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The Radar Equation Introduction to Radar Systems The Radar Equation 361564_P_1Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Disclaimer of Endorsement and Liability • The video courseware and accompanying viewgraphs presented on this server were prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor the Massachusetts Institute of Technology and its Lincoln Laboratory, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, products, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors or the Massachusetts Institute of Technology and its Lincoln Laboratory. MIT Lincoln Laboratory 361564_P_2Y.ppt• The views and opinions expressed herein do not necessarily state or ODonnell 06-13-02 reflect those of the United States Government or any agency thereof or any of their contractors or subcontractors Introduction – The Radar Range Equation Propagation Waveform Transmitter Medium Generator Signal Processor Target Cross Pulse Doppler Section Receiver A / D Antenna Compression Processing Main Computer Console / Tracking & Display Detection Parameter Estimation Recording The Radar Range Equation Connects: 1. Target Properties - e.g. Target Reflectivity (radar cross section) 2. Radar Characteristics - e.g. Transmitter Power, Antenna Aperture 3. Distance between Target and Radar - e.g. Range 4. Properties of the Medium - e.g. Atmospheric Attenuation. 361564_P_3Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Outline • Introduction • Introduction to Radar Equation • Surveillance Form of Radar Equation • Radar Losses • Example • Summary 361564_P_4Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Radar Range Equation Power density from P = peak transmitter P t uniformly radiating antenna t power 2 transmitting spherical wave 4 π R R = distance from radar R 361564_P_5Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Radar Range Equation (continued) Power density from P t Pt = peak transmitter isotropic antenna 4 π R2 power R = distance from radar Power density from Pt Gt directive antenna G = transmit gain 4 π R2 t Gain is the radiation intensity of the antenna in a given direction over that of an isotropic (uniformly radiating) source . Gain = 4 π A / λ2 361564_P_6Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Definition of Radar Cross Section (RCS or σ) R Incident Energy Radar Antenna Target Reflected Energy Radar Cross Section (RCS or σ ) is a measure of the energy that a radar target intercepts and scatters back toward the radar σ = radar cross section Power of reflected P G t t σ units (meters)2 signal at target 4 π R2 Power density of Power density of reflected Pt Gt σ reflected signal falls signal at the radar 4 π R2 4 π R2 off as (1/R2 ) 361564_P_7Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Radar Range Equation (continued) Power density of reflected Pt Gt σ signal at radar 4 π R2 4 π R2 R Radar Target Antenna Reflected Energy The received power = the power density at the radar times the area of the receiving antenna Power of reflected Pt Gt σ Ae Pr = power received signal from target and Pr = 2 2 received by radar 4 π R 4 π R Ae = effective area of receiving antenna 361564_P_8Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Sources of Noise Received by Radar • The total effect of these Galactic Noise noise sources is represented by a single Solar Noise noise source at the antenna output terminal. Atmospheric Noise • The noise power at the receiver is given by: N = k Bn Ts Man Made Courtesy of Lockheed Martin. Receiver Interference Ground Noise Used with permission. ( Radars, Radio Stations, etc) Transmitter k = Boltzmans constant -23 o (Receiver, waveguide, and duplexer noise) = 1.38 x 10 joules / deg K Ts= System Noise Noise from Many Sources Competes Temperature Bn = Noise bandwidth of with the Target Echo receiver 361564_P_9Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Radar Range Equation (continued) Signal Power reflected Pt Gt σ Ae Pr = from target and 4 π R2 4 π R2 received by radar Average Noise Power N= k Ts Bn Assumptions : Signal to Noise Ratio S / N = Pr / N Gt = Gr L = Total System Losses o 2 2 To = 290 K Pt G λ σ S / N = 3 4 (4 π ) R k Ts Bn L Signal to Noise Ratio (S/N or SNR) is the standard measure of a radar’s ability to detect a given target at a