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# Correct way to think about thermal noise?

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I have just started learning about thermal noise in op-amps and while studying could not find if the noise given in op-amps data sheets is random sample to sample regardless of the time interval between the samples or if the randomness of noise is thought about in terms of unit time.

If a data sheet gives the thermal noise (of +3/-3 standard deviations) as 1 uVpp does it mean that out of every thousand samples, 3 will have noise more than ±1 uV at any sample rate? 1000 sps will lead to 3 samples having more than ±1uV noise in a second, 2000 sps will lead to 6 samples having more than ±1uV noise in a second, and so on.

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If a data sheet gives the thermal noise (of +3/-3 standard deviations) as 1 uVpp does it mean that out of every thousand samples, 3 will have noise more than ±1 uV at any sample rate? 1000 sps will lead to 3 samples having more than ±1uV noise in a second, 2000 sps will lead to 6 samples having more than ±1uV noise in a second, and so on.

Your interpretation is correct. When a datasheet specifies “peak-to-peak” noise within ±3 standard deviations, they are specifying the 99.7 percentile peaks.

I’ve put “peak-to-peak” in quotes, because peak-to-peak of a Gaussian white noise is ±∞ from the purely mathematical point of view.

RMS is a better specification for Gaussian white noise than peak-to-peak. RMS has a mathematical property that it’s equal to standard deviation when the signal has zero mean (no DC component). If a datasheet specifies RMS, then it implies ±1 standard deviations, and it doesn’t need to specify the number of standard deviations.

RMS may be easier to measure with a digital oscilloscope than catching thousands of peaks.

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