Chapter Radar Cross Section ( R C S ) 엄효준교수 한국과학기술원
Contents.1. RCS Definition.. RCS Prediction Methods.3. RCS Dependency on Aspect Angle and Frequency.4. RCS Dependency on Polarization.5. RCS of Simple Objects Sphere, Ellipsoid, Circular Flat Plate, Truncated Cone, Cylinder Rectangular Flat Plate,Triangular Flat Plate.6. RCS of Complex Objects.7. RCS Fluctuations and Statistical Models
.1. RCS Definition (1) Transmitter Receiver P Di R P r P r 4πR Radar antenna 가 far field 에있다고가정. R P Di target Transmitter 와 receiver (antenna) 위치가같으면 monostatic RCS Transmitter 와 receiver (antenna) 위치가다르면 bistatic RCS : incident power density on a target : distance between target and radar : reflected power from a target Pr = P Di (.1) :target radar cross section (RCS)
.1. RCS Definition () P Dr :scattered power density at receiving antenna P Dr Pr = (.) 4π R (.1) 과 (.) 로부터 = P Dr 4πR = lim 4πR R PDi P P Dr Di t t : total target scattered RCS = 1 4π π π φ = 0θ = 0 s s ( θ, φ ) sin θ dθ dφ s s 주로 optical region 에서 far field monostatic RCS 가이책에서쓰임. s s s
.. RCS Prediction Methods Exact method: Maxwell 방정식또는적분방정식응용 Approximate method: target 의정확한 RCS 예측은계산상의어려움이수반되므로여러가지형태의근사식이사용됨. Geometrical Optics (GO) Physical Optics (PO) Geometrical Theory of Diffraction (GTD) Physical Theory of Diffraction (PTD)
.3. RCS Dependency on Aspect Angle/Freq RCS 는 aspect angle 과주파수의함수임. Isotropic 인경우 : radar 1.0 m RCS=1m RCS=1m Composite RCS=m 1.0 cosθ θ θ 1.0 m Electrical spacing = (1.0 cosθ ) λ λ : 파장
.4. RCS Dependency on Polarization (1).4.1. Polarization wave 가 z 방향으로진행하는경우 : E = E sin( ωt kz) x 1 E = E sin( ωt kz+ δ ) y 1 ω : wave frequency δ : phase difference r E = ae ˆ sin( ωt kz) + ae ˆy sin( ωt kz+ δ ) x aˆ x, ˆ y a : Unit vectors k = π λ z E x EE x ycosδ Ey + = E E E E 1 1 (sin δ ) Polarization Ellipse
.4. RCS Dependency on Polarization () z z z linearly polarized RCP LCP E 1 = 0 linearly polarized in y-direction E E ο = E, δ 90 = E, δ = 90 1 = 1 ο left circularly polarized (LCP) right circularly polarized (RCP)
.4. RCS Dependency on Polarization (3).4.. Target Scattering Matrix Backscattered RCS 는 Scattering matrix [S] 로표현가능함 s i i E 1 E 1 s11 s1 E 1 = [ S] = s { i i { E E { s1 s E Scattering 산란 field matrix 입사 field 11 1 = 4π R s 11 1 1 s1 s s [S] 는다양한 polarization basis 로표현이가능함.
.5. RCS of Simple Objects (1).5.1. Sphere : Mie series Perfectly conducting sphere 경우 Normalized RCS (db) Rayleigh region Mie region Optical region Sphere circumference in wavelengths < 완전도체구의 normalized RCS>
.5. RCS of Simple Objects ().5.. Ellipsoid approximate backscattered RCS = ( sinθ) ( cosφ) + ( sinθ) ( sinφ) + ( cosθ).5.3. Circular Flat Plate π abc a b c For non-normal incidence, approximate backscattered RCS 4 J (krsin θ ) 1 = π θ kr kr sinθ ( cos ) 1 () J : Bessel function of the first kind of order 1
.5. RCS of Simple Objects (3).5.4. Truncated Cone.5.5. Cylinder.5.6. Rectangular Flat Plate.5.7. Triangular Flat Plate 다양한 simple object 의 RCS 는 Maxwell 방정식 또는적분방정식에경계조건을적용하여해석가능.
.6. RCS of Complex Objects 복잡한 target RCS 는간단한 target RCS 의 coherent combination 으로계산가능함. 복잡한 target RCS 는간단한 target 의 individual scattering centers 의합으로표시함. 복잡한 target 이동일한 simple scattering centers 의합으로표시되는경우 : Swerling 1 or targets 복잡한 target 이한개의 dominant scattering center 와다수의 smaller scattering centers 로표시되는경우 : Swerling 3 or 4 targets
.7 RCS Fluctuations & Statistical Models (1) 실제 RCS 는크기와위상이시간에대해변함 (fluctuation). glint: 위상변화 scintillation: 크기변화 RCS 는 random process 로모델링함..7.1. RCS Statistical Models Chi-Square of Degree m m 1 m m pdf : f ( ) = e Γ( m) av av Γ( m ) : gamma function av : average m av
.7 RCS Fluctuations & Statistical Models () Swerling I and II (Chi-Square of Degree ) 1 pdf : f ( ) e = av av - completely correlated during scan - uncorrelated from scan to scan (slow fluctuation) Swerling I - uncorrelated from pulse to pulse (rapid fluctuation) Swerling II - many independent fluctuating point scatterers of equal dimensions
.7 RCS Fluctuations & Statistical Models (3) Swerling III and IV (Chi-Square of Degree 4) 4 pdf : f ( ) e av = av - uncorrelated from scan to scan Swerling III - uncorrelated from pulse to pulse Swerling IV - 한개의dominant scatterer 와다수의작은 reflector 가존재하는경우