PRÁCTICA 2. ACCELEROMETER (2017)
Pràctica InglésUniversidad  Universidad Politécnica de Cataluña (UPC) 
Grado  Ingeniería de Aeronavegación  3º curso 
Asignatura  Aviónica 
Año del apunte  2017 
Páginas  7 
Fecha de subida  24/06/2017 
Descargas  0 
Subido por  areig 
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Alba Martín, Anna Reig
INERTIAL SYSTEMS: ACCELEROMETER
Simulation with Lab View software
OBJECTIVES
Implement signal processing by an inertial system
Use LabView in a more fluently way and get introduced in new LabView libraries
Learn how to use the data acquisition card KUSB3100 from KEITHLEY
Learn how to use and how to calibrate the accelerometer MMA6270QT from Freescale
Learn how from an accelerometer through a data acquisition card it is possible to get real acceleration
data
Work with analogue and digital worlds at the same time
Apply mathematical equations to transform voltage data obtained from the accelerometer into
acceleration data to then integrate and compute velocity and position data
1. Introduction
The main aim of this exercise is to experimentally develop a signal processing with signals generated by an
inertial system. The inertial system used is an accelerometer which generates analogue signals processed by
a data acquisition card (DAC). This DAC generates, in turn, digital signals readable by the computer.
The process needed for this implementation is summed up as follows. First, the specifications of the
accelerometer and the DAC are needed to carry out the next steps. Once got, both devices can be connected
between them without conditioning necessity. Subsequently, the adquisition card can be connected to the
computer acting as a voltage generator for the sensor. Now the sensor is on and generates a voltage
equivalent to the measured acceleration. Consequently, it must be converted to acceleration values making
use of LabView. Then integrating them, the velocity and the position can be computed. Finally, as the sensor
has systematic error as all electronic devices, the system has to be calibrated so to get accurate results.
2. Technical specifications and relevant parameters
First of all, the specifications and values relatives to the accelerometer sensor and the DAC are needed to carry
out all the following steps. The DAC used in the laboratory corresponds to the KUSB3100 model from Keithley
and the one concerning to the accelerometer is the MMA6270QT from Freescale.
DATA ACQUISITION CARD
INPUT
Number of analogic acquisition channels
Input voltage range for signal acquisition
Number of bits for A/D converter
A/D converter resolution
1
8 channels
±10 V
12 bits
4,88mV
Alba Martín, Anna Reig
DATA ACQUISITION CARD
OUTPUT
Number of signal generation channels
Output voltage range for signal generation
Number of bits for D/A converter
D/A converter resolution
OTHERS
Maximum sampling frequency
Input Impedance
2 channels
±10 V
12 bits
4,88mV
50kbauds
10MΩ, 100pF
Table 1 KUSB3100 DAC characteristics [1]
ACCELEROMETER
Full scale voltage and typical voltage supply
Sensibility of the characteristic equation
Uncertainty of the sensibility
Offset of the characteristic equation
Uncertainty of the offset
Output impedance
3,3V
800 mV/ g
±7,5% (±60 mV/ g)
1,65V
±10% (±0.165 V)
1kΩ, 0.1µF
Table 2 MMA6270QT accelerometer characteristics [2]
Most of the previous values have been obtained from the datasheet of already mentioned devices. However,
some of them have been calculated. Let’s see how they have been got.

A/D and D/A converter resolution
𝑉𝑚𝑎𝑥 − 𝑉min 10𝑉 − (−10𝑉)
ΔR =
=
= 4,88𝑚𝑉
2𝑛𝑏𝑖𝑡𝑠
212

Uncertainty of the sensibility
𝑆𝑒𝑛𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =

𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 860𝑚𝑉 − 740𝑚𝑉
=
· 100 = 7.5%
2 · 𝑉𝑡𝑦𝑝
2 · 800𝑚𝑉
Uncertainty of the offset
𝑂𝑓𝑓𝑠𝑒𝑡 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =
𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 1,815𝑉 − 1,485𝑉
=
· 100 = 10%
2 · 𝑉𝑡𝑦𝑝
2 · 1,65𝑉
3. Theoretical approximation
Once got all the specifications in mind and before starting connecting devices, it is important to evaluate if
there is a significant load effect produced between the sensor and the DAC when connecting them without
any conditioning. To do so, the following schema must be considered where Vin is the voltage given by the
sensor and Vo is the voltage received by the DAC, besides R1=1kΩ and R2=1MΩ.