given range from the radar “ S/N = 13 dB on a 1 m2 target at a range of 1000 km” radar cross section of target 361564_P_10Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 System Noise Temperature • The System Noise Temperature, TS , is divided into 3 components : Ts = Ta + Tr + Lr Te • Ta is the contribution from the antenna – Apparent temperature of sky (from graph) – Loss within antenna • Tr is the contribution from the RF components between the antenna and the receiver – Temperature of RF components • Lr is the loss of input RF components • Te is the temperature of the receiver – Noise factor of receiver 361564_P_11Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Outline • Introduction • Introduction to Radar Equation • Surveillance Form of Radar Equation • Radar Losses • Example • Summary 361564_P_12Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Track Radar Range Equation Track Radar Equation 2 2 Pt G λ σ S / N = 3 4 (4 π ) R k Ts Bn L • When the location of a target is known and the antenna is pointed toward the target. Track Example 361564_P_13Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Track & Search Radar Range Equations Search Radar Equation Track Radar Equation 2 2 Pt G λ σ Pav Ae ts σ S / N = 3 4 S / N = 4 (4 π ) R k Ts Bn L 4 π Ω R k Ts L • When the location of a • When the target’s location is target is known and the unknown, and the radar has to antenna is pointed toward search a large angular region the target. to find it. Search Volume Track Example Where: Pav = average power Ω = solid angle searched ts = scan time for Ω Αe = antenna area Search Example 361564_P_14Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Search Radar Range Equation Pav Ae ts σ S / N = 4 4 π Ω R k Ts L Re-write as: f (design parameters) = g (performance parameters) Angular coverage Range coverage Measurement quality 4 π Ω R4 (S/N) Pav Ae = Time required kTs L σ ts Target size 361564_P_15Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Scaling of Radar Equation S P A t σ 4 = av e s P = 4π R Ω k Ts L (S/N) N 4 av 4π R Ω k Ts L Ae ts σ • Power required is: – Independent of wavelength – A very strong function of R – A linear function of everything else Example Radar Can Perform Search at 1000 km Range How Might It Be Modified to Work at 2000 km ? Solutions Increasing R by 3 dB (x 2) Can Be Achieved by: 1. Increasing Pav by 12 dB (x 16) or 2. Increasing Diameter by 6 dB (A by 12 dB) or 3. Increasing ts by 12 dB or 4. Decreasing Ω by 12 dB or 5. Increasing σ by 12 dB or 6. An Appropriate Combination of the Above 361564_P_16Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Search Radar Performance 100 K R = 3000 km R = 300 km R = 1000 km ASR- 9 10 K ARSR- 4 Airport Surveillance Radar WSR-88D/NEXRAD R = 100 km 1 K ASR- 9 TDWR Search 1 sr 100 In 10 sec for 1 sq m Target R = 30 km S/N = 15 dB Average Power (W) Loss = 10 dB T = 500 deg 10 Courtesy of Northrop Grumman. ASDE- 3 Used with permission. R = 10 km 1 0.1 1 10 100 (Equivalent) Antenna Diameter (m) 361564_P_17Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Search Radar Performance 100 K ASDE- 3 R = 3000 km Airport Surface Detection R = 300 km R = 1000 km Equipment 10 K ARSR- 4 WSR-88D/NEXRAD R = 100 km 1 K ASR- 9 TDWR Search 1 sr 100 In 10 sec for 1 sq m Target R = 30 km S/N = 15 dB Average Power (W) Loss = 10 dB 10 T = 500 deg Courtesy Lincoln Laboratory ASDE- 3 R = 10 km 1 0.1 1 10 100 (Equivalent) Antenna Diameter (m) 361564_P_18Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Search Radar Performance ARSR- 4 100 K Air Route Surveillance Radar R = 3000 km R = 300 km R = 1000 km 10 K ARSR- 4 WSR-88D/NEXRAD R = 100 km 1 K ASR- 9 TDWR Search 1 sr ARSR- 4 Antenna 100 In 10 sec for 1 sq m Target (without Radome) R = 30 km S/N = 15 dB Average Power (W) Loss = 10 dB 10 T = 500 deg ASDE- 3 R = 10 km 1 0.1 1 10 100 (Equivalent) Antenna Diameter (m) Courtesy of Northrop Grumman. Used with permission. 361564_P_19Y.ppt MIT Lincoln Laboratory ODonnell 06-13-02 Search Radar Performance 100 K R = 3000 km WSR-88D / NEXRAD R = 300 km R = 1000 km 10 K ARSR- 4 WSR-88D/NEXRAD R = 100 km 1 K ASR- 9 TDWR Search 1 sr 100 In 10 sec for 1 sq m Target R = 30 km S/N = 15 dB Average Power (W) Loss = 10 dB 10 T = 500 deg ASDE- 3 Courtesy of NOAA.
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