# Sensor performances and equivalent magnetic noise

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## Cross-eld eect

As illustrated in Figure 3.13, the AMR sensor is generally sensitive to a magnetic eld vector in its sensitive axis. However, all the magnetoresistive sensors have an inherent sensitivity to the perpendicular eld to the sensitive axis. This eect is the so called cross-eld eect or cross-eld error is represented by Hx in Equation (3.13). This eect mostly comes from the dimensional characteristics of the sensor layout and has an inverse relation to the sensor sensitivity [57]. By increasing Hk, obviously, the cross-eld eect will be reduced, but on the other hand, the sensitivity also behaves the same way. In order to investigate the dependency of the anisotropy eld with the geometry of the sensor or strip, we need to consider an additional component to the free energy of the system in the Equation (3.1). This parameter is usually known as shape anisotropy eld Hd = NMs (where N is the demagnetizing factor) [58]. Almasi and co-workers [59] proposed to use the shape anisotropy as a method to decrease the anisotropy eld of a thin lm material by the following equation: Hk = t w 􀀀 t l M 􀀀 Hko.

### Power consumption of ipping method

In general, the typical ipping frequency is about 100-200 Hz for low frequency measurement. However, in some cases the ipping frequency can be exceeded to tens of kilohertz in order to achieve the maximum resolution of the sensor. In low frequency application, low frequency noise is the main critical problem. In all front end electronic design this noise exists in power supplies, sensors, ampliers, resistors, etc. Chopper stabilization is one of the eective methods that can be employed to remove the low frequency noise of the ampliers [63]. This method is based on the modulation and demodulation technique (Figure 3.13 (a)). As depicted in Figure 3.13 (b), rst, the sensor output that contains of signal and noise is modulated by a carrier to higher frequencies where the low frequency noise of the amplier is less (c). Note that the modulation frequency should be greater than the corner frequency of the amplier noise. In addition, due to this modulation, the odd harmonics of the sensor signal appear as well. After the amplication and adding the amplier noise (d), the signal is demodulated by the same frequency as modulation and turn back to its previous frequency. This new operation converts the signal harmonics to even harmonics, and since the amplier noise is modulated once, its odd harmonics will appear. Finally, in order to recover the clean output signal from the modulation noise and harmonics, a low pass lter is implemented at the end of the chain (e). In AMR sensors, ipping method operates as a modulation. Consequently, as mentioned earlier, this modulation helps to shift the sensor signal to a higher frequency to improve the sensor resolution. Meanwhile the ipping frequency depends on the corner frequency of the electronic low frequency noise.
However, one should not forget that using the ipping method increases the power consumption of the sensor and this can be viewed as a serious problem in most of the applications. In order to apply the pulse magnetic eld, a simple RC circuit can be used consisting of half or full-bridge of transistors with a low drain source resistance.
Moreover, to reduce the thermal drift of the sensor measurement, the power dissipated should be much lower via the set/reset strap compared to the sensor power consumption. Although, this strap needs a high current (few amps) to re-align the magnetic domains, the pulse duration is quite small. For instance, the HMC102X from Honeywell needs at least a pulse width current of around ve micro seconds.

#### Sensor performances and equivalent magnetic noise

Most of the AMR sensors available today do an excellent job of sensing magnetic eld within the Earth’s magnetic elds, and they can measure both linear and angular positions. Furthermore, the AMR sensors are the most stable of the magnetoresistance sensors and their bias remains constant during the sensor life. However, these advantages can only be obtained by using some techniques for improving the sensor performances that will be explained in the following sections.

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Vector magnetometer error modeling

The microelectromechanical systems (MEMS) type magnetometer is commonly used nowadays in many applications. Inertial navigation systems use a magnetometer as a digital compass for heading, with the combination of the accelerometer and the gyroscope.
However, these sensors have drawbacks in terms of noise, dierent sensitivities, bias drift and nonlinearity response. Hence, much research and additional eorts have been devoted to enhancing the performances of motion sensors such as accelerometers, gyroscopes, magnetic sensors and barometers. Signal processing, estimation algorithms, special electronic design and sensor calibration can be mentioned. Compared to other motion sensors, calibrating the DC magnetometer needs more eort and experiences because this process is always subject to perturbation of the magnetic eld. Several methods and algorithms have been proposed for calibrating magnetometers.
Most of them have the same fundamental and use a scalar calibration algorithm that needs to rotate the magnetometer in all possible directions in a constant uniform magnetic eld [65], [66], [67], [68], [69].
Generally, the main source of errors can be separated into two categories: those caused by disturbances in the magnetic elds surrounding the sensor, and those due to the manufacturing defects and limitation in the sensors. These errors for three-axis sensors are detailed below.

Abstract
Acknowledgements
List of Figures
List of Tables
1 Introduction
2 Review of magnetic sensors
2.1 Hall sensors
2.2 Search coil
2.3 Flux-gate
2.4 Magnetoresistance and Magnetoimpedance magnetometer
2.4.1 AMR
2.4.2 GMR and TMR
2.4.3 GMI
2.5 Magneto-Electric sensor
2.6 Application
3 Anisotropic Magnetoresistance Sensor
3.1 Principle
3.2 Temperature eect
3.3 Cross-eld eect
3.4 Flipping
3.4.1 Cross-eld error compensation
3.4.2 Temperature drift on the bias measurement
3.4.3 Power consumption of ipping method
3.5 Low-cost electronic design
3.6 Sensor performances and equivalent magnetic noise
4 Calibration algorithm and sensor error modeling
4.1 Vector magnetometer error modeling
4.1.1 Scale factor
4.1.2 Misalignment error
4.1.3 Soft iron error
4.1.4 Hard iron error
4.1.5 Sensor bias
4.2 Calibration process
5 Novel compensation method of the cross-axis eect
5.1 Introduction
5.1.1 Methods using additional electronic design
5.1.1.1 Flipping method
5.1.1.2 Feedback loop
5.1.2 Sensor fabrication process
5.1.3 Methods using numerical computation
5.2 Numerical compensation method of cross axis in Earth’s magnetic eld.
5.2.1 Compensation method without ipping
5.2.2 Compensation method using ipping
5.3 Experimental result
5.3.1 Sensor board
5.3.2 Scale factors
5.3.3 Method to nd scale factors
5.3.4 Results
5.3.4.1 Non ipped sensor
5.3.4.2 Flipped sensor
6 Indoor calibration
6.1 Indoor magnetometer calibration system (IMCS)
6.1.1 Theory of operation
6.1.2 Hardware Overview
6.1.2.1 Driver board
6.1.2.2 Study of the Helmholtz coil design
6.1.2.3 Mu-metal box design
6.1.2.4 Sensor board
6.1.3 Experimental results
6.1.3.1 Evaluate the performance of IMCS
6.1.3.2 Calibration results
6.1.3.3 Arbitrary position
6.2 On-board solution (auto-calibration)
6.2.1 Theory of operation
6.2.2 Experimental results
6.2.2.1 Evaluation of the performance of the oset coil for calibrating the AMR sensors
6.2.2.2 Results
7 Conclusion
A Helmholtz coil
A.1 Magnetic eld provided by a current loop
A.2 Magnetic eld provided by a combination of two coils
A.3 Simulating the eect of an angular error of one coil on the uniformity of the magnetic eld of two coil combinations
B Mu-metal box
B.1 Shape
B.2 Size
B.3 Distance between the layers
B.4 Number of layers

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