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Optical Measurement of Currents in Power Converters

  • DiGOS Potsdam GmbH
Optical Measurement of
Currents in Power
Master’s Degree Project in
Electrical Measurement Technology
report no. XR-EE-MST 2006:001
Stockholm, Sweden 2006
Optical Measurement of Currents in
Power Converters
Master’s thesis project
Sascha Liehr
Supervisor: Hans Sohlström
Microsystem Technology Group
School of Electrical Engineering
Royal Institute of Technology
Stockholm, March 2006
Conventional current measurement in high-voltage and high-EMI (Electromagnetic
Interference) environments generally require complex devices due to the necessary
insulation and shielding of the device and the signal line. This paper investigates the
possibility of instead using a Faraday effect-based opto-magnetic field sensor
technique for fault detection in IGBT-switched current lines.
Firstly, possible techniques, optical and non-optical, are reviewed with a special
focus on optical sensing techniques. An optical sensing technique using a high-
rotation Faraday film sensor is chosen. Then a FEM simulation of the magnetic
field pattern encompassing a parallel conductor geometry is conducted and its
favourable results on the magnetic field pattern are presented. Characterization and
sensitivity determination of a present Faraday YIG sensor are conducted. The
favourable magnetic field behaviour predicted by the simulation is then confirmed
in experiments. The sensor electronics have been redesigned and electronic signal
processing circuitry for failure handling has been added. Finally, first tests in an
application-similar set-up with switched currents were conducted. The proposed
sensing technique gave promising first results for reliable and instant current fault
detection in high-EMI environments.
1. Introduction ................................................................................................................. 1
1.1. Motivation and Specification of the Problem.................................................... 2
2. Investigation of applicable Techniques ...................................................................... 4
2.1. Non-Optical Current Transformers .................................................................. 4
2.1.1. Current Transformer .............................................................................4
2.1.2. Rogowski Coil.......................................................................................5
2.1.3. Search-Coil Magnetometer ...................................................................6
2.1.4. Flux-Gate Magnetometer ......................................................................7
2.1.5. Shunt .....................................................................................................7
2.1.6. Hall Sensor............................................................................................8
2.1.7. Magnetodiode........................................................................................8
2.1.8. Magnetotransistor..................................................................................9
2.1.9. Magnetoresistor................................................................................... 10
2.1.10. SQUID Magnetometer ...................................................................... 11
2.1.11. Optically Pumped Magnetometer .....................................................11
2.1.12. Nuclear-Precession Magnetometer ...................................................11
2.1.13. Conclusion of the Applicability of Non-Optic Magnetic Field
Sensors ..........................................................................................................11
2.2. Optical Current Transformers (OCTs)........................................................... 12
2.2.1. Introduction.........................................................................................12
2.2.2. OCTs based on the Faraday Effect .....................................................15 Explanation of the Faraday Effect................................................ 15 Magnetic Field Sensing................................................................23 Magnetic Concentrator with Optical Measurement .....................27 Bulk Optics...................................................................................29 Optical Fibre Sensing Elements ...................................................31 Unlinked Type..............................................................................34
2.2.3. Interferometric Principles ...................................................................37
2.2.4. OCTs based on Bragg Gratings ..........................................................39
2.2.5. Micromechanical Sensors with Optical Readout................................42
2.2.6. Other Optical Current Sensing Principles........................................... 44
2.2.7. Conclusion Optical Current Transformers.......................................... 44
2.3. Conclusion of the Technology Investigation ................................................... 45
3. FEM Simulation of the Magnetic Field Pattern ...................................................... 47
3.1. Introduction ....................................................................................................... 47
3.2. Normal Working Condition.............................................................................. 49
3.3. Case of Failure ................................................................................................... 53
3.4. Conclusion .......................................................................................................... 57
4. Experiments ............................................................................................................... 59
4.1. The Sensors ........................................................................................................ 59
4.2. Characterization of the Sensors ....................................................................... 60
4.2.1. Sensitivity............................................................................................60
4.2.2. Temperature Behaviour.......................................................................65
4.2.3. Modification of the Electronics...........................................................67
