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Institute of Vehicle System Technology Chair of Rail System Technology Prof. Dr.-Ing. Peter Gratzfeld Bachelor Thesis Simulation of a hall sensor in ANSYS Maxwell with Integration in MATLAB/Python cand. mach. Enrique Barrientos García Placeholder Image Project Manager Jost, Franz No.: List StA- and DA Transfer 16-B-0013 Karlsruhe, July 2016 Institute of Vehicle System Technology Chair of Rail System Technology Prof. Dr.-Ing. Peter Gratzfeld Bachelor Thesis Mr. B.Sc. Enrique Barrientos García Matr.-No.: 1798441 Simulation of a hall sensor in ANSYS Maxwell with Integration in MATLAB/Python The thesis is to be elaborated in close interaction with the institute and stays its property. Any publication or distribution requires the instituteโs permission. Topic issued on: TT.MM.JJJJ Thesis handed in on: TT.MM.JJJJ Supervisor: Project manager: (Prof. Dr.-Ing. Peter Gratzfeld) Author: (Jost, Franz) Address: City Street Phone Karlsruhe Willy Andreas Allee Nr.1 +49 1578 4196328 (B. Sc. Enrique Barrientos García ) Heads of the institute: Prof. Frank Gauterin Prof. Dr.-Ing. Marcus Prof. Dr.-Ing. Peter Prof. Dr.-Ing. Frank Henning Dr.rer.nat. Geimer Gratzfeld Rintheimer Querallee 2, Geb. 70.04 Tel.: +49 721 608-48610 76131 Karlsruhe Fax: +49 721 www.bahnsystemtechnik.de 608-48639 Definition of task for Mr. B.Sc. Barrientos García, Enrique (Matr.-No.: 1798441) Simulation of a hall sensor in ANSYS Maxwell with Integration in MATLAB/Python Space for the description of the task. Declaration of Originality I hereby formally declare that I have written the submitted thesis independently. I did not make use of any outside support except for the use of the quoted literature and the sources mentioned in the paper. Furthermore, I assure that all quotations and statements that have been inferred literally or in a general manner from published or unpublished writings are marked as such. I am aware that the violation of this regulation will lead to failure of the thesis. Karlsruhe, DD.MM.YYYY Acknowledgment First of all, I would like to thank the KIT, in particular the Institut für Fahrzeugsystemtechnik and Franz Jost, for helping me achieve this great work. I would like to thank as well the Universidad Pontificia de Comillas I.C.A.I. for inspiring, teaching and helping me grow as an engineer and as a person. All the same, I want to thank my parents, with whom all their support and care have made me achieve this accomplishment. Last but not least, I want to thank my brother the most, for being there now and always, every time I needed him, without you this would not have been possible. Abstract The abstract concerns mostly factual texts. Most commonly, these texts belong to sorts of journalistic forms. The writer of an abstract has to adopt style and contextual intentions of the textual source. Contents 1. 2. Introduction .................................................................................................................... 1 1.1. Motivation ................................................................................................................ 4 1.2. Objective ................................................................................................................. 5 1.3. Outline..................................................................................................................... 5 Basic concepts ............................................................................................................... 7 2.1. The Hall Effect......................................................................................................... 7 2.2. Hall Effect Sensor ..................................................................................................12 2.2.1. Basic Hall Effect Sensor ..................................................................................13 2.2.2. Analog Output Sensors ...................................................................................14 2.2.3. Digital Output Sensors ....................................................................................19 2.3. 2.3.1. Magnetic Fields ...............................................................................................23 2.3.2. Magnetic Materials and their Specifications .....................................................23 2.3.3. Basic Magnetic Design Considerations ...........................................................24 2.3.4. Magnet Materials Summary.............................................................................26 2.3.5. Magnetic Systems ...........................................................................................27 2.4. 3. Electrical Considerations ........................................................................................32 2.4.1. Introduction to the electrical considerations .....................................................32 2.4.2. Digital Output Sensors ....................................................................................33 2.4.3. Analogical Output Sensor ................................................................................34 2.5. Application of the Hall Effect Sensing Devices .......................................................36 2.6. ANSYS Maxwell approaches ..................................................................................37 Solution Approaches .....................................................................................................38 3.1. Model Construction ................................................................................................38 3.1.1. Coil..................................................................................................................38 3.1.2. Target and sensors .........................................................................................39 3.1.3. Model Set ........................................................................................................41 3.2. 4. Magnetic Considerations ........................................................................................22 Simulations ............................................................................................................44 Results ..........................................................................................................................45 4.1. Simulations ............................................................................................................45 5. 4.1.1. Simulation A ....................................................................................................48 4.1.2. Simulation B ..................................................................................................... 6 4.1.3. Simulation C ..................................................................................................... 2 4.1.1. Simulation D ..................................................................................................... 2 Conclusion and Prospect................................................................................................ 3 5.1. Conclusion .............................................................................................................. 3 5.2. Prospect .................................................................................................................. 3 List of Figures ........................................................................................................................ 2 Bibliography .......................................................................................................................... 6 Register of symbols Formula Symbols Dimensions Unit ๐ Magnetic force [N] q Electrical charge [-] E Electric field [NฮC-1] v Velocity [m/s] B Magnetic Field [Teslas] I Electrical current [A] w Width [m] VH Hall Voltage [V] d Thickness [m] n Mobile charges [-] j Density of charge carries [-] RH Hall Coeficient [-] µe Electron mobility [-] µr Hole mobility [-] ฦฅ Hole concentration [-] [-] [-] [-] Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 1. Introduction Rail vehicles are highly complex systems, where different techniques from the field of mechanical engineering, electrical engineering and information technology are integrated. Continuously increasing demands regarding even greater installed capacity, lighter weight, less wear, higher efficiency, higher crash resistance and greater security to a utilization of the installed equipment to the limits of what is physically feasible. Here, the boundaries between traditional disciplines become increasingly blurred. Functions that have been realized by electrical or mechanical subsystems are increasingly replaced by integral solutions in which electrical engineering and information technology are closely intertwined (Mechatronics). (KIT, 2016) The wear on wheel and rail is one of the largest cost items in the maintenance of rolling stock and maintenance of rail networks. In particular, with very tight corners, as these pass usually through the movement of the tram along its way, there appears a large approach angle of attack between wheel and rail, which deteriorates the mechanism. Therefore, this leads to increased wear. (KIT, 2016) In order to downsize this cost of the wear, a research is being done in which not only a robust control of the start angle becomes optimum along the track in the curve, but also ensures a stable behavior on straight track. There are also methods to calculate the quantification the behavior of the wear. (KIT, 2016) Yunfan Wei develops the idea of โDirectly steered wheels (DSW)โ, which can be become a solution for this issue. Wei joins the work of an active tracking through its explanation of a regime of an โactively steered wheel pair (AGR)โ. The actively steered pair corresponds to the principle of an expansion of the actively controlled idler gear ratio by a steering angle, and has not yet been studied in detail. (Göser, 2015) Figure 1-1 Active steered wheel pair (Wei, 2014) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 