Formula for adding noise

[Nishmaster]

Greeting gents,

I have a bit of a math question. I understand the formula for adding uncorrelated noise is:

Total Noise = Sqrt(N1^2 + N2^2)

Let's say I have two devices with noise floor at -120dB and -90dB. I can't seem to use these numbers in this formula in any way that makes sense to me.

EDIT: Corrected junk thread title spelling.

 

[rodabod]

Try converting your dB figures to real values (with respect to unity, ie. 1) and then use your formula before converting back to dB.

The answer is still pretty much -90dB though (consider the factor between -90dB and -120dB).

 

[JohnRoberts]

Greeting gents,

I have a bit of a math question. I understand the formula for adding uncorrelated noise is:

Total Noise = Sqrt(N1^2 + N2^2)

Let's say I have two devices with noise floor at -120dB and -90dB. I can't seem to use these numbers in this formula in any way that makes sense to me.

You have to convert those numbers to voltages first.. dB is a (power) ratio not an absolute amplitude.

While your example is not worth doing the math, the result will be close to the -90dB? level I'll play along.

I ASSume you are talking about dBu  or 0 dBu= .775V

(-90 dbu is 24.5 uv, that ^2 = 6 E-10 )+(-120 dBu is .78 uV  ^2= 6E-13) , so QSRT of sum( -90dB + -120 dB)= 24.52 uV or -89.995 dB

Note: If I choose dBV or some other similar dB voltage reference the result will be the same.
-------
*From inspect the noise will be dominated by noisiest source.
* combining two similar level noise sources will degrade noise floor 3db
* noise increases another 3dB for every doubling of similar noise sources. i.e. 4 sources +6db, 8 sources +9 dB... etc

JR

 

[Nishmaster]

Thanks guys.

I had not yet put my brain in my skull today and a few minutes later realized I was being quite foolish.