Radar equation review 1/19/10. Radar eq (Rayleigh scatter) The only variable is h, the pulse length...
Transcript of Radar equation review 1/19/10. Radar eq (Rayleigh scatter) The only variable is h, the pulse length...
Radar equation review
1/19/10
Radar eq (Rayleigh scatter)
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P r =π 3
16⋅64 ⋅ln 2
⎡
⎣ ⎢
⎤
⎦ ⎥⋅
PtG2θφh
λ2
⎡
⎣ ⎢
⎤
⎦ ⎥⋅
K 2
r 2vol
∑ Di6
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
= c ⋅K 2
r 2⋅Z
The only variable is h, the pulse lengthMost radars have a range of h values.
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Z = c3P rr2
Rewrite the radar eq as:
Convert to log form:
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Z = C3 + P r + 20log10(r)
Radar equation, Mie scatter
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P r =1
π 2 ⋅16⋅64 ⋅ln 2
⎡
⎣ ⎢ ⎤
⎦ ⎥⋅ PtG2λ2θφh[ ]⋅
1
r 2vol
∑ σ i
⎡
⎣ ⎢
⎤
⎦ ⎥
= c'⋅η
r 2
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 1. Specifications for the dual frequency, dual pol radar system. Frequency 9.4-9.6 GHz 34-36 GHz Polarization H and V (STAR) H and V (STAR) Phase stability (I don’t have a firm number for this, but we will use a low-phase noise design)
±2° ±2°
Pulse lengths 0.2 – 2.0 s 0.2 – 1.0 s PRF 250 – 2500 Hz 2000 – 10,000 Hz Minimum detectable Z at 10 km -30 dBZ (6 /deg s; 10:1
pulse compression, 1 s compressed pulse width;
1% duty)
-35 dBZ (6 /deg s; 20:1 pulse compressio ; n 0.4 s compressed pulse;
3% duty) Antenna dish diameter 8 ft Beam widt h (max) 1° 0.25° First side lobe (one way) -17 dB -17 dB Cross-polar isolation -25 dB spec; -30 dB goal
-25 dB spec; -30 dB
goal Bore site poin tangle error ±0.1° ( weneed to check thi )s azim/elev pointing accuracy ±0.1° Max scanning rate 36 / deg sin azimut ,h 6 /deg s in elevation Range gates (minimum) 1024 1024
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 stability (see comment above for X-Ka band spec)
±2°
Minimum detectable Z at 5 km -40 dBZ (1.6 s integration tim ;e 30 m range resolution)
Antenna dish diameter 24” Beam width 0.25 degrees First side lobe (one way) -17 dB Cross-polar isolation -25 dB spec
-30 dB goal
Beam width estimate
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θ1 =1.27λ
DFor D = 8 ft (2.44 m): if = 3.2 cm, then θ = 1.27(0.032)/2.44 * 57.3 = 0.95 deg
if = 8.6 mm, then θ = 1.27(0.0086)/2.44 * 57.3 = 0.26 deg
For D = 2 ft (0.61 m):if = 3.2 mm, then θ = 1.27(.0032)/0.61 * 57.3 = 0.38 deg
3.2 cm 9.4 GHz8.6 mm 35 GHz3.2 mm 94 GHz
These are estimates; need to conduct test on antenna range to get actual value
Radial profile of Zmin for WSR-88D
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.
-45.0
-40.0
-35.0
-30.0
-25.0
-20.0
-15.0
-10.0
-5.0
0.0
0 10 20 30 40 50 60 70 80 90 100
Range (km)
r = 2 km
end