3 Wei has designed a robust controller for this system and has proved it with simulations. The measurements variables he has used are steering angle ฯ๐ฟ , the lateral offset V๐ฟ and the approach angle ฮฑ of the wheels. Here, the steering angle on the actuator can be tapped while the lateral offset and the approach angle must be measured continuously. (Göser, 2015) The work of Wei, which comprises the first step of the design of a robust controller for the system, is based on the awareness of all sizes and is limited in terms of the measuring principles only on fundamental considerations. The reaction of the sensor thus constitutes an essential step in the development of the concept "actively steered wheel pair" is. Closely linked with the selection of sensors, the question arises as new concepts for the installation of sensors and possible installation locations. (Göser, 2015) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 4 1.1. Motivation At the chair of railway vehicle systems of the KIT a research for the improvement on the rolling behavior on the tracks of the mechatronic bogies is being done. An active steered bogie has been developed for further improvements; in which a control algorithm has been implemented and validated using a multibody physics simulation software. (Jost, 2015) The next step is the investigation of a necessary sensor technology. An interesting solution could be the usage of Hall sensors. In order to develop this solution, a deep a study in to magnetic fields, Hall Effect, Hall sensor,as well as other details such as the material used in integrated circuits is to be carried out. However, not only a theoretical investigation is needed, but also the development of the model in Maxwell and the post processing of the output signals in MATLAB. (Jost, 2015) The main reason for the usage of these Hall Sensors is to prevent wrong measurements, which could be recorded because of physical factors such as dust, snow, or great temperatures changes. Therefore, the thesis is firstly focused on the study of Hall effects and Hall Sensors. Hall Sensors are built on the Hall Effect. (KIT, 2016) The correct use of the Hall sensors for the new boogie, can provide very useful information about the angle and space between the wheel and the rail. Therefore, this information can be used in order to reduce the cost. This costs which are generated by the wear of rail and wheel. (KIT, 2016) The Hall sensors are very simple to use and has shown already the diversity of its applications in the mechanical fields. Since the hall sensors give as output a voltage signal it is independent of the rate of the field. Furthermore, the hall sensors are not affected by ambient conditions. Dust, humidity and vibrations affect many other physical sensors, whereas Hall sensors are not affected. The hall sensors is not in contact with neighboring mechanical parts, and therefore this strengthens their sensibilty. In addition, unlike the rail or the wheel, the hall sensors do not wear over time. The Hall Effect sensors use semiconductor materials, which display a low density of electrical charges; hence, the voltage is larger since the conductivity is smaller. The dependency on the moving charges erases the possibility of wrong measurements due to perturbations. Moreover, one of the most important features of the Hall sensors is that it has a wide range of operating temperatures. (Sensors, 2012) Within their applications, they are divided in two groups. The Hall Sensors working with Analog output are used for, current sensing motor control protection, power supply sensing, motion sensing, rotary encoders, vibration sensors and rotational speed sensor. The digital Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 5 output sensor application include, pressure sensors, proximity sensors, lens position sensors and wireless communication. (Sensors, 2012) 1.2. Objective Due to limitations of conventional tracking, especially when passing through curves, alternatives are sought for better tracking. Thereby the active tracking can be implemented in different ways. In order to understand the feasibility of the proposed improvement, the following objectives are to be covered. This project presents the basic concepts of the Hall Effect sensors. In it, both the theory pertaining this sensors and their modus operandi, with all its specifications to analog and digital output sensors are examined. In the following chapters, the principles of magnetism are presented along with other theoretical concepts needed to understand correctly the function of the sensor. All this extensive analysis will create the bases to designing the magnetic systems that operate Hall Effect sensors. (Honeywell International Inc, 2016) Along with the objective of understanding the Hall Effect sensors, the project also studies which materials are the most suited to be used in the integrated circuits. Such deep study involving different magnetic and electrical factors makes it mandatory to establish several considerations and to learn how the ANSYS Maxwell program works and is implemented in MATLAB to carry out simulations that present realistic outputs. These simulations are based in the development of a simple model, in which the input is an alternating magnetic field. Through the correct development of the model, another goal is to be met: the postprocessing of the outputs reached in the simulations from MATLAB. Once this goal is achieved, a comparison of the outputs obtained with the outputs obtained by a Hall Effect sensor that is currently on the market is presented. 1.3. Outline The first task of this project is to gather information about the Hall Effect and the hall sensors. The research is focused in the first part on the theory of Hall Effect, with the intention to understand which will be the important features of the Hall Sensors. The main points that to be acquired from this research are: the discovery of this effect, its mathematical background and functioning. The information will be displayed with the following structure. Firstly introducing the basics of each of the effects mentioned, which will provide information about the discovery, performance and applications. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 6 Subsequently the research focused on Hall sensors must be precise, since the applications of the Hall sensors are of a wide range. Therefore, this second research is of greater importance and greater difficulty than the research of Hall Effect theory. The mains points that are covered through this research are, basic functioning of the sensor, classification of sensors, magnetic and electrical considerations and applications. The implementation of the theory or effect into the purpose of the thesis; following the same example would be, the use of the Hall Effect in Hall Sensors, their applications and advantages and disadvantages. Consequently, the first section of the thesis will consist on studying the effect and the Hall Sensor, focusing on the theory behind the effect, the different applications and the several considerations to have when using the effect for sensing. The study of the different materials used in the sensoring and the devices will also be revised during this section. The magnetic and the electrical considerations are studied deeply in a section. Hereafter the useful information has to be implemented to the case study, which is the development of the sensor. The learning outcomes have to be very clear, these are, the capability to create a model of the case to study. This model has to contain a coil through which an electrical current has to flow. It is important to enter different types of currents, such as sinusoidal currents. The simulation will also contain a simple target and in between these two elements, the hall sensors have to be positioned. Once the model is built the simulations take part. The characteristics of the simulations change in order to observe the effects of these changes. Finally, the measurements are studied and compared, in order to obtain solid conclusions. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 7 2. Basic concepts This section is an introduction to the Hall Effect. In it, the discovery of the effect and its applications are described. 2.1. The Hall Effect The Hall Effect is named after the American physicist Edwin Herbert Hall who discovered the effect in 1879, during his studies on his doctoral degree at the Johns Hopkins University investigating Kelvinโs electron theory. (Pengra, Stoltenberg, Van Dyck, & Vilches, 2015) Hall noticed that if a conducting material is placed in a magnetic field and an electric current passes through it, the material suffers a voltage difference proportional to both the magnetic field and the electric current. This voltage difference, points in a perpendicular direction to both the current and the magnetic field. The effect of developing the voltage difference is known as the Hall Effect. Through his measurements, Hall was able to determine the presence of moving electrical charges along a conductor. (Pengra, Stoltenberg, Van Dyck, & Vilches, 2015) In the 1950s the effect was first used to measure microwave power. However, it was not until the mass production of semiconductors, which allowed a better understanding of the effect, that it was found how useful it could be in other industries such as the computer industry, the automobile industry or the medical industry. For example, in 1968 the keyboard sector was able to take one of its biggest steps forward and introduce in the market the first solid state keyboard thanks to the application of the Hall Effect to measure different parameters. (Nave, 2012) Theoretically, the Hall effect is the generation of a voltage difference (the Hall voltage) throughout an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current. (Sensors, 2012) Figure 2-1 shows an electrical conducting material connected to an electrical current in presence of a perpendicular magnetic field. The electrons flowing through the