# Neural Networks

Topics: Dimension, René Descartes, Cartesian coordinate system Pages: 34 (3380 words) Published: December 29, 2012
Freescale Semiconductor
Application Note

AN3107
Rev 0, 05/2005

Measuring Tilt with Low-g Accelerometers
by: Michelle Clifford and Leticia Gomez
Sensor Products, Tempe, AZ

INTRODUCTION
This application note describes how accelerometers are
used to measure the tilt of an object. Accelerometers can be used for measuring both dynamic and static measurements of
acceleration. Tilt is a static measurement where gravity is the acceleration being measured. Therefore, to achieve the
highest degree resolution of a tilt measurement, a low-g, highsensitivity accelerometer is required. The Freescale MMA6200Q and MMA7260Q series accelerometers are good
solutions for XY and XYZ tilt sensing. These devices provide a sensitivity of 800 mV/g in 3.3 V applications. The
MMA2260D and MMA1260D are also good solutions for 5 V
applications providing a sensitivity of 1200mV/g for X and Z, respectively. All of these accelerometers will experience
acceleration in the range of +1g to -1g as the device is tilted from -90 degrees to +90 degrees.
1g = 9.8 m/s

+1 g

MODULE
A simple tilt application can be implemented using an 8 or
10-bit microcontroller that has 1 or 2 ADC channels to input the analog output voltage of the accelerometers and general
purpose I/O pins for displaying the degrees either on a PC
through a communication protocol or on an LCD. See Figure 1
for a typical block diagram. Some applications may not require a display at all. These applications may only require an I/O channel to send a signal for turning on or off a device at a determined angle range.

LCD
Accelerometer

Microcontroller
with

Interface
Circuit
RS232,
USB

Figure 1. Typical Tilt Application Block Diagram

MOUNTING CONSIDERATIONS
Device selection depends on the angle of reference and
how the device will be mounted in the end application. This will allow you to achieve the highest degree resolution for a given solution due to the nonlinearity of the technology. First, you need to know what the sensing axis is for the accelerometer. See Figure 2 to see where the sensing axes are for the

MMA7260Q. To obtain the most resolution per degree of
change, the IC should be mounted with the sensitive axis
parallel to the plane of movement where the most sensitivity is desired. For example, if the degree range that an application will be measuring is only 0° to 45° and the PCB will be
mounted perpendicular to gravity, then an X-Axis device

would be the best solution. If the degree range was 0° to 45° and the PCB will be mounted perpendicular to gravity, then a Z-Axis device would be the best solution. This is understood more when thinking about the output response signal of the

device and the nonlinearity.
Sensing Axis
Z for Z-Axis

Z-Axis

X-Axis
X-Axis
Accelerometer
Accelerometer

PC
PCB

Z-Axis
Accelerometer
Accelerometer

PCB
PCB

SSensing
ensing
AAxis
xis

X

1g
1g

Sensing
Sensing
Axis
Axis

Sensing Axis
for Y-Axis

Sensing Axis
for X-Axis

Gravity
Gravity

1
1gg

Y
MMA7260Q
Series
Accelerometer

Gravity
Gravity

Figure 2. Sensing Axis for the
MMA7260Q Accelerometer With X, Y,
and Z-Axis for Sensing Acceleration

Figure 3. Gravity Component of a
Tilted X-Axis Accelerometer

Figure 4. Gravity Component of a
Tilted Z-Axis Accelerometer

NONLINEARITY
As seen in Figure 5, the typical output of capacitive, micromachined accelerometers is more like a sine function. The figure shows the analog output voltage from the accelerometer for degrees of tilt from -90° to +90°. The change in degrees of tilt directly corresponds to a change in the acceleration due to a changing component of gravity acted on the accelerometer.

The slope of the curve is actually the sensitivity of the device.

As the device is tilted from 0°, the sensitivity decreases. You see this in the graph as the slope of output...