Radar 2009 a 7 radar cross section 1

IEEE New Hampshire SectionRadar Systems Course 1Radar Cross Section 1/1/2010 IEEE AES Society

Radar Systems Engineering Lecture 7 –

Part 1

Radar Cross Section

Dr. Robert M. O’DonnellIEEE New Hampshire Section

Guest Lecturer

Radar Systems Course 2Radar Cross Section 1/1/2010

IEEE New Hampshire SectionIEEE AES Society

Block Diagram of Radar System

Transmitter

WaveformGeneration

PowerAmplifier

T / RSwitch

Antenna

PropagationMedium

TargetRadarCross

Section

Photo ImageCourtesy of US Air ForceUsed with permission.

PulseCompressionReceiver Clutter Rejection

(Doppler Filtering)A / D

Converter

General Purpose Computer

Tracking

DataRecording

ParameterEstimation Detection

Signal Processor Computer

Thresholding

User Displays and Radar Control

This lecture



Definition -

Radar Cross Section (RCS or σ)

Radar Cross Section

(RCS) is the hypothetical area, that would intercept the incident power at the target, which if scattered isotropically, would produce the same echo power at the radar, as the actual target.

Figure by MIT OCW.



Factors Determining RCS

Figure by MIT OCW.



Threat’s View of the Radar Range Equation

Transmitted Pulse

Received Pulse

Target Cross Section σ

Antenna Gain GTransmit Power PT

Figure by MIT OCW.

Distance from Radar to Target

Radar Range Equation

R

SN =

Pt G2 λ2

σ

(4π)3

R4

k TS

Bn

L

Cannot Control

Can ControlCannot Control



Outline

• Radar cross section (RCS) of typical targets– Variation with frequency, type of target, etc.

• Physical scattering mechanisms and contributors to the RCS of a target

• Prediction of a target’s radar cross section– Measurement– Theoretical Calculation



Radar Cross Section of Artillery Shell

M107 Shellfor

155mm HowitzerAspect Angle (degrees)

0 20 40 60 80 100 120 140 160

180

Rad

ar C

ross

Sec

tion

(dB

sm)

0

-60

-20

-30

-40

-50

-10

Typical Artillery Shell

RCS vs. Aspect Angle of an Artillery Shell

Courtesy US Marine Corps



Radar Cross Section of Cessna 150L

S BandV V

Polarization

Measured at RATSCAT (6585th

Test Group) Holloman AFB for FAA

Courtesy of Federal Aviation Administration

Aspect Angle (degrees)0 90 180 270 360

Rad

ar C

ross

Sec

tion

(dB

sm)

0

-20

20

40

Cessna 150L (in takeoff) Cessna 150L (in flight)

Scott Studio Photography with permissionScott Studio Photography with permission



Aspect Angle Dependence of RCSCone Sphere Re-entry Vehicle (RV) Example

Figure by MIT OCW.



Examples of Radar Cross Sections Square meters

Conventional winged missile

0.1Small, single engine aircraft, or jet fighter

1Four passenger jet

2Large fighter

6Medium jet airliner

40Jumbo jet

100Helicopter

3

Small open boat

0.02Small pleasure boat (20-30 ft)

2Cabin cruiser (40-50 ft)

10Ship (5,000 tons displacement, L Band)

10,000

Automobile / Small truck

100 -

200Bicycle

2Man

1Birds (large -> medium)

10-2 - 10-3

Insects (locust -> fly)

10-4 - 10-5

Radar Cross Sections of Targets Span at least 50 dBAdapted from Skolnik, Reference 2



Outline






RCS Target Contributors

• Types of RCS Contributors– Structural

(Body shape, Control surfaces, etc.)– Avionics

(Altimeter, Seeker, GPS, etc.)– Propulsion (Engine inlets and exhausts, etc.)

