CEM Workshop Lectures (1/11): ABC of CEM and RCS

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ABC of CEM and RCS
Basics explained for beginners

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©ZeusNumerixPvtLtd:ConfidentialDocument
About the Training Programme
ABC of CEM and RCS
 This is an introductory course in computational electromagnetics (CEM)
 The emphasis is on foundations and methods of predicting Radar Cross Section
(RCS) of Aerial Targets
 The course is neither targeted towards scientists who wish to develop their own
application nor towards engineers who wish to use a proprietary software for solving
their own problems
 Demonstrations on the last two days are for illustrating steps required to calculate
RCS
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Contents
ABC of CEM and RCS
 Basics of stealth and importance of RCS
 Electromagnetic wave, Frequency, wave number and Poynting vector, electrical and
magnetic field
 Frequencies and bands used in Radar
 Detection, inverse scattering, Types of scattering and types of RCS
 Units of RCS, Range equation, Polarisation and scattering matrix
 RCs of simple shapes, scattering regions, RCS of flying object and maritime objects
 Classification of RADAR echoes
 Some information of IR and acoustics stealth
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ABC of CEM and RCS
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Survivability vs. Altitude & Speed for Aircraft
Flight altitude
Speed of the aircraft
Excellent
survivability
very good
survivability
good
survivability
low
survivability
Stealth technologies can
improve the survivability for
aircraft for a given flight
envelop.
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ABC of CEM and RCS
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Stealth Technologies and their Usefulness
Stealth technology Applications in
Aerospace
Application in Navy Applications in Army
 Radar  High  High  Medium
 Infrared  Medium  Medium  High
 Acoustics  Low  High  Low
 Contrail  Low  High  High
 Visual  Low  Low  Medium
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Electromagnetic Wave
ABC of CEM and RCS
 Electromagnetic wave has two fields: Electrical field and Magnetic field
 The direction of electrical field dictates the polarisation
 Energy density = energy / volume = ( E2 + H2) Joules / m3
 Flux of energy S = E x H watts / m2
 Power ~ (amplitude)2
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E – electrical filed
Horizontally polarised electromagnetic wave
E – electrical filed
Vertically polarised electromagnetic wave
amplitude
Wave length 
Frequency f = c/ 
Wave no k = 2/
Poynting vector
S = E x H (watts /m2)
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ABC of CEM and RCS
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Electromagnetic Radiation vs Light
Visible light
Radar waves
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Nomenclature of Bands
ABC of CEM and RCS
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ELF (Extremely Low Frequency) 30 Hz 10,000 km
VF (Voice Frequency) 300 Hz 1,000 km
VLF (Very Low Frequency) 3 kHz 100 km
LF (Low Frequency) 30 kHz 10 km
MF (Medium Frequency) 300 kHz 1 km
HF (High Frequency) 3 MHz 100 mm
VHF (Very High Frequency) 30 MHz 10 mm
UHF (Ultra High Frequency) 300 MHz 1 mm
L 1 GHz 30 cm
S 2 GHz 15 cm
C 4 GHz 7.5 cm
X 8 GHz 3.75 cm
Ku 12 GHz 2.5 cm
K 18 GHz 1.67 cm
Ka 27 GHz 1.1 cm
V 40 GHz 7.5 mm
W 75 GHz 4 mm
Mm 110 GHz 2.73 mm
NATO Band Frequencies
A 0 Hz –
B 250 MHz 1.2 m
C 500 MHz 60 cm
D 1 GHz 3 cm
E 2 GHz 15 cm
F 3 GHz 10 cm
G 4 GHz 7.5 cm
H 6 GHz 5.0 cm
I 8 GHz 3.75 cm
J 10 GHz 3.0 cm
K 20 GHz 1.5 cm
L 40 GHz 0.75 cm
M 60 GHz 0.5 cm (up to 100 GHz / 0.3cm
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RCS : Detection of Target
Incident power
scattered or reflected power is
collected by different antennas
Bi-static Configuration
Mono-static Configuration
scattered or reflected power is
collected by the same antenna
Rst
Rtf
Rst
Incident power
scattered power
Transmitting and also receiving antenna
Transmitting antenna
receiving antenna
ABC of CEM and RCS14-Sep-2012

