Calculate the Max Detection Radar Range

[MattH150197]

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

 

[marcusl]

Your math is wrong. Correct the losses and Psig.

 

[MattH150197]

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

 

[marcusl]

You slipped a sign

 

[MattH150197]

Sorry I am unsure if you still mean the losses is wrong or the Psig

 

[marcusl]

Psig

 

[MattH150197]

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.

 

[marcusl]

Why do you say that I can’t actually do it? Of course it’s possible. How do you convert dBW to W?

 

[MattH150197]

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?

 

[marcusl]

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!

 

[MattH150197]

Perhaps should have shown you this at the start but this is the formula I am going off

 

[marcusl]

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.

 

[MattH150197]

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!

 

[marcusl]

Good! Glad to have helped.