4.2.4. Noise ...................................................................................................70
4.2.5. Characterization of the Sensor Sensitivity..........................................70
4.3. Validation of the Simulation Results ............................................................... 77
4.3.1. Measurement Set-up ...........................................................................77
4.3.2. Conclusion of the Simulation and Measured Results .........................81
4.4. Phase Shift Measurements................................................................................ 81
4.5. Current Fault Measurements........................................................................... 83
4.5.1. Test Conductor Set-up ........................................................................83
4.5.2. Magnetic Field Measurement Results................................................. 83
4.5.3. Design of the Detection Electronics....................................................85 Delay measurement of the detection electronics.......................... 88
4.5.4. Current fault detection ........................................................................89
5. Conclusion ................................................................................................................. 91
6. Outlook....................................................................................................................... 92
Acknowledgements ........................................................................................................ 93
References...................................................................................................................... 94
Symbols and Abbreviations ......................................................................................... 101
List of Figures.............................................................................................................. 104
List of Tables................................................................................................................ 108
Chapter 1
1. Introduction
The electrical power industry is an important and growing branch of industry. Not
only in electrical power plants, power converters and transformer stations, but also
in industrial high-power applications metering, monitoring and control of high
currents is essential. The main challenge with conventional current transformers in
high-voltage environments is the need for safe separation between the main circuit
carrying the current to be measured and the control circuit in which the measured
signal will be utilized. Therefore, the sensor has to be galvanically insulated. Another
challenge for measurements in high-current and high-field environments is the
influence of EMI (
nterference) on the sensor and its signal.
Consequentially, there is a need to shield the sensor and the signal line from EMI in
order to get a reliable signal. Shielding and insulation however, results in complex
and massive structures that make conventional current transformers in high-current
and high-voltage applications very costly.
There is a need and trend to develop alternative sensing technologies to overcome
these obstacles. Different approaches, predominantly using optical sensing and/or
signal transmission techniques, have been developed during the last 20 years. There
is potentially a large market for this technology but commercial success is still being
waited for.
The thesis work presented here arose in this context.
A fast and reliable current sensor technique to immediately detect a current fault in a
conductor, rather than a precise current metering sensor is investigated. The project
is launched by the company ABB and is accomplished at the Royal Institute of
Technology (KTH) in Stockholm. The sensor technology part of the project is the
subject of my thesis and is carried out at the Microsystem Technology research
group at KTH.
The purpose of the work is to find a suitable technique in order to reliably and
instantly (within 3µs) detect a current fault in a high-voltage environment with a
high level of Electromagnetic Interference.
In chapter 2, possible techniques with the focus on optical techniques are described,
and one is chosen. A finite element method simulation of the magnetic field
encompassing the conductor and its results are presented in chapter 3. Some first
experiments with the chosen sensing technique and tests in an application-similar
set-up and environment are presented in chapter 4.
Chapter 1
1.1. Motivation and Specification of the Problem
In electrical high power converters and other high-power applications, IGBTs
ransistors) are widely used to rapidly switch large currents at
high voltage potentials. IGBTs are capable of switching high currents (>3000A) at
voltages of more than 2500V. These devices must be connected in series in order to
provide sufficient voltage handling capability. In such designs, the failure mode of
the series connected devices becomes a crucial consideration. One solution is to
utilize IGBT components with encapsulation, e.g. ABB “StackPack”, that exhibit
short-circuit failure mode. Standard industrial IGBT modules on the other hand
may be problematic because the bond wires may burn causing internal arcing in the
device. However, it is advantageous to use standard industrial type IGBT devices as
they represent the main-stream component type, which are economical and available
from several manufacturers.
It has been proposed by ABB to implement standard IGBT devices in series
connection (>10) of parallel pairs of devices in a stack as shown in Fig. 1.
Fig. 1: Proposed geometry with parallel IGBTs
In normal operation, the devices share the total current and both devices perform
switching according to the desired PWM (
odulation) pattern. If one
device fails and stops conducting, a sensor should immediately detect that fault and
command the remaining parallel device to conduct continuously. As switching
losses are then eliminated in the device, it will be capable of conducting the total
current in one device. For that case, additional IGBT stages are installed in the stack
to prevent excess voltage. The stack can remain in duty depending on how many
additional stages are installed in the stack. The defect IGBTs only have to be
exchanged at the next check routine. Using this technique is expected to be
considerably cheaper than using the expensive “StackPacks”.