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Detection vs Inverse Scattering
Incident wave
scattered wave has
time varying amplitude
Inverse scattering technique
provides method of estimating
(a) Size of target
(b) Shape of target
Inverse scattering technique is
more sophisticated than RCS
which is only for detection of
target
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Scattered Power
Mono-static radar RCS : Energy scattered towards the source is called backscattered energy
Bi-static RCS: Energy scattered in any other directions
RCS (normally denoted by ) is defined as
 = 4 ( Ps / Pi); Ps scattered or reflected power per solid angle (w/sold
angle)
Pi incident power density (w/m2)
Radiation intercepted by an object can be reflected, absorbed, or transmitted through the target
Incident energy
absorbed energy
transmitted energy
scattered energy
reflected energy
diffracted energy
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 RCS depends up on:
 Shape of the target
 Orientation of target with respect to source of radiation
 Orientation of the receiving radar with respect to target (only for Bi-static RCS)
 Material of the surface
Plane wave incident on flat plate
conductor will reflect the entire
energy backwards
Reflected energy is not restricted
in the backward direction
Reflected energy is primarily in
forward direction, except at nose
diffraction
If RCS is reduced in one direction, it will necessarily increase in some other direction
scattered power
scattered power scattered power
Incident power Incident power Incident power
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Scattered Power and RCS

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RCS also depends up on orientation of the surface. Consider a flat plate:
Mono-static RCS varies from 0 to a large value as the orientation changes to broad-side orientation
Note: We have neglected edge diffractions and tip diffractions
No scattered power
scattered power
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Scattered Power

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Ev
i
incident
scattered
Ev
s
Ev
i
incident
scattered
Ev
s
Ev
s = avv Ev
i EH
s = aHv Ev
i
Cross polarization / depolarization
EH
S aHH aHV EH
I
=
Ev
S aVH aVV EV
I
Scattering Matrix :
Co-polarization
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Polarization and Scattering Matrix

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A Definition : Radar Cross Section (RCS) of a target is the (fictitious) area intercepting that amount of
power which, when scattered equally in all directions, produces an echo at the radar equal to that from
the target
From the definition:  Ii / (4) = Ir R2
where
 Ii / (4) is fraction of power scattered by target per unit solid angle
(Ir Ar )/(Ar / R2) IrR2 is power scattered into area (Ir Ar) divided by solid angle that the area makes
(Ar/R2)
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Definition of RCS

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Definition of RCS
Amount of energy scattered by aircraft = energy scattered by sphere
Aircraft scatters different amount of energy in different direction; RCS is different in different directions
 = (power reflected by the target per solid angle) / (incident power density / 4)
= limit 4 R2 | Er / Ei | or
R  
= limit 4 R2 | Hr / Hi|
R  
= limit 4 R2 | Ir / Ii |, I is power density
R  
RCS (expressed in db): db = 10 log [( in m2)/(1 m2)]
Equivalent
sphere
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10000 m2 40 Battle ship
1000 m2 30 Classical bomber
100 m2 20 B – 52 bomber
10 m2 10 Classical fighter
Sphere of cross section 1 m2 1 m2 0
0.1 m2 -10 Stealth fighter
Birds 0.01 m2 -20 F-22 Raptor
Insects 0.001 m2 -30
B -2 Spirit
0.0001 m2 -40
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Typical RCS Values in m2 and in dB

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 Power density at the target (St )
(Psource Gtransmission_antenna) / (4 Rsource-to-target
2), where
Psource = Power transmitted by source radar &
Gtransmission_antenna = gain of the transmitting antenna
Power received by target (Pincident )
= Ssource  = (Psource Gtransmission_antenna ) / (4R2
source-to-target), where
 = surface area of target
For (PEC) perfectly electrical conductor, the entire power is scattered. If the scattered
energy is isotropic (not a function of the direction), then scattered energy by receiving
radar (Sscattered)
Sscattered = Pincident / (4R2
target-to-receiver) = (Ps Gs )/[(4R2
source-to-target)(4R2
target-to-receiver)]
Range for Given RCS Value
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h
d
 =  d h2 / 
for h = 1 m, d = 0.5 m
 = 50 m2 for x band and
 = 16 m2 for s band
d
 =  (d/2)2
for d = 1 m
 = 0.785 m2 for x band and
 = 0.785 m2 for s band
σ = 4  l4 / 2
for l = 1 m,
σ = 12300 m2 for x band and
σ = 1300 m2 for s band
l
l
Note that:
RCS is an order of magnitude larger
than geometric area
RCS decreases as frequency
increases
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RCS of Simplest Objects

