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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
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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 institute’s 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
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Tel.: +49 721 608-48610
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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a general manner from published or unpublished writings are marked as such.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
𝑓
Magnetic force
[N]
q
Electrical charge
[-]
E
Electric field
[N·C-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
[-]
ƥ
Hole concentration
[-]
[-]
[-]
[-]
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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 “Directly steered wheels (DSW)”, 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 “actively steered wheel pair (AGR)”. 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)
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Wei has designed a robust controller for this system and has proved it with simulations. The
measurements variables he has used are steering angle ψ𝐿 , the lateral offset V𝐿 and the
approach angle α 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)
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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
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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.
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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.
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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 Kelvin’s 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)
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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: 𝑓 = 𝑞(𝐸 + 𝑣 × 𝐵)
Where 𝑓 is the magnetic force, 𝑞 the charge, 𝐸 electric field, 𝑣 the velocity of this particle
and 𝐵 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 ‘line of sight’. 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)
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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 𝐼. (Fitzpatrick, 2007)
In the first case, (the one on the left side), the positive charges, commonly known as “holes”
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.
“A 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 solids” (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)
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Therefore, at this point where the forces are balanced the following equation can be written:
Formula 2: 0 = 𝐸𝑦 − 𝑣𝑥 𝐵𝑧
Taking into account the width of the conductor 𝑤 and the Hall Voltage 𝑉𝐻 , the electric field
𝐸𝑦 can be written as:
Formula 3: 𝐸𝑦 =
𝑉𝐻
𝑤
After Formula 3 is substituted in Formula 2 and rearranged, Formula 4 is obtained:
Formula 4: 𝑉𝐻 = 𝑣𝑥 𝐵𝑧 𝑤
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: 𝐼 = 𝑞 ∙ 𝑛 ∙ 𝑤 ∙ 𝑑 ∙ 𝑣𝑥
When Formula 5 is combined with Formula 4, the following expression is reached:
Formula 6: 𝑉𝐻 =
𝐼𝐵𝑧
𝑞𝑛𝑑
Thus, the Hall voltage is also proportional to the current 𝐼 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 𝑗𝑥 and the electrical field, 𝐸𝑦 .
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Formula 7: 𝑅𝐻 =
𝐸𝑦
𝑗𝑥 𝐵𝑧
If the equation is expressed in units from the International System of Units, (hereinafter
referred to as “SI”):
Formula 8: 𝑅𝐻 =
𝐸𝑦
𝑗𝑥 𝐵𝑧
=
𝑉𝐻 𝑑
𝐼𝐵
1
= − 𝑛𝑒
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. “For moderate magnetic fields the Hall coefficient is”
(Kasap, 2001):
Formula 9: 𝑅𝐻 =
𝑝𝜇2 ℎ −𝑛𝜇2 𝑒
𝑒(𝑝𝜇ℎ +𝑛𝜇𝑒 )2
Where, 𝑛 is the electron concentration, 𝑝 is the hole concentration, 𝜇𝑒 the electron mobility,
𝜇ℎ the hole mobility and 𝑒 the elementary charge.
“For 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. “ (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. “At room temperature, the charge density comes largely from
intentional dopants and either electrons (from donors) or holes (from acceptors) will
dominate” (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.
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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)
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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 (“CMV”). 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,
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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)
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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. “It 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.” (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)
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Figure 2-7 Simple analog output sensor (Honeywell International
Inc, 2016)
2.2.2.1.
Output vs. Power Supply Characteristics
“Analog output sensors are available in voltage ranges of 4.5 to 10.5, 4.5 to 12, or 6.6 to
12.6 VDC”, (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 “illustrates 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 “rail-to-rail” operation. That is, its
output varies from almost zero (0.2 V typical) to almost the supply voltage (Vs 0.2 V typical)”, (Honeywell International Inc, 2016).
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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:

Sensitivity: “Sensitivity 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 sensor…” (Honeywell International
Inc, 2016)

Null offset: “…null offset is the output from a sensor with no magnetic field

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 offset…” (Honeywell International Inc, 2016)
Span: “…span 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)”, (Honeywell International Inc, 2016)
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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 “illustrates the sensitivity shift over temperature for the miniature ratio-metric
linear Hall Effect sensor.” (Honeywell International Inc, 2016)
Figure 2-10 Sensitivity shift versus temperature (Honeywell International Inc, 2016)
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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 “ON” or “OFF”. 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)
“The 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.” (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)
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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)
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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:
“Maximum 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.”
(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.
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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)
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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 doesn’t 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 𝑊𝑒𝑏𝑒𝑟𝑠 ∗ 𝑚𝑒𝑡𝑒𝑟 −2or 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)
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Figure 2-17 Magnetization curve (Honeywell International
Inc, 2016)
On the previous figure, the vertical axis describes the flux density of the magnetic field (𝐵)
expressed in Gauss units, while the horizontal axis expresses the magnetizing force (𝐻) on
oesterds. Following, an analysis of the content of Figure 2-17:

First quadrant: starting from the origin of the graph (𝐵 = 0, 𝐻 = 0), the material is
unmagnetized, and gradually increasing its magnetizing force, taking to from 0 to
𝐵𝑀𝐴𝑋 , where the material cannot be magnetized any further.