material will experience a magnetic force, which will produce a voltage difference. (Nave, 2012) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 8 Figure 2-1 Sample of a Hall probe This magnetic force experienced is the Lorentz force, which is based in the following equation: Formula 1: ๐ = ๐(๐ธ + ๐ฃ × ๐ต) Where ๐ is the magnetic force, ๐ the charge, ๐ธ electric field, ๐ฃ the velocity of this particle and ๐ต the magnetic field. If the magnetic field is not present while the charge carriers are moving, these follow an apparently straight line, or the so called โline of sightโ. With the magnetic field acting perpendicularly on the conductor, this force accumulates one type of the charge carriers on one of the sides of the conductor. As a consequence, an equal amount of opposite charges is left on each face of the conductor. The separation of the charges generates an electric field opposite to the direction of the magnetic force, preventing a greater displacement of charges and establishing a steady electrical potential. (Sensors, 2012) The uncertainty of the polarity of the moving charges arises several other questions. Therefore, a brief study of the two possibilities, (the charges can be positive or negative), must be carried out. Figure 2-2 shows both situations. Figure 2-2 Hall effect for positive charge carriers (left) and negative charge carriers (right) (Fitzpatrick, 2007) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 9 As shown in the previous figure, the magnetic field enters the surface and the electric current flows in the same direction in both cases. The study of classical electromagnetism determines that electrons will move in the opposite direction to the one followed by the current ๐ผ. (Fitzpatrick, 2007) In the first case, (the one on the left side), the positive charges, commonly known as โholesโ are moving from left to right. This implies that the magnetic force acting on them pushes the positive charges upwards, hence separating the charges. As a consequence of the separation, an electric field pointing downwards is generated. Therefore, when the positive charges move from the left to right, the potential difference is positive. (Fitzpatrick, 2007) In the second case, the magnetic force acting on the charges pushes the negative particles to the top of the surface and the positive ones downwards. The electric field generated by this separation of the charges generates an upwards going electric field. This field implies a negative measurement of the potential difference (Fitzpatrick, 2007) The study on whether the moving particles are positive or negative proves that the electric currents in metals are carried out by electrons and not by protons. (Fitzpatrick, 2007) In both cases, the potential difference measured is the Hall Voltage. It is a common mistake to think that de value for both voltages is the same. However, reality proves to be different. โA common source of confusion with the Hall Effect is that holes moving to the left are really electrons moving to the right, so one expects the same sign of the Hall coefficient for both electrons and holes. This confusion, however, can only be resolved by modern quantum mechanical theory of transport in solidsโ (Ashcroft & Mermin, 1976) The Hall Voltage can be obtained from the expression of Lorentz force. The following figure, assumes that the charges are balanced due to the equilibrium of the magnetic and the electrical force. Therefore, the charges only move from in the direction set by the x-axis. Figure 2-3 Hall Effect principle with positioning (Wikipedia Commons, 2012) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 10 Therefore, at this point where the forces are balanced the following equation can be written: Formula 2: 0 = ๐ธ๐ฆ โ ๐ฃ๐ฅ ๐ต๐ง Taking into account the width of the conductor ๐ค and the Hall Voltage ๐๐ป , the electric field ๐ธ๐ฆ can be written as: Formula 3: ๐ธ๐ฆ = ๐๐ป ๐ค After Formula 3 is substituted in Formula 2 and rearranged, Formula 4 is obtained: Formula 4: ๐๐ป = ๐ฃ๐ฅ ๐ต๐ง ๐ค Hence, the Hall voltage is directly proportional to the magnitude of the magnetic field. However, the Hall voltage is not only proportional to the magnetic field but also to the current. The following equations demonstrate this statement. If the thickness of the conductor is d and it contains n mobile charges, per unit volume. The current flowing through the conductor can be expressed with the following equation: Formula 5: ๐ผ = ๐ โ ๐ โ ๐ค โ ๐ โ ๐ฃ๐ฅ When Formula 5 is combined with Formula 4, the following expression is reached: Formula 6: ๐๐ป = ๐ผ๐ต๐ง ๐๐๐ Thus, the Hall voltage is also proportional to the current ๐ผ and also inversely proportional to the thickness of the conductor and the density of charges flowing per unit volume. In order to build an efficient Hall probe, the material should carry few charge carriers per unit volume and withstand large electrical currents through it. Another important expression to mention is the Hall coefficient, which links the current density of the charge carriers ๐๐ฅ and the electrical field, ๐ธ๐ฆ . Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 11 Formula 7: ๐ ๐ป = ๐ธ๐ฆ ๐๐ฅ ๐ต๐ง If the equation is expressed in units from the International System of Units, (hereinafter referred to as โSIโ): Formula 8: ๐ ๐ป = ๐ธ๐ฆ ๐๐ฅ ๐ต๐ง = ๐๐ป ๐ ๐ผ๐ต 1 = โ ๐๐ However, the Hall Effect measured in semiconductors has a few differences, since the charge carriers are both holes and electrons, creating uncertainties of the density and different mobility of both carriers. โFor moderate magnetic fields the Hall coefficient isโ (Kasap, 2001): Formula 9: ๐ ๐ป = ๐๐2 โ โ๐๐2 ๐ ๐(๐๐โ +๐๐๐ )2 Where, ๐ is the electron concentration, ๐ is the hole concentration, ๐๐ the electron mobility, ๐โ the hole mobility and ๐ the elementary charge. โFor metals, the exact value of the charge carrier density and the sign of the Hall coefficient depend on the energy band structure of the particular metal. For alkali metals (Li, Na, K, etc.) and some of the transition metals (Cu, Ag, Au), the charge carriers are electrons (negative) and the charge carrier density is approximately one electron per atom. โ (D. B. Pengra, 2015) For semiconductors, the band structure can give rise to either electron or holes effective charge carriers, where the density and the mobility are the factors which determine the electrical conductivity. โAt room temperature, the charge density comes largely from intentional dopants and either electrons (from donors) or holes (from acceptors) will dominateโ (D. B. Pengra, 2015). The higher the temperature gets, the greater conductivity the material has and the more complex to understand the Hall coefficient gets. Nevertheless, at room temperatures, the density of the charge carries is much smaller than the density of the metals, and therefore the Hall voltage is much greater if the same electrical current and magnetic field is applied. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 12 2.2. Hall Effect Sensor One of the big steps in the sensing technology was the use of the Hall Effect Sensor. This sensor is built from a thin sheet of conducting material. Where the output connections are perpendicular to the electrical current flow. In the presence of a magnetic field, the sensor answers with a potential difference (voltage) which is proportional to the force of the magnetic field. However, this output is too small and, in order to obtain a measurable output, additional electronics are required. Consequently, the sum of all these associated electronic elements generates the Hall Sensor. (Honeywell International Inc, 2016) The Hall Effect Sensor is not only suitable to measure magnetic fields, but it can also measure temperature, pressure, currents, position, etc. The Hall Effect Sensor has a great number of utilities. However, the main principle of the sensor is having a magnetic field to measure. The figure below describes the working process of a Hall Effect Sensor. (Honeywell International Inc, 2016) Figure 2-4 General Sensor Based on the Hall Effect (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 13 As seen on Figure 2-4, once the magnetic field is acting the sensing device will receive an input, and consequently the system responds to the physical quantity through the input interface. The output interface converts the electrical signal to a signal that meets the requirements of the application. Within the following sections, the different parts of this system are explained in more detail. (Honeywell International Inc, 2016) 2.2.1. Basic Hall Effect Sensor One of the most basic magnetic field sensor is the Hall Element. In order to make the output useable for most applications, it requires signal conditioning, which the ones needed are an amplifier stage and temperature compensation. Furthermore, when operating from an unregulated supply a voltage regulation is needed. The following figure shows a basic hall sensor: Figure 2-5 Basic Hall Effect sensor (Honeywell International Inc, 2016) In case that there is no magnetic field present, the output voltage will be zero. Nevertheless, the output will not be zero if measured with respect to the ground, which is referred to as the common mode voltage (โCMVโ). The CMV has the same value in all output terminals. It is the potential difference what is equal to cero. The element in charge to amplify only this potential difference (Hall voltage) is the amplifier shown at Figure 2-5. (Honeywell International Inc, 2016) The potential difference obtained, Hall voltage, is considered to be a low-level signal since the order of it is about 30 micro-volts when a one gauss magnetic field is applied. Therefore, Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 14 the amplifier required to measure it must be an amplifier with low noise, high input impedance and moderate gain. The integration of this type of amplifier can be carried out through the use of standard bipolar transistor technology. The integration of the temperature is easy. (Honeywell International Inc, 2016) The purpose of