Calculate speed in a copper wire

[dont_know]

Okey, I have a problem now. I´m suposed to sketch a graf of how long range on a copper wire some different speeds have ex 256 kbit/s etc.

I have 225 channels of each 4kHz and it can transfer 4000 symbols/sec. The effect on each channel is 0.1mW and the noise is -100dBm.

The signal is reduced by 18 db/km

I´m using QAM-256 that means i can transfer 8 bits/symbol. It demands a SNR of 30db. Now i´m going to sketch a graf of the distance of some different speeds.


This far have I come (or am I totally lost?):

The bandwith is 900Mhz and SNR of the channel is 30db (30db = 10 log 1000 = S/N=1000) that gives: C=B log2 (1+S/N) C=900M*log2(1+1000)=7.2 Mbit/s

or a single channel:

C=4000*log2(1+1000)=398.7 kbit/s and then we have 225 channels that makes: 225*398.7=89,7 Mbit/s

Which one is the correct? If one is that say... That is speed att approximate 1 m and then I have to calculate the range of the speed with the 18 db/km?

But what about the symbols and bits? The effect of the channels and the noise?

Feeling quite lost now. Would be grateful for some help!

//Dont_know

 

[learningphysics]

C=900M*log2(1+1000)=7.2 Mbit/s

how are you getting 7.2Mbit/s here? I'm getting the same number you got using single channels and multiplying by 225.

 

[dont_know]

Oh. That is correct. When I checked what I wrote. I see some mistakes from my side. It shouldn´t be 900M but 900k.

I have looked at it on many different angles now. I´m staring to get somewhere now. But the limit in this channel is 8.97 Mbit/s. With the right equation:

C=900k*log2(1+1000)=8.97 Mbit/s

 

[learningphysics]

Not sure if I'm fully understanding the question... it's been years since I did this stuff... But are you supposed to pick rates in bits/s and then plot the range for them... ie the distance when the signal to noise ratio becomes less than 30dB?

So what is the signal to noise ratio at the source... and how does it change with distance... is that what you need to work out?

just thinking out loud...