RCS PREDICTION and REDUCTION TECHNIQUES Doğuş University  ECE Department Doğuş University  ECE Department ÇAĞATAY ULUIŞIK B52 F117

RCS is defined as : and given by : Radar Cross Section (RCS) The absolute magnitude of RCS is given in terms of area, typically in units of square meters (m 2 ) Relative magnitude is given in terms of dBm 2, where RCS is the area a target would have to occupy to produce the amount of reflected power (echo) that is detected back at the radar.

Radar Cross Section (RCS)

RCS frequency regions :  Rayleigh Region (low frequencies) Target dimensions are much less than the radar wavelength (l<< ). In this region RCS is proportional with the fourth power of the frequency  Resonance Region (medium frequencies) Target dimensions and the radar wavelength are in the same order (l  ).  Optical Region (high frequencies) Target dimensions are very large compared to the radar wavelength (l>> ). In this region RCS is roughly the same size as the real area of target.

Radar Cross Section (RCS) RCS of a target is dependent on several factors, such as,  Orientation (Viewing direction)  Radar frequency  Polarization of the radar signal (vertical, horizontal, circular)  Physical size of the target  Geometry of the target  Composition of the target (Surface Quality) When RCS of a target is of interest these parameters should be given :  Angle of incidence  Angle of scatter  Incident field polarization  Scattered field polarization  Frequency and target geometry  RCS value

Radar Cross Section (RCS) Cross Section of Real Targets The cross section of complex targets are complicated functions of the viewing aspect, frequency and polarisation. The most accurate method of determining the cross section of a target is by measurement. However it is often impractical to measure this over all aspect angles in azimuth and elevation. Target cross section is often related to their physical size, but under certain circumstances it may be much larger. For example a corner reflector has an extremely large target cross section in relation to its size, whereas a B2-B stealth bomber has a very small cross section.The RCS of a B26 bomber exceeds 35 dBm 2 (3100m 2 ) from certain aspect angles. In contrast, the RCS of the B2 stealth bomber is about – 40dBm 2. Because it is made up of reflections from a large number of scatterers, even very small changes in the aspect angle of the target results in relative phase changes between the scatterers and an altered cross section. Experimental cross section of the B-26 two engine bomber at 10 cm wavelength as a function of azimuth angle Experimental cross section of a Toyota pickup truck at 35 GHz as a function of azimuth angle

Radar Cross Section (RCS)

RCS PREDICTION Numerical Techniques FDTD : Finite Difference Time Domain (direct discretization of Maxwell’s Equation ) TLM : Transmission Line Matrix (3-dimensional transmission line matrix representation) MoM : Method of Moments (requires derivation of Green’s function) PE : Parabolic Equation (one-way axial propagation simulation) FE : Finite Element (requires discretization in terms of patches) Analytical Asymptotic Methods (High Frequency) GO : Geometric Optics (reflection + refraction) GTD : Geometric Theory of Diffraction (reflection + refraction + diffraction) PO : Physical Optics (reflection + refraction) PTD : Physical Theory of Diffraction (reflection + refraction+ diffraction)

RCS PREDICTION Time Domain Methods FDTD : Finite Difference Time Domain (Field Theory) TLM : Transmission Line Matrix (Circuit Theory) Frequency Domain Methods MoM : Method of Moments PE : Parabolic Equation FE : Finite Element GO : Geometric Optics GTD : Geometric Theory of Diffraction PO : Physical Optics PTD : Physical Theory of Diffraction

RCS PREDICTION SCATTERING  Reflection  Refraction  Diffraction  Tip Diffraction  Edge Diffraction GO, PO GTD, PTD Reflection Edge DiffractionTip Diffraction

RCS PREDICTION Geometric Optics Method Radar Cross Sections of Simple Canonical Objects

RCS PREDICTION MoM using NEC x y z x y z x y z

RCS PREDICTION MoM using NEC

RCS PREDICTION FDTD using F-SNRCS and F-BIRCS SNRCS.INP or BIRCS.INP Monostatic RCSBistatic RCS

