# How to determine minimal detectable acceleration on accelerometer?

How can it be determined the minimal detectable acceleration on analog and digital accelerometers? In datasheets I found only specification like sensitivity, noise etc. And how the minimal time for detecting can be found?

As example, product site and its datasheet

• If you'd post a copy of the data sheet or - at the bare minimum - a link, then we'd all be on the same page. Jan 22 '15 at 12:34
• "I found only specification like sensitivity, noise etc." - Sounds really unlikely, at least for digital devices. Are you sure you didn't just overlook the relevant infos? Jan 22 '15 at 12:36
• @EMFields I've added product site and its datasheet Jan 22 '15 at 12:40

Resolution of the accelerometer depends upon the power spectral density and bandwidth. Quoting from Accelerometer Terminology Guide by Freescale semiconductors:

Resolution: The smallest detectable increment in acceleration. It is necessary to know what the smallest change is that needs to be detected. The accelerometer bandwidth will determine the measurement resolution, but filtering can be used to lower the noise floor and improve resolution further. The resolution can be improved by decreasing the bandwidth of the output low-pass filter. The trade-off with better resolution is a longer enable time. The resolution is calculated by the following equation:

$$R=N\times\sqrt{BW_{LPF}\times 1.6}$$

where N is the power spectral density noise in $\dfrac{\mu g}{\sqrt{Hz}}$. he power spectral density noise value is characteristic of the accelerometer.

NOTE: If the resolution of the A/D converter is less than the resolution calculated for the accelerometer, then the system will be limited by the A/D converter. Otherwise the limitation is due to the noise and filter using the equations above.

So for analog accelerometers, R gives the resolution. For digital accelerometers, the resolution of ADC or R, which ever be worse (usually the resolution of ADC) will give the final resolution.

• So, if it said that the resolution is 1024 LSB/ g, than the minimal detectable acceleration is 1/1024 g? Am I right? Jan 22 '15 at 12:58
• And if the resolution is in bits, than the minimal acceleration is 1/2^n g , where n is resolution in bits? Jan 22 '15 at 13:09
• That sounds correct to me. If you have 1024 "steps" of acceleration, then each "step" is 1/1024 of the full scale. Jan 22 '15 at 13:10
• I'm not sure. It looks like it depends on the filter (big filter = lower noise = longer time), but I haven't looked at this guide too closely. Jan 22 '15 at 13:27
• And how to determine the minimal time during which this acceleration should affect to produce the reaction form sensor? Jan 22 '15 at 13:30

Unless you are already very familiar with signal processing concepts such as PSD and bandpass filters I would recommend you design a simple experiment to test your sensor instead of trying to use the data sheet. Also that data sheet lacks some data you'll need to accurately simulate the sensor response, like a PSD or Allan Variance plot or the densities of the different kind or noises (white, flicker, random walk, etc...). I guess this short paper would be a good start if you want to start going that road.

I'm assuming you are only interested in change in acceleration, otherwise with that device you'll have a hard time going under 100mg only because of the nonlinearity and change in temperature, which have been plotted on the datasheet.

You could strap the sensor to something heavy and take measurements in different output data rate settings. Do this in firm flooring like the concrete floor on a cellar or underground car parking with not too much transit. Then for example the highest peak to valley difference in this signal is a worst case accuracy for a single shot measurement with the sensor. You can also take the standard deviation if you are not worried about worst case and would like to know how the sensor would perform with a filter that doesn't lags the signal too much.

Using the digital resolution as you said in previous comments is not a good idea. The sensor's accuracy may be all over the place in term of bits, firing up for example the lower three bits randomly even when no acceleration is present. Also, you could get sub-bit resolution by filtering, for example by taking the average of many samples.