The company ABB has launched a project at KTH to test the proposed technique.
A small-scale set-up with an IGBT firing control is being built at the department of
Chapter 1
electrical engineering within the thesis work of Martin Skoglund [Skog06]. The set-
up will be able to switch currents up to 180A at voltages of 500V. An essential part
of the technique is to reliably and rapidly detect a fault of one of the IGBTs to
command the remaining device to conduct continuously.
This current fault detection is the objective of this work. A desired maximum time
delay for the detection of a fault is 3µs. A suitable sensor technology has to be
found to detect a fault in the objective of the actual application. The expected
currents in the full-scale application are in the range of several kA and will be
switched at potentials of 10-50kV. Hence, a considerable level of EMI is expected.
The sensor has to be immune to EMI and also be insulated from the high voltage
An appropriate sensing technique will have to be chosen, tested and integrated in
the mentioned set-up. An optical sensing technique using the Faraday effect seems a
promising option and will be focused on. The measurement part of the project is
therefore conducted at the Microsystem Technology research group of KTH due to
competences in magneto-optic field sensing.
Chapter 2
Investigation of applicable Techniques
2. Investigation of applicable Techniques
In this chapter, principles for measuring an electric current are presented and
evaluated in terms of applicability to the purpose of sensing a current fault in the
proposed geometry under the given demands.
Most current sensor principles are based on some kind of magnetic field
measurement technique. Therefore magnetic field sensing techniques are also
investigated for current metering purposes. Thus the term “current sensor” is
somewhat extended in this work also covering magnetic field sensors as “potential”
current sensors.
The following investigation is divided into two groups: conventional, or non-optical
current transformers and optical current transformers. Considering that the
capabilities of optical principles are interesting and promising, the following review
has a stronger focus on optical technologies.
2.1. Non-Optical Current Transformers
2.1.1. Current Transformer
The most-used device for measurements of alternating currents in electrical high-
and medium-voltage networks is the CT (
ransformer). A current transformer
transforms the current down to a reasonable level and provides an isolation barrier
between the primary winding and the secondary winding at ground potential. The
primary current of the transformer is translated to the secondary current (I1=n·I2) by
the turns ratio n and I2 is measured by an ampèremeter or other conventional
methods. The secondary winding, or measurement winding, have to be isolated
from high voltages to prevent short circuits and the resulting heat has to be
dissipated. For that reason the transformers are often filled with oil which causes a
risk of explosion. These devices are reliable and have long life cycles but become
very costly and massive with increasing voltages. An example of a current
transformer with indication of its size is shown in Fig. 2.
Chapter 2
Investigation of applicable Techniques
Fig. 2: Conventional ABB transformer for high voltages [ABB06]
The current transformer is based on Ampère’s law, whereby the line integral of the
magnetic field H
ralong any closed path equals the enclosed current I.
Equation (1)
Most current transformers consist of a ferromagnetic core entirely enclosing the
conductor. Hence, measurements are independent of the position of the current
carrying conductor in the core. Measurement windings are wound around the core
and a voltage is induced according to Faraday’s induction law. With low resistance in
the measurement winding, the resulting current is proportional to the primary
current and cancels most of the field in the core. At low frequency however, the
driving voltage can no longer create a current that is proportional to the primary
current. Also the core will be saturated. That implies that the current transformer
can only be used for AC measurement. For DC measurements, more complex
devices with Hall elements are often used.
2.1.2. Rogowski Coil
A Rogowski coil is a core-less coil toroidally placed around a conductor forming a
closed loop, Fig. 3.
