1. Radar equation review 1/19/10

2. Radar eq (Rayleigh scatter) The only variable is h, the pulse length Most radars have a range of h values. Rewrite the radar eq as: Convert to log form:

3. Radar equation, Mie scatter

4. Uses of the radar equation Convert P r to Z Used for specifications, such as minimum detectable signal (minimum detectable reflectivity at some standard range) The general form of the radar equation also applies to sodars and lidars

5. Important radar parameters Wavelength (cm vs mm) Peak transmit power Pulse vs. continuous wave (CW) Pulse length Pulse repetition frequency Beam width Minimum detectable signal Duty cycle: PW/PRT or P avg /P peak Receiver bandwidth Antenna size (gain) Scan rate

6. Lidar equation But, additional terms representing absorption and extinction are important.

9. Beam width estimate For D = 8 ft (2.44 m): if  = 3.2 cm, then  = 1.27(0.032)/2.44 * 57.3 = 0.95 deg if = 8.6 mm, then  = 1.27(0.0086)/2.44 * 57.3 = 0.26 deg For D = 2 ft (0.61 m): if = 3.2 mm, then  = 1.27(.0032)/0.61 * 57.3 = 0.38 deg 3.2 cm 9.4 GHz 8.6 mm 35 GHz 3.2 mm 94 GHz These are estimates; need to conduct test on antenna range to get actual value

10. Radial profile of Z min for WSR-88D At 50 km: Z = 58.4 dB + (-107 dBm) +20 log 10 (50) = -20.6 dBZ. At 10 km: Z = 58.4 +(-107) + 20log 10 (10) = -28.6 dBZ. Range (km)  r = 2 km end