Inlet

Control SurfacesAltimeter

SeekerBody Shape

Exhaust



Single and Multiple Frequency RCS Calculations with the FD-FD Technique

• RCS Calculations for a Single Frequency– Illuminate target with incident sinusoidal wave– Sequentially in time, update the electric and magnetic fields, until

steady state conditions are met– The scattered wave’s amplitude and phase can the be calculated

• RCS Calculations for a Multiple Frequencies– Illuminate target with incident Gaussian pulse– Calculate the transient response– Calculate to Fourier transforms of both:

Incident Gaussian pulse, and Transient response

– RCS at multiple frequencies is calculated from the ratios of these two quantities



Scattering Mechanisms for an Arbitrary Target

Tip Diffraction atAircraft Nose

Diffraction atCorner

ReturnFrom

Engine Cavity

Edge Diffraction

Tip Diffraction from

Fuel Tank

Specular Surface

ReflectionMultiple

Reflection

Wave Echo from Traveling Wave

Gap, Seam, orDiscontinuity

Echo

Backscatter from

Creeping Wave

CurvatureDiscontinuity

Return



Measured RCS of C-29 Aircraft Model

Full Scale C-29 BAE Hawker 125-800

Aspect Angle (degrees)

RC

S (d

Bsm

)

0 60 120 180 240 300 360

20

-20

-10

0

10

-30

1/12 ScaleModel

Measurement

X-BandHH PolarizationWaterline Cut

Wing LeadingEdge

FuselageSpecular

Courtesy of Arpingstone

Adapted from Atkins, Reference 5Courtesy of MIT Lincoln Laboratory



Outline






Techniques for RCS Analysis

Scaled Model MeasurementsTheoretical Prediction

Full Scale Measurements

Courtesy of MIT Lincoln LaboratoryUsed with Permission



Full Scale Measurements

Target on Support

• Foam column mounting– Dielectric properties of Styrofoam close to those of free space

• Metal pylon mounting– Metal pylon shaped to reduce radar reflections– Background subtraction can be used

Derived from: http://www.af.mil/shared/media/photodb/photos/050805-F-0000S-003.jpg




Full Scale Measurement of Johnson Generic Aircraft Model (JGAM)

RATSCAT Outdoor Measurement Facility at Holloman AFB Courtesy of MIT Lincoln Laboratory

Used with Permission



Compact Range RCS MeasurementRadar Reflectivity Laboratory (Pt. Mugu) / AFRL Compact Range (WPAFB)

Courtesy of U. S. Navy.

Target

MainReflector

FeedAntenna

PlaneWave

Low RCSPylon

Sub-Reflector



Scale Model Measurement

SubscaleMeasure at frequency S x F

Scale FactorS

(Reduced Size)

Full ScaleMeasure at frequency f

MQM-107 Drone in 0.29, 0.034, and 0.01 scaled sizes




Scaling of RCS of TargetsScale Factor

S

Length

L

L´

= L / S

Wavelength

λ λ´ = λ

/ S

Frequency f

f´

= S f

Time

t

t´

= t / S

Permittivity

ε ε´ = ε

Permeability

μ μ´ = μ

Conductivity

g

g´

= S g

Radar Cross Section

σ σ´ = σ

/ S2

Quantity Full Scale Subscale



Outline






Radar Cross Section Calculation Methods

• Introduction– A look at the few simple problems

• RCS prediction– Exact Techniques

Finite Difference-

Time Domain Technique (FD-TD) Method of Moments (MOM)

– Approximate Techniques Geometrical Optics (GO) Physical Optics (PO) Geometrical Theory of Diffraction (GTD) Physical Theory of Diffraction (PTD)

• Comparison of different methodologies



Radar Cross Section of Sphere

Rayleigh Regionλ >> aσ = k / λ4

Mie or ResonanceRegion

OscillationsBackscattered wave interferes with creeping wave

Optical Regionλ

<< aσ = π a2

Surface and edge scattering occur

Circumference/ wavelength = 2πa / λ

Rad

ar C

ross

Sec

tion

/ πa2

10

1

10-3

10-2

10-1

0.1 0.2 0.4 0.7 1 2 4 7 10 20

RayleighRegion

Resonance or MieRegion

OpticalRegion

a

Higher Wavelengths Lower Wavelengths

Figure by MIT OCW.