the regulator in Figure 2-5 is to adjust and hold the current constant so that the output of the sensor measures only the intensity of the magnetic field, since the Hall voltage is also a function of the input current. However, some systems have already a regulated supply available and thus some Hall Effect sensors may not include an internal regulator. (Honeywell International Inc, 2016) 2.2.2. Analog Output Sensors The basic Hall Effect Sensor is a basic analog output device. These sensors provide an output voltage proportional to the magnetic field given. In order to simplify the application additional functions were added; nevertheless, it is a complete device. (Honeywell International Inc, 2016) The sensed magnetic field can be either positive or negative. Therefore, the output of the amplifier will be driven positive or negative, and hence both plus and minus power supply is required. In order to avoid having to power supplies, a fixed offset or bias is introduced into the differential amplifier. When no magnetic field is present, the bias value appears on the output and is referred to as a null voltage. The output increases above the null voltage if a positive magnetic field is sensed. And in the same way, when a negative magnetic field is sensed, the output decreases below the null voltage, but remains positive. This concept is illustrated in Figure 2-6. (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 15 Figure 2-6 Null voltage concept (Honeywell International Inc, 2016) The limits imposed by the power supply cannot be exceeded by the output of the amplifier. In fact, before the limits of the power supply are reached, the amplifier saturates. This saturation is illustrated in Figure 2-6. โIt is important to note that this saturation takes place in the amplifier and not in the Hall element. Thus, large magnetic fields will not damage the Hall Effect sensors, but rather drive them into saturation.โ (Honeywell International Inc, 2016) An open emitter, open collector, or push-pull transistor is added to the output of the differential amplifier to further increase the interface flexibility of the device. Figure 2-7 shows a complete analog output Hall Effect sensor incorporating all of the previously discussed circuit functions. (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 16 Figure 2-7 Simple analog output sensor (Honeywell International Inc, 2016) 2.2.2.1. Output vs. Power Supply Characteristics โAnalog output sensors are available in voltage ranges of 4.5 to 10.5, 4.5 to 12, or 6.6 to 12.6 VDCโ, (Honeywell International Inc, 2016) . With the purpose of operating accurately, they usually require a regulated supply voltage. Figure 2-8 Ratio-metric linear output sensor (Honeywell International Inc, 2016) Figure 2-8 โillustrates a ratio-metric analog sensor that accepts a 4.5 to 10.5 V supply. This sensor has a sensitivity (mV/Gauss) and offset (V) proportional (ratiometric) to the supply voltage. This device has โrail-to-railโ operation. That is, its output varies from almost zero (0.2 V typical) to almost the supply voltage (Vs 0.2 V typical)โ, (Honeywell International Inc, 2016). Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2.2.2.2. 17 Transfer function The transfer function of an analog output expresses the relationship between an input, the magnetic field (gauss), and an output, the Hall voltage. The transfer function can either be expressed with an equation or with a graph. The transfer function for a typical analog output sensor is illustrated in Figure 2-8. (Honeywell International Inc, 2016) Figure 2-9 Transfer function of an Analog output sensor (Honeywell International Inc, 2016) The main characteristics of an analog output sensor are the following: ๏ท Sensitivity: โSensitivity is defined as the change in output resulting from a given change in input. The slope of the transfer function illustrated in Figure 2-8 corresponds to the sensitivity of the sensor. The factor of {B (6.25 x 10-4 x VS)} in equation 2-2 expresses the sensitivity for this sensorโฆโ (Honeywell International Inc, 2016) ๏ท Null offset: โโฆnull offset is the output from a sensor with no magnetic field ๏ท excitation. In the case of the transfer function in Figure 2-8, null offset is the output voltage at 0 gauss and a given supply voltage. The second term in Equation 2-2, (0.5 x VS), expresses the null offsetโฆโ (Honeywell International Inc, 2016) Span: โโฆspan defines the output range of an analog output sensor. Span is the difference in output voltages when the input is varied from negative gauss (north) to positive gauss (south)โ, (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 18 Over their span, the analog output sensors are supposed to be linear. However, there are no perfectly linear sensors. The maximum error that results from assuming the transfer function is a straight line is defined as the specification linearity. The basic Hall device is sensitive to changes in temperature. In order to compensate for these effects, signal conditioning electronics may be incorporated into Hall Effect sensors. Figure 2-10 โillustrates the sensitivity shift over temperature for the miniature ratio-metric linear Hall Effect sensor.โ (Honeywell International Inc, 2016) Figure 2-10 Sensitivity shift versus temperature (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2.2.3. 19 Digital Output Sensors This section consists in the analysis of the digital Hall Effect Sensor. The output of this sensor can only be โONโ or โOFFโ. To convert the analog output sensor like the one showed in Figure 2-4 into a digital output sensor, a Schmitt trigger circuit has to be added. Figure 2-11 exposes the internal regulation of a digital output Hall Sensor (Honeywell International Inc, 2016) Figure 2-11 Digital output Hall Effect sensor (Honeywell International Inc, 2016) โThe Schmitt trigger compares the output of the differential amplifier (Figure 2-11) with a preset reference. When the amplifier output exceeds the reference, the Schmitt trigger turns on. Conversely, when the output of the amplifier falls below the reference point, the output of the Schmitt trigger turns off.โ (Honeywell International Inc, 2016). In the Schmitt Trigger, the hysteresis is already included for jitter-free switching. 2.2.3.1. Transfer function Figure 2-12 shows the transfer function for a digital output Hall Effect sensor that has a hysteresis incorporated. In the diagram, the operate point; the release point and the deviation between the two are the principal characteristics of the input and the output. There will be no change in the output of the sensor while the magnetic field increases until the operate point is reached. Once reached, any increase of the magnetic field will have no effect and the sensor will change its state from OFF to ON. In case of decrease of the magnetic field lower than the release point, the sensor will switch back to OFF where it originally started. The purpose for this difference between the operating and releasing point is to erase any type of false triggering caused by minor variations in the input. (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 20 Figure 2-12 Hysteresis transfer function from a digital output Hall Effect Sensor (Honeywell International Inc, 2016) The same way as in the analog sensor an output transistor is used to obtain greater application flexibility. In the following diagram the basic details of the digital output are presented. (Honeywell International Inc, 2016) Figure 2-13 NPN (Current Sinking) Digital Output Sensor (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2.2.3.2. 21 Power and Supply Characteristics There are two available configurations for the power supply in the digital sensors: regulated and unregulated sensors. In most cases, supply is regulated and the range of the power varies from 3.8 to 24 VDC. On the other hand, the cases where supple is unregulated are used for special applications, and are applied with logic circuits adding a 5 volt power supply. (Honeywell International Inc, 2016) 2.2.3.3. Input Characteristics The main characteristics of the input, which are defined by the operate and release points and the deviation between both, can alter due to a change in temperature or to using different sensors. Each sensor has a specified maximum and minimum value. In one of their reports, the company Honeywell defines this critic values as: โMaximum Operate Point refers to the level of magnetic field that will insure the digital output sensor turns ON under any rated condition. Minimum Release Point refers to the level of magnetic field that insures the sensor is turned OFF.โ (Honeywell International Inc, 2016) The following figure shows the characteristics of the input and describes the typical unipolar digital output sensor. The reason for the sensor being unipolar is that both the maximum and minimum release points are positive. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 22 Figure 2-14 Unipolar input characteristics of a Digital Output Sensor (Honeywell International Inc, 2016) A bipolar sensor shows a positive maximum release point (South Pole) and a negative minimum release point (North Pole). In Figure 2-15 the transfer function of three different bipolar sensor devices is shown. A realistic device would only correspond to the second one, which will always have a positive operate point and a negative release point. (Honeywell International Inc, 2016) Figure 2-15 Bipolar input characteristics of a Digital Output Sensor (Honeywell International Inc, 2016) 2.3. Magnetic Considerations The physical phenomena that arises from the force caused by magnets, which produce attracting or repelling fields, is called Magnetism. Due to the Lorentz force, the magnetic field exerts a force on particles. The electrical currents and magnetic materials are the ones in charge of creating these magnetic fields. (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 23 In this section, the basics concepts of magnetism and its relations with Hall Sensors are explained. 