Download Angular orientation reconstruction of the Hall sensor

Angular orientation
reconstruction of the Hall sensor
calibration setup
By Zdenko van Kesteren
Supervisor: prof. dr. Frank Linde
Outline
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Hall sensors
Calibration set up
Determining internal parameters
Angular orientation analysis
ATLAS muonspectrometer
3D magnetic field sensor
• 3D sensor with 10-4 precision
• Prototype designed &
built by NIKHEF
• Need to be
calibrated
• Felix Bergsma (CERN)
Hall effect
(semi)conductor
in magnetic field
Hall effect
VH = IB/nqd
q = charge
carrier
n = carrier
density
Hall sensor calibration
• Rotate sensors over two orthogonal axes
in accurately known homogeneous
magnetic field
• Repeat for several field strengths and
temperatures
• Angular orientation should be measured
very precisely, order of 10-5 rad
Hall sensor calibration
• Calibration set up #1 @ CERN (F. Bergsma)
(magnet with B about 3 x 10-5 T)
• Calibration set up #2
Jaap Kuijt,
Henk Boterenbrood,
Fred Schimmel
Currently @ NIKHEF
Calibration setup
Coil measurements
Noise levels
Angular orientation
• Need to know  and  < 10-4 both
• Calibration setup offers several ways to
measure  and :
– Absolute encoder readout
– 3 orthogonal coils integrated on probe
– Reference Hall board (will not
be covered here)
Determining internal parameters
• Constructing a model to describe coils
• Imperfections in set up ->
parameters in model
– Rotation axes parameters
– Coil geometry parameters
– Coil electronics parameters
• Fitting model to coil data
Rotation axes geometry
Coil geometry
Plus 3 angles to fix coils in space: 1, 2 , 1
Coil electronics
• Pedestal voltage
• Electronical gain
• RC-times
Shell
internal parameters
• Rotation geometry
– 1 2  1  2  2
• Coils geometry
– 12 13 23 1 2 1
• Coil electronics
– Gi Pi i (i = 1, 2, 3)
20
parameters!
Coil voltage vs. time
Modeled coil data
Internal parameters
• Values and errors of the parameters
are not reliable
• Wrong assumption to fix i in fit
• Normalized 2 on noise RMS
• Parameters are used to analyse the
angular orientation
Obtaining orientation
• Set up offers two ways to obtain
angular information:
– Direct from the absolute encoders
relies on 1 2 1 2 2
– By using the coil measurements
relies on all parameters
Coil measurement method
• Values of C1, C2 and C3 gives rise to a
reconstructed trec (found by fitting)
• 1 trec and 2 trec give rotation angles x, y
• Rotation angles relate to angular
orientation , 
Absolute Encoder method
• Encoder readout give AX and AY
• AX and AY relate to rotation angels x, y
• Rotation angles relate to angular
orientation , 
Angular orientation
→
Trajectory x
Results
• ,  reconstruction
• <10-4 rad precision not met
• Internal parameters not reliable
Conclusions
• Data not reliable
– ADCs coils do not behave properly
• Bergsma reconstructed B; B of 10-3 T
• Fit not reliable
– The i should be floating parameters in fit
– Including i in fit yields correlations between
parameters