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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)


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


Near Field

0.62 D 2


Radar System Design

Far-Field Approach

0 /2 2D2/

D


Near Field

0 /2 2D2/

D


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)


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=


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.


Radar System Design

Rectangular Aperture (Uniform)

Rectangular Aperture Antenna Pattern


Radar System Design

Circular Aperture (Uniform)

Circular Aperture Antenna Pattern


Radar System Design

E-Plane v.s. H-Plane

Rectangular Aperture Circular Aperture


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-------------

=


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


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


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----


Radar System Design

Beamwidth Const. v.s. Sidelobe

Line Aperture Circular Aperture


Radar System Design

Aperture Efficiency v.s. SidelobeLine Aperture Circular Aperture


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)


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


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


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


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


Radar System Design

Phased-Array Antenna (Applications)

愛國者飛彈射控雷達神盾雷達系統


Radar System Design

Phased-Array Antenna

Features

•Ability to steer a beam without moving a large mechanical structure

•Multibeam

•High Cost and Complexity


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


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=


Radar System Design

Phased-Array Antenna Pattern (No Scan)

Case 2:

•

•No scan

•Grating at

and .

d =

0 90=

0 90–=


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–=


Radar System Design


Case 2:

•

•Grating lobesanywhere

d =


Radar System Design


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–=


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


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


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


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


Radar System Design

Parabolic Reflector Antenna (Applic.)


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


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.


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


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

chapter 6 radar antenna - fju.edu.t · pdf filechapter 6 radar antenna chapter 6: radar...

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