We notice the assertion that A/D converter quantization noise is equal to ADU/SQRT(12), where ADU is the quantization unit or LSB. We saw this in Hobbs’ excellent book Building Electro-Optical Systems, Making It All Work.
So, we decided to derive this. Took us a while to get the ‘trick’, and to remember how to perform calculus, to get that pesky root-mean-squared function.
Think of the quatization error as a sawtooth function that repeats. Then work out the RMS noise of that sawtooth wave (it happens to be the same as a triangle wave). And, yes, it does work out to that value.
Now the next part is Hobbs’ assertion that this quantization noise is not a Gaussian distribution. Get to work.