λ

>> a

λ << a



Radar Cross Section Calculation Issues

• Three regions of wavelength Rayleigh (λ

>> a) Mie / Resonance (λ

~ a) Optical

(λ

<< a)

• Other simple shapes– Examples: Cylinders, Flat Plates, Rods, Cones, Ogives– Some

amenable to relatively straightforward solutions in some

wavelength regions

• Complex targets:– Examples: Aircraft, Missiles, Ships)– RCS changes significantly with very small changes in frequency

and / or viewing angle See Ref. 6 (Levanon), problem 2-1 or Ref. 2 (Skolnik) page 57

• We will spend the rest of the lecture studying the different basic methods of calculating radar cross sections



High Frequency RCS Approximations (Simple Scattering Features)

Scattering Feature

Orientation

Approximate RCS

Corner Reflector

Axis of symmetry along LOS

Flat Plate

Surface perpendicular to LOS

Singly Curved Surface


Doubly Curved Surface


Straight Edge

Edge perpendicular to LOS

Curved Edge

Edge element perpendicular to LOS

Cone Tip

Axial incidence

Where:

22eff /A4 λπ

22 /A4 λπ

22 /A4 λπ

21 aaπ

πλ /2

2/a λ

)2/(sin42 αλ

Adapted from Knott is Skolnik Reference 3



Radar Cross Section Calculation Issues

• Three regions of wavelength Rayleigh (λ

>> a) Mie / Resonance (λ

~ a) Optical

(λ

<< a)

• Other simple shapes– Examples: Cylinders, Flat Plates, Rods, Cones, Ogives– Some

amenable to relatively straightforward solutions in some

wavelength regions

• Complex targets:– Examples: Aircraft, Missiles, Ships)– RCS changes significantly with very small changes in frequency

and / or viewing angle See Ref. 6 (Levanon), problem 2-1 or Ref. 2 (Skolnik) page 57

• We will spend the rest of the lecture studying the different basic methods of calculating radar cross sections



RCS Calculation -

Overview

• Electromagnetism Problem– A plane wave with electric field, , impinges on the target of

interest and some of the energy scatters back to the radar antenna

– Since, the radar cross section is given by:

– All we need to do is use Maxwell’s Equations to calculate the scattered electric field

– That’s easier said that done

– Before we examine in detail these different techniques, let’s review briefly the necessary electromagnetism concepts and formulae, in the next few viewgraphs

IEr

2

I

2

S2

r E

Er4lim r

r

π=σ∞→

SEr



Maxwell’s Equations

• Source free region of space:

• Free space constitutive relations:

0)t,r(B0)t,r(D

t)t,r(D)t,r(H

t)t,r(B)t,r(E

=⋅∇

=⋅∇

∂∂

=×∇

∂∂

−=×∇

→

→

rr

rr

rrrr

rrrr

)t,r(H)t,r(B

)t,r(E)t,r(D

o

orrrr

rrrr

μ=

ε= = Free space permittivity

= Free space permeability

oε

oμ



Maxwell’s Equations in Time-Harmonic Form

• Source free region:

• Time dependence

0)r(B

0)r(D

)r(Di)r(H

)r(Bi)r(E

=⋅∇

=⋅∇

ω−=×∇

ω=×∇→

→

rr

rr

rrrr

rrrr

{ }{ }ti

ti

e)r(HRe)t,r(He)r(ERe)t,r(E

ω−

ω−

=

=rrrr

rrrr



Boundary Conditions

• Tangential components of and are continuous:

• For surfaces that are perfect conductors:

• Radiation condition:

