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Radar System Design
Chapter 6Radar Antenna
6 - 1Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Basic Antenna Theory
xsinx
------------
N 2 x sin1 2 x sin
---------------------------------
With the uniform amp. andphase array you willapproximate
(Continuous)
(discrete)
6 - 2Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Antenna Pattern Regions•Near-Field (Reactive): Fields are predominantly reactive
• Inter-mediate Region (Fresnel): Radiated near field angulardependence is a function of distance from the antenna (i.e., thingsare still changing rapidly)
•Far-Field (Fraunhofer): Radiated far field angular dependence isindependent of distance R the region of interest
g r
0 /2 2D 2 /
D
reactive radiatedNear Field Radiated far Field
Near Field
0 /2 2D 2 /
D
reactive radiatedNear Field Radiated far Field
Near Field
0.62 D 2
6 - 3Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Far-Field Approach
0 /2 2D2/
D
reactive radiatedNear Field Radiated far Field
Near Field
0 /2 2D2/
D
reactive radiatedNear Field Radiated far Field
Near Field
R
R 2 D 2 4+
D 2
Pointtarget
Case: Receiving signal from point target
•Assume the point target radiates field
•The phase difference between points (a) and (b) due to signal from point target is
, where wave number . Assumption: .
•Using
e jkR– R
k r2 D 2
4------+ r–
8--- PB PA–=
16------= k 2
------= r D»
r 1 D 2
4r2---------+ r 1 D 2 8r2+ = r 1 D 2 8r2+ r–
16------ D 2 8r 2 16 r 2D 2 = = =
(a)
(b)
6 - 4Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Point Target Approach
0 /2 2D2/
D
reactive radiatedNear Field Radiated far FieldNear Field
0 /2 2D2/
D
reactive radiatedNear Field Radiated far FieldNear Field
d
Case: Transmitting with antenna that has constant phase across aperture if we
assume beam-width . Usually .
•At the criteria , , or
•We select , .
•If the target is sufficiently small with respect to spot size d then the wave incident on thetarget is approximately uniform in phase and amplitude
BW 0.5 D = BW L---
r 2D 2 = d r BW 2D 2
----------
0.5D
------------- D= = =
BW 2 D = d 4D=
6 - 5Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Primary Parameters•Gain, Beamwidth, Sidelobe level:
— These three are interdependent
— A number of source aperture distribution have been developed so asto optimize with respect to one or more of these parameters
0-10 -5
3 dB beamwidth
major lobe
sidelobe
null
(minor lobe)
-3 dB
back lobe
•Uniform aperture produces the narrowest mainlobe obtainable with linear or constant phaseacross the aperture but at the expense of sidelobe levels (~ 13 dB first sidelobe)
•For he Dolph Chebychev distribution, the optimum pattern is defined asthe one that produce the narrowest beamwidth between first nulls (oneach of main lobe) with no sidelobe higher than a stipulated level.
6 - 6Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Rectangular Aperture (Uniform)
Rectangular Aperture Antenna Pattern
6 - 7Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Circular Aperture (Uniform)
Circular Aperture Antenna Pattern
6 - 8Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
E-Plane v.s. H-Plane
Rectangular Aperture Circular Aperture
6 - 9Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Some Common RF Decibel UnitsOnly one number is needed if the other is a known, standardvalue:
•dBm = dB referred to 1 mW
•dBW = dB referred to 1 W
•dBi = dB referred to an isotropic source
•dBd = dB referred to a dipole = dBi - 2.15 dB
dBm 10 log P1 mW-------------------
=
dBW 10 log P1 W-------------
=
6 - 10Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Free-space Path Loss
gainPrPt------- G1G2
4d------------
2
G1G2c
4df---------------
2
G1G23 810
4d 1 310 f 1 610 --------------------------------------------------------------
2
= = = =
loss(dB) 32.44 20 log d 20 log f G1 dB – G2 dB –++=
Path Gain
for d in km, f in MHz
Path Loss = 1 / (Pr/Pt)
distance d
antenna 1 antenna 2
P rP t G1 G2
frequency f or wavelength
6 - 11Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Antenna Gain
Pr sin d d0
0
2
=
• = power accepted by antenna
• = power radiated by antenna
• = radiation efficiency =
Po
Pr
Pr Po
= Radiation intensity
= average radiation intensity
:Directivityrelative
to isotropic antenna
: Gain
avg Pr 4=
D avg
-------------------------- Pr 4
---------------------------= =
G D Po 4
---------------------------= =
P R R
---------------------------------------------
R 2-------------------------- G
Po4R 2------------= = =
Po
Pr
D G
6 - 12Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Antenna Aperture
: Effective Area
: Antenna efficiency
: Physical area of antenna’s aperture
: the peak or maximum value of
: Peak gain of antenna
: Standard directivity
: product of several factors
: aperture illumination efficiency, whichreduce the gain of antenna. Loss in gainresulting from tapering the aperturedistribution to produce sidelobs lower thanthose achievable from a uniform illumination
Ae 2
4------G =
aAeA-----=
A
Ae Ae
G a4A2
--------- aGo= =
Go4A2
---------=
a i123=
i
Half-power beamwidth BW of an antennais related to the beamwidth constant
BW = (Linear aperture)
BW = (Circular aperture)
2sin 1– 2L------
L----
2sin 1– 2L------
D----
6 - 13Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Beamwidth Const. v.s. Sidelobe
Line Aperture Circular Aperture
6 - 14Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Aperture Efficiency v.s. SidelobeLine Aperture Circular Aperture
6 - 15Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Gain Loss v.s. SidelobeLine Aperture Circular Aperture
•cosn aperture
•Gain loss: afeed in front ofa reflector ->Blockage
•Line source oflength L
•Lb: centrallylocatedblockage oflength Lb
•Loss (Line) >Loss (circular)
6 - 16Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
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 - 17Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Antenna Types and Parameters
•Narrow beams (at least in one plane) andrelatively low sidelobe levels are required.
