Resolution calculations

John Khan

Other Parts Discussed in Thread: MSP430F5438A

Hi, I am using MSP430F5438A and learning about accelerometer interfacing. I am trying to do the single axis tilt meter using ADXL335B.

Wixey tilt meter:

www.wixey.com/.../index.html

The thing is that wixey digital gauge has following specs.

Range: +/- 180 degrees
Resolution: 0.1 degrees
Accuracy: +/- 0.2 degrees

How can I specify my system in the same way as wixey did ? I tried the following approach. Please tell me that am I on the right track.

The thing is that I am using ADXL335B with 12 bit ADC. My power supply is 3.3V and Aref = 5V. I am doing single axis tilt calculations.

The data sheet of the sensor is as follows

http://www.analog.com/media/en/technical-documentation/data-sheets/ADXL335.pdf

My calculations are as follows

Desired Range = 0 to 180 degrees.

1. ) Resolution : 3.3 / 4096 = 0.8 mV
2.) ADC_out = ((3.3) / 5 ) x 4096= 2703.36

3) (1.99-1.65) = 0.34 ; 1.99 corresponds to 90 degree and 1.65 V correspond to 0 degree.

0.8mV / 90 = 0.008 mV / degree

But i am lost here. what is the angle resolution in degrees?

How can I calculate the accuracy of my system?

The thing is that I also found the following paper on page 2. It uses arcSin() to calculate the angle resolution

http://www.nxp.com/files/sensors/doc/app_note/AN3107.pdf

It calculates the resolution in a different way and I get confused which method is correct.

over 10 years ago

0 Ryan Brown1 over 10 years ago

TI__Guru**** 219477 points

Hello John,

The difference between 0 and 90 degrees is 340 mV and your ADC resolution is 0.8 mV, this would lead me to believe that the angle resolution is (90/340)*0.8 = 0.2 degrees. I don't follow how an Aref of 5 V is involved in this system, the MSP430F5438A's Veref+ pin should not surpass AVcc which is a maximum of 3.6 V. If anything Aref should be equivalent to your system Vcc of 3.3 V, in which case it isn't necessary since the ADC can reference AVcc directly.

Regards,
Ryan

0 John Khan over 10 years ago in reply to Ryan Brown1

Prodigy 70 points

You are right. But what about the following paper from nxp. Please read page 4. The paper says that at 90 degrees with 12 bit ADC, the resolution is 1.63 degrees not 0.2 degrees. Please advise whish one is correct.

www.nxp.com/.../AN3107.pdf

0 Clemens Ladisch over 10 years ago in reply to John Khan

Guru 318740 points

The Freescale Application Note describes a sensor that outputs a non-linear voltage:

A 12-bit ADC cuts 3.3V supply into 4095 steps of 0.8mV for each step. Therefore, by taking one ADC reading of the MMA6260Q again at 0g (0° of tilt for an x-axis device), would now result in the following:
0°: 1650mV + 0.8mV = 1650.8mV
90°: 2450mV + 0.8mV = 2450.8mV
This results in a 0.057 degree resolution at the highest sensitivity point (0°) and 1.63 degree resolution at the lowest sensitivity point (90°).

With a sensor that outputs a linear voltage, you have the same resolution everywhere.

0 John Khan over 10 years ago in reply to Clemens Ladisch

Prodigy 70 points

Hi,

1. I have no clue that my sensor ADXL335B is giving me a linear reading or non linear reading.
2. How did you reach the number 0.057 resolution? I am unable to get the math behind it.

Thanks

0 Clemens Ladisch over 10 years ago in reply to John Khan

Guru 318740 points

The ADXL335 datasheet does not mention the word "linear", but it specifies the sensitivity in units of mV/g.
1650.8 mV = 0.057°; 2450.8 mV = 91.63°

0 John Khan over 10 years ago in reply to Clemens Ladisch

Prodigy 70 points

Hi,

But 1.65 / 0.3 is equal to 5.5 . How did you get 0.057 degrees?

0 Clemens Ladisch over 10 years ago in reply to John Khan

Guru 318740 points

AN3107 describes how to compute the angle from the ADC voltage.

(And I was wrong calling the ADXL335 linear; all sensors output a voltage that is linear with the acceleration, but you have to use arcsin or arccos to compute the angle.)

0 John Khan over 10 years ago in reply to Clemens Ladisch

Prodigy 70 points

Hi,

AN3107 does not explain how to calculate the angle. It just gave the numbers. I tired couple of things but did not manage to get the right answer.

So , ( 1.65 - 1.6) / 0.8 = 0.0625, arc Sin ( 0.0625) = 3.5 degrees. its not 0.057 degrees.

0 Clemens Ladisch over 10 years ago in reply to John Khan

Guru 318740 points

It's the last formula in the "Calculating degree of tilt" section.

0 John Khan over 10 years ago in reply to Clemens Ladisch

Prodigy 70 points

Yes, and I did the calculations using that formula in my last post. The answer is wrong. I get different angle than 0.057.

0 Clemens Ladisch over 10 years ago in reply to John Khan

Guru 318740 points

asin((1658.8 − 1658) / 800 / 9.8) = 0.0058465 °
(They used 8 mV instead of the correct 0.8 mV for the calculation.)

0 John Khan over 9 years ago in reply to John Khan

Prodigy 70 points

Hi,

I converted the radian values into degrees given in the following paper page 4

www.nxp.com/.../AN3107.pdf

( 12 bit ADC) :

for zero degree -----> 0.067 radians ------> 3.8 degrees

for 90 degrees -----> 1.63 radians ------> 93 degrees

The paper says that the 3.8 degrees is the resolution at the highest sensitivity point and 93 degrees is the resolution at the lowest sensitivity point.

What does it mean?

For 12 bit ADC, the 1LSB = 0.8mV. Does it mean that 3.8 degrees is equal to 0.8mV and 93 degrees is equal to ?? I am confused. Please provide some direction.

0 Clemens Ladisch over 9 years ago in reply to John Khan

Guru 318740 points

0.8 mV is the resolution of the ADC, over its entire range. That is, the ADC can detect changes by 0.8 mV. This difference corresponds to differents amount of rotation, so the resolution, when measured in degrees, also differs.

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Resolution calculations