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Angular orientation reconstruction of the Hall sensor calibration setup

Angular orientation reconstruction of the Hall sensor calibration setup. By Zdenko van Kesteren Supervisor: prof. dr. Frank Linde. Outline. Hall sensors Calibration set up Determining internal parameters Angular orientation analysis. ATLAS muonspectrometer. 3D magnetic field sensor.

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Angular orientation reconstruction of the Hall sensor calibration setup

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  1. Angular orientation reconstruction of the Hall sensor calibration setup By Zdenko van Kesteren Supervisor: prof. dr. Frank Linde

  2. Outline • Hall sensors • Calibration set up • Determining internal parameters • Angular orientation analysis

  3. ATLAS muonspectrometer

  4. 3D magnetic field sensor • 3D sensor with 10-4 precision • Prototype designed & built by NIKHEF • Need to be calibrated • Felix Bergsma (CERN)

  5. Hall effect (semi)conductor in magnetic field

  6. Hall effect VH = IB/nqd q = charge carrier n = carrier density

  7. 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

  8. 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

  9. Calibration setup

  10. Coil measurements

  11. Noise levels

  12. 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)

  13. 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

  14. Rotation axes geometry

  15. Coil geometry Plus 3 angles to fix coils in space: 1, 2 ,1

  16. Coil electronics • Pedestal voltage • Electronical gain • RC-times Shell

  17. 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!

  18. Coil voltage vs. time

  19. Modeled coil data

  20. Internal parameters • Values and errors of the parameters are not reliable • Wrong assumption to fix iin fit • Normalized 2 on noise RMS • Parameters are used to analyse the angular orientation

  21. 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

  22. Coil measurement method • Values of C1, C2 and C3 gives rise to a reconstructed trec (found by fitting) • 1trec and 2trec give rotation angles x, y • Rotation angles relate to angular orientation , 

  23. Absolute Encoder method • Encoder readout give AX and AY • AX and AY relate to rotation angels x, y • Rotation angles relate to angular orientation , 

  24. Angular orientation

  25. Trajectory x →

  26. Results • ,  reconstruction • <10-4 rad precision not met • Internal parameters not reliable

  27. Conclusions • Data not reliable • ADCs coils do not behave properly • Bergsma reconstructed B; B of 10-3 T • Fit not reliable • The ishould be floating parameters in fit • Including iin fit yields correlations between parameters

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