Radar equation review
1/19/10
Radar eq (Rayleigh scatter)
  3
 PtG 2h  K 2
Pr  
 
  2
2
16 64  ln 2    
 r
 c
K2
r
2

vol

6
Di 


Z
The only variable is h, the pulse length
Most radars have a range of h values.

Rewrite the radar eq as:
Z  c 3 Pr r
Convert to log form:
Z  C3  Pr  20log10 (r)
2
Radar equation, Mie scatter
1


1
2 2
Pr   2
 PtG  h   2

 16 64  ln 2
r
 c'

r2

vol

 i 

Uses of the radar equation
• Convert Pr 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
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 Pavg/Ppeak
Receiver bandwidth
Antenna size (gain)
Scan rate
Lidar equation
• But, additional terms representing
absorption and extinction are important.
Table 2. Specifications for a W-band FMCW radar.
Frequency
95 GHz
Antenna type
zenith pointing, transmit and receive antennas
Power
1 W CW
PRF
1-10 kHz
Range Resolution
5-100 m
Polarization (receiving antenna)
orthogonal
Phase stabili ty (see comment
2
above for X-Ka band spec)
Minimum detectable Z at 5 km
-40 dBZ (1.6 s integration time; 30 m range
resolution)
Antenna dish diameter
24Σ
Beam width
0.25 degrees
First side lobe (one way)
-17 dB
Cross-polar isolation
-25 dB spec
-30 dB goal
Beam width estimate
1.27 
1 
D
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
 m):
For D = 2 ft (0.61
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
Radial profile of Zmin for WSR-88D
Range (km)
0.0
-5.0
0
10
20
30
40
50
60
70
80
90
100
-10.0
-15.0
-20.0
-25.0
-30.0
-35.0
r = 2 km
-40.0
-45.0
At 50 km: Z = 58.4 dB + (-107 dBm) +20 log10(50) = -20.6 dBZ.
At 10 km: Z = 58.4 +(-107) + 20log10(10) = -28.6 dBZ.
end