# Dual-Axis Tilt Sensor with ADXL203

Hi,

Referring to the datasheet ADXL203, AN-1057 and CN-0189 I would like to implement a system that measures the angle of inclination of a vehicle (Roll, Pitch).
For the project I made the following choices:

- Accelerometer is oriented on both its x-axis and y-axis
are parallel to the earth's surface
- Bandwidth Settings: 1Hz (Cx = Cy = 4.7 uF)
- RMS-noise (BW = 1Hz) = 138 ug (0.138 mg)
- RMS peak-peak = 6 x rms = 0.83 mg
- Tilt range ± 30 °

The Sensitivity ADXL203 is 1000 mV/g (typ). AN-1057 shows how to calculate the single axis acceleration (in my case both for the x axis and for the y axis):

Ax, out = 1g x sin (θ)
Ay, out = 1g x sin (θ)

Because the output resolution is a constant acceleration, the resolution in degrees of inclination is variable, with the best resolution close to 0° and the worst resolution at ±90°. The incremental sensitivity is the output change, shown in mg, per inclination angle step (In my case 1°).

For example, designing for a maximum step size of 1°, a resolution of at least 15 mg/LSB is necessary for a range of ±30°

What does mg/LSB mean? 15 mg to how many mV corresponds?

For example, suppose you want to use a two-input SAR ADC with Vdd = Vref = 3.3V. LSB = Vref / (2^n ) thus

n = 8 bits    --->   LSB = 12.9 mV
n = 10 bits  --->   LSB = 3.2 mV
n = 12 bits  --->   LSB = 0.8 mV

Which is the best ADC resolution that should be chosen in my application? How can I estimate LSB in my application?

Sincerely

Centered image
[edited by: mike_war at 9:55 AM (GMT 0) on 29 Jan 2019]
Parents
• The mg/LSB is the units for sensitivity, when using a digital accelerometer.  In your case, that will represent the output of the ADC in your system.

Thank you for your this post! When making similar consideration, I would start with making sure that the quantization noise level was lower than the total noise in the system. q = mg/LSB divided by the square root of 12 (classic ADC formula)

Quantization noise = 0.8mV/sqrt(12) x 1mg/1mV = 0.23mg

Using a 1Hz bandwidth, you have determined that the total noise will be 0.83mg, which is greater than the quantization noise of the 12-bit resolution that you estimate.

Since you will want to accommodate bias and sensitivity tolerance and to fit the nominal bias in the middle of the ADC range, you probably will want to consider scaling the +5V accelerometer output down, by a factor of 5/3.3 and perhaps, divide the power supply down to 3.3V for the ADC reference, since the ADXL203 is a ratiometric ADC.  If you do that, then you would need to reduce your noise estimate down to 0.54mg (0.83 x 3.3 / 5), which is still greater than the 0.23mg quantization noise, for the 12-bit ADC (3.3V range).

I hope that this helps.

Out of curiosity, why not use the ADC that is recommended in CN-0189?

• Coming to the question I asked how to estimate the best resolution of the ADC for my application because I wanted to understand the criterion that was below for the choice in general.

what I can not understand is how to check if the minimum required resolution of 15 mg/LSB to have a tilt range ± 30° is satisfied?
in relation to my application would have been had I adopted a 14-bit SAR ADC? I would like to understand how to make the best choice in relation to my application for example

Sincerely

• First of all thank you you are very kind and patient. One thing I can not understand is this: in the AC-0189 is presented Dual Axis Tilt Measurement System with 1° over 90° accuracy. In particular, the accelerometer is mounted with an axis parallel to the earth's surface and the other parallel to the gravitational vector. This makes sensitivity and other advantages constant. My case is different, the accelerometer planks it with both axes parallel to the earth's surface so that we can measure the inclination along the x and y axis. Basically, I was worried about the fact that sensitivity is not constant. What I want to understand ensure the right resolution to achieve a tilt range of ± 30°. When the ± 30° threshold is reached, for example, the alarm can be triggered, for example. I have to worry that the ± 30° read them well bearing in mind that at ± 90° the vehicle will never get there. How to ensure that the system reads an inclination of at least ± 30° with a single axis?

• You are welcome.

With respect to CN-0189, I can't speak for that document. I didn't write this document, nor was our team involved with its creation.  Aside from that, I am happy to focus on your current needs and help you with questions that help us get there.

To be honest, I feel like I have already offered you credible guidance, which will help you in achieving your goals.  If you want to support a window detector, which will alert you when the tilt has exceeded + 30 or -30 deg, with an accuracy of +/-1deg, 1.22mg/LSB appears to be sufficient.

Arcsin(30 deg) - Arcsin(29) = 15mg, which 10x greater than the resolution that you will achieve with the 12-bit ADC.

What is the problem?