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

• 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-timesShell

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)

20parameters!

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