TLE5011 Calibration

February 2009
TLE5011
GMR-Based Angular Sensor
Application Note
TLE5011 Calibration
V 1.1
Sensors
Edition 2009-02-26
Published by
Infineon Technologies AG
81726 München, Germany
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TLE5011 GMR-Based Angular Sensor
Revision History: 2009-02-26, V 1.1
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Table of Contents
Table of Contents
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1
Giant Magneto-Resistance Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2
2.1
2.1.1
2.1.2
2.2
2.3
Calibration of TLE5011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Extraction of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Min-Max Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Exact Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Final Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Temperature-dependent Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3
Angle Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
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List of Figures
List of Figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
X, Y output signal (raw values) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Angle performance without parameter correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
X, Y output signals (offset corrected) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
X, Y output signals (amplitude normalized) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Angle performance after parameter correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Calibration routine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Min-Max method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Orthogonality error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Correction of orthogonality error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Temperature coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Implementation of angle calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
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TLE5011 Calibration
Giant Magneto-Resistance Parameters
1
Giant Magneto-Resistance Parameters
The output signals of the TLE5011 can be factored into a sine (Y) and a cosine (X). These signals can be
expressed by Equation (1).
(1)
X = AX * COS (α + ϕ X ) + OX
Y = AY * SIN (α + ϕY ) + OY
AX .. Amplitude of X(COS) signal
AY .. Amplitude of Y(SIN) signal
OX .. Offset of X(COS) signal
OY .. Offset of Y(SIN) signal
ϕX .. Phase of X(COS) signal
ϕY .. Phase of Y(SIN) signal
The three parameters that affect the angle calculation are the amplitude, the offset, and the phase. Figure 1
displays the output of X and Y signals. The scale in the figure has been exaggerated to make them easier to see.
X, Y Output [digits]
TLE5011 (X, Y Output)
(raw values)
0
45
90
135
180
225
270
315
360
Angle [°]
sin (Y)
Figure 1
cos (X)
X, Y output signal (raw values)
The direct angle calculation (Equation (2)) will result in an elliptical shape (Figure 2).
(2)
Y
α = arctan( )
X
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TLE5011 Calibration
Giant Magneto-Resistance Parameters
Y
Y
α
X
X
Figure 2
Angle performance without parameter correction
To minimize the angle error, it is important to achieve a circular shape. Therefore some corrections are necessary.
First the offset has to be corrected (Figure 3).
X, Y Output [digits]
TLE5011 (X, Y Output)
(offset corrected)
0
45
90
135
180
225
270
315
360
Angle [°]
sin (Y)
Figure 3
cos (X)
X, Y output signals (offset corrected)
The next step is the amplitude normalization (Figure 4), followed by the correction of the non-orthogonality
(Figure 8).
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TLE5011 Calibration
Giant Magneto-Resistance Parameters
X, Y Output [digits]
TLE5011 (X, Y Output)
(amplitude normalized)
0
45
90
135
180
225
270
315
360
Angle [°]
sin (Y)
Figure 4
cos (X)
X, Y output signals (amplitude normalized)
After all corrections have been made, the resulting vector of X and Y signal will have a circular shape.
Y
Y
α
X
Figure 5
X
Angle performance after parameter correction
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TLE5011 Calibration
Calibration of TLE5011
2
Calibration of TLE5011
This chapter explains how to determine the Giant MagnetoResistance (GMR) parameters such as amplitude,
offset, and the phase of X- and Y-channels.
The end-of-line calibration can be accomplished using the following sequence (Figure 6):
1.) left turn measurement
3.) right & left turn w/o measurement
4.) right turn measurement
90°
180°
0°
Start
End
270°
Figure 6
1.
2.
3.
4.
5.
6.
Calibration routine
Turn magnetic field 360° left and measure X and Y values
Calculate amplitude, offset, phase correction values of left turn
Turn further 90° left and 90° back right without measurement
Turn magnetic field 360° right and measure X and Y values
Calculate amplitude, offset, phase correction values of right turn
Calculate mean values of amplitude, offset, phase correction
The calibration has to be done at room temperature with a magnet in the specified magnetic field range. The signal
amplitude T25 of the temperature measurement path must also be measured afterwards. This is done by setting
the TEMP_EN bit at address 0CH. The temperature can then be read out via X-path (XL, XH). Store this value in
digits; it is not necessary to convert it into °C.
