# Signal-to-Noise Ratio

I need to design a channel with the transfer rate 20Mb/s and a bandwidth of 3MHz. What kind of signal-to-noise ratio can this channel tolerate?
Microsoft SQL ServerMicrosoft SQL Server 2008

Last Comment
joeyc801

8/22/2022 - Mon
joeyc801

This is actual a question for my class, so if someone can help with I would greatly appreciate it.
sfmny

Look up Shannon channel capacity theorem.

Max Channel Data rate = Bandwidth x log base 2 ( 1 + SNR )

SNR is Signal to Noise Ratio

So you get

log base 2 (1 + SNR) = 6.99

1 + SNR = 127.11

SNR = 126.11, as a decibel 2.1 db

Am I seriously helping out with class assignments now? Dude, not cool :-) The question category is not database, should be networks
joeyc801

Sorry dude, I needed help. And I have never used this site before, so I wasn't sure what to pick. And not to mention I am completely lost, so asking for a little help is not so bad. I knew about the formula but I did the math wrong. I know that I am rookie, but could you further explain how you got 6.99? And the rest of the answer? I already handed in the homework and definitely got it wrong, but like I said looking for a little help.
sfmny

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joeyc801

Ok, thank you very much for your help. I really do appreciate it. Just one more question. I see everything you have laid out except one spot.  20 x 1024 Kbps = 20 x 1024 x 1024 bps, where does the 1024 come from?
joeyc801

Also I am struggling with with where you got 127.11? Sorry
sfmny

Mbps is Mega bits per second
Kbps is Kilo bits per second

MBps is Mega bytes per second
KBps is Kilo bytes per second

In this case we don't need to worry about converting bytes to bits. It's already expressed in bits per second.

1 Mega bps = 1024 Kilo bps
1 Kilo bps = 1024 bps

Therefore 20 Mbps = 20 x 1024 x 1024 bps

In computer science, while representing data, the units are always powers of 2 (binary operations). Therefore it's 1024 not 1000 (2 ^ 10 = 1024).

However when it comes to frequency there is no such constraint. For the 127.11:

log base 2 (1 + SNR) = 6.99 is where we begin.

If you review logarithms, 10 ^ 2 = 100 is represented as log base 10 (100) =2. In another words if the power if 10 is 2, you get 100. 10 is the base, 2 is the exponent and 100 is the result.

We now use 2 as the base not 10. Given that, the equation in bold says, if we raise 2 to the power 6.99 we get (1 + SNR). Therefore 2 ^ 6.99 = (1 + SNR) = 127.11

You might want to check out Khan Academy if you want to review math. It's a series of video posts that walks you through math fundamentals and it's free.
sfmny

The unit conversions should be based on what the course conventions are. If your professor uses 1000 vs 1024 then use 1000. I've had conflicting experiences with both.

Here's the norm that's currently used WITHOUT the 1024 for Kbps. In you course if they just use 1024 for everything data related, then just use that. But if they have drawn a distinction, use 1000 instead. Either way, state your assumption.
joeyc801