– As

Er

Hr

21

21

Hxn̂Hxn̂

Exn̂Exn̂rr

rr

=

=

0Exn̂ =r

r1)r(Er ∝∞→

rr

2222

1111

HE

HErr

rr

εμ

εμ n̂Surface

BoundaryMedium 1

Medium 2



Scattering Matrix

• For a linear polarization basis

• The incident field polarization is related to the scattered field polarization by this Scattering Matrix -

S

• For and a reciprocal medium and for monostatic radar cross section:

• For a circular polarization basis

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

HI

VI

HHHV

VHVVikr

HS

VSS E

ESSSS

re

EEE

r

2VHVH

2HHHH

2VVVV

S4

S4

S4

π=σ

π=σ

π=σ

RLLLRR ,, σσσ

HVVH σ=σ

Scattering Matrix -

S



Radar Cross Section Calculation Methods

• Introduction– A look at the few simple problems

• RCS prediction– Exact Techniques

Finite Difference-

Time Domain Technique (FD-TD) Method of Moments (MOM)

– Approximate Techniques Geometrical Optics (GO) Physical Optics (PO) Geometrical Theory of Diffraction (GTD) Physical Theory of Diffraction (PTD)

• Comparison of different methodologies



Methods of Radar Cross Section Calculation

RCS Method

Approach to Determine Surface Currents

Finite Difference- Time Domain (FD-TD)

Solve Differential Form of Maxwell’s Equation’s for Exact Fields

Method of Moments (MoM)

Solve Integral Form of Maxwell’s Equation’s for Exact Currents

Geometrical Optics (GO)

Current Contribution Assumed to Vanish Except at Isolated Specular Points

Physical Optics (PO)

Currents Approximated by Tangent Plane Method

Geometrical Theory of Diffraction (GTD)

Geometrical Optics with Added Edge Current Contribution

Physical Theory of Diffraction (PTD)

Physical Optics with Added Edge Current Contribution



Finite Difference-

Time Domain (FD-TD) Overview

• Exact method for calculation radar cross section

• Solve differential form of Maxwell’s equations– The change in the E field, in time, is dependent on the change in the H

field, across space, and visa versa

• The differential equations are transformed to difference equations– These difference equations are used to sequentially calculate the E

field at one time and the use those E field calculations to calculate H field at an incrementally greater time; etc. etc.

Called “Marching in Time”

• These time stepped E and H field calculations avoid the necessity of solving simultaneous equations

• Good approach for structures with varying electric and magnetic properties and for cavities



Maxwell’s Equations in Rectangular Coordinates

• Examine 2 D problem –

no dependence:

• Equations decouple into H-field polarization and E-field polarization

ZoXY

YoZX

XoYZ

Et

Hy

Hx

Ht

Ex

Ez

Et

Hz

Hy

∂∂

ε=∂∂

−∂∂

∂∂

μ−=∂∂

−∂∂

∂∂

ε=∂∂

−∂∂

ZoXY

YoZX

XoYZ

Ht

Ey

Ex

Et

Hx

Hz

Ht

Ez

Ey

∂∂

μ−=∂∂

−∂∂

∂∂

ε=∂∂

−∂∂

∂∂

μ−=∂∂

−∂∂

0y

=∂∂

• H-field polarization • E-field polarization

ZXY EEH ZXY HHE

y



Maxwell’s Equations in Rectangular Coordinates

• Examine 2 D problem –

no dependence:

• Equations decouple into H-field polarization and E-field polarization

0y

=∂∂

• H-field polarizationZXY EEH

• E-field polarizationZXY HHE

ZoXY

YoZX

XoYZ

Et

Hy

Hx

Ht

Ex

Ez

Et

Hz

Hy

∂∂

ε=∂∂

−∂∂

∂∂

μ−=∂∂

−∂∂

∂∂

ε=∂∂

−∂∂

ZoXY

YoZX

XoYZ

Ht

Ey

Ex

Et

Hx

Hz

Ht

Ez

Ey

∂∂

μ−=∂∂

−∂∂

∂∂

ε=∂∂

−∂∂

∂∂

μ−=∂∂

−∂∂

= 0

= 0

= 0

= 0

y



• H-field polarization:

