Re: Summing Noise Sources

Phil Allison wrote:
** Hi all,

Ok, lets have another go.


Following on from the " Familiar formula ? " thread:

If we have two or more random ( band limited) noise sources ( be they pink, white or whatever ) and we sum them, then the TOTAL noise is found by either summing the individual power levels OR by taking the RMS voltage of each noise source, squaring the values, summing the results and then taking the square root of that sum.

The latter gives a total RMS noise voltage while the former gives the total noise power.

OK ??

But what about the peak value ?????

Any steady noise source will have a "peak to average ratio" or Crest Factor ( CF) - which is the number ratio of the magnitude of the peak value to the steady RMS voltage level.

This is my point, is a noise rource is truly random then exactly what does the peak value mean? At what point is a value reached that can not be exceeded? What I am trying to bring into question, is does the CF you are using have a real meaning. And so is it valid to assume that you can simply add two of them together.

As Arni, has said, yes, its possible for two large values to add, but it will occur far less often than the large value occuring in the single source. If its so rare that this occurs, is it not likely, that this combined value will not be seen in any normal sample period.

This is where my point about sample period. I would think that the peak value measured in a sample, would only have any significance if the sample was big enough to be statistically valid. If so, then maybe the reason for the confusion, if the sample period would need to be much much bigger to see the collision of two peak values in the resultant output.

Its ok, to consider a random source as being generated by a software like function rand(x) where x denotes the maximum value returned, but in reality, is it like that? Hence my question about the level of noise generated if all the electrons in the resistor moved in the same direction at the same time.

And this then takes us to the distribution. A gausian distribution doesn't get to zero does it?

--
Nick
.

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