2.3.1. Magnetic Fields When a charge moves in the same direction as a current, it experiences a perpendicular force. This force results from the magnetic field that surrounds the cable through which the electrical current travels. This magnetic field is only one of the many types that exist. Other magnetic fields are created by permanent magnets. Humans are insensitive towards magnetic fields. However, it doesnโt mean that they do not exist. On the contrary, they are present everywhere and have countless applications. Regarding the Hall Effect sensors, for example, the application of a magnetic field is to provide the input. (Honeywell International Inc, 2016) The following figure shows the flux lines of a permanent magnet. The density of these lines is used to explain the size of the magnetic field. Some of the units used to measure the size of a magnetic field are ๐๐๐๐๐๐ โ ๐๐๐ก๐๐ โ2or Teslas. However, the most commonly used one is Gauss. The flux lines rise on the north pole of the magnet and die at the south, with the following shape. (Honeywell International Inc, 2016) Figure 2-16 Representation of a magnetic field and its flux lines (Honeywell International Inc, 2016) 2.3.2. Magnetic Materials and their Specifications In order to clearly understand the practical magnet specification for magnetic material and their characteristics, the following curve is used. (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 24 Figure 2-17 Magnetization curve (Honeywell International Inc, 2016) On the previous figure, the vertical axis describes the flux density of the magnetic field (๐ต) expressed in Gauss units, while the horizontal axis expresses the magnetizing force (๐ป) on oesterds. Following, an analysis of the content of Figure 2-17: ๏ท First quadrant: starting from the origin of the graph (๐ต = 0, ๐ป = 0), the material is unmagnetized, and gradually increasing its magnetizing force, taking to from 0 to ๐ต๐๐ด๐ , where the material cannot be magnetized any further. ๏ท Second quadrant: when reducing the magnetic force, instead of retracing to the original point, it decreases to a point known as the Residual Induction (๐ต๐ ). From this point the magnetic force is reversed in direction and increased, bringing it to HC, the Coercive Force. The shadowed area of the diagram is of great importance for the designers of permanent magnets. This zone represents the Demagnetization Curve, and it is used to calculate the Peak Energy Product (๐ต๐ท ๐ป๐ท (๐๐ด๐) ), which helps as criteria for comparing one magnetic material with another. (Honeywell International Inc, 2016) 2.3.3. Basic Magnetic Design Considerations There are numerous factors affecting the flux density of a magnet, and some of these factors are length, cross sectional area, material and shape, as well as the environment surrounding the flux. Therefore, these factors are of high significance for designing the Hall Sensor. (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 25 When considering a magnet to provide a specific flux, it is useful to divide the magnetic circuit in two parts: the magnet itself and the path that the flux takes from the positive pole to the negative. Taking the magnet into consideration, it is of the utmost importance to study the magnetโs demagnetization curve, in which the peak flux density is represented. The flux density will always be below the maximum and will depend on the ๐ตโ๐ป ration (permeance) for a given geometry. The figure below shows a fixed value of permeance. The point in which it crosses the demagnetization curve determines the peak flux density available from this magnet. (Honeywell International Inc, 2016) Figure 2-18 Characteristic magnet material load lines (Honeywell International Inc, 2016) Considering a magnet with a length ๐ฟ and the magnetic strength of the magnetic field being a distance ๐ from the magnet, as shown in Figure 2-19, the following proportions arise: (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 26 Formula 10: ๐ต๐ โ Formula 11: ๐ต๐ โ 1 ๐2 (๐๐๐๐กโ ๐๐๐๐) 1 (๐+๐ฟ)2 (๐๐๐ข๐กโ ๐๐๐๐) Figure 2-19 Magnet (Honeywell International Inc, 2016) This points out that the use of sensing magnetic devices is only effective in short distances and that at point ๐ the strength of the field is also relatively proportional to the area of the pole face. (Honeywell International Inc, 2016) 2.3.4. Magnet Materials Summary The following table of figure 2-20 illustrates a relative comparison between some magnetic materials. Figure 2-20 Comparison table of magnetic materials (Honeywell International Inc, 2016) Where: - BR: Flux Density measured in Gauss - HC: Demagnetizing force measured in Oersteds - BDHD: Peak Energy product. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2.3.5. 27 Magnetic Systems As explained earlier, the Hall Sensor converts a magnetic field into a useful output in the form of an electrical signal. Magnetic systems on the other hand, have the task to convert the physical quantity into a magnetic field which can be sensed by the hall sensor. (Honeywell International Inc, 2016) There are different methods to get a Hall Sensor working. One of them is the unipolar head-on mode. The term head-on refers to the manner in which the magnet moves relative to the sensor´s reference point. In this type of sensors, the magnets move towards and away from the sensor. Therefore, the magnetic flux lines pass through the sensor´s reference point. The South Pole of the magnet will be positioned facing the front of the sensor. (Honeywell International Inc, 2016) The flux lines have a specific direction due to their vector character, which goes from the North Pole to the South Pole. If the direction of the flux is the same as the one from the sensorโs reference direction, then the flux has a positive polarity. In Figure 2-21, the arrow states the direction of the reference. For this type, the lines detected are the ones, which have the same direction as the reference. Therefore, this mode is called unipolar. (Honeywell International Inc, 2016) Figure 2-21 Unipolar head-on mode Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 28 When using the head-on mode, the relationship between the distance and gauss is given by the inverse square law, where the distance is measured from the South Pole of the magnet to the face of the sensor. (Honeywell International Inc, 2016) Using a digital (ON/OFF) Hall Sensor the magnetic curve from Figure 2-21 is used to demonstrate this application. At the level G1, the sensor will have an operate (ON) and at level G2, it will be a release. When the magnet is moving toward the sensor reaching the point D1, the flux density will be big enough to turn the sensor to mode ON. In case of inverting the motion of the magnet and reaching point D2. At this point the magnetic field is not sufficient and the mode will turn in to OFF. (Honeywell International Inc, 2016) In Figure 2-22, the Unipolar Slide-by Mode is shown. The magnet moves in a horizontal direction which is beneath the sensible face of the sensor. In this case, the shape of the gauss versus distance curve is a bell curve. The gap (distance marked in the figure) decides the size of the peak. The smaller the gap, the higher the peak. (Honeywell International Inc, 2016) As in the previous example, the digital Hall Sensor operates at G1 and releases at G2 value. As the sensor moves closer to the reference point of the sensor the curve reaches +D1, at this point the sensor starts operating. If it keeps moving to the right, the sensor will remain at the same mode (ON) until it reaches -D2, in which, it will release. (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 29 Figure 2-22 Unipolar slide-by mode (Honeywell International Inc, 2016) Another mode is the โbipolar slide-by modeโ, represented in the Figure below. The components of this mode include two magnets, which move in the same way as the one in the unipolar slide-by mode. The reason for this mode being bipolar is explained by the company Honeywell International: โIn this mode, distance is measured relative to the center of the magnet pair and the sensorโs reference point. The gauss versus distance relationship for this mode is an โSโ shaped curve which has both positive and negative excursions, thus the term bipolarโ, (Honeywell International Inc, 2016). The closure of the magnetโs North or South Pole and the side of the sensorโs reference point at which it is placed result in the positive and negative halves of the curve. Figure 2-23 Bipolar slide-by mode (Honeywell International Inc, 2016) A digital (ON-OFF) Hall Effect Sensor with an operate and release value of G1 and G2, respectively, will demonstrate the effect of the curve. Moving the magnet structure counter clockwise, point D2 is reached. At that point the sensor will be operated. If the movement Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 30 is continuous, the sensor will operate until point D4 is reached. Therefore, in a counter clockwise movement, the sensor operates on the steep portion of the curve. When the movement is clockwise, the contrary occurs. Figure 2-24 is a variation of the slide-by mode. In this structure, the distance that separates both magnets is fixed. Due to this factor, the steepness of the center portion of the curve is reduced. Figure 2-24 Variation of a Bipolar Slide-by Mode (Honeywell International Inc, 2016) Figure 2-25 is another variation of the bipolar slide-by mode. The difference here is that: โโฆ a magnet with its south pole facing the sensorโs reference point is sandwiched between two magnets with the opposite orientationโฆโ (Honeywell International Inc, 2016). This variation results in a symmetrical curve. The symmetry of this curve is along the distance axis. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 31 Figure 2-25 Variation of a Bipolar Slide-by Mode (2) (Honeywell International Inc, 2016) The use of a digital output Hall Effect Sensor will imply that either on the left or the right slope of the curve actuation will occur. The width of the beat, which results from the width of the magnet placed in the center, will set the distance between the operate points. Figure 2-26 Magnetic System Comparison Chart (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 32 The previous figure is a comparison between the different modes and variation of these modes that have been previously analysed. 