• Discrete form:

• Electric and magnetic fields are calculated alternately by the marching in time method

Discrete Form of Maxwell’s Equations

( ) ( )

( )t,y,xEx

t,y,xEz

t,y,xHt

Z

XYo

∂∂

−

∂∂

=∂∂

μ−

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Δ

+−⎟⎠⎞

⎜⎝⎛ Δ

+Δ+Δ

−

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Δ

+−⎟⎠⎞

⎜⎝⎛ Δ+

Δ+

Δ=

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Δ

−Δ

+Δ

+−⎟⎠⎞

⎜⎝⎛ Δ

+Δ

+Δ

+Δμ

−

oZ

ooZoZ

oXoZX

ooX

oXoZoX

oXZ

To

Zo

XoY

To

Zo

XoY

T

o

t,2

z,xEt,2

z,xE1

t,z,2

xEt,z,2

xE1

2t,

2z,

2xH

2t,

2z,

2xH

z

xy

Ex

EZ

HY Yee’sLattice(2-D)



FD-TD Calculations and Absorbing Boundary Conditions (ABC)

• Absorbing Boundary Condition (ABC) Used to Limit Computational Domain– Reflections at exterior boundary are minimized– Traditional ABC’s model field as outgoing wave to estimate field quantities outside

domain– More recent perfectly matched layer (PML) model uses non-physical layer, that

absorbs waves

Ex

EZ

HY

Perfect ConductorLayer Perfectly Matched0H

x21

tc1

txc1

y2

2

2

2

2

2

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∂∂

+∂∂

∂2nd

Order ABC

1st

Order ABC 0Htc

1xz2

1y =⎟

⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

Total Field

Target

Domain of Computation

Absorbing Boundary

0ETAN =

Scattered Field



RCS Calculations Using the FD-TD Method

• Single frequency RCS calculations– Excite with sinusoidal incident wave– Run computation until steady state is reached– Calculate amplitude and phase of scattered wave

• Multiple frequency RCS calculations– Excite with Gaussian pulse incident wave– Calculate transient response– Take Fourier transform of incident pulse and transient

response– Calculate ratios of these transforms to obtain RCS at multiple

frequencies

From Atkins, Reference 5Courtesy of MIT Lincoln Laboratory



Description of Scattering Cases on Video

Finite Difference Time Domain (FDTD) Simulations

Ei Hi

Hi

Ei

15 deg 15 degHi

Ei

Case 1 –

Plate I Case 2 –

Plate II Case 3 –

Plate III

Case 4 –

Cylinder I Case 5 –

Cylinder II Case 6 –

Cavity

Hi

EiHiEiEi Hi

Courtesy of MIT Lincoln Laboratory Used with Permission



FD-TD Simulation of Scattering by Strip

0.5 m

Ey

4 m

• Gaussian pulse plane wave incidence• E-field polarization (Ey

plotted)• Phenomena: specular reflection

Case 1

Courtesy ofMIT Lincoln LaboratoryUsed with Permission



Case 1




FD-TD Simulation of Scattering by Strip

Case 1




FD-TD Simulation of Scattering by Cylinder

0.5 mHy

2 m

• Gaussian pulse plane wave incidence• H-field polarization (Hy

plotted)• Phenomena: creeping waveCase 5




Case 5




FD-TD Simulation of Scattering by Cylinder

Case 5




Backscatter of Short Pulse from Sphere

Creeping Wave Return

SpecularReturn

Radius of sphere is equal to the radar wavelength

Figure by MIT OCW.

Radar 2009 a 7 radar cross section 1

Engineering

Transcript of Radar 2009 a 7 radar cross section 1