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ABC of CEM and RCS
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Relative RCS Values for some Targets
Target RCS Features
Cylinder
 = 2ab2/
 Non-specular along radial
direction
 Low RCS for size
 Specular along axis
Sphere
 = a2
 Non-specular
 Lowest RCS
 Radiates isotropically
Dipalne
 = 8a2b2/2
 Large value of RCS
 Specular perpendicular to one
axis
 Good target for testing
polarisation
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ABC of CEM and RCS
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Target RCS Features
Triangular
trihedral
 = 4a4/(32)
 Non-specular
 Can not be used for testing
polarisation
Square
trihedral
 = 12a4/2
 Large RCS
 Non-specular
 Cannot be used for cross
polarised measurements
Circular
trihedral
 = 0.5073a4/2
 Large RCS
 Non-specular
 Cannot be used for cross
polarised measurements
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ABC of CEM and RCS
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Target RCS Features
Flat plate
 = 4a2b2/2
 Largest RCS
 Specular along both axes,
difficult to align
Top hat
 =
4ab2/(cos3())
 Low RCS
 Difficult to align rotated
seam
Bruderhedral
 =
4ab2/(cos3())
 Large RCS
 Easier to align for rotation
 Moderately specular along
one axis
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Factors Affecting RCS
ABC of CEM and RCS
 RCS depends on several factors:
 Geometry and physical size of the target measured in terms wave length
 Illumination and viewing direction
 Polarization of the radar signal (vertical, horizontal, circular)
 Material of the target
 RCS calculations require following parameters:
 Angle of incidence
 Angle of scatter
 Incident field polarization
 Scattered field polarization
 Frequency and target geometry
 RCS units
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 ii ,θ 
 ss ,θ 
 iθi E,E 
 sθs E,E 
 λl 
 22
dBmormin
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Variation of RCS with Electrical Size
ABC of CEM and RCS
 There are three regions based on size of the target relative to wave length
 Rayleigh region : ka = (2/) a << 1
 Mie region (Resonance region): ka = (2/)a ~ 1
 Optical region: ka = (2/) a >> 1
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Polarised
along axis
of cylinder
Polarised
along the
diameter
Rayleigh Mie Optical
E
E
|| = k a L2
2a
L
 = k a
L2
1
0.1
4
0.1 101
/kaL2
ka
Normally || > 
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Scattering Regions
ABC of CEM and RCS
 Low-frequency region : electrical size << 1
 Rayleigh scattering
 Distinctive features can not be identified
 RCS, i.e.  ~ -4
 RCS varies smoothly
 RCS ~ (volume)2
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Scattering Regions
ABC of CEM and RCS
 High-frequency region : electrical size >> 1
 Optical scattering
 Diffraction dominant
 Distinctive features can be identified
 RCS is smooth and independent of wavelength
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ABC of CEM and RCS
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RCS of Aerial Targets
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ABC of CEM and RCS
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RCS vs Aerodynamic Performance
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RCS Reduction by Shaping
ABC of CEM and RCS
 RCS reduction is first attempted by shaping
 To reduce RCS further Radar Absorbing materials (RAM) are used
 RAMs are usually Multi-layered composite structures RAM match the impedance
with free space
 Energy is progressively absorbing and dissipated as heat
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F 117 : RCS reduction by Shaping
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RCS of Maritime Targets
ABC of CEM and RCS
 The aspect of a target () is its orientation to the axis of the radar beam
 Grazing angle () is the angle measured in the vertical plane between the ray and a
reflecting surface
RCS of a ship in X, S and L bands is given by empirical formula:  = 52 f1/2 D3/2 where
 - Radar cross section, f - frequency in MHz, D - full load displacement in kilo-tons
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Top view side view