Chapter 2
Investigation of applicable Techniques
Fig. 3: Scheme of a Rogowski coil [Xiao03]
It is also based on the induction law. A voltage proportional to the rate of change of
the current is induced into the uniformly wound coil with constant cross-sectional
area. Due to the absence of a magnetic core, the sensor shows good linearity, no
saturation, as well as high current capability (up to 100kA) and bandwidth (0.1Hz to
100MHz) [Xiao03]. Similarly as for other induction-based sensors, the Rogowski
coil can not detect currents of low frequency. In contrast to the conventional
transformer with a closed iron core, the output is not completely independent of the
primary conductor position. There are also problems with reproducibility and
2.1.3. Search-Coil Magnetometer
The search-coil magnetometer is also based on Faraday’s induction law. It typically
consists of an iron magnetic core and a coil wound around it. When the magnetic
flux through the coiled conductor changes, a voltage proportional to the rate of
change is induced in the coil and can be measured between its leads. This sensor can
measure fields over a very wide range from 1pT to 1kT depending on the design of
the magnetic core. According to the induction law, only the change of the magnetic
field can be detected. The useful frequency range of this sensor is typically between
1Hz and 1MHz [Lenz90], but also static fields can be detected with a search-coil
magnetometer when the coil is rotated in the field. A principle of the search coil
magnetometer is shown in the figure below.
Fig. 4: Scheme of a search-coil magnetometer [Lenz90]
Chapter 2
Investigation of applicable Techniques
2.1.4. Flux-Gate Magnetometer
The most common type of a Flux-Gate magnetometer consists of two coils, a
primary and a secondary, wrapped around a ferromagnetic core. The magnetic
induction in the core changes with the external magnetic field. A signal, for example
10kHz, applied to the primary coil causes the core to oscillate between saturation
points. The secondary winding outputs a signal coupled to the primary signal by the
iron core. This signal is influenced by any change of core permeability (slope of the
B-H curve) and appears as variation of the amplitude at the secondary output. The
value for the magnetic field strength can be obtained by using a phase-sensitive
detector and following signal processing. Phase-sensitive detection is a useful
technique to recover small signals that are obscured by larger and/or background
signals with the help of a reference or modulation signal.
Fig. 5: Fluxgate magnetometer operation [Caru98]
A fluxgate magnetometer can precisely measure direction and magnitude of
constant or changing magnetic fields at sensitivities down to 1nT. The bandwidth
however, is limited to some kHz and the dynamic range covers fields from 1nT to
1mT [Xiao03]. The Fluxgate magnetometer is therefore not suitable for fault
2.1.5. Shunt
Shunts are low resistance sensing elements that are directly inserted in the main
current path. They operate on the principle of the Ohmic voltage drop and are
suitable to measure currents. Shunts are relatively cheap and can be used to measure
direct currents and alternating currents up to tens of MHz [Xiao03]. But since they
have to be integrated directly into the circuit, efficiency decreases, especially at high
currents and low voltages. Moreover, the output voltage is directly connected to the
current to be measured. Shunts can therefore normally not be used with high
Chapter 2
Investigation of applicable Techniques
2.1.6. Hall Sensor
This sensor is based on the Hall effect, discovered by Edwin H. Hall in 1879. He
found a potential difference (Hall voltage) on the sides of a thin sheet of conducting
material in a magnetic field perpendicular to the surface when a current flows along
the sheet, Fig. 6.
Fig. 6: Scheme of a Hall Effect Sensor [Lenz90]
This voltage is the result of the Lorentz force that every electron that moves
through a magnetic field experiences. This force is perpendicular to both the
magnetic field and the direction of motion of the electron. Electrons moving in the
sheet perpendicular to the magnetic field will therefore be deflected to one side of
the sheet resulting in the Hall voltage.
Hall elements made of semiconductors have a much larger effect than those made
of metallic conductors. Nowadays, Hall sensors are produced at low costs due to
standard CMOS technologies and are mostly made of silicon or III-V
semiconductors. They have good temperature characteristics, bandwidths from
static fields up to 100MHz, resolutions of 100nT and a dynamic range from 50µT to
30T [Maci00].
2.1.7. Magnetodiode
A magnetodiode is basically a semiconductor diode where the p-region is separated
from the n-region by an area of undoped silicon. The silicon layer lies between, for
example, a Sapphire substrate and a SiO2-layer, Fig. 7.