2.4. Electrical Considerations 2.4.1. Introduction to the electrical considerations The Hall Effect technology brings along several electric principles that are mandatory in order to a correct operation of the sensor. In the last two sections, the structure, components and inputs of the sensor have been covered. This section will analyze all the electrical specifications related with the sensor and its output. As mentioned before, the Hall Effect Sensor offers two different types of outputs: analogical and digital. Each output has its own characteristics and methodologies. These will be treated in this section. Analogical sensors provide analogical output voltages which are proportional to the intensity of the fieldโs input. While digital sensor offers binary outputs: 1 or 0, ON or OFF, respectively. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2.4.2. 33 Digital Output Sensors Digital Hall Effect Sensorsโ outputs are NPN, where the current sinks and the collector is open. Figure 2-27 shows outputs on actuated state, ON. Figure 2-27 NPN Output (Honeywell International Inc, 2016) The reason for the current to sink is that the current flows from the load into the sensor. Devices in which the current sinks contain integrated NPN circuit chips The sensor allows the current to pass throw when turned ON and blocks it when turned OFF. The difference with these switches is that โUnlike an ideal switch, a solid state sensor has a voltage drop when turned ON, and a small current (leakage) when turned OFF. The sensor will only switch low level DC voltage (30 VDC max.) at currents of 20 mA or less. In some applications, an output interface may be current sinking output, NPNโ, (Honeywell International Inc, 2016). Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 34 Figure 2-28 NPN Output Hall Effect Sensor (Honeywell International Inc, 2016) In the circuit configuration of the NPN Sensor, when the sensor is actuated by a magnetic field, the current flows through the load into the output. The output voltage of the sensor is measured between the collector and the ground. Depending on whether the sensor is ON or OFF, the following may happen: โWhen the sensor is not actuated, current will not flow through the output transistor (except for the small leakage current). The output voltage, in this condition, will be equal to VLS (neglecting the leakage current). When the sensor is actuated, the output voltage will drop to ground potential if the saturation voltage of the output transistor is neglected. In terms of the output voltage, an NPN sensor in the OFF condition is considered to be normally highโ, (Honeywell International Inc, 2016). 2.4.3. Analogical Output Sensor The โHall Effect Sensing and Applicationโ report of Honeywell International Inc., explains that: โThe output of an analog Hall effect sensor is an open emitter (current sourcing) configuration intended for use as an emitter followerโ, in which โThe output transistor provides current to the load resistor RLOAD producing an analog voltage proportional to the magnetic field at the sensing surface of the sensorโ, (Honeywell International Inc, 2016). Figure 2-29 represents an Analog Output Hall Effect Sensor. Figure 2-29 Analog output Hall Sensor (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 35 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 36 2.5. Application of the Hall Effect Sensing Devices The number of parameters that can be measured with a Hall Effect Sensor is high. However, the same design principles can be used to measure each and every one of these parameters. This section will analyze the design of the general sensing device. The designs of all sensing technologies are approached the same way. As seen in Figure, the first thing to be done is to define the parameter that is pursued to be measured. Once defined, several conceptual approaches must be made that regard to more specific matters that the parameter implies. After these analyses, the fundamental concepts are defined and evaluated. And, once the most suited fundamental is chosen, the sensor is designed. Figure 2-30 General sensing device design approach (Honeywell International Inc, 2016) Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2.6. 37 ANSYS Maxwell approaches ANSYS Maxwell is a program that allows modeling Hall Effect Sensor with different applications. This permits the measurement of magnetic fields with different geometries while taking into account all the flux flinging and nonlinear magnetic supplies. These measurements lead to the determination of the most suitable configurations and placements of the Hall Effect Sensors for specific applications. Combining the ANSYS Maxwell with ANSYS Optimetrics allows the study of different scenarios and the generation of equivalent circuits of Hall Effect Sensors, which can be included in a system-level simulation model through ANSYS Simplorer. The functioning of these models can be modeled ensuring the consideration of all respective design requirements. Figure 2-31 Example of a Magnetic Flux density and Flux lines plot toothed wheel (ANSYS, 2016) โANSYS Maxwell is the premier low frequency electromagnetic field simulation software for engineers tasked with designing and analyzing 2-D and 3-D electromagnetic and electromechanical devices, including motors, actuators, transformers, sensors and coils. Maxwell uses the accurate finite element method to solve static, frequency-domain, and time-varying electromagnetic and electric fieldsโ, (ANSYS, 2016). Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 38 3. Solution Approaches This chapters explains the construction and decision taking on the several options to carry out the simulations of a Hall Sensor model. The software used for these simulations is Ansys Maxwell. In order to understand the functioning of this software, Maxwell provides their users with several workshops. Throughout these workshops the users learn to use all the basic commands working con on 2-Dimensional space and 3-Dimensional space. Moreover, the user learns how to solve magnetic and electric problems. The magnetic problems taught in the workshop go through Magneto static, Eddy Currents and Transient problems. The main focus will be held on the Transient problems. 3.1. Model Construction The main idea thought for this model is to measure the magnetic field crossing through the hall sensors. Therefore, for this model a transient magnetic field is needed. This magnetic field is provided by a Coil. A sinusoidal current will flow through this coil, creating a changing magnetic field which will cross through the Hall sensors. Moreover, a target piece is also constructed for this model. This target simulates to be the railway. The material chosen for this piece is steel. 3.1.1. Coil This piece is in charge of providing the alternate magnetic field. The material chosen for the coil is copper. The main reason for this choice is that copper is not very expensive and is a great conductor for the purpose of it. This are the characteristics of the material: - Relative permeability:0.99991 N·Aโ2 Bulk conductivity: 58000000 siemens/m Through the coil a sinusoidal current is entered, this current has the following initial characteristics: ๐ผ(๐ก) = 5 โ ๐ ๐๐(2๐ โ 50000 โ ๐ก) ๐ด In which ๐ก is the variable of time. The frecuency arranged for the electrical current is 50๐๐ป๐ง. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 39 Figure 33 Coil description The measurements are the following: - Height: 40 mm - Interior radius: 6,5 mm - Exterior radius: 8 mm 3.1.2. Target and sensors The target simulates to be the railway tracks of the boogie, the material chosen for the piece is steel. It is the material used by the railway producers and therefore same has been chosen. Carbon among other characteristics has a high weldability and very good projection. (AZoM, 2012) The steel chosen is steel_1008, it has the following characteristics: Bulk Conductivity: 2000000 Siemens/m - Carbon 0,10% Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 40 The sensors are simulated as squared surfaces placed in between the target and the coil. The dimensions of the surface are 0, 25 × 0, 25๐๐ , the reason for such a small size is that instead of having the whole sensor represented, the active size of it is shown. On the following image you can observe the disposition of these two elements: Figure 34 Target-Sensor Top view Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 41 Figure 35 Target-Sensors Side view As can be observed in the images, the elements are separated, initially the distance between each other 2 ๐๐. The size of the target is: - Height 3 ๐๐ - Length:20๐๐ - Width:20 ๐๐ 3.1.3. Model Set On the following images the set of the model is described. The elements are positioned in order to have the most efficiency on the measurements. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Figure 36 Model Set The elements are initially positioned in the following structure: - Distance Coil- sensors: 1๐๐ - Distance Sensors-Target: 2๐๐ 42 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 43 Figure 37Model Set- top view There are 21 sensors positioned across the circular section of the coil to obtain a many measurements as possible, and observe a clear difference of the variation of the magnetic field. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 44 Figure 38Model Set- Side view 3.2. Simulations The simulations are carried out with the following procedure: 1. Input: sinusoidal current : ๐ผ(๐ก) = 5 โ ๐ ๐๐(2๐ โ 50000 โ ๐ก) ๐ด 2. Time set: the measurements are recorded from the ๐ก0 = 2 โ 10โ5 until ๐ก๐ = 16 โ 10โ5 , and the times step taken in between ๐ก๐ = 5 โ 10โ7 In order to calculate the flux of the magnetic field which goes through the sensors, the following formula is used: โ โ ๐ = |๐ต| โ |๐| โ cos ๐ ๐ท = โซ ๐ต โ ๐๐ = ๐ต Separately calculate each of the flux densities for each target, and analysing the data through the graphs. Furthermore, there is also a study on the sizes of the magnetic fields on the different elements of the set. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 45 4. Results 4.1. Simulations In this chapter the results of the simulations are exposed and explained. Each simulation is divided in three sectors. These sectors depend on the positioning of the active surface of each sensor. Since the sensors are symmetrically distributed across the sections of the coil, there is no need to study and represent each result of all of the sensors. Thus, the results are divided in the following three sectors: - - Sector 1: Sensors 1-3 (inclusive): These sensors are the ones positioned from the furthest side of the target to the beginning of the inner circumference of the coil. Sector 2: Sensors 4- 7 (inclusive): Sensors positioned in the inner section of the coil, in which the magnetic field has a greater presence. Sector 3: Sensors 8-12 (inclusive): Middle of the inner section of the coil. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Figure 39 Sector division 46 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Figure 40 Sensor distribution 47 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 4.1.1. 48 Simulation A In this simulation the characteristics are the following: - Current: 5A Frequency: 50 kHz Distance: 3 mm On the following pages, the results of the simulation are exposed. Thus, there is a description on these results: - Sector 1: On this graph the value of the magnetic field flux varies from 3E-9 Wb to 1.5E-08 Wb. This variation is due to the position of the sensors. On the graph it can be observed how the function with the lowest values is the one representing the sensor number one, which is the furthest from all the sensors. As the sensors get closer to the coil, the value of the flux increases. - Sector 2: On this sector a clear increase in the value of the flux is observed, however there is still a variation, from one sensor to the other. The highest value observed is 2,65E-8 Wb, which is acquired by the sensor number 8, and the lowest value is 2,05E-8 Wb reached by sensor number 5. Although the variation is appreciable, is not as vast as on the previous sector. - Sector 3: The variations observed are much smaller, this is due to the small difference of the value of the magnetic field. The magnetic field in the middle of the coil is quite constant in value. Nevertheless, in comparison with the first sector the variation is very significant. The highest value is a little higher than 2,8E-8 Wb and the smallest is a little lower than 2,8E-8 Wb. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 41 1rst Sector 5A 50kHz Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2 Figure 42 2nd Sector 5A 50kHz Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 43 3rd Sector 5A 50kHz Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 On the following images, the size and value of the magnetic field is seen. The three frames that are shown are the three most characteristic values of the magnetic field through the sinusoidal function of the current. The first frame represents the positive peak value of the intensity function in which the top value is 5 A. Therefore as can be seen in the image the average color of the arrows, which are the ones representing the magnetic field, is yellow. Thus, the average magnetic field coming out of the inside of the coil is between (5, 2352E-1 and 5, 9891E-1). Figure 44 Magnetic field 5A 1rst frame Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2 The third frame shows the negative value of the intensity, -5 A, and therefore the direction of the magnetic field changes, pointing in the other direction. However the value of the magnetic field is the same. Figure 45 Magnetic Field Coil 5A 3rd frame Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 3 The second frame is illustrates the value of the magnetic field when the current is 0 A, and therefore the value of the magnetic field is undetectable. Figure 46 Magnetic Field Coil 5A 2nd frame Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 4 The following next three images represent the value of the of the magnetic field going through the sensors. The frames shown have the same charactetristics as the ones previously shown. Figure 47 Magnetic Field Sensor 5A 1rst frame Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 5 Figure 48 Magnetic Field Sensor 5A 2nd frame As can be seen, the value of the magnetic field on the first and second frame are very similar, however in comparison with the magnetic fields of the coil the color changes to green, and therefore it has a lower value, between 4,4879E-1 T and 3,7394E-1 T. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 4.1.2. 6 Simulation B In this simulation the characteristics are the following: - Current: 50A Frequency: 50 kHz Distance: 3 mm For this second simulation, the current has changed its value to 50 A to understand whether it has a great impact or not. On the graphs the value do not seem to be altered, apart from the fact that the value has increased in all of them. However the variation between the different sensors is basically the same. Here is some of the data recorded: - Sector 1: Interval of the maximum values 1,5E-8 โ 2,5E-9 Sector 2: Interval of the maximum values 2,6E-7 โ 2,25E-8 Wb Sector 3: Interval of the maximum values 2,8E-7 Wb Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2 Figure 49 1rst Sector 50A 50kHz Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 3 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 4 Figure 50 2nd Sector 50A 50kH Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 5 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2 Figure 51 3rd Sector 50A 50kHz Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Figure 52 Magnetic Field Coil 50A 1 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 53 Magnetic Field Sensor 50A The last two images represent, the magnetic field of the coil and sensor, respectively. The form has not changed, however the value has been increased proportionately to the intensity. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 4.1.3. 2 Simulation C In this simulation the characteristics are the following: - Current: 5A Frequency: 50 kHz Distance: 9 mm In this simulation, the initial values of the electrical current have rested. However the target of steel has been moved away from the sensors and coil, in order to observe how the sensors react to this. The target has been moved 9 mm apart from the lowest part of the coil. Figure 54 Simulation displacement of Target On the following graphs the results of this simulation are shown: - Sector 1: The difference in between the different sensors varies similarly to the previous simulations. However there is an important variation on the value of the flux, which indicates that the movement of the target affects and is sensed by the active surfaces. The interval of the maximum values is 1E-8 โ 0 Wb the smaller values are very close to zero. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 3 - Sector 2: In this sector the variations within the different sector as well very similar to the ones in the first simulation. As expected, the value has however decreased like in the first sector. The interval of values is 2,5E-8 โ 1,9E-8 Wb - Sector 3: The same effects are observed in this sector. The interval of values is 2,8E-8 โ 2,2E-8 Wb, Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2 Figure 55 1rst Sector 5A 50kHz - Target 9mm away Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 56 2nd Sector 5A 50kHz - Target 9mm away Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 57 3rd Sector 5A 50kHz - Target 9mm away Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 58 Magnetic Field Sensor 5A - Target 9 mm away The previous figure shows the quantity of magnetic field going through the sensors. As can be appreciated the value on this simulation is smaller compared to the initial one. The value on this one is approximately 3,5E-1 T. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 4.1.1. 2 Simulation D In this simulation the characteristics are the following: - Current: 5A Frequency: 50 kHz Distance: 1 mm The main change of this simulation is that the target has been moved closer to the plane where the sensors are placed. On the following graph the flux values of the different magnetic fields is shown: - - Sector 1: There is a significance increase in the flux of the magnetic field compared to the previous simulation. The value of the flux in this simulation is the following: 1,525E-8 Wb. Sector 2: In this sector the effects are similar as well. The values of the following 3,14E-8 Wb Sector 3: This sector has also a variation on the flux value of the magnetic field 3,27E-0,8 The variation of the values is a good sign that the simulation are working. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 59 1rst Sector 5A 50kHz - Target 2mm closer Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 60 2nd Sector 5A 50kHz - Target 2mm closer Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 Figure 61 3rd Sector 5A 50kHz - Target 2mm closer Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 1 The next image shows the magnetic field produced by the coil. It can be seen that the magnitude of the field is the same as on the first simulation. Thus, the initial values have not changed but the displacement of the target affects to the sensor. Figure 62 Magnetic Field Coil 5A Target 2mm closer Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 2 In this image however the value of the magnetic field is greater than on the first simulation. Figure 63 Magnetic Field Sensor 5A Target 2mm closer Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. Error! Use the Home tab to apply Überschrift 1 to the text that you want to appear here. 5. 