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A 16-bit data acquisition board input range can be set to various ranges like +/-10V or +/-0.5V ect.

If our input signal’s range is +/-0.3V with a noise floor of 1mV does it make sense to set the range to +/-0.5V instead of +/-10V?

For +/-10V range the ADC resolution becomes 20/(2^16)=0.3mV. And for +/-0.5V range the ADC resolution becomes 0.015mV. But our noise floor is 1mV.

Can we say the DAQ input range here doesn't have any effect on the overall resolution?

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    \$\begingroup\$ I think I remember something along the lines of improving accuracy by averaging/filtering readings of more resolution than is required. I think the catch was that it doesn't work if the "true value" is at or below the noise floor since any readings between zero and the noise floor will measure as the noise floor. I could be mis-remembering though. \$\endgroup\$
    – DKNguyen
    Apr 19, 2019 at 18:39
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    \$\begingroup\$ 1mV is not a noise floor – you'd typically specify the noise floor by it's power spectral density (e.g. dBm/Hz) , or the noise power (eg. W), or the equivalent noise std deviation density (e.g. nV/sqrt(Hz)). Can you elaborate on what your 1 mV is? an offset? The square root of noise variance, maybe? \$\endgroup\$ Apr 19, 2019 at 18:50
  • \$\begingroup\$ 1mV is not offset. My question is not about accuracy but resolution. Think 1mV is lets say white noise super imposed on DC input. So the input will be a voltage of +/-0.3V DC plus that 1mV white noise superimposed. \$\endgroup\$
    – user16307
    Apr 19, 2019 at 19:02
  • \$\begingroup\$ @user16307 white noise in what bandwidth? \$\endgroup\$
    – Neil_UK
    Apr 19, 2019 at 20:05
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    \$\begingroup\$ @danmcb I'm not disagreeing with that – when you say "RMS" (or: standard deviation) then things become something that one can work with; I think I explicitly asked for whether the 1 mW might be a square root of noise variance. So, I think we're arguing for the same thing; it's just that even if OP calls it noise flooar, in the original question it's not specified whether it's an offset, RMS, or some other measure. \$\endgroup\$ Apr 7, 2021 at 8:55

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Noise would not typically be what determines your input scaling. You should aim to condition your input signal (whatever it is) in a way that fits your application (whatever that is) and, in doing so, match it to the chosen range of your ADC. Looking at signal to noise and ADC resolution is all a part of that, and must be considered from a system point of view.

So long as you keep the "information" part of your signal above whatever noise is present, and your DAC has enough resolution to preserve it, you did what you need. It's often the case that the 12 or 16 bits of a DAC is much more than needed for the app anyway, and system noise is greater than one LSB - but that may not be an issue.

Other factors (such as what system power supplies are available and their quality) also play a part.

For example if you are making a high end audio DAC, you have a totally different set of goals and constraints compared to a designer of a strain gauge amp for mechanical measurements.

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The short answer is that - in data acquisition - you should typically use the smallest full range that accommodates your signal + noise. The RMS noise should be always much bigger than the Least Significant Bit (LSB) size.

What you discern as "1 mV noise" can contain a great deal of information that could be lost to discretization effects if you used a larger LSB size. DKNguyen's comment suggested this. Given the signal is stable over time and the noise is white, you can use averaging or Delta-Sigma modulation to obtain a reading with virtually infinite precision as long as the useful signal is sufficiently dithered by noise.

The more noise you see, the better for accuracy. If your RMS noise gets even close to the LSB size, you start to see aliasing and this will alter your reading and look e.g. like a fake offset. The limit where spurs become a serious concern is a noise of 1 LSB. If noise is lower than that, your signal is no longer properly dithered by its own noise. Even with slightly higher noise, this effect is not instantly gone, but decays exponentially (if the noise follows a Gaussian distribution).

Maths was requested:

The white rounding error std. dev. introduced by digitization is always \$LSB/2/\sqrt3\$. This noise gets added to your signal when digitizing, thus reducing SNR. Digitizing can never enhance SNR - only reduce it. If the noise std. dev. is e.g. \$2 LSB\$ to begin with, you end up with \$ \sqrt{2^2+1/12} = 2.02 LSB\$ of noise, a 1% reduction in SNR. The more noisy bits, the weaker the SNR reduction.

It is a small effect, but as it is completely avoidable - namely by using the smallest full range accomodating the signal+noise - one should be aware of it.

For slow and low resolution converters, the RMS noise in the measured signal can easily be even below 1 LSB when using no pre-gain. In this case, the rounding can constitute the majority of the noise in the digitized signal.

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