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Alba Martín, Anna Reig
SENSOR
DATA
ACQUISITON
CARD
Figure 1 Connection scheme between the sensor and the data acquisition card
Theoretically,
𝑉𝑜𝑢𝑡_1 = 𝑉𝑖𝑛
In practice,
𝑉𝑜𝑢𝑡_2 =
𝑅𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛 𝑐𝑎𝑟𝑑
10𝑀Ω
· 𝑉𝑖𝑛 =
· 𝑉 = 0,9999001 · 𝑉𝑖𝑛
𝑅𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛 𝑐𝑎𝑟𝑑 + 𝑅𝑠𝑒𝑛𝑠𝑜𝑟
10𝑀Ω + 1𝑘Ω 𝑖𝑛
Consequently, the error committed can be computed as follows.
𝑉𝑜𝑢𝑡_1 − 𝑉𝑜𝑢𝑡2 = 𝑉𝑖𝑛 · (1 − 0,9999001) → 𝐸𝑟𝑟𝑜𝑟𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 = 10−4 · 𝑉𝑖𝑛
To better appreciate the magnitude of this error, let’s estimate a range of values for Vin. Thus, knowing the
value of the sensibility and the offset of the characteristic equation of the accelerometer, it is possible
obviously to get its equation.
𝑉𝑖𝑛 = 0,8V · 𝑋 + 1,65𝑉
As what is going to be measured is the acceleration that experiences the sensor at rest over a table in different
positions, the measured acceleration will vary between 1g and 1g, that is:
𝑉𝑖𝑛𝑚𝑎𝑥 = 0,8V · 1 + 1,65𝑉 = 2,45𝑉
𝑉𝑖𝑛𝑚𝑖𝑛 = 0,8V · (−1) + 1,65𝑉 = −0,85𝑉
Therefore, the maximum absolute error takes the next value.
𝐸𝑟𝑟𝑜𝑟𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 = 10−4 · 𝑉𝑖𝑛 = 2,45 · 10−4 𝑉
Hence, to know how significant is this error, the resolution obtained when connecting the sensor directly to
the DAC without previous conditioning must be calculated. If this resolution is higher than the error, the error
will not be noticed by the card. Otherwise, the error will have to be considered for later computations.
𝑔𝑚𝑎𝑥 − 𝑔min 𝑉𝑜𝑢𝑡 𝑚𝑎𝑥 − 𝑉𝑜𝑢𝑡 𝑚𝑖𝑛
ΔR · sensibility =
·
· sensibility
2𝑛𝑏𝑖𝑡𝑠
𝑉𝑖𝑛 𝑚𝑎𝑥 − 𝑉𝑖𝑛 𝑚𝑖𝑛
1 − (−1) 10𝑉 − (−10𝑉)
=
·
· sensibility = 2,96 · 10−3 𝑔 · sensibility
212
2,45𝑉 − (−0,85𝑉)
0,8𝑉
= 2,96 · 10−3 𝑔 ·
= 2,368 · 10−3 𝑉
𝑔
The obtained resolution is almost 10 times greater than the error due to the load effect, consequently, it can
be neglected avoiding extra errors which will simplify a lot the next steps of the practice.
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Alba Martín, Anna Reig
4. Initial simulations
After the previous theoretical part, the practical part is composed by three different programs developed with
LabView. The two first ones are introductory to the accelerometer tool to have a better understanding about
how the DAC works. In these parts, the DAC is assumed to be connected to the computer with an USB.
