What is ADC RMS noise? It would be helpful if someone could theoretically explain ADC RMS noise.Say a ADC has RMS noise of 11nV@4.7Hz.What does that mean?

• is that a real value of adc noise or something you've plucked from thin air? An example spec of a particular ADC Might benefit – Andy aka Nov 9 '13 at 11:20
• Hi Andy aka, it is real value of AD7192. Could you please explain what is RMS noise in theory . – abhilash Nov 9 '13 at 12:09

If I were calculating it I would go down this path: -

The device specifies 15.5 noise-free bits at a sampling rate of 2400Hz and looking at page 12 on the data sheet this is about the same for 4.7Hz sampling. Assuming the reference input is set at 3V, 15.5 bits represents 65uV of peak to peak noise.

Usually this can be divided by 6 (sigma) to make an estimation of RMS noise and this becomes 11uV RMS. There is a gain of 128 in the device and therefore the equivalent noise voltage before a gain of 128 is 84nV RMS.

But there all sorts of filters that may be used within the ADC that can take this noise figure down further and without spending hours going through this I'm assuming 11nV at a sampling rate of 4.7Hz is reasonable.

Page 16 appears to imply that the error free resolution when filters are applied at about 4Hz sampling is 19.5 bits so maybe if i plugged this in to what I wrote earlier it would be closer: -

19.5 error free bits in 3V represents a p-p voltage of 4.1uVp-p and dividing by 6 gives an RMS of 674nV. Then dividing by 128 gives 5.3nV - near enough for jazz!

The RMS value of a noise signal, just like with any other type of signal, is the value that you would use to calculate the power of the signal, which is the parameter that designers are most interested in. After all, signal-to-noise ratios are power ratios, so you want to compare the RMS value of the signal to the RMS value of the noise, in whatever units are appropriate to the application at hand.

The "11 nV RMS @ 4.7 Hz" you see on the front page of the datasheet is just one entry (the "best" entry) from the table found on page 14, which relates different sample rates and gain settings to the overall noise figure.

Noise is a random process, and thus, it cannot be characterized by simply an amplitude. It's average value (or time integral) is 0 so the method to characterizing noise is by stating the power of the noise. RMS (root mean square) is the root of the squared value for the noise voltage, which is the power of the noise voltage signal.

In data converter systems, noise is not generally stated as a single value, but as noise density over frequencies since several methods are applicable to limit the noise in the whole bandwidth to arrive at a smaller equivalent noise voltage right before the conversion happens. The noise density has the unit $V/\sqrt(Hz)$ which is actually equivalent to $V^2/Hz$, stating the power at that specific frequency. To account for all the noise in your conversion, you have to integrate this density function for your frequency band of interest.

If an ADC says it has 11nV @ 4.7 Hz noise, it means that the square root integral of the noise density function squared from 0 Hz to 4.7 Hz is 11nV, which is an exceptionally good value. It also shows me that it is using a method to filter out flicker noise such as chopping. Flicker noise is a low frequency noise effect which has a $1/f$ characteristic, and is the dominant noise effect for low frequencies.

There are many things going on in that one measurement. What they are trying to encapsulate for you in this one measurement is essentially how sensitive the device is if you operate it in precisely the same way. From there , understanding the noise sources etc. you can move forward with you own design/configuration.

This is what is known as "input referred noise" there is noise in any conversion process, even an ideal ADC will have noise, and then there is the noise shaping that happens in Sigma/delta designs and noise from op-amps inside etc.

The nice thing about Analog devices is that they have all sorts of excellent app notes detailing the noise processes etc. The data-sheet for that device even enumerates noise levels at different gains and sampling rates.

So if you have a signal that needs to be sampled at 4.7 Hz (is this within your noise bandwidth ?) and you have certain criteria for noise contribution (i.e. the ADC cannot contribute more than 1/10 th the noise or 3 dB of the noise) then you can rapidly determine if this is the right device for your application.

Say you have a signal that has 47 nV of noise in a band of 4.7 Hz. The noise bandwidth for a first order system is $\frac{\Pi}{2}*F_{3dB} = 1.57 * F_{3dB}$. The noise in the system adds as RSS (Root sum of squares) $sqrt(47^2 + 4.7^2) = 47.23 [nV]$ so you see that for THAT scenario the ADC doesn't contribute very much.