SINGLE – RCS of a PLATE SNRCS.INP x y z E SNRCS.INP x y z E SNRCS.INP x y z E SNRCS.INP x y z E  i =  s =90   i =  s =0     i =  s =90   i =  s =0     i =  s =90   i =  s =0     i =  s =90   i =  s =0   

SINGLE – RCS of a PLATE  i =  s =90   i =  s =90     i =  s =90   i =  s =90     i =  s =90   i =  s =90     i =  s =90   i =  s =0    SNRCS.INP x y z E : FDTD : GO : NEC  10 4 SNRCS.INP x y z E SNRCS.INP x y z E SNRCS.INP x y z E

F-SNRCSNEC En uzun kenar:l=10 cm Segment uzunluğu  =0.25 cm  =0.5 cm Minimum dalga boyu min =2.5 cm min =5 cm Maksimum frekansf max =12 GHzf max =6 GHz  i =  s =90   i =  s =90    SNRCS.INP x y z E : FDTD : GO : NEC  10 4 SINGLE – RCS of a PLATE SNRCS.INP x y z E  i =  s =90   i =  s =90    SNRCS.INP x y z E Geometric Optics

SINGLE – RCS of a 4 Element Vertical Array F-SNRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1 cm Minimum dalga boyu min =10 cm Maksimum frekansf max =3 GHz  i =  s =90   i =  s =0     i =  s =90   i =  s =30    x y z E SNRCS.INP : FDTD : NEC SNRCS.INP x y z E : FDTD : NEC x y z E

SINGLE – RCS of a Square Dihedral  i =  s =45   i =  s =90    Geometric Optics F-SNRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm  =2cm Minimum dalga boyu min=10 cm min=20 cm Maksimum frekansfmax =3 GHzfmax=1.5 GHz SNRCS.INP x y z E : FDTD : GO : NEC : FDTD : GO : NEC x y z E SNRCS.INP x y z E

SINGLE – RCS of a Square Trihedral  i =  s =45   i =  s =45    Geometric Optics F-SNRCSNEC 635 segments En uzun kenar:l=40 cm Segment uzunluğu  =1cm  =4 cm Minimum dalga boyu min =10 cm min =40 cm Maksimum frekansf max =3 GHzf max =750 MHz x y z E : FDTD : GO : NEC

SINGLE – RCS of a Square Trihedral  i =  s =45   i =  s =45    Geometric Optics F-SNRCSNEC 2640 segments En uzun kenar:l=40 cm Segment uzunluğu  =1cm  =2 cm Minimum dalga boyu min =10 cm min =20 cm Maksimum frekansf max =3 GHzf max =1.5 GHz x y z E : FDTD : GO : NEC

SINGLE – RCS of a Rectangular Prism x y z E  i =  s =90   i =  s =0    SNRCS.INP : FDTD : GO : NEC Geometric Optics

BISTATIC – RCS of a Plate BIRCS BIRCS.INP l= f =3 GHz  i =90   i =90   s =90   s =0:1:360 Eta=0  (  polar.) x y z E BIRCSNEC En uzun kenar:l=10 cm Segment uzunluğu  =0.25 cm  =0.5 cm Minimum dalga boyu min =2.5 cm min =5 cm Maksimum frekansf max =12 GHzf max =6 GHz Geometric Optics NEC 0 dB   8.97 dB : FDTD : PO 30 dB   8.71 dB 30 dB   9.01 dB

BISTATIC – RCS of a Plate BIRCS BIRCS.INP l=2 f =6 GHz  i =90   i =90   s =90   s =0:1:360 Eta=0  (  polar.) Geometric Optics NEC 0 dB   2.7 dB : FDTD : PO 30 dB   3.14 dB 30 dB   2.99 dB x y z E Physic Optics :  : RCS as a function of angle (m 2 ) a, b : Sides of the plate (m)

