### Application Note Using MagAlpha in Off-Axis Mounting

```Application Note
Using MagAlpha in Off-Axis Mounting
October 2014
Introduction
The MagAlpha is an angle sensor that locally detects the direction of
the magnetic vector. Therefore, only the strength and the direction of
magnetic field at the sensor position (package center) matters. This
leaves some freedom to the user to optimally adapt the magnet-sensor
configuration to his application.
In the present note, we consider cylinder magnets diametrically
magnetized.
Minimum field
The MagAlpha can be placed at any position where the in-plane field
strength remains above its operational limit, i.e. 20 mT or 60 mT
depending on the MagAlpha version. In general, the magnetic field
strength varies upon rotating the magnet. Thus, the smallest field value
within one complete turn of the magnet must be considered.
Non-linearity
If the sensor is placed on the rotation axis, the magnetic field direction
is proportional to the mechanical angle. Hence, the output of a sensor
is linear (in ideal case). If the position of the sensor is eccentric, it
probes a magnetic field out of the rotation axis. In this case, the
magnetic field amplitude varies as a function of the angle. This
variation comes along with an angle deviation with respect to a
perfectly uniform magnetic field. When decomposing the magnetic
field, it can be observed that its radial and tangential components
behave as sine and cosine functions, with different amplitudes (see
Figure 1). This is sometimes called an "elliptic" error. As a
consequence the angle of the field vector does not move proportionally
to the mechanical angle anymore. The sensor output is therefore nonlinear. We define the ellipticity ratio as:
where
and
respectively.
are the radial and tangential field amplitude
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October 2014
Figure 1: Left: Example of Radial and Tangential Magnetic Field Off-Axis. Right: Resulting NonLinearity.
The integral non-linearity (INL) is defined as the maxium deviation from
the perfect straight-line response. For a given ellipticity , the INL is:
If this non-linearity exceeds the user requirements, the MagAlpha can
be configured to compensate this error. For this, the user needs to
adjust the trimming parameters BCT, ETX and ETY (see MagAlpha
datasheets and the guidelines below).
Direction of rotation
In the peripheral region, i.e. where the eccentricity is greater than the
magnet radius, the direction of the radial field is reversed, while the
tangential field keeps the same direction. The result is that the
direction of rotation is reversed.
Figure 2: The Direction of the Rotating Magnetic Field (Red Arrow) at the Sensor
Position is Reversed when the Eccentricity is Greater than the Magnet Radius.
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October 2014
Example
Assume the magnet has the characteristics:
Diameter
Height
Remanent field
mm
mm
T
5
2.5
1
The sensitive region of the MagAlpha (which is in the package center)
can be placed anywhere inside the surface limited by the color lines in
Figure 3 left. For instance, if the lower limit is 20 mT the sensor must
be somewhere within the violet line. The ellipticity is indicated in Figure
3, right. Note: the sign change reflects the change of sign of the
radial field, and therefore the direction change.
Figure 3: Left: The Minimum Field Amplitude over a Complete Turn. Right: The Ellipticity
Ratio.
For instance, if the user decides to position the Magalpha center at the
position e = 2 mm and z = 4 mm, the minimum field within one rotation
would be 20 mT. At this point, the ellipticty ratio is between 0.6 and
0.8. Note that along a curve in the e-z plane (light blue line) the
ellipticity is -1. Along this curve
, in other words, the sensor
output is linear without any trimming.
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October 2014
Guidelines for off-axis sensor positioning
Whether a certain sensor position is suitable for MagAlpha and what is
the optimal setting are determined from the values
and
. These
values can be estimated from the graphs of Figure 4. Note that the
parameters are normalized by the magnet height:
for the magnet
diameter,
for the eccentricity and
for the sensor vertical
position. The field values are given for a remanent field
1 T. For
different remanent field, multiply
and
by the ratio
.
Once
and
are known, go through the list below:
1. Check that the minimum field
is above the lower limit of
MagAlpha. The minimum field is the lower value between
and
:
20 mT
2. Determine the ellipticity ratio:
and estimate the
3. If the
without correction:
is too large, determine the ellipticity correction:
ETX
ETY
1
0
0
1
BCT
The BTX, BTY settings assumes that the sensor is positioned as
displayed on the left. If rotated by 90°, the ETX - ETY settings are
reversed.
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October 2014
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October 2014
Figure 4: Mapping of the Radial and Tangential Fields for a 1 T Remanent Field Magnet with Several aspects
Ratios
.
Example
Consider the magnet-sensor configuration. The chip is positionned as
displayed on the left.
Diameter
Height
Remanent field
Eccentricity
Height
(mm)
(mm)
(T)
(mm)
(mm)
5
2.5
1.1
5
1.25
The normalized coordinates are:
Normalized Parameter
Value
2
2
0.5
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October 2014
The sensor position is shown by the red dots in Figure 5. The table
below indicates the values extracted from the graph. Note that the
normalized values must be multiplied by 1.1 since
T.
Figure 5 : Sensor Position in the Magnetic Field of a Permanent Magnet.
Normalized field
Field
Both
and
Unit
mT
55
60.5
Tangent
30
33
are more than 20 mT, therefore the position is OK.
The ellipticity ratio is
. Therefore without trimming, the
would be 16.3°:
Therefore to correct the non-linearity, the MagAlpha should be
programmed with :
Because the chip is rotated by 90 ° (see picture above) and
trimming should occur along the Y axis:
the
ETX = 0
ETY = 1
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October 2014
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