So, firstly, a signal is generated with the power supply and is introduced to the DAC through an analogue input.
Then a simple code with LabView is developed so to see the value of the power supply voltage in the screen
of the computer and appreciate how this output varies when changing the value of the power supply.
Subsequently, a second program is developed aiming to vary from the computer the value of the output
voltage of the DAC through an analogue output. A digital multimeter is used to measure the values obtained
in the output of the DAC which then are compared with the inputted values in the program so to check the
correspondence in between and the validity of themselves. In practice, very similar results are get when
varying the voltage value between 2,5V and 3,3V thus approving the correct performance of the system.
Once up to here, the sensor and the DAC can be connected without conditioning necessity as well as the
adquisition card and the computer so to have the card on and thus acting as a power supply for the sensor.
The connections between these devices can be appreciated in the following schema.
SENSOR
VDD
VSS
X
Y
Voutput 0+
Voutput ref 0+
Vground ref
Vinput 1
Vinput 0
DATA
ACQUISITION
CARD
USB
Figure 2 Schema of the connections between the devices interacting in the practice
After making the previous connections, the third program is developped which, from the computer, controls
the voltage output of the DAC which supplies 3,3V to the sensor. Now the sensor is on and it generates a
voltage equivalent to the measured acceleration. So, to be able to interpret correctly this voltage, it must be
converted to acceleration in m/s2. This conversion is executed by the software with voltage values obtained
from the sensor, acquired by the DAC (Vinput_0 and Vinput_1), sent to the computer to then been plotted.
Hence, the acceleration can be computed by means of an easy conversion.
𝑉 − 1,65
𝑎𝑋,𝑌 = 9,8 ·
[𝑚/𝑠 2 ]
0,8
This equation has been obtained from the parameters mentioned in section 2, where;
 1,65 V is the typical offset value for a 3,3V input voltage
 0,8 V/g is the sensitivity for a 1,5g full scale
 9,8 m/s2 is the conversion factor from gm/s2
In this first version of the accelerometer, the user has the possibility of changing the input voltage given by
the computer to the DAC which corresponds to the output voltage of the DAC. This initial approach is
necessary to consolidate all the data computed so far and to verify that the idea initially conceived is correct.
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Alba Martín, Anna Reig
5. Acceleration, velocity and position computations
The main objective of this project is to develop a useful system for air navigation where acceleration is not
enough to meet the necessary requirements. As the basic resource used is the accelerometer sensor, it is
relatively simple to link up all the constraints. From physics, the velocity can be extracted integrating once the
acceleration, and finally integrating twice in order to get the position.
𝑣𝑋 = ∫ 𝑎𝑋 · 𝑑𝑋 ,
𝑣𝑌 = ∫ 𝑎𝑌 · 𝑑𝑌
𝑋 = ∫ 𝑣𝑋 · 𝑑𝑋,
𝑌 = ∫ 𝑣𝑌 · 𝑑𝑌
Applied to the case at hand, the characteristic equation would finally be:
𝑣𝑥𝑖 = 𝑎𝑥𝑖−1 · 𝑡 + 𝑣𝑥𝑖−1 𝑣𝑦𝑖 = 𝑎𝑦𝑖−1 · 𝑡 + 𝑣𝑦𝑖−1
𝑥𝑖 = 𝑣𝑥𝑖−1 · 𝑡 + 𝑥𝑖−1 𝑦𝑖 = 𝑣𝑦𝑖−1 · 𝑡 + 𝑦𝑖−1
6. Calibration
Up to here, the program carries out all the functionalities required initially within a single drawback, it is not
calibrated. Nowadays, all devices not calibrated are devices without a valid initial reference, consequently the
measured values are not accurate and have a considerable error which oscillates between the expected values.
If one wants accurate measures, devices measuring directly parameters as for instance a sensor must be
calibrated. This process can be performed by modifying the characteristic equation of the sensor in such a way
that the typical values of sensibility and offset are removed and replaced by the measured and calculated ones
since known sensor positions.
