For a particular current transducer,
http://www.digikey.com/catalog/en/partgroup/ho-p-sp33-series/49533,
it states an "Output rms voltage noise (spectral density)" of 6.13 uV / sqrt{Hz}.
If the frequency of interest is from 1 Hz to 100 Hz,
what would be the resulting peak-to-peak voltage variation of the output?
Would it be:
meaning the resulting output voltage of the transducer is likely gonna vary by ~403uV peak-to-peak from noise within the transducer?
(NOTE: The 6.6 presumably is some number related to statistical probably of the resulting peak to peak voltage)
Best Answer
When you have gaussian noise you have a picture like this: -
The RMS value of the noise occurs at 1\$\sigma\$ (one standard deviation) and that means the signal is constrained as a peak-to peak signal to this RMS number for 68% of the time. That's not great for estimating p-p amplitude so, some people go for 6 \$\sigma\$ i.e. multiply the RMS value by 6 to get p-p but that is only true 99.7% of the time. Some people use 6.6 \$\sigma\$ and that guarantees the p-p value is constrained in amplitude to 6.6 x RMS for 99.9% of the time. This is the general norm but, some folk might want to go much higher and maybe use 7 or 8: -
Your CT's data sheet appears to say that the spectral density is constant from DC i.e. there is no flicker-noise (low frequency) effects so, if you have a bandwidth of 1 Hz to 100 Hz then the output noise will be: -
6.13 uV x \$\sqrt{99}\$ = 61 uV RMS (402.6 uVp-p using 6.6 \$\sigma\$).
However, this assumes a perfect brick-wall filter above 100 Hz. If you have a 1st order, low pass filter shaping the upper spectrum, the voltage noise will be \$\sqrt{\pi/2}\$ times higher at 504.5 uVp-p or 76.4 uV RMS. The hike of \$\sqrt{\pi/2}\$ is due to the noise equivalent bandwidth (in case you want to look it up). Here is a table that relates the filter order to the factor you have to use for powers and, thanks to @carloc, correcting my earlier mistake, these values need to be square rooted when talking about voltage noise: -
Also, the above table is for a butterworth type filtering. If different filters are used, the values are somewhat altered.