•types
- Mechanical movement
- Electromechanical and electricalscanning feed mechanism
- Electrically scanning an array
- Design specifications, cost, risk trade-offs
6 - 18Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Linear Antenna
a2---
a2---–
xZ
x sin
E A x
E A xej2x sin
----------------–
xda 2–
a 2
=
: current, uniformly distributedA x
E ej2x sin
----------------–
xda 2–
a 2
=
ej2x sin
----------------–
a 2–
a 2
j2 sin
-------------–-------------------------------------------= Ao
a
------ sinsin
a
------ sin-------------------------------=
: Gain of the antenna
: Power Gain of the antenna
E 0=
Ao=
G 0= Ao2=
E
6 - 19Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Pattern of a Dipole Antenna
•E-Plane pattern: magnitude of the normalized fieldstrength versus for a constant .
•E-Plane pattern: magnitude of the normalized fieldstrength versus for a constant .
E j Idl4
--------- e jR–R
--------------- o sin= H j Idl
4--------- e jR–
R--------------- sin=
E 0= ER 0
H 0= HR 0
6 - 20Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Antenna (Applications)
愛國者飛彈射控雷達 神盾雷達系統
6 - 21Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Antenna
Features
•Ability to steer a beam without moving a large mechanical structure
•Multibeam
•High Cost and Complexity
6 - 22Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
General Phased-Array - Beam Steering
7
6
5
4
3
2
1
0
beam direction equiphasewavefront
radiators
phaseshifters
feednetwork
input
Broadside Array
•Linear
•Array Factor
•Peak Gain
•Bandwidth
•Sidelobes
•Beamwidth ->Scanning Angle
Grating lobs
•Wavelength
•Space
•Scanning Angle
6 - 23Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Antenna Pattern (No Scan)
Case 1:
•
•No scan
•No grating
•N up BW down
•N = constant, upL up BW
Down
d 2=
6 - 24Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Antenna Pattern (No Scan)
Case 2:
•
•No scan
•Grating at
and .
d =
0 90=
0 90–=
6 - 25Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Antenna Pattern (Scan)
Case 1:
•
•No grating forscanning angle
•As or
, Gratinglobe happens at
or
•The greaterScanning angle.the greaterbeamwidth
d 2=
60– 0 60
63 0
63– 0
0 90=
0 90–=
6 - 26Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Antenna Pattern (Scan)
Case 2:
•
•Grating lobesanywhere
d =
6 - 27Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Antenna Pattern (Scan)
Case 3:
•Scanning angle
,
•No grating lobehappens
•As or
,Grating lobehappens at
or
60– 0 60
d 0.54
60 0
60– 0
0 90=
0 90–=
6 - 28Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Pattern (Calculation)
•Far Field case: Difference in phase of thesignals in adjacent elements is
•One can show that for an array of sourceseach with pattern . The pattern for
the array is , where
: isotropic, AF: Array Factor
•Simple uniform amp. and phase array:
d sin
----------------2 2d sin
-----------------------= =
f g f AF=
f e jkr–=
AF 1 e j kd –sin e j2 kd –sin e j N 1– kd –sin + + + + e j n 1– kd –sin
n 1=
N
= =
AF e j kd –sin 1– e jN kd –sin 1–= , where : the progressive phase shift bet. elements
AF e j N 1– 2 kd –sin N 2 kd –sin sin1 2 kd –sin sin
----------------------------------------------------------- , We define kd –sin= =
AFN 2 sin1 2 sin
----------------------------------= AF 0lim N 2 N 2 cos
1 2 1 2 cos--------------------------------------------
0
N= = AF n 1N---
N 2 sin1 2 sin
----------------------------------=
normalized
6 - 29Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Phased-Array Antenna (Grating)
kd – sin kd osin= = , k 2 =
2d sin osin– =
AF n1N---
N 2 sin1 2 sin
----------------------------------=
AF n1N---
Nd sin osin– sin
d sin osin– sin-----------------------------------------------------------------------------=
Gain AF n AF n AF n2 1
N 2-------
sin2 Nd sin osin– sin2 d sin osin–
------------------------------------------------------------------------------= = =
Gain due to array factor (AF)
o
•It is important to space the elements sufficiently close to avoid grating lobes thatare caused by the periodic nature of the structure
•The pattern has maxima whenever , n= 0, 1,2...: Mainbeam grating
lobes. For , Grating lobes at .