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Radar Absorbing Materials
ABC of CEM and RCS
 Cockpit windows are covered with conductive materials to minimise penetration into
the cockpit,
 Air intakes are covered with mesh, or follow convoluted paths designed to ensure
that the radar signal is reflected many times and mostly absorbed before it exits.
 Research is being conducted to create a plasma that can cover the aircraft. Plasma
makes an excellent RAM as is not reflective but offers high attenuation.
 Under certain circumstances, a 10mm thick plasma could reduce the radar
reflectivity of the underlying surface by 20dB.
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Types of Radar Echoes
ABC of CEM and RCS
 RCS fluctuates from one echo to the next. The fluctuation is caused by:
 Target scintillation
 Multipath effects
 Environmental effects as caused by atmosphere / seastate
 Changes due to aspect / grazing angles
 These are treated statistically and properties can be determined:
 RCS mean or median value
 Shape of the probability density function (PDF)
 Autocorrelation function (ACF)
 There are five (Peter Swerling) distinct cases describing typical radar echo
fluctuations
 Knowing the type of case helps in radar range calculations 32
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Types of Radar Echoes
ABC of CEM and RCS
 Swerling case 1 (Echoes from aerial/maritime targets)
 Echoes do not fluctuate much from one radar pulse to the next
 However echoes from two successive scans are independent from each other.
 Swerling case 2 (Rapidly fluctuating target)
 Echoes can vary from pulse to pulse
 Echos vary from scan to scan
 For Case 1 & Case 2 PDF is given by:
 P() = (1/ave) e –(/ave)
 Case 3 and Case 4
 These apply to target targets having one dominant reflecting surface For these Swerling
cases PDF is given by P() = (4/(ave)2) e –(2/ave)
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Electronic Counter Measures
ABC of CEM and RCS
Anti stealth technology includes the following techniques:
 Radar with wavelengths longer than the aircraft
 Bi-static and multi static radar configurations. These can use dedicated transmitters or
existing FM or even mobile phone broadcasts!
 Wide-band radar because it is difficult to make good wide-band RAM
 Wake and exhaust detection and tracking; neither of these can be completely eliminated
 Wingtip vortex detection as vortices generate low density regions capable of significant
changes in refractive index and hence generating radar echoes
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What about IR and Visible Range?
ABC of CEM and RCS
Important difference between Radar and IR / Visible frequency detection are:
 Laser targets are always larger than beam size
 Targets appearing smooth in microwave will appear as rough targets are wavelength
is smaller
 Diffuse surface at Radar frequencies may appear as a collection specular scatterer
 At higher IR and visible radiation cross section is  = GA
 where
  - cross section (m2)
  - reflectivity of surface
 G - gain of target
 A – projected physical area
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 Engineering Electromagnetics, 2nd
edition,
 N. Ida, Springer Verlag, NY, May 2004.
 Antenna Theory (Analysis and
Design)
 Constantine A. Balanis, John Wiley &
Sons, INC
 Radar Principles
 Peyton Z. Peebles, Jr., John Wiely and
Sons Inc.
 Electromagnetics
 Joseph A. Edminister, International
Edition, Schaum’s Radar Cross Section
Lectures
 Radar Cross Section Lectures
 Allen E. Fuhs, AIAA, 1633 Bradway,
New York, 100 19
 Radar Absorbing Materials (from
theory to Design and
Characterisation)
 K. J. Vinoy and R. M. Jha, NAL
Bangalore
 Time Domain Electromagetics
 S. M. Rao (editor), Academic Press
ABC of CEM and RCS
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Recommended Books / Report
14-Sep-2012

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www.zeusnumerix.com
+91 72760 31511
Abhishek Jain
abhishek@zeusnumerix.com
Thank You !

CEM Workshop Lectures (1/11): ABC of CEM and RCS

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CEM Workshop Lectures (1/11): ABC of CEM and RCS