5.1. Conclusion 5.2. Prospect 3 Conclusion and Prospect Illustration of questions yet to be answered and new suggestions for further research 1 2 List of Figures Figure 1-1 Active steered wheel pair (Göser, 2015) ............................................................... 1 Figure 2-1 Sample of a Hall probe ......................................................................................... 8 Figure 2-2 Hall effect for positive charge carriers (left) and negative charge carriers (right) (Fitzpatrick, 2007).................................................................................................................. 8 Figure 2-3 Hall Effect principle with positioning (Wikipedia Commons, 2012) ........................ 9 Figure 2-4 General Sensor Based on the Hall Effect (Honeywell International Inc, 2016) ....12 Figure 2-5 Basic Hall Effect sensor (Honeywell International Inc, 2016) ...............................13 Figure 2-6 Null voltage concept (Honeywell International Inc, 2016).....................................15 Figure 2-7 Simple analog output sensor (Honeywell International Inc, 2016) ........................16 Figure 2-8 Ratio-metric linear output sensor (Honeywell International Inc, 2016) .................16 Figure 2-9 Transfer function of an Analog output sensor (Honeywell International Inc, 2016) .............................................................................................................................................17 Figure 2-10 Sensitivity shift versus temperature (Honeywell International Inc, 2016) ............18 Figure 2-11 Digital output Hall Effect sensor (Honeywell International Inc, 2016) .................19 Figure 2-12 Hysteresis transfer function from a digital output Hall Effect Sensor (Honeywell International Inc, 2016) .........................................................................................................20 Figure 2-13 NPN (Current Sinking) Digital Output Sensor (Honeywell International Inc, 2016) .............................................................................................................................................20 Figure 2-14 Unipolar input characteristics of a Digital Output Sensor (Honeywell International Inc, 2016) .............................................................................................................................22 Figure 2-15 Bipolar input characteristics of a Digital Output Sensor (Honeywell International Inc, 2016) .............................................................................................................................22 Figure 2-16 Representation of a magnetic field and its flux lines (Honeywell International Inc, 2016) ....................................................................................................................................23 Figure 2-17 Magnetization curve (Honeywell International Inc, 2016) ...................................24 Figure 2-18 Characteristic magnet material load lines (Honeywell International Inc, 2016) ...25 Figure 2-19 Magnet (Honeywell International Inc, 2016).......................................................26 Figure 2-20 Comparison table of magnetic materials (Honeywell International Inc, 2016) ....26 Figure 2-21 Unipolar head-on mode .....................................................................................27 Figure 2-22 Unipolar slide-by mode (Honeywell International Inc, 2016) ..............................29 Figure 2-23 Bipolar slide-by mode (Honeywell International Inc, 2016) ................................29 Figure 2-24 Variation of a Bipolar Slide-by Mode (Honeywell International Inc, 2016) ..........30 3 Figure 2-25 Variation of a Bipolar Slide-by Mode (2) (Honeywell International Inc, 2016) .....31 Figure 2-26 Magnetic System Comparison Chart (Honeywell International Inc, 2016) ..........31 Figure 2-27 NPN Output (Honeywell International Inc, 2016) ...............................................33 Figure 2-28 NPN Output Hall Effect Sensor (Honeywell International Inc, 2016) ..................34 Figure 2-29 Analog output Hall Sensor (Honeywell International Inc, 2016) .........................34 Figure 2-30 General sensing device design approach (Honeywell International Inc, 2016) ..36 Figure 2-31 Example of a Magnetic Flux density and Flux lines plot toothed wheel ..............37 Figure 33 Coil description .....................................................................................................39 Figure 34 Target-Sensor Top view .......................................................................................40 Figure 35 Target-Sensors Side view.....................................................................................41 Figure 36 Model Set .............................................................................................................42 Figure 37Model Set- top view ...............................................................................................43 Figure 38Model Set- Side view .............................................................................................44 Figure 39 Sector division ......................................................................................................46 Figure 40 1rst Sector 5A 50kHz ............................................................................................. 1 Figure 41 2nd Sector 5A 50kHz............................................................................................. 2 Figure 42 3rd Sector 5A 50kHz ............................................................................................. 1 Figure 43 Magnetic field 5A 1rst frame .................................................................................. 1 Figure 44 Magnetic Field Coil 5A 3rd frame........................................................................... 2 Figure 45 Magnetic Field Coil 5A 2nd frame .......................................................................... 3 Figure 46 Magnetic Field Sensor 5A 1rst frame ..................................................................... 4 Figure 47 Magnetic Field Sensor 5A 2nd frame ..................................................................... 5 Figure 48 Magnetic Field Sensor 5A 3rd frame....................... 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Figure 49 1rst Sector 50A 50kHz ........................................................................................... 2 Figure 50 2nd Sector 50A 50kH ............................................................................................ 4 Figure 51 3rd Sector 50A 50kHz ........................................................................................... 2 Figure 52 Magnetic Field Coil 50A ......................................................................................... 1 Figure 53 Magnetic Field Sensor 50A.................................................................................... 1 Figure 54 Simulation displacement of Target ......................................................................... 2 Figure 55 1rst Sector 5A 50kHz - Target 9mm away ............................................................. 2 Figure 56 2nd Sector 5A 50kHz - Target 9mm away ............................................................. 1 Figure 57 3rd Sector 5A 50kHz - Target 9mm away .............................................................. 1 4 Figure 58 Magnetic Field Sensor 5A - Target 9 mm away ..................................................... 1 Figure 59 1rst Sector 5A 50kHz - Target 2mm closer ............................................................ 1 Figure 60 2nd Sector 5A 50kHz - Target 2mm closer ............................................................ 1 Figure 61 3rd Sector 5A 50kHz - Target 2mm closer ............................................................. 1 Figure 62 Magnetic Field Coil 5A Target 2mm closer ............................................................ 1 Figure 63 Magnetic Field Sensor 5A Target 2mm closer ....................................................... 2 5 6 Bibliography ANSYS. (2016). ANSYS Maxwell. Abgerufen am http://www.ansys.com/Products/Electronics/ANSYS-Maxwell June 2016 von Ashcroft, N., & Mermin, N. (1976). Solide State Physics. Holt, Rinehart and Winston. AZoM. (23. August 2012). AISI 1008 Carbon Steel (UNS http://www.azom.com/article.aspx?ArticleID=6538 abgerufen G10080). D. B. Pengra, J. S. (June 2015). The Hall Effect. http://courses.washington.edu/phys431/hall_effect/hall_effect.pdf abgerufen Von Von Fitzpatrick, R. (July 2007). The Hall Effect. Von http://images.google.de/imgres?imgurl=http%3A%2F%2Ffarside.ph.utexas.edu%2Fte aching%2F302l%2Flectures%2Fimg795.png&imgrefurl=http%3A%2F%2Ffarside.ph. utexas.edu%2Fteaching%2F302l%2Flectures%2Fnode74.html&h=229&w=654&tbnid =BjQvRXAIFtROrM%3A&docid=qsFcYayDoQ abgerufen Göser, H. (2015). Konstruktive Untersuchung eines aktiv gelenkten. Karlsruhe. Honeywell International Inc. (2016). HALL EFFECT SENSING AND APPLICATION. Abgerufen am Juni 2016 von http://sensing.honeywell.com/hallbook.pdf Jost, F. (2015). Entwicklung eines mechatronischen Fahrwerks für Straßenbahnen. Von http://www.fast.kit.edu/bst/947_3828.php abgerufen Kasap, S. (6. November 2001). Hall effect in semiconductors. Abgerufen am Juni 2016 von http://kasap3.usask.ca/samples/HallEffectSemicon.pdf KIT, F. (2016). Eisenbahn als mechatronisches http://www.fast.kit.edu/bst/5540.php abgerufen System. Nave, C. R. (August 2012). HyperPhysics. Abgerufen am June http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/hall.gif 2016 Von von Pengra, D. B., Stoltenberg, J., Van Dyck, R., & Vilches, O. (June 2015). The Hall Effect. Abgerufen am June 2016 von http://courses.washington.edu/phys431/hall_effect/hall_effect.pdf Sensors, A. (22. JUNE 2012). Hall Effect http://www.azosensors.com/Article.aspx?ArticleID=16 abgerufen Sensors. Von 7 Wikimedia, F. (January 2008). Hall effect https://en.wikipedia.org/wiki/Hall_effect abgerufen - Wikipedia. Wikipedia Commons. (27. March 2012). Hall Effect Measurement Setup for Electrons. Von