Electronics > Metrology

Noise Spectral Density (NSD)

**macaba**:

I recently built a LNA (bandwidth 0.1 to 10hz) and have been measuring various noise sources (such as this) and wanted to investigate the effect of record length.

The NSD is computed with a power spectrum FFT, the results square rooted, and an average taken of many runs. I initially started with a fixed number of points (1Mpts) and did 10s (100kSa/s) record lengths, then tried 20s (50kSa/s) and 50s (20kSa/s) where I discovered the apparent noise dropped each time. I then wondered if this is related to sample rate, so did 10Mpts at 100s (100kSa/s) and it doesn't seem to be related. I also tried different window functions and whilst they can change the trace slightly, it doesn't cause them all to converge to the same level.

[attachimg=1]

I did some reading and it would seem that the longer the record length, the closer to the true NSD (that's my interpretation anyway, not 100% sure).

So what record lengths do datasheets tend to use?

One of the things I've been measuring is the performance of my LT3042 design, which gets close to datasheet specifications and if I took a longer record length, would probably match it perfectly.

**TexasRanger**:

Hi, you have to average the power spectral density and then take the square root. Also don't use window functions for noise analysis as they alter the power of your Signal.

NSD should be Independent of sampling speed and lenght, for 1/f I usally average like 128 plots over 3 hours at something like 2ksps and for white noise 32 averages are usally suficient.

**David Hess**:

--- Quote from: TexasRanger on June 13, 2020, 04:37:47 pm ---NSD should be Independent of sampling speed and lenght

--- End quote ---

I agree. Something is amiss with the results.

--- Quote ---Hi, you have to average the power spectral density and then take the square root. Also don't use window functions for noise analysis as they alter the power of your Signal.

--- End quote ---

There is a compensation factor to produce a RBW (resolution bandwidth) of 1 Hz for noise spectral density which depends on the FFT bin width which depends on sampling rate, and the window function.

Also beware of noise higher than the Nyquist frequency aliasing down into the results.

https://www.edn.com/dsos-and-noise/

https://www.edn.com/ffts-and-oscilloscopes-a-practical-guide/

**macaba**:

Thank you TexasRanger - your insightful post prompted me to check my maths again with your comments in mind - I found I was computing power spectrum, and not power spectrum density. :palm:

Just running the analysis again...

**macaba**:

That's better!

[attachimg=1]

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