (center feed) - Splash Plate - Parabolic Cylinder - Cassgrain - Offset feed Lens Discrete (Antenna Array) Diploes Waveguide Slots 6-16 Antenna Types and Parameters Narrow beams (at least in one plane) and relatively low sidelobe levels are required. types - Mechanical movement - Electromechanical and electrical scanning feed mechanism - Electrically scanning an array - Design specifications, cost, risk trade-offs 6-17
10 Linear Antenna a 2 E A xe j2x sin = dx a 2 A x: current, uniformly distributed a 2 E e j2x sin = dx a 2 e j2x sin a a sin sin a 2 = j sin = A o a sin a -- 2 Z A x a -- 2 E x xsin E E = A : Gain of the antenna = 0 o G = A 2 : Power Gain of the antenna = 0 o 6-18 Pattern of a Dipole Antenna E-Plane pattern: magnitude of the normalized field strength versusfor a constant. E-Plane pattern: magnitude of the normalized field strength versusfor a constant. E j Idl e = jr 4 R o sin H j Idl e jr = R sin E = 0 E R 0 H = 0 H R
11 Phased-Array Antenna (Applications) 愛國者飛彈射控雷達 神盾雷達系統 6-20 Phased-Array Antenna Features Ability to steer a beam without moving a large mechanical structure Multibeam High Cost and Complexity 6-21
12 General Phased-Array - Beam Steering Broadside Array Linear Array Factor beam direction equiphase wave front Peak Gain Bandwidth Sidelobes Beamwidth -> Scanning Angle Grating lobs radiators phase shifters Wavelength Space feed network Scanning Angle input 6-22 Phased-Array Antenna Pattern (No Scan) Case 1: d = 2 No scan No grating N up BW down N = constant,up L up BW Down 6-23
13 Phased-Array Antenna Pattern (No Scan) Case 2: d = No scan Grating at 0 = 90 and 0 = Phased-Array Antenna Pattern (Scan) Case 1: d = 2 No grating for scanning angle As 63 0 or 63 0, Grating lobe happens at 0 = 90 or 0 = 90 The greater Scanning angle. the greater beamwidth 6-25
14 Phased-Array Antenna Pattern (Scan) Case 2: d = Grating lobes anywhere 6-26 Phased-Array Antenna Pattern (Scan) Case 3: Scanning angle , No grating lobe happens d0.54 As 60 0 or 60 0, Grating lobe happens at 0 = 90 or 0 =
15 Phased-Array Pattern (Calculation) Far Field case: Difference in phase of the signals in adjacent elements is = d sin = d sin One can show that for an array of sources each with pattern f. The pattern for the array is g = f AF, where f = e jkr : isotropic, AF: Array Factor Simple uniform amp. and phase array: AF = 1 + e jkd sin + e j2 kd sin + + e jn 1kd sin = e j n 1 N n = 1 kd sin AF e jkd sin 1 = e jn kd sin 1, where : the progressive phase shift bet. elements AF e j N 12 kd sin sinn 2 kd sin = , We define = kdsin sin1 2 kd sin sin N 2 N 2 cos N 2 1 sin N 2 AF = lim AF = = N AF sin cos 1 2 n = N sin normalized 6-28 Phased-Array Antenna (Grating) = kdsin = kd sin o, k = 2 = 2d sin sin o AF 1 sin N 2 n = N sin sinnd sin sin o AF n = N sind sin sin Gain due to array factor (AF) Gain AF n AF n AF 2 1 n sin2 Nd sin sin o = = = N 2 sin 2 d sin sin For a broadside array, o = 0, and then Gain sin2 Nd sin = It is important N 2 sin to space 2 d the sin elements sufficiently close to avoid grating lobes that are caused by the periodic nature of the structure o The pattern has maxima whenever sin= n d, n= 0, 1,2...: Mainbeam grating lobes. d sin = n For d =, Grating lobes at = 90. Beam is scanned. Grating lobes atd sin sin o = n o Man beam o Grating lobes 6-29
16 Other Aspects of Phased-Array o up BW up: as the array is scanned, the half-power beamwidth increases tn plane of scan The beamwidth is approximately inversely proportional to cos, where : scan angle o measured from the normal to the array B B 0 o = : BW in thedirection at scan cos o angle o. B 0 : Beamwidth at broadside. For small scan angle o, B 0 = in radians Ndcos o The peak gain for typical illumination function may be approximated by G0 0 = B 0 B 0 B 0, B 0 in degree B 0, B 0 down G0 0 up o B o broadside B 0 B 0 o B 0 G ARRAY ANTENNA PATTERNS (Spacing =/2) (in rectangular coordinates) 1 1 Normalized Magnitude N = 4 Normalized Magnitude N = /2 1 2/ /2 1 2/3 2 Angle of Radiation Angle of Radiation 6-31
17 Parabolic Reflector Antenna (Applic.) 6-32 Parabolic Reflector Antenna Design rules Sidelobe level: Select side level (Distribution) Beamwidth constant: Select beamwidth constant via consideration of Fig (circular aperture BW v.s. sidelobe level) Aperture Efficiency: Select aperture efficiency via consideration of Fig (aperture efficiency v.s. sidelobe) Gain: Find G = a G o. Assume a is dominant efficiency consideration Beamwidth: Find BW --- D using beamwidth constant Weighting Distribution: A complex analysis to design feed with a proper weighting based on - Edge Taper - Beamwidth of feeder - Space Attenuation Scanning Techniques Scan entire antenna Scan feed within reflector 6-33
18 Weighting Design rules Parabolic Reflector Antenna Design(1) Sidelobe level: Select H-plane edge taper from Fig necessary to obtain desired sidelobe level. (Edge taper is determined by beamwidth of feeder and space attenuation) Space attenuation: Given f/d, find intercepted angle from Fig In order to determine space attenuation Parabolic Reflector Antenna Design (2) Using Fig to find space attenuations Fig to determine 10dB beamwidth of feed horn BW 10dB = 2 10dB, given intercepted angle. Use BW 10dB = 88 B (degree), B 2.5 for E-plane, BW 10dB = A (degree), A 3 for H-plane - BW 10dB : pattern width in degrees at -10dB level. B: E-plane horn aperture A: H-plane horn aperture A B E H 6-35
19 An Example Design the feed horn for an antenna with f/d = 0.7 using the technique describe above. It is required that the edge illumination should be 20dB down. Assume a wavelength of 3cm. f D = 0.7 total feed angle = 80 o, = 40 space attenuation 1dB. G h = 40 = 20 1 = 19dB 10dB 1.4, = 40 10dB = 29 BW 10dB = 58, E-plane, BW 10dB = 88 B B = = 4.55cm B, = H-plane, BW 10dB = A A = = 8.78cm A, = From Fig. 6-11, first sidelobe = -40dB = 71 BW --- D for Taylor distribution From Fig. 6-11, first sidelobe = -40dB a = 1.1dB, G = a db + G o db. E H B Feeder Horn -10B edge taper A 58 o 6-36
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