Second quadrant: when reducing the magnetic force, instead of retracing to the
original point, it decreases to a point known as the Residual Induction (𝐵𝑅 ). 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 (𝐵𝐷 𝐻𝐷 (𝑀𝐴𝑋) ), 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)
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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 magnet’s demagnetization curve, in which the peak flux density is represented. The flux
density will always be below the maximum and will depend on the 𝐵⁄𝐻 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 𝐿 and the magnetic strength of the magnetic field being
a distance 𝑑 from the magnet, as shown in Figure 2-19, the following proportions arise:
(Honeywell International Inc, 2016)
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Formula 10: 𝐵𝑁 ∝
Formula 11: 𝐵𝑆 ∝
1
𝑑2
(𝑁𝑜𝑟𝑡ℎ 𝑝𝑜𝑙𝑒)
1
(𝑑+𝐿)2
(𝑆𝑜𝑢𝑡ℎ 𝑝𝑜𝑙𝑒)
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 𝑃 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.
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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
sensor’s 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
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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)
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Figure 2-22 Unipolar slide-by mode
(Honeywell International Inc, 2016)
Another mode is the “bipolar slide-by mode”, 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: “In this mode, distance is measured relative to the center
of the magnet pair and the sensor’s reference point. The gauss versus distance relationship
for this mode is an “S” shaped curve which has both positive and negative excursions, thus
the term bipolar”, (Honeywell International Inc, 2016). The closure of the magnet’s North or
South Pole and the side of the sensor’s 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
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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: “…
a magnet with its south pole facing the sensor’s reference point is sandwiched between two
magnets with the opposite orientation…” (Honeywell International Inc, 2016). This variation
results in a symmetrical curve. The symmetry of this curve is along the distance axis.
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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)
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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 field’s input. While digital sensor offers binary outputs: 1 or 0, ON or OFF,
respectively.
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2.4.2.
33
Digital Output Sensors
Digital Hall Effect Sensors’ 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 “Unlike 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, NPN”, (Honeywell
International Inc, 2016).
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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: “When 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 high”, (Honeywell International Inc, 2016).
2.4.3.
Analogical Output Sensor
The “Hall Effect Sensing and Application” report of Honeywell International Inc., explains
that: “The output of an analog Hall effect sensor is an open emitter (current sourcing)
configuration intended for use as an emitter follower”, in which “The output transistor
provides current to the load resistor RLOAD producing an analog voltage proportional to
the magnetic field at the sensing surface of the sensor”, (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)
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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)
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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)
“ANSYS 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 fields”, (ANSYS, 2016).
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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·A−2
Bulk conductivity: 58000000 siemens/m
Through the coil a sinusoidal current is entered, this current has the following initial
characteristics:
𝐼(𝑡) = 5 ∙ 𝑠𝑖𝑛(2𝜋 ∙ 50000 ∙ 𝑡) 𝐴
In which 𝑡 is the variable of time. The frecuency arranged for the electrical current is 50𝑘𝐻𝑧.
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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%
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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, 25𝑚𝑚 , 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
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Figure 35 Target-Sensors Side view
As can be observed in the images, the elements are separated, initially the distance
between each other 2 𝑚𝑚. The size of the target is:
- Height 3 𝑚𝑚
- Length:20𝑚𝑚
- Width:20 𝑚𝑚
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.
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Figure 36 Model Set
The elements are initially positioned in the following structure:
- Distance Coil- sensors: 1𝑚𝑚
- Distance Sensors-Target: 2𝑚𝑚
42
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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.
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Figure 38Model Set- Side view
3.2. Simulations
The simulations are carried out with the following procedure:
1. Input: sinusoidal current : 𝐼(𝑡) = 5 ∙ 𝑠𝑖𝑛(2𝜋 ∙ 50000 ∙ 𝑡) 𝐴
2. Time set: the measurements are recorded from the 𝑡0 = 2 ∗ 10−5 until 𝑡𝑓 = 16 ∗
10−5 , and the times step taken in between 𝑡𝑠 = 5 ∗ 10−7
In order to calculate the flux of the magnetic field which goes through the sensors, the
following formula is used:
⃗ ∙ 𝑆 = |𝐵| ∙ |𝑆| ∙ cos 𝜃
𝛷 = ∫ 𝐵 ∙ 𝑑𝑆 = 𝐵
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.
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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.
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Figure 39 Sector division
46
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Figure 40 Sensor distribution
47
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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.
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Figure 41 1rst Sector 5A 50kHz
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Figure 42 2nd Sector 5A 50kHz
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Figure 43 3rd Sector 5A 50kHz
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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
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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
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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
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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
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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.
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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 – 2,5E-9
Sector 2: Interval of the maximum values 2,6E-7 – 2,25E-8 Wb
Sector 3: Interval of the maximum values 2,8E-7 Wb
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Figure 49 1rst Sector 50A 50kHz
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Figure 50 2nd Sector 50A 50kH
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Figure 51 3rd Sector 50A 50kHz
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Figure 52 Magnetic Field Coil 50A
1
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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.
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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 – 0 Wb the
smaller values are very close to zero.
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- 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 – 1,9E-8 Wb
- Sector 3: The same effects are observed in this sector. The interval of values is
2,8E-8 – 2,2E-8 Wb,
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Figure 55 1rst Sector 5A 50kHz - Target 9mm away
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Figure 56 2nd Sector 5A 50kHz - Target 9mm away
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Figure 57 3rd Sector 5A 50kHz - Target 9mm away
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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.
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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.
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Figure 59 1rst Sector 5A 50kHz - Target 2mm closer
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Figure 60 2nd Sector 5A 50kHz - Target 2mm closer
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Figure 61 3rd Sector 5A 50kHz - Target 2mm closer
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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
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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
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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....................... Error! Bookmark not defined.
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