2.1
Extraction of Parameters
There are two possible methods for extracting these parameters. The methods will be discussed in more detail in
the next two sections.
2.1.1
Min-Max Method
Xmax, Xmin, Ymax and Ymin have to be extracted out of every full-turn measurement (Figure 7).
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TLE5011 Calibration
Calibration of TLE5011
Y
Ymax
X(Ymax)
Y(Xmax)
Xmin
Y(Xmin)
Xmax
SensorZeropoint
X
X(Ymin)
Ymin
Figure 7
Min-Max method
Afterwards, amplitude (Equation (3), Equation (4)) and offset (Equation (5), Equation (6)) can be calculated:
AX =
AY =
X max − X min
2
(3)
Ymax − Ymin
2
OX =
X max + X min
2
OY =
Ymax + Ymin
2
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TLE5011 Calibration
(4)
(5)
(6)
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TLE5011 Calibration
Calibration of TLE5011
The corresponding maximum and zero-crossing points of the SIN and COS signals do not occur at the precise
distance of 90°. The difference between X and Y phases is called the orthogonality error (Equation (7)):
(7)
ϕ = ϕ X − ϕY
φX
sin (Y)
cos (X)
0,800
0,300
-0,200
0
45
90
135
180
225
270
315
360
φY
-0,700
-1,200
Figure 8
Orthogonality error
There is another more accurate way to determine the orthogonality error. The orthogonality can be calculated out
of the magnitude of two 90° angle shifted components. Possible angle combinations are 45° and 135°, 135° and
225°, 225° and 315° or 315° and 45°.
The angle value is given by the angle sensor. No reference is necessary. Therefore the final parameters of
amplitude and offset (Chapter 2.2) should be used.
At an angle output of 45° the corresponding Y(sin) and X(cos) values can be read out. This has been done also
at 135° (Figure 9).
Next step is to calculate the length of the magnitudes (Equation (8)):
2
M 45 = X 45 + Y45
2
2
M 135 = X 135 + Y135
(8)
2
M45, M135.. Magnitude at 45° and 135°
X45, X135 .. Cosine values at 45° and 135°
Y45, Y135 .. Sine values at 45° and 135°
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Calibration of TLE5011
With these magnitudes the orthogonality can be calculated (Equation (9)):
ϕ = 2 * arctan(
M 135 − M 45
)
M 135 + M 45
(9)
Y
(SIN)
45°
135°
M45
M135
X
(COS)
Figure 9
Correction of orthogonality error
2.1.2
Exact Method
This method uses the Discrete Fourier Transform (DFT) to extract the parameters out of the measurements.
Therefore an accurate reference system is necessary. This method is done using 2m measurement points at 360°
(e.g. m = 8; n = 2m = 28 = 64).
DFT Offset Calculation:
The offset is calculated by the summation of the X- or Y- measurements divided by the number of measurement
points (Equation (10)):
Ox = [ X (1) + X (2) + .. + X (n )] / n
(10)
OY = [Y (1) + Y (2) + .. + Y (n )] / n
X(n) .. X value at measurement point n
Y(n) .. Y value at measurement point n
n .. Measurement points
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TLE5011 Calibration
Calibration of TLE5011
DFT Amplitude and Phase Calculation:
To determine the amplitude, the real and imaginary parts must be calculated. This has been done with
Equation (11) for the X values and Equation (12) for the Y values. β describes the reference angle (e.g. n = 64;
measurement every 360° / 64 = 5.625° step).
DFT _ X _ r = [X (1) * COS (β 1) + X (2 ) * COS (β 2 ) + .. + X (n ) * COS (βn )]* 2 / n
DFT _ X _ i = [X (1) * SIN (β 1) + X (2 ) * SIN (β 2 ) + .. + X (n ) * SIN (βn )]* 2 / n
DFT _ Y _ r = [Y (1) * COS (β 1) + Y (2) * COS (β 2) + .. + Y (n ) * COS (βn )]* 2 / n
DFT _ Y _ i = [Y (1) * SIN (β 1) + Y (2) * SIN (β 2) + .. + Y (n ) * SIN (βn )]* 2 / n
(11)
(12)
Now the amplitude and phase can be calculated (Equation (13), Equation (14))
(13)
AX = ( DFT _ X _ r ) 2 + ( DFT _ X _ i ) 2
AY = ( DFT _ Y _ r ) 2 + ( DFT _ Y _ i ) 2
(14)
DFT _ X _ i
ϕ X = arctan
DFT _ X _ r
DFT _ Y _ i
π
ϕ Y = − arctan
2
DFT _ Y _ r
ϕ = ϕ X − ϕY
2.2
Final Parameters
No matter what calibration method is used, you still have to calculate the symmetrical values of the parameters.
