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# SNR Calculation Formula

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#### fgavin

##### Newbie level 6
I am reading a blog, author: Cadence PCB Solutions, title: What is Signal to Noise Ratio and How to calculate it?

''As I stated earlier, calculating SNR can be involved, as well. So, for complex calculations, you divide the value of the desired signal by the amount of the noise and then take the common logarithm of the result, i.e., log (S ÷ N). After this, if the signal strength measurements are in watts (power), you will then multiply by 20. However, if they are units of voltage, then you will multiply by 10."

I believe the log of voltage ratio is multiplied by 20, but the blog tells me to multiply by 10. Is the blog correct?
Furthermore, the result of power ratio, and voltage ratio, is unit less. When to multiply by 10, or 20 to have units of SNR in dB?

The blog shows an example in the next paragraph:
"Furthermore, for power, SNR = 20 log (S ÷ N) and for voltage, SNR = 10 log (S ÷ N). Also, the resulting calculation is the SNR in decibels. For example, your measured noise value (N) is 2 microvolts, and your signal (S) is 300 millivolts. The SNR is 10 log (.3 ÷ .000002) or approximately 62 dB."

In this calculation, I got approximately 52 dB. Is the blog correct?
Thank you in advance.

The blog has everything wrong.
Ratio in dB = 20 * log(voltage ratio) = 10 * log(power ratio).
Easy to remember:
Double power is +3 dB.
Double voltage is 4x power = +6 dB.

The last example: 20 * log(300 mV / 2 uV) = 103.5 dB

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