BISTATIC – RCS of a Plate BIRCS BIRCS.INP l= f =3 GHz  i =90   i =60   s =90   s =0:1:360 Eta=0  (  polar.) y x z E BIRCSNEC En uzun kenar:l=10 cm Segment uzunluğu  =0.25 cm  =0.5 cm Minimum dalga boyu min =2.5 cm min =5 cm Maksimum frekansf max =12 GHzf max =6 GHz NEC 0 dB   9.8 dB : FDTD : PO 30 dB   9.64 dB 30 dB   dB

BISTATIC – RCS of a Plate BIRCS BIRCS.INP l=2 f =6 GHz  i =90   i =60   s =90   s =0:1:360 Eta=0  (  polar.) y x z E BIRCSNEC En uzun kenar:l=10 cm Segment uzunluğu  =0.25 cm  =0.5 cm Minimum dalga boyu min =2.5 cm min =5 cm Maksimum frekansf max =12 GHzf max =6 GHz NEC 0 dB  dB : FDTD : PO 30 dB   3.75 dB 30 dB   7.36 dB

BISTATIC – RCS of a 4 Element Vertical Array BIRCS NEC 0 dB   3.25 dB BIRCS.INP l=4 f =3 GHz  i =90   i =0   s =90   s =0:1:360 Eta=0  (  polar.) x y z E BIRCS 30 dB  dB BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm Minimum dalga boyu min =10 cm Maksimum frekansf max =3 GHz

BISTATIC – RCS of a 4 Element Vertical Array NEC 0 dB   4.99 dB  i =90   i =0   s =90   s =0:1:360 Eta=0  (  polar.) x y z E BIRCS 30 dB  –0.86 dB l =2 f =1.5 GHz BIRCS.INP l=2 BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm Minimum dalga boyu min =10 cm Maksimum frekansf max =3 GHz

BISTATIC – RCS of a 4 Element Vertical Array NEC 0 dB   2.63 dB BIRCS.INP l= f =750 MHz  i =90   i =0   s =90   s =0:1:360 Eta=0  (  polar.) x y z E BIRCS 30 dB  3.10 dB BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm Minimum dalga boyu min =10 cm Maksimum frekansf max =3 GHz

BISTATIC – RCS of a 4 Element Vertical Array BIRCS.INP l= / 2 f =375 MHz  i =90   i =0   s =90   s =0:1:360 Eta=0  (  polar.) x y z E BIRCS 30 dB  5.38 dB NEC 0 dB  5.46 dB BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm Minimum dalga boyu min =10 cm Maksimum frekansf max =3 GHz

BISTATIC – RCS of a 4 Element Vertical Array BIRCS.INP l= f =750 MHz  i =90   i =45   s =90   s =0:1:360 Eta=0  (  polar.) x y z E BIRCS 30 dB   0.25 dB NEC 0 dB   4.67 dB BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm Minimum dalga boyu min =10 cm Maksimum frekansf max =3 GHz

BISTATIC – RCS of a 4 Element Vertical Array BIRCS.INP l= f =750 MHz  i =90   i =75   s =90   s =0:1:360 Eta=0  (  polar.) x y z E NEC 0 dB   7.01 dB BIRCS 30 dB   3.64 dB BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm Minimum dalga boyu min =10 cm Maksimum frekansf max =3 GHz

BISTATIC – RCS of a Square Dihedral BIRCS.INP l= f =750 MHz  i =45   i =90   s =45   s =0:1:360 Eta=0  (  polar.) BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm  =2cm Minimum dalga boyu min=10 cm min=20 cm Maksimum frekansfmax =3 GHzfmax=1.5 GHz x y z E NEC 0 dB  5.59 dB BIRCS 30 dB  6.06 dB Geometric Optics

