How do you convert from Decibels to SNR for use with Shannon's equation?

[Comscistudent]

Hi all,

It's been many years since I did Mathematics last and I'm having trouble converting from db to the format required by Shannon's formula.

I've googled and looked in the textbook but it's all a bit technical for me, I see logs and formula manipulation and go cross-eyed.

I understand that decibels represent a ratio of S/N. Can someone maybe show me how to convert from 20db to the relevant Snr for shannons? Please explain as if trying to teach it to a 5 year old :)

I have found the SNR = 10log(S/N) ,where log is to the base 10, and I have a worked example using this but I get lost with the manipulations. Is there any rough and ready conversion?

I'm studying for an exam, this isn't a case of I have a simple question to convert from 20db, if it helps please pick an arbitrary number of db for the example.

Many thanks in advance

 

[Comscistudent]

In case more info is needed -

35db is the SNR in the question
SNR(db) = 35 = 10log(SNR) (all logs are base 10)
SNR = 10^35/10 = 10^3.5

Where does the 35/10 come from? if it was 20 db would it just be 20/10?

 

[Comscistudent]

Ok so it turns out all you do is divide the decibels by 10 and raise 10 to this power. Example = 27 decibels = 10^2.7