Step by step, the user will calibrate the sensor with 2 simple movements. In LabView, the software has been
developed by a Flat Sequence Structure that allows to divide the software and thus the calibration in different
steps as shown.

First calibration: The user is asked to place the sensor in the table steadily. In this position, the
acceleration in X and Y axis is equal to zero. Before
the countdown achieves zero, the program takes
the voltage measured by the sensor. Once it
achieves zero, the mean is done for the array of
measured voltage values in X axis and in Y axis.
These means are then assumed to be the offset
value of the characteristic equation of the sensor for
X and Y axis respectively.
Figure 3 Calibration 1

Second calibration: The user must place the sensor
at 90º until the countdown arrives at 0, as before. In
this position, the acceleration in X axis equal to 9,8
m/s2 and the acceleration in Y is null. Before the
countdown achieves zero, the program takes the
voltage measured by the sensor and gets the
sensibility by applying:
𝑉𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑𝑥 − 𝑉𝑜𝑓𝑓𝑠𝑒𝑡
𝑥
𝑆𝑒𝑛𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 =
1𝑔𝑥
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Figure 4 Calibration 2
Alba Martín, Anna Reig
Once the countdown achieves zero, the mean is done for the array of measured sensibility values in
X axis. This mean is then assumed to be the sensibility value of the characteristic equation of the
sensor for X axis.

Third calibration: The user has to place the sensor
with the shorter part on the table and wait for the
countdown to be at zero. In this position, the
acceleration in Y axis equal to 9,8 m/s2 and the
acceleration in X is null. Before the countdown
achieves zero, the program takes the voltage
measured by the sensor and gets the sensibility by
applying:
𝑉𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑𝑦 − 𝑉𝑜𝑓𝑓𝑠𝑒𝑡
𝑦
𝑆𝑒𝑛𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 =
1𝑔𝑦
Figure 5 Calibration 3
Once the countdown achieves zero, the mean is done
for the array of measured sensibility values in Y axis. This mean is then assumed to be the sensibility
value of the characteristic equation of the sensor for Y axis.
The whole application developed through this project can be seen in the following figure where the current
acceleration, velocity and position are plotted as a function of time for X and Y axis, calculated from every
given voltage output of the sensor for both axis. In the first column of plots, the behaviour of acceleration can
be appreciated after having placed the sensor in the four basic positions, at rest and within acceleration
positive and negative in X axis and then in Y axis. In the second column, for both axis, the velocity increase and
decreases when turning the sensor to the next position when going from g to g. Finally, the position cannot
be well determined as it is very relative to the initial reference; it varies a lot due to the fact that the random
error of the system increases exponentially when integrating a measured value. This is because the sensor
used is not really accurate and it is pretty old and used.
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Figure 6 Accelerometer tool 3.0
Alba Martín, Anna Reig
7. Conclusions
The main objective of this project was to develop an accelerometer sensor in order to be conscious about all
the processes needed to carry out any avionics system that is to be used in an aircraft.
On the beginning is very important to have a good knowledge of the parameters involved in the whole process.
Once the concerning information has been extracted from the datasheets, some calculations have been done
that have helped to adapt all the devices correctly as well as to be aware of possible errors or possible
variations on the devices.
The key and basic step is in well performing the changes between acceleration, velocity and position which
are the possibilities offered by the tool developed. Even though, this is not enough if a reliable sensor wants
to be developed.
Finally, as a necessity appears the calibration. Although the variation in the measurements were initially
considered as known, all devices have a tolerance that determines the difference between a good sensor and
a useless for aviation. For some determined positions, the values measured in those positions have been
considered as an offset and substituted by zero. It could be said that we have managed to fulfil all the
objectives initially marked, which included developing with ease in the libraries of LabView.
8. References
[1]. KUSB3100 User’s Manual. KUSB310090001 Rev. A, January 2005.
[2]. MMA6270QT Rev 4, April 2008. Freescale Semiconductor. Technical Data.
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