Document created by analog-archivist on Feb 23, 2016
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### Q

For my application, timing is nearly no problem. I would rotate the sensor
slowly (3 rev/min) around the axis which inclination should be determined. The
measured acceleration shows a sine-dependency with rotation angle, where the
amplitude is proportional to the tilt angle of the rotation axis. Thus the
total measurement is insensitive to the sensor's offset. I am now concerned
about the temperature stability and temperature hyteresis of the sensitivity.
The operating temperature range is planned to be 5-45°. We could do a precise
factory calibration of the sensitivity at 25°C to compensate for sensor to
sensor-variations. Thus we would also limit the temperature deviation from this
reference measurement to +/-20°C. We can allow the in-field deviation of the
sensitivity with respect to our in-factory calibration of 0.01°/5° = 0.2%. The
values from the datasheets of both sensors are are larger but also given for
larger operating temperature ranges. From fig.12 of the datasheet for ADXL213,
it would seem as if the example curves for this sensor would meet my
requirements. Do you know how the sensitivity behaves in this limited
temperature range for both models, also concerning hysteresis, and if they will
fulfil my requirements? For sensor ADXL213, the temperature effect on the
sensitivity accounts for 0.3%. The sensitivity is specified from 27 to 33%/g.
What effects account for the remaining deviation? Is the remaining deviation
fixed (with time and other parameters) and can be compensated using one
individual measurement? An accuracy of 0.01° corresponds to 1.7e-4 g. To
achieve this, the noise should be below this value. Can I expect for the
digital outputs of both sensors, that the noise after averaging over timt t
follows a 1/sqrt(t) behaviour? In that case, both sensors would meet my
requirements after slightly more than 1 second of averaging. The digital
resolution of the ADIS16209 is 0.244 mg = 0.014° and thus above my accuracy
goal. I expect, that with averaging I will nevertheless achieve this goal. On
page 8 of the datasheet for ADXL213 you state: "As a result, there is
essentially no quantization error or nonmonotonic behavior". Can you quantify
"essentially no" or tell me at least that it is better than what I need? The
measurement would be sensitive to drifts of the offset value while measuring.
Can you specify or at least comment on the stability of the offset on this long
time scale, assuming the temperature would be constant?

### A

I sent four questions to another engineer, who has a little more insight into
the ADXL213 operation than I do, and here is the summary of the responses:

Q: Have you seen any customer accomplish 0.01 degrees of accuracy using the
A: No. That doesn't mean it's not been done though. Still, 170µG accuracy seems
impractical to me (resolution, maybe - but not accuracy).

Q: Thermal hysteresis over 5-45 degC.
A: I have no data for such a small temperature range, but my guess would be
0.5mg. (over a temperature range of 160°C I have occasionally seen as much as
8mg, so over a temperature range that is one quarter as large  I would guess
that it would be ~one sixteenth).

Q: Noise: In a previous discussion, I believe that you offered that the 1/f
frequency was approximately 0.25Hz.  Would I be correct in that 160ug x
sqrt(1.57*0.25) = 100ug is the lowest noise we could expect?
A: Seems reasonable.

Q: Pulse-width timing: I have never used an accelerometer in this fashion.
Does this become a performance limit, or has this factor already been
incorporated into the sensitivity graphs?
A: If the PWM period is set to  10ms (100Hz) with a scale factor of 30%/g, one
g has a pulse width of 3ms. So 100µg would be 0.3µs (not very long). The timer
used would need to have a count time of half this (150ns) or less.

With regards to "end of life," we have not been able to test to the level of
accuracy you are describing.  Getting to ~0.1 degree of dimensional stability
in test platforms has been challenging, but that represents the level we have
taken this too up to this point.  We have reason to believe that the device
will perform better, but believe the fixturing and test methods are handicapped
in their ability to isolate true sensor behaviors.  Based on the information I
have, I can't offer assurance to the level of performance you seek on either

I understand your approach to calibrating PCB shifts but my question was
focused on planarity/flatness over temp cycles, moisture absorption, vibration,
etc.  2um is a dimensional accuracy that took decades to accomplish at the
silicon level.  I am not saying this is impossible on PCBs, but I would not be
surprised if it required consideration at some point.

With regards to the ADC input, these typical values are normally pretty
conservative and make some allowance for anticipated drifts, but keep in mind,
they are listed as typicals, and not min/max limits.

The only parting thought I would have regarding the ADIS16209 would center on
its calibration over temperature and supply.  While it was not targeted at the
same performance level, you may find value in the first-order corrections for
your pursuit of the tighter performance level over a more narrow temperature
range.