Chapter 2
Investigation of applicable Techniques
Fig. 7: Structure of a Magnetodiode [Lenz90]
When a potential is applied between the p- and n-region, holes and electrons are
injected into the silicon and move in opposite directions resulting in a current flow.
In absence of a magnetic field, mainly recombination contributes to the resistance,
especially at the surface Si-SiO2 and Si-Sapphire. When a magnetic field is applied,
the electrons and holes are diverted in the same direction to one of the surfaces.
Since the possibility to recombine at the Si-Sapphire surface is much greater than at
the Si-SiO2 surface, the resistance is higher when the charge carriers are diverted
towards the Si-Sapphire surface.
Magnetodiodes have higher responses than Hall elements [Lenz90] at similar
bandwidths and resolutions up to 0.5µT, but they suffer from a high temperature
dependency [Here93].
2.1.8. Magnetotransistor
The magnetotransistor is a version of an npn-transistor. Like a transistor, it consists
of an n-doted emitter separated by a p-doped base from the n-doped collector. The
difference is that there are two collectors instead of one, Fig. 8.
Fig. 8: Principle of a Magnetotransistor [Lenz90]
Chapter 2
Investigation of applicable Techniques
Without any external magnetic field, equal numbers of charge carriers reach the two
collectors. When a magnetic field is applied perpendicular to the direction of motion
of the charge carriers, they will be deflected toward one collector or the other. The
two collector voltages are fed to a differential amplifier, whose output is
proportional to the applied magnetic field. Magentodiodes are about 100 times more
sensitive than Hall elements, have a bandwidth up to 1MHz [Lando] and are based
on more standard fabrication technologies (CMOS) than the magnetodiode
2.1.9. Magnetoresistor
The MR (
esistance) effect describes the relative change of resistance of a
conductor at the presence of a magnetic field. According to the orientation of the
magnetic field vector and the electric current vector, the effect is named either
longitudinal MR effect (magnetic field and current parallel) or transversal MR effect
(magnetic field and current perpendicular). Several effects are known today:
The AMR (
esistance) effect occurs in magnetic materials such as
Permalloy (Ni-Fe alloy). This material is given an easy direction in the direction of
the current. When a magnetic field is applied, the resistance will change with the
angle between the field and the direction of the current. When the magnetic field is
applied perpendicularly to the current, the magnetic orientation will rotate in
direction of the field. This rotation is dependent on the magnitude of the field.
Rotation results in higher resistance since electrons that move in direction of the
magnetization have a higher probability to be scattered.
The GMR (
esistance) effect occurs in stacks of very thin layers of Fe
and Cr with antiparallel magnetization of neighbouring layers. When the
magnetization of the single layers is rotated to parallel magnetization due to an
external magnetic field, the resistance will significantly change. Resistance changes
of up to 50% are possible compared to the AMR effect where the resistance
changes 3% at maximum. Fields from static to 5MHz can be measured [Xiao03].
AMR and GMR are both used as read/write heads in hard disc drives.
The CMR (
esistance) effect is the strongest magnetoresistive effect
known. It occurs mostly in manganese-based perovskite oxides and changes the
electrical resistance of the material in the order of magnitudes at the presence of a
magnetic field. This relatively newly found effect is subject to current research.
Typically, magnetoresistors for field sensing have a dynamic range of B=1µT to
B=1T, a resolution of 10nT and a bandwidth from dc to 10MHz [Maci00].
Magnetoresistors do however, not give information about the direction of the field.
Chapter 2
Investigation of applicable Techniques
2.1.10. SQUID Magnetometer
The most sensitive magnetometer is the SQUID (
evice) with a resolution of fT. The SQUID is based on the Josephson effect that
arises in superconducting rings with a “weak link” (thin layer of insulator).
Josephson discovered, that a current can flow through the weak link as an oscillating
function of the magnetic field intensity. Typically, the ring is inductively coupled to
a radio frequency circuit that both, supplies a known bias field and serves as
detector output. Changes in the ring current alter the resonant frequency of the
circuit. The change of the magnetic field can be measured by counting the maxima
and minima. If there are two weak links in the circuit (DC SQUID), the voltage
difference between them can be measured directly. This voltage also periodically
changes with the change in magnetic field. [Lenz90]
SQUIDs are very precise and expensive magnetic field sensors and need liquid
Nitrogen cooling to allow superconductivity. They typically have a dynamic range
from B=1pT to B=0.1mT, a resolution of 100fT and a low bandwidth from dc to
5Hz [Maci00] and are therefore not suitable for current fault detection.
