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Radar Systems Engineering Lect 7

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- 1. IEEE New Hampshire Section Radar Systems Course 1 Radar Cross Section 1/1/2010 IEEE AES Society Radar Systems Engineering Lecture 7 – Part 1 Radar Cross Section Dr. Robert M. O’Donnell IEEE New Hampshire Section Guest Lecturer
- 2. Radar Systems Course 2 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Block Diagram of Radar System Transmitter Waveform Generation Power Amplifier T / R Switch Antenna Propagation Medium Target Radar Cross Section Photo Image Courtesy of US Air Force Used with permission. Pulse Compression Receiver Clutter Rejection (Doppler Filtering) A / D Converter General Purpose Computer Tracking Data Recording Parameter Estimation Detection Signal Processor Computer Thresholding User Displays and Radar Control This lecture
- 3. Radar Systems Course 3 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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.
- 4. Radar Systems Course 4 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Factors Determining RCS Figure by MIT OCW.
- 5. Radar Systems Course 5 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Threat’s View of the Radar Range Equation Transmitted Pulse Received Pulse Target Cross Section σ Antenna Gain G Transmit Power PT Figure by MIT OCW. Distance from Radar to Target Radar Range Equation R S N = Pt G2 λ2 σ (4π)3 R4 k TS Bn L Cannot Control Can Control Cannot Control
- 6. Radar Systems Course 6 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 7. Radar Systems Course 7 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Radar Cross Section of Artillery Shell M107 Shell for 155mm Howitzer Aspect Angle (degrees) 0 20 40 60 80 100 120 140 160 180 RadarCrossSection(dBsm) 0 -60 -20 -30 -40 -50 -10 Typical Artillery Shell RCS vs. Aspect Angle of an Artillery Shell Courtesy US Marine Corps
- 8. Radar Systems Course 8 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Radar Cross Section of Cessna 150L S Band V 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 RadarCrossSection(dBsm) 0 -20 20 40 Cessna 150L (in takeoff) Cessna 150L (in flight) Scott Studio Photography with permissionScott Studio Photography with permission
- 9. Radar Systems Course 9 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Aspect Angle Dependence of RCS Cone Sphere Re-entry Vehicle (RV) Example Figure by MIT OCW.
- 10. Radar Systems Course 10 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Examples of Radar Cross Sections Square meters Conventional winged missile 0.1 Small, single engine aircraft, or jet fighter 1 Four passenger jet 2 Large fighter 6 Medium jet airliner 40 Jumbo jet 100 Helicopter 3 Small open boat 0.02 Small pleasure boat (20-30 ft) 2 Cabin cruiser (40-50 ft) 10 Ship (5,000 tons displacement, L Band) 10,000 Automobile / Small truck 100 - 200 Bicycle 2 Man 1 Birds (large -> medium) 10-2 - 10-3 Insects (locust -> fly) 10-4 - 10-5 Radar Cross Sections of Targets Span at least 50 dB Adapted from Skolnik, Reference 2
- 11. Radar Systems Course 11 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 12. Radar Systems Course 12 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 Surfaces Altimeter Seeker Body Shape Exhaust
- 13. Radar Systems Course 13 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 14. Radar Systems Course 14 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Scattering Mechanisms for an Arbitrary Target Tip Diffraction at Aircraft Nose Diffraction at Corner Return From Engine Cavity Edge Diffraction Tip Diffraction from Fuel Tank Specular Surface Reflection Multiple Reflection Wave Echo from Traveling Wave Gap, Seam, or Discontinuity Echo Backscatter from Creeping Wave Curvature Discontinuity Return
- 15. Radar Systems Course 15 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Measured RCS of C-29 Aircraft Model Full Scale C-29 BAE Hawker 125-800 Aspect Angle (degrees) RCS(dBsm) 0 60 120 180 240 300 360 20 -20 -10 0 10 -30 1/12 Scale Model Measurement X-Band HH Polarization Waterline Cut Wing Leading Edge Fuselage Specular Courtesy of Arpingstone Adapted from Atkins, Reference 5 Courtesy of MIT Lincoln Laboratory
