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Hi engineer team,

I was looking on the ADXL1002 datasheet and I was wondering about something : is that significant and accurate to measure a voltage difference which is less than 2mV or 1mV with the ADXL1002 ? We know that the sensitivity is 40mV/g, and the ADXL1002 is made for a huge range +/-50g, so basically the main purpose is not to measure low variation.

I saw as well that the sensitivity due to the temperature is 5% of 40mV/g. So I assume than measuring an acceleration which is lower than 5% of 1g (which means 2mV) is not really accurate.

I am currently asking this cause we are reflecting about which ADC we are gonna use, and I am wondering if a 12bit ADC with a 4V VREF is enough (which allow us to have a resolution of 0.97mV).

Florent

• Thank you for your post.  While you are correctly citing the sensitivity error and measurement range from the ADXL1002 datasheet, I do not understand how that limits the capability of the ADXL1002 as a vibration sensor, nor do I understand why the sensitivity error would drive the resolution requirement for a complementary ADC.  Page 11 of the ADXL1002 datasheet actually recommends the use of a 16-bit ADC (AD4000).

I didn't write the ADXL1002 datasheet, nor did I select the AD4000 for this purpose, but I can guess at what the author's motivation was.  I suspect that the resolution of this ADC was driven by making sure that its (ADC) quantization noise was less than the total noise contribution from the ADXL1002, for the stated bandwidth of the application (5kHz  in this context).  This is often an important criteria for those who do not want the ADC to limit the resolution of a particular signal. So let's do some math and see how this works out:

• Sensor noise: assume single pole filter, which has a -3dB frequency of 5kHz and a nominal noise density (25ug/sqrt(Hz)):
• Total Noise = Noise Density x sqrt(Noise Bandwidth)
• Total Noise = 25 x 10^-6 g/sqrt(Hz) x sqrt[1.57 x 5000Hz] = 2215ug
• Total Noise = 2215 ug x 40mV/g x 1g/1000000ug = 0.0886mV
• ADC Quantization noise, assume Vref = 5V, 16-bits and full use of the ADC input range
• q = 5V / (2^16-1) = 0.0763mV
• Quantization noise = q/sqrt(12) = 0.022mV
• So, it would appear like the (5kHz) total noise of the ADXL1002 (0.0886mV) is greater than the quantization noise of the ADC (0.022mV).
• If we make the same assumptions about a 12-bit ADC, its quantization noise (0.352mV) is actually larger than the total noise of the ADXL1002 (0.022mV), which means that the ADC will limit the resolution of the vibration observation.
• q = 5V / (2^12-1) = 1.22mV
• Quantization noise = q/sqrt(12) = 0.352mV

• Mark has it correct.  The ADC is typically recommended so that it will not limit the performance of the sensor.  The Sensitivity change over temperature will slightly change the output response over the temperature range, it does not suggest that vibration at low signal level cannot be observed.

Mark has done an excellent job at explaining the resolution impact on the combined performance.

The noise floor and bandwidth of the ADXL1002 allows it produce response for low magnitude vibrations typically found in machine health monitoring.

• Hi Mark,

• The limits of the capability of the ADXL1002 as a vibration sensor impact the choice of the ADC because if the accuracy limit is 2mV, then it is pointless to select an ADC which got a resolution of ,less than 2mV (aka AD4000) and a 12 bit ADC is enough.
• The ADXL1002 is a 11khz bandwidth accelerometer, so i guess you selected 5Khz as it is an average value, am I  right ?
• Ok I got your calculations,exepted this one :  Quantization noise = q/sqrt(12). Where does the 12 come from ?

Your thinking make sens to me now, and I understand that the ADC noise has to be smaller than the sensor noise.

So according to your calculation, the total noise of the ADXL1002 is 0.0886mV. So does it means there will always gonna be this amount of voltage which is garbage ? So this is pretty much the limit of the ADC so ? I mean that we cannot measure a voltage of less than 0.0886mV otherwise this won't make sense ?

Thanks for your help, much appreciated  !

• You are welcome!  Here is a breakdown of your questions, as I understand them.

QUESTION>> The limits of the capability of the ADXL1002 as a vibration sensor impact the choice of the ADC because if the accuracy limit is 2mV, then it is pointless to select an ADC which got a resolution of ,less than 2mV (aka AD4000) and a 12 bit ADC is enough.

ANSWER>>  While I appreciate your kind words, you seem to be re-stating the same position that you started with in this question, but also acknowledging our motivation for encouraging the use of a 16-bit ADC.  I am confused, but let's presume that you are still wondering if a 12-bit ADC will preserve all available performance in the ADXL1002... From a fundamental signal processing point of view, resolution is not the same thing as absolute accuracy.  In fact, they would seem to be somewhat unrelated.  In simple terms, the absolute accuracy quantifies how well the sensor will represents a vibration signal, which is much larger than the noise in its output.  Resolution represents the smallest vibration signal, which the sensor will respond to.  In the following article, we proposed that if the vibration magnitude was the same as the sensor's inherent noise, it would raise the root-mean-square of the sensor output by 3dB or 40%.

So, to be very clear, we believe that a system will need at least 16-bits of resolution in its ADC, in order to preserve the resolution that the ADXL1002 is capable of, in a vibration monitoring application.

QUESTION>> The ADXL1002 is a 11khz bandwidth accelerometer, so i guess you selected 5Khz as it is an average value, am I  right ?

ANSWER>> No, I didn't put that much thought into selecting 5kHz for this example; I took it from the section of the datasheet, which offers the AD4000 as a complementary ADC. In a real application, this will be set by the vibration profile that the system is trying to monitor.

QUESTION>> Ok I got your calculations,exepted this one :  Quantization noise = q/sqrt(12). Where does the 12 come from ?

ANSWER>> This is a fundamental relationship in quantization theory.  Deriving this industry-recognized formula is outside of what I can support in this forum, but I can help you get started, if you want dig into its origin and derivation. Check page 57 of this reference, which lists this formula, along with a reference to one of the original books on sampled data theory, which was published in 1948.  I hope that this helps.

QUESTION(S)>> Your thinking make sens to me now, and I understand that the ADC noise has to be smaller than the sensor noise. So according to your calculation, the total noise of the ADXL1002 is 0.0886mV. So does it means there will always gonna be this amount of voltage which is garbage ? So this is pretty much the limit of the ADC so ? I mean that we cannot measure a voltage of less than 0.0886mV otherwise this won't make sense ?

ANSWER>> I am not sure that I would go as far as calling this information "garbage," but I guess that is a fair statement, in this case.  I would prefer to say that the total noise is a key factor in the resolution of the sensor. I hate to be repetitive, but I would recommend reading this article and depending on your time/depth of motivation, perhaps start digging into electronic noise theory.  Motchenbacher's "Low Noise in Electronic System Design" is a classic reference on this topic.

I hope that this helps!

• Hi Mark,

Yes, I got the difference between the resolution and the absolute accuracy !

All right I understand the example now, there is the same for aiming 10Khz vibration straight after (this is what I am looking for). I am just wondering why in the second example (aiming the 10Khz) the frequency of the low pass filter are 33Khz and 16.5Khz?  The filter is supposed to reduce all the harmonics which got a frequency greater than the Nyquist frequency isn’t it?

Ok so this is purely theory formula, I was wondering because I thought it could have been some other parameter.

Yes, I mean by garbage not reliable data, even if it is based on some real signal. Okep I will have a look on this article.

Thanks again for your help, much appreciated and useful!