This is done using the mean value of the clock-wise (cw) rotation parameters and counterclock-wise (ccw) rotation
parameters. This calculation has to be done with X and Y parameters. These parameters have to be used for the
signal correction.
Acw + Accw
2
O + Occw
OM = cw
2
ϕ + ϕ ccw
ϕ M = cw
2
AM =
(15)
(A,O,ϕ)M .. Mean parameters
(A,O,ϕ)CW .. Parameters of clock-wise rotation
(A,O,ϕ)CCW .. Parameters of counterclock-wise rotation
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Calibration of TLE5011
2.3
Temperature-dependent Behavior
The temperature offset gradients (KTOX, KTOY) for both channels depend on the value at 25°C. These gradients
are neccesary for the temperature offset compensation.
KTOx = tco _ d _ x + (tco _ k _ x * OX 25 )
(16)
KTOY = tco _ d _ y + (tco _ k _ y * OY 25 )
tco_d_x, tco_d_y .. Offset temperature coefficient base (in digits/K)
tco_k_x, tco_k_y .. Offset temperature coefficient gain (in 1/K)
The coefficients (tco_d_x, tco_d_y, tco_k_x, tco_k_y) have to be determined for every sensor separately. This has
been done at two different temperatures (e.g. T25 and HT).
Offset
tco_d
P1(T 1/O 1)
P2 (T2/O2)
0
Figure 10
HT
T25
Temperature
Temperature coefficients
The offset of X and Y channels at two temperatures has to be known before the coefficients can be calculated with
Equation (17) and Equation (18).
tco _ k =
(17)
O2 − O1
T2 − T1
(18)
tco _ d = O1 − tco _ k * T1
The temperature offset compensation should be used to achieve more accurate angle values over the whole
temperature range.
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TLE5011 Calibration
Angle Calculation
3
Angle Calculation
To get highly accurate angle values, the following angle calculation must be performed. Figure 11 shows the
implementation within a microcontroller.
CalibrationsAlgorithm
Sensor X
Sensor Y
Figure 11
Offset_
corr
Gain_
corr
+
*
+
*
Angle_
corr
X_tmp
atan
(Cordic)
Y_tmp
Y-Corr
Implementation of angle calculation
Offset Correction (Offset_corr)
To increase the accuracy, the temperature-dependent offset drift can be compensated for. The temperature of the
chip has to be read out. The offset values OX and OY can be described by the following equations:
Ox = O X 25 +
KTOX
* (T − T25 )
ST
OY = OY 25 +
KTOY
* (T − T25 )
ST
(19)
OX25 .. Offset of X(COS) signal at room temperature (in digits)
OY25 .. Offset of Y(SIN) signal at room temperature (in digits)
KTOX .. Gradient of X-offset (in digits/K)
KTOY .. Gradient of Y-offset (in digits/K)
ST .. Temperature sensor sensitivity (in digits/K)
T .. Temperature (in digits)
T25 .. Temperature at room temperature (in digits)
After the X and Y values are read out, the temperature-corrected offset value must be subtracted (Equation (20)):
(20)
X 1 = X − OX
Y1 = Y − OY
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TLE5011 Calibration
Angle Calculation
Amplitude Normalization (Gain_corr)
The next step is to normalize the X and Y values by using the mean values determined in the calibration.
X2 =
Y2 =
X1
AXM
(21)
Y1
AYM
Non-Orthogonality Correction (Angle_corr)
The influence of the non-orthogonality can be compensated for by using Equation (22), in which only the Y
channel must be corrected.
Y3 =
Y2 − X 2 * sin( −ϕ )
cos( −ϕ )
(22)
Resulting Angle
After correction of all errors, the resulting angle can be calculated using the arctan function1).
α = arctan(
Y3
) −ϕX
X2
(23)
1) Microcontroller library function “arctan2(Y3,X2)” works better to resolve 360°
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