Calculate the Max Detection Radar Range

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SUMMARY

The discussion centers on calculating the maximum detection range of a radar system with specific parameters: Transmitter Power (Pt) of 10 kW, Radar Cross Section (RCS) of 1 m², frequency of 3 GHz, losses (Ls) of 5 dB, radar dish radius (r) of 0.5 m, and a noise level (N) of -140 dBW. The correct formula for radar range incorporates antenna gain, which must be calculated from the dish radius and wavelength. The participants identified errors in the initial calculations, particularly regarding the conversion of losses and noise levels, leading to a more accurate range calculation of approximately 1891 meters after corrections.

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  • Knowledge of dB conversions and signal-to-noise ratio (SNR)
  • Familiarity with antenna gain calculations
  • Basic grasp of radar system components and their functions
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MattH150197
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Homework Statement


I am asked to find the Max detection range of the following radar system:
Transmitter Power, Pt = 10Kw
RCS = 1 m sq.
Frequency = 3Ghz
Losses, Ls = 5dB
radar dish radius, r = .5m
Noise level, N = -140dbW
SNR= 13 dB

Homework Equations


Radar Max range = ((Pt*(G^2)*RCS*(Wavelength^2)*Ls)/((4pi^3)*(r^4)*SNR) )^1/4

The Attempt at a Solution


So i first converted freq. to wavelength by 3x10^8 / 3x10^9 = 0.1.
Then converted losses from dB to get 1x10^-5
Converted Noise level from dBW to Watts to get 1x10^-14 (not totally sure of this step)
Then put the noise level into SNR gives 13dB = 10log(Psignal/1x10^-14) and solving for Psignal gives 1.99x10^13
Putting this into equation i get a range of 252 metres obviously this is far too small, as you can tell I am struggling a bit with the dB conversions.Can anybody spot where I've gone wrong? Would really appreciate some help been trying to figure this out for a while with no joy. Thanks
 
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Your math is wrong. Correct the losses and Psig.
 
Okay i can see where I've gone wrong for losses, 10log(y) = 5dB > y = 10^(5/10) = 3.16 is this correct? however I am unsure where I've gone wrong for the Psig
 
You slipped a sign
 
Sorry I am unsure if you still mean the losses is wrong or the Psig
 
Psig
 
So SNR 13dB = 10log(Psignal/PNoise) and converting PNoise into Watts is what I am unsure of because i know you can't actually convert -130dbW into Watts so I am not sure if it converts as -1x10^14 or 1x10^-14 but the latter gave a more favourable result.
 
Why do you say that I can’t actually do it? Of course it’s possible. How do you convert dBW to W?
 
Ahh yeah sorry i see what you mean now it should be 1.99x10^-13 however I am still getting a fairly low value of 1891m
this is what my whole equation looks like:
4th root (( 10x10^3 * 0.1^2 * 3.16) / (4pi^3 * 0.5^4 * 1.99^-13))
Am i right in assuming gain should be taken as 1 if not stated?
 
  • #10
No, G is the gain of the antenna which you have to calculate from its radius and the wavelength. Look up the formula. Also your equation should not have the factor of r^4 in the denominator, go back and re-derive it.
EDIT: Also the way you've defined Loss as a positive number in dB implies that the loss term should be in the denominator. Losses always reduce range, not increase it!
 
  • #11
Perhaps should have shown you this at the start but this is the formula I am going off
 

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  • #12
That equation is wrong, your prof messed up cross-multiplying the range. Also as I said, you have inverted the losses.
You can find the correct range equation online at hundred of sites. Here's a slide presentation that looks particularly clear
https://www.google.com/url?sa=t&rct...amentals.pdf&usg=AOvVaw3Y8TMdtCy7x02XfvdCAo4l
with antenna gain on slide 14 and range on 17. But honestly you can find it in any radar book or site.
 
  • #13
He seems to have made so many mistakes in the notes! I will use the notes you provided from now on, putting the loss in the denominator and entering a gain value gives a much more reasonable answer. Thank you very much for being so patient, you have helped tremendously!
 
  • #14
Good! Glad to have helped.
 
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