Signal to Noise Ratio

[andrew257]

Hi Guys

Can someone correct me if i am making a mistake withthe basic formula

SNR= 20 log (Vsignal / Vnoise)

The above is what i believe it to be however i have seen so many posts on the internet that say it is

SNR=10 log (Vsig/Vnoise)

can someone clear this up for me

Thank you

Andy

 

[the_risk_master]

SNR=20 log (Vs/Vn) is correct

or you may do SNR=10 log (Ps/Pn)

remember: P=V²/R (thats why it is 20 log...)

Note: subscripts with s refers to signal and n for noise

 

[andrew257]

Hi,

Can you explain why P=v2/r = 20 log..... etc?

Cheers

Andy

 

[mondunno]

hi andy,
thats the basic identity, anyway i'd explain it

log(a*a) = log(a) + log(a) = 2log(a)

 

[qureshi]

Hi, andrew257!

Actually, the Signal to Noise ratio is in "db" u can write in two ways, such like that:

SNR (db) = 10 log Ps/Pn
where,
Ps = Signal Power
Pn = Noise Power

Since,

Ps = Vs²/Rs² and Pn= Vn²/Rn²

Let, Rs = Rn hence , we get

Ps/Pn = Vs²/Rs² ÷ Vn²/Rs² since Rs = Rn

Ps/Pn = Vs²/Vn²
OR
Ps/Pn = (Vs/Vn)²

Now,

SNR (db) = 10 log (Vs/Vn)²

SNR (db) = 20 log (Vs/Vn) Using Logrithmic Property


I hope u understand easily, this mathematically phenomenon.

Enjoy.............