A1332 Datasheet, PDF (14/20 Pages) Allegro MicroSystems – Precision Hall Effect Angle Sensor IC with I2C Interface

A1332
Precision Hall Effect Angle Sensor IC with I²C Interface
Linearization
Magnetic fields are generally not completely linear throughout
the full range of target positions. This can be the result of non-
uniformities in mechanical motion or of material composition.
In some applications, it may be required to apply a mathematical
transfer function to the angle that is reported by the A1332.
The A1332 has built-in functions for performing linearization on
the acquired angle data. It is capable of performing one of two
different linearization methods: harmonic linearization and piece-
wise (segmented) linearization.
Segmented linearization breaks up the output dynamic range
into 16 equal segments. Each segment is then represented by the
equation of a straight line between the two endpoints of the seg-
ment. Using this basic principle, it is possible to tailor the output
response to compensate for mechanical non-linearity.
One example is a fluid level detector in a vehicle fuel tank.
Because of requirements to conform the tank and to provide
stiffening, fuel tanks often do not have a uniform shape. A level
detector with a linear sensor in this application would not cor-
rectly indicate the remaining volume of fuel in the tank without
some mathematical conversion. Figure 11 graphically illustrates
the general concept.
Harmonic linearization utilizes the Fourier series in order to
compensate for periodic error components. In the most basic of
terms, the Fourier series is used to represent a periodic signal
using a sum of ideal periodic waveforms. The A1332 is capable
of utilizing up to 15 Fourier series components to linearize the
output transfer function.
While it can be used for many applications, harmonic lineariza-
tion is most useful for 360-degree applications. The error curve
for a rotating magnet that is not perfectly aligned will most often
have an error waveform that is periodic. This is phenomenon is
especially true for systems where the sensor is mounted off-axis
relative to the magnet. Figure 12 illustrates this periodic error.
An initial set of linearization coefficients is created by character-
izing the application experimentally. With all signal processing
options configured, the device is used to sense the applied mag-
netic field, B: at a target zero-degrees of rotation reference angle
and at regular intervals. For segmented linearization, 16 samples
are taken: at nominal zero degrees and every 1/16 interval (22.5°)
of the full 360° rotational input range. Each angle is read from
the ANG[ANGLE] register and recorded.
These values are loaded into the Allegro ASEK programming
utility for the device, or an equivalent customer software pro-
gram, and to generate coefficients corresponding to the values.
The user then uses the software load function to transmit the
coefficients to the EEPROM. Each of the coefficient values can
be individually overwritten during normal operation by writing
directly to the corresponding SRAM.
Meter and
Sender
Fill pipe
Uniform walls
Linearized rate
Angled walls
Wall stiffener cavities
Angled walls, uneven bottom
Fuel Volume
0
Figure 11: Varying Volumes in an Integrated Vehicle Fuel Tank
An integrated vehicle fuel tank has varying volumes according to depth due to structural elements. As shown in the chart, this results in a
variable rate of fuel level change, depending on volume at the given depth, and a linearized transfer function can be used against the integral
volume.
Allegro MicroSystems, LLC
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Worcester, Massachusetts 01615-0036 U.S.A.
1.508.853.5000; www.allegromicro.com