- 16. Radar Systems Course 16 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 17. Radar Systems Course 17 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Techniques for RCS Analysis Scaled Model Measurements Theoretical Prediction Full Scale Measurements Courtesy of MIT Lincoln Laboratory Used with Permission
- 18. Radar Systems Course 18 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 Courtesy of MIT Lincoln Laboratory Used with Permission
- 19. Radar Systems Course 19 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Full Scale Measurement of Johnson Generic Aircraft Model (JGAM) RATSCAT Outdoor Measurement Facility at Holloman AFB Courtesy of MIT Lincoln Laboratory Used with Permission
- 20. Radar Systems Course 20 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Compact Range RCS Measurement Radar Reflectivity Laboratory (Pt. Mugu) / AFRL Compact Range (WPAFB) Courtesy of U. S. Navy. Target Main Reflector Feed Antenna Plane Wave Low RCS Pylon Sub-Reflector
- 21. Radar Systems Course 21 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Scale Model Measurement Subscale Measure at frequency S x F Scale Factor S (Reduced Size) Full Scale Measure at frequency f MQM-107 Drone in 0.29, 0.034, and 0.01 scaled sizes Courtesy of MIT Lincoln Laboratory Used with Permission
- 22. Radar Systems Course 22 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Scaling of RCS of Targets Scale 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
- 23. Radar Systems Course 23 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 24. Radar Systems Course 24 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 25. Radar Systems Course 25 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Radar Cross Section of Sphere Rayleigh Region λ >> a σ = k / λ4 Mie or Resonance Region Oscillations Backscattered wave interferes with creeping wave Optical Region λ << a σ = π a2 Surface and edge scattering occur Circumference/ wavelength = 2πa / λ RadarCrossSection/πa2 10 1 10-3 10-2 10-1 0.1 0.2 0.4 0.7 1 2 4 7 10 20 Rayleigh Region Resonance or Mie Region Optical Region a Higher Wavelengths Lower Wavelengths Figure by MIT OCW. λ >> a λ << a
- 26. Radar Systems Course 26 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 27. Radar Systems Course 27 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 Surface perpendicular to LOS Doubly Curved Surface Surface perpendicular to LOS Straight Edge Edge perpendicular to LOS Curved Edge Edge element perpendicular to LOS Cone Tip Axial incidence Where: 22 eff /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
- 28. Radar Systems Course 28 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 29. Radar Systems Course 29 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 IE r 2 I 2 S2 r E E r4lim r r π=σ ∞→ SE r
- 30. Radar Systems Course 30 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Maxwell’s Equations • Source free region of space: • Free space constitutive relations: 0)t,r(B 0)t,r(D t )t,r(D )t,r(H t )t,r(B )t,r(E =⋅∇ =⋅∇ ∂ ∂ =×∇ ∂ ∂ −=×∇ → → rr rr rr rr rr rr )t,r(H)t,r(B )t,r(E)t,r(D o o rrrr rrrr μ= ε= = Free space permittivity = Free space permeability oε oμ
- 31. Radar Systems Course 31 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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(H e)r(ERe)t,r(E ω− ω− = = rrrr rrrr
- 32. Radar Systems Course 32 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Boundary Conditions • Tangential components of and are continuous: • For surfaces that are perfect conductors: • Radiation condition: – As E r H r 21 21 HxnˆHxnˆ ExnˆExnˆ rr rr = = 0Exnˆ = r r 1 )r(Er ∝∞→ rr 2222 1111 HE HE rr rr εμ εμ nˆ Surface BoundaryMedium 1 Medium 2
- 33. Radar Systems Course 33 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 VHVV ikr HS VS S E E SS SS r e E E E r 2 VHVH 2 HHHH 2 VVVV S4 S4 S4 π=σ π=σ π=σ RLLLRR ,, σσσ HVVH σ=σ Scattering Matrix - S
