Radar Range Equation

1. Radar Range Equation

2. Objectives • Calculate range for a pulsed radar system. • Calculate and interpret minimum range, unambiguous range and range resolution • Outline the derivation of the simplified radar range equation • Solve for maximum radar range using the simplified radar range equation.

3. Basic Range • Range = c Dt 2 • Dt = total time • elapsed for 2 – way trip • for pulse 16.5 ms 16.5 ms 4.95 km • Example: How far away is a contact if it takes 33msecs for the pulse to return? • R = (3X108 m/s)(33x10-6 s) = 9900 m = 4.95 km 2 2

4. Range Calculations Shortest range at which radar can first detect a target Range beyond which target appears as “second time around” The min distance between 2 targets at nearly the same range that generate 2 separate returns

5. “Simplified” Radar Range Equation

6. Power Out • Assume pulse radiates uniformly out from antenna in all directions Power density at any given point is

7. Effective Antenna Aperture • Ae is a measure of actual antenna performance • both transmit and receive • The larger the aperture, the better the radar’s performance • But no 100% efficient antenna, r is a decimal # < 1.0 A = antenna physical area ρ = antenna [in]efficiency Ae = antenna aperture

8. Directional Gain • Omni-directional beam spreads spherically surface area = 4R2 • Directional beam surface area = (R)(R) = R2  • Directional Gain = Maximum Radiation Intensity Average Radiation Intensity = Maximum power per steradian Total power radiated isotropic • Based purely on dimensions/shape of antenna R R R

9. L W Power Gain • Also simply called Gain…power out with respect to signal losses between transmitter and antenna. • Remember for radar antennas   = k/L therefore; • Includes efficiency of radar based on shape/spill over/losses  =k / Length  = k / Width

10. Gain Example What is the gain of an AN/APS-116 (S-3 radar) that is operating at 9.8 GHz? The antenna is 1.07 m wide and 0.61 m high with an efficiency estimated at 77%.

11. Power Gain Combine with Power Gain (G) of a directed antenna…

12. Radar Cross Section

13. Reflection Effective area that reflects the Radar Energy back to the receiver is Radar Cross Section “σ” Returned Ray Incident Rays

14. Return Signal Spreading Signal undergoes spherical spreading on way back to receiver Pr = Power Returning from target

15. Received at Antenna • Only a small amount of return pulse is collected • Effective Antenna Aperture Ae determines amount of energy received A = area antenna ρ = antenna efficiency

16. Detection When the Minimum Signal for Detection (Smin) is equal to the power density at the receiver, target detection will result. Therefore,

17. Rmax Solve for Maximum Range for Detection Units check!

18. Example: SPS-49 2D Air Search Radar • Radar Parameters • Peak Power: 500 kW • Antenna Dimensions: 8m wide x 4m high (Orange Peel Parabolic design) • Frequency: 700 MHz (approx. mid range) • Antenna Gain: 34 dB • PRF: 230pps / 800 or 1000pps • PW: 75 μs (compressed) or 2 μs (short range) • Determine horizontal and vertical beamwidths • Calculate Directional Gain (Gdir), efficiency and (Ae) • Calculate Rmax for a 1 square meter RCS and Smin of 1pW • Change peak power to 6400 kW . Determine new max range for the same target.

19. Objectives • Calculate range for a pulsed radar system. • Calculate and interpret minimum range, unambiguous range and range resolution • Outline the derivation of the simplified radar range equation • Solve for maximum radar range using the simplified radar range equation.