BISTATIC – RCS of a Square Dihedral BIRCS.INP l= f =750 MHz  i =45   i =90   s = 0:1  :360   s = 90  Eta=0  (  polar.) x y z E BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm  =2cm Minimum dalga boyu min=10 cm min=20 cm Maksimum frekansfmax =3 GHzfmax=1.5 GHz x y z E NEC 0 dB  5.59 dB BIRCS 30 dB  6.12 dB

BISTATIC – RCS of a Square Dihedral BIRCS.INP l= f =750 MHz  i =45   i =315   s = 45   s = 0:1  :360  Eta=0  (  polar.) BIRCSNEC En uzun kenar:l=40 cm Segment uzunluğu  =1cm  =2cm Minimum dalga boyu min=10 cm min=20 cm Maksimum frekansfmax =3 GHzfmax=1.5 GHz x y z E NEC 0 dB   4.44 dB BIRCS 30 dB  – 4.17 dB

BISTATIC – RCS of a Square Trihedral  i =45   i =315   s = 45   s = 0:1  :360  Eta=0  (  polar.) x y z E NEC En uzun kenar:l=1 m Segment uzunluğu  =0.1 m Minimum dalga boyu min=1 m Maksimum frekansfmax=300 MHz f =300 MHz NEC 0 dB  dB NEC 0 dB  5.79 dB f =150 MHz Geometric Optics

BISTATIC – RCS of a Rectangular Prism BIRCS BIRCS.INP l= f =375 MHz  i =90   i =0   s =90   s =0:1:360 Eta=0  (  polar.) NEC 0 dB  0.30 dB x y z E BIRCS 30 dB  – 1.77 dB Geometric Optics:

BISTATIC – RCS of a Rectangular Prism BIRCS BIRCS.INP l= f =375 MHz  i =90   i =60   s =90   s =0:1:360 Eta=0  (  polar.) NEC 0 dB   3.18 dB x y z E BIRCS 30 dB  – 3.79 dB

BISTATIC – RCS of a Rectangular Prism BIRCS.INP l= f =375 MHz  i =45   i =60   s =90   s =0:1:360 Eta=0  (  polar.) NEC 0 dB  2.35 dB x y z E BIRCS 30 dB  3.15 dB

x y z E BISTATIC – RCS of a Roketa NEC En uzun kenar:l = 4.5 m Segment uzunluğu  =0.25 m Minimum dalga boyu min=2.5 m Maksimum frekansfmax=120 MHz BIRCS  i =0   i =0   s =0   s =0:1:360 Eta=0  (  polar.) f =120 MHz 0 dB   dB f =60 MHz  i =0   i =0   s =0   s =0:1:360 Eta=0  (  polar.) 0 dB   dB

x y z E BISTATIC – RCS of a Roketa NEC En uzun kenar:l = 4.5 m Segment uzunluğu  =0.25 m Minimum dalga boyu min=2.5 m Maksimum frekansfmax=120 MHz BIRCS 0 dB  dB  i =90   i =0   s =90   s =0:1:360 Eta=0  (  polar.) f =60 MHz 0 dB  dB f =120 MHz  i =90   i =0   s =90   s =0:1:360 Eta=0  (  polar.)

x y z E BISTATIC – RCS of a Roketa NEC En uzun kenar:l = 4.5 m Segment uzunluğu  =0.25 m Minimum dalga boyu min=2.5 m Maksimum frekansfmax=120 MHz 0 dB  dB  i =45   i =0   s =45   s =0:1  :360  Eta=0  (  polar.) f =60 MHz 0 dB  5.63 dB f =120 MHz  i =45   i =0   s =45   s =0:1:360 Eta=0  (  polar.)

BIRCS REFERENCES  “Complex Electromagnetic Problems and Numerical Simulation Approaches” by Levent Sevgi, Doğuş University, IEEE Press, May  “Ece 5490/6490 RCS - Basic Concepts” by Dr. Randy J. Jost, Utah State University.  “Introduction to Radar Systems” by M.Skolnik, McGraw Hill,  “Sensors and Signals Notes” by H.Durrant-Whyte.