- 34. Radar Systems Course 34 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 35. Radar Systems Course 35 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 36. Radar Systems Course 36 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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
- 37. Radar Systems Course 37 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 E t H y H x H t E x E z E t H z H y ∂ ∂ ε= ∂ ∂ − ∂ ∂ ∂ ∂ μ−= ∂ ∂ − ∂ ∂ ∂ ∂ ε= ∂ ∂ − ∂ ∂ ZoXY YoZX XoYZ H t E y E x E t H x H z H t E z E y ∂ ∂ μ−= ∂ ∂ − ∂ ∂ ∂ ∂ ε= ∂ ∂ − ∂ ∂ ∂ ∂ μ−= ∂ ∂ − ∂ ∂ 0 y = ∂ ∂ • H-field polarization • E-field polarization ZXY EEH ZXY HHE y
- 38. Radar Systems Course 38 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Maxwell’s Equations in Rectangular Coordinates • Examine 2 D problem – no dependence: • Equations decouple into H-field polarization and E-field polarization 0 y = ∂ ∂ • H-field polarization ZXY EEH • E-field polarization ZXY HHE ZoXY YoZX XoYZ E t H y H x H t E x E z E t H z H y ∂ ∂ ε= ∂ ∂ − ∂ ∂ ∂ ∂ μ−= ∂ ∂ − ∂ ∂ ∂ ∂ ε= ∂ ∂ − ∂ ∂ ZoXY YoZX XoYZ H t E y E x E t H x H z H t E z E y ∂ ∂ μ−= ∂ ∂ − ∂ ∂ ∂ ∂ ε= ∂ ∂ − ∂ ∂ ∂ ∂ μ−= ∂ ∂ − ∂ ∂ = 0 = 0 = 0 = 0 y
- 39. Radar Systems Course 39 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society • 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,xE x t,y,xE z t,y,xH t Z XYo ∂ ∂ − ∂ ∂ = ∂ ∂ μ− ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ +−⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ +Δ+ Δ − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ +−⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ+ Δ + Δ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ − Δ + Δ +−⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ + Δ + Δ + Δ μ − o Z ooZo Z oXoZ X oo X oXoZo X oX Z T o Z o X oY T o Z o X oY T o t, 2 z,xEt, 2 z,xE 1 t,z, 2 xEt,z, 2 xE 1 2 t, 2 z, 2 xH 2 t, 2 z, 2 xH z xy Ex EZ HY Yee’s Lattice (2-D)
- 40. Radar Systems Course 40 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 Matched 0H x2 1 tc 1 txc 1 y2 2 2 2 2 2 =⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ∂ ∂ − ∂ ∂ + ∂∂ ∂ 2nd Order ABC 1st Order ABC 0H tc 1 xz2 1 y =⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ +⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ Total Field Target Domain of Computation Absorbing Boundary 0ETAN = Scattered Field
- 41. Radar Systems Course 41 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 5 Courtesy of MIT Lincoln Laboratory
- 42. Radar Systems Course 42 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Description of Scattering Cases on Video Finite Difference Time Domain (FDTD) Simulations Ei Hi Hi Ei 15 deg 15 deg Hi 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 Ei Hi EiEi Hi Courtesy of MIT Lincoln Laboratory Used with Permission
- 43. Radar Systems Course 43 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society 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 of MIT Lincoln Laboratory Used with Permission
- 44. Radar Systems Course 44 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Case 1 Courtesy of MIT Lincoln Laboratory Used with Permission
- 45. Radar Systems Course 45 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society FD-TD Simulation of Scattering by Strip Case 1 Courtesy of MIT Lincoln Laboratory Used with Permission
- 46. Radar Systems Course 46 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society FD-TD Simulation of Scattering by Cylinder 0.5 m Hy 2 m • Gaussian pulse plane wave incidence • H-field polarization (Hy plotted) • Phenomena: creeping waveCase 5 Courtesy of MIT Lincoln Laboratory Used with Permission
- 47. Radar Systems Course 47 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Case 5 Courtesy of MIT Lincoln Laboratory Used with Permission
- 48. Radar Systems Course 48 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society FD-TD Simulation of Scattering by Cylinder Case 5 Courtesy of MIT Lincoln Laboratory Used with Permission
- 49. Radar Systems Course 49 Radar Cross Section 1/1/2010 IEEE New Hampshire Section IEEE AES Society Backscatter of Short Pulse from Sphere Creeping Wave Return Specular Return Radius of sphere is equal to the radar wavelength Figure by MIT OCW.

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