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Equations:
For one echo pulse |
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(S/N)P
= ((P x G2
x λ2
x δ) / ((4 x pi)3
x R4
x (kTB) x L )) |
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For
some integrated pulses |
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S/N =
((P x G2
x λ2
x δ x n ) / ((4 x pi)3
x R4 x (kTB) x L )) |
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S/N
total |
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S/Nt
= ((P x G2
x
λ2
x δ x (Ti x PRF)
x T) / (4 x pi)3
x R4
x (kT) x L)) |
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Where: |
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P = transmitted power ( in Watt) |
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G = antenna gain (figure not dB) |
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λ
= wavelength (m) |
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δ
= Radar Cross Section (RCS) sq. m |
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R = target range |
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kTB
= k= Boltzmann-Constant
(1.38-23),
T = absolute Temperature in
degree Kelvin,
T
is related to - 273 deg. Kelvin at 17°C
Roomtemperature
T
is assumed = 290
B = Receiver IF
Bandwidth (Hertz)
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T
= transmitted pulse width |
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n
= number of target-hits (returned rf echos) |
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n
= (Ti(PRF)) = ((BW° x PRF) /( 6 x RPM)) |
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L
= losses (within the system and environmental, figure
not dB) |
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BW°
= radar Beam Width |
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PRF = Pulse Repetition Frequency |
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RPM = antenna Revolution Per Minute |
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Example: SNR for one echo
pulse |
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P G2
λ2
δ
(4 x pi)3 R4
k To B |
((1 000
000 x 10 000 000 x 0.008327 x 1) / (1984.4 x 2.821
x 1.38-23
x 290 x 1 000 000))
= 3.7 (5.7 dB) |
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Example: SNR for some
integrated pulses |
((1 000 000
x 10 000 000 x 0.008327 x 1 x 10) / (1984.4 x
2.821
x 1.38-23
x 290 x 1 000 000))
= 37 (15.7 dB) |
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Example:
S/N total |
((1
000 000 x 10 000 000 x 0.008327 x 1 x 10 x 0.000
001) / (1984.4 x 2.821
x 1.38-23
x 290))
= 37 |
In simple words:
The Target Signal is 37 times stronger
then the receiver (system) noise power.
(Equation by: Hovanessian,
S.A) |