•Beam is scanned. Grating lobes at
sin n d=d sin n= d = 90=
d sin osin– n=
For a broadside array, , and theno 0=
Gain 1N 2-------sin
2 Nd sin sin2 d sin
---------------------------------------------------=
Grating lobes
Man beam
6 - 30Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Other Aspects of Phased-Array
• up BW up: as the array is scanned, thehalf-power beamwidth increases tn plane of scan
•The beamwidth is approximately inverselyproportional to , where : scan angle
measured from the normal to the array
: BW in the direction at scan
angle .
• : Beamwidth at broadside. For small scan
angle , . in radians
•The peak gain for typical illumination function may
be approximated by .
, in degree
• , down up
o
ocos o
B o B 0
ocos---------------=
o
B 0
o B 0 0.886Nd ocos----------------------=
G 0 0 32 000B 0B 0-----------------------------=
B 0B 0
B 0B 0 G 0 0
o
B 0
B o
B 0 B 0
G 0 0
broadside
6 - 31Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
ARRAY ANTENNA PATTERNS(Spacing = /2)
(in rectangular coordinates)
Angle of Radiation
Nor
mal
ized
Mag
nitu
de
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
1/2
2/3 2
N = 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
N = 8
1
Nor
mal
ized
Mag
nitu
de
0
1/2
2/3 21
Angle of Radiation
6 - 32Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Parabolic Reflector Antenna (Applic.)
6 - 33Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Parabolic Reflector Antenna
Design rules
•Sidelobe level: Select side level (Distribution)
•Beamwidth constant: Select beamwidth constant viaconsideration of Fig. 6-5. (circular aperture BW v.s.sidelobe level)
•Aperture Efficiency: Select aperture efficiency viaconsideration of Fig. 6-6. (aperture efficiency v.s.sidelobe)
•Gain: Find . Assume is dominant efficiency
consideration
•Beamwidth: Find using beamwidth constant
•Weighting Distribution: A complex analysis todesign feed with a proper weighting based on
- Edge Taper
- Beamwidth of feeder
- Space Attenuation
G aGo= a
BW D----
Scanning Techniques
•Scan entire antenna
•Scan feed within reflector
6 - 34Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Parabolic Reflector Antenna Design(1)
Weighting Design rules
•Sidelobe level: Select H-plane edge taper from Fig. 6.11 necessary to obtain desired sidelobelevel. (Edge taper is determined by beamwidth of feeder and space attenuation)
•Space attenuation: Given f/D, find intercepted angle from Fig. 6.12. In order to determine spaceattenuation.
6 - 35Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
Parabolic Reflector Antenna Design (2)
•Using Fig. 6-13 to find space attenuations Fig. 17.17 todetermine 10dB beamwidth of feed horn
, given intercepted angle .
•Use (degree), for E-plane,
(degree), for H-plane
- : pattern width in degrees at -10dB level.
BW10dB 210dB=
BW10dB 88 B= B 2.5
BW10dB 31 79+ A= A 3
BW10dB
B: E-plane horn apertureA: H-plane horn aperture
H
EA
B
6 - 36Chapter 6: Radar Antenna Dr. Sheng-Chou Lin
Radar System Design
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 illuminationshould be 20dB down. Assume a wavelength of 3cm.
• total feed angle = 80o, space attenuation 1dB.
• , ,
•E-plane, , .
•H-plane, , .
•From Fig. 6-11, first sidelobe = -40dB for Taylor distribution
•From Fig. 6-11, first sidelobe = -40dB , .
f D 0.7= 40=
Gh 40= 20 1– 19dB= = 10dB 1.4 40= 10dB 29= BW10dB 58=
BW10dB 88 B= B 88 3 58 4.55cm= = B 1.52 2.5=
BW10dB 31 79+ A= A 79 3 58 31– 8.78cm= = A 2.93 3=
71= BW D----
a 1.1dB–= G a dB Go dB +=
HE
edge taper A
B-10B
58o
Feeder Horn