2.1.11. Optically Pumped Magnetometer
The optically pumped magnetometer is based on the Zeeman effect and precisely
measures a scalar magnetic field. The measurand is the resonance frequency of a
radio frequency source at which the electrons in a Caesium or Helium vapour
change their spin angular momentum. The energy required to flip the electron spins,
and thus the radio frequency, depends on the strength of the magnetic field. This
sensor however, is relatively large, has a high power consumption, a sensitivity range
from B=1nT to B=0.1mT and a low bandwidth from dc to 5Hz [Lenz90], [Maci00],
which makes it unsuitable the purpose of this work.
2.1.12. Nuclear-Precession Magnetometer
This magnetometer exploits the response of protons to a magnetic field in a
hydrocarbon fluid, such as benzene. The precession frequency of the protons at a
present magnetic field is proportional to the magnetic field strength and is picked up
by a coil. Again, this magnetometer has a low sensitivity range (10pT to 100µT) and
is rather expensive.
2.1.13. Conclusion of the Applicability of Non-Optic Magnetic
Field Sensors
All presented sensing principles suffer from electromagnetic interference that is
expected to be at a very high level in the application environment. Especially
Lorentz force-based sensors, such as Hall element, magnetodiode and
magnetotransistor are sensitive to EMI due to their typically low signal levels. The
same holds for the search-coil magnetometer. The flux-gate magnetometer suffers
Chapter 2
Investigation of applicable Techniques
from its low bandwidth. Shunts are not suitable owing their lack of insulation and
the magnetoresitor does not detect the sign of the field. Costly high-precision
magnetometers such as the SQUID, the optically pumped magnetometer and the
nuclear precession magnetometer are not suitable due to their cost, dynamic range
and low bandwidth limitations.
Concluding this, there are no real alternatives to the conventional current sensors,
such as current transformer and Rogowski coil among the presented non-optical
2.2. Optical Current Transformers (OCTs)
2.2.1. Introduction
A logical step to overcome the problems caused by electromagnetic interference on
the sensor signal is to use a signal transmission that is immune to electromagnetic
fields. Optical signal transmission using optical fibres are the best solution for that
purpose. Normally, the optical signal is not influenced by electromagnetic fields. In
a suitable designed sensor however, several properties of the light that is used as the
signal carrier can be influenced, e.g. intensity, state of polarization, spectral
properties and phase delay. Ideally, the sensor signal is directly generated by the
interaction of the magnetic field with the sensor medium. Several such magneto-
optical effects are known to occur in magneto-optic active materials.
The most interesting magneto-optic effect in transmission for magnetic field sensing
is the Faraday effect. It causes the polarization of linearly polarized light to rotate at
the presence of a magnetic field when propagating in a material exhibiting the
Faraday effect. It is widely used for magnetic field sensing and will be explained in
detail in chapter Another effect in transmission is the Zeeman effect, which
causes the split of a spectral line into several components at the presence of a
magnetic field.
The most important effect in reflection is the MOKE (
ffect). It
occurs for example in thin magnetized metal films and exists in three different
geometries: The PMOKE (
ffect) occurs with the
magnetization direction perpendicular to the surface of the film, the LMOKE
ffect) with the magnetization in the film plane and
also in the plane of incidence. In TMOKE (
geometry, the magnetization direction is in the film plane but perpendicular to the
plane of incidence. These effects are for example used in magneto-optic disks for
reading the data with help of the Kerr effect but are not suitable for magnetic field
measurements because of their non-linearity. Other magneto-optic effects are the
Voigt effect, the Cotton-Mouton effect and the Majorana effect.
Chapter 2
Investigation of applicable Techniques
But not only direct magneto-optic conversion is used as a sensor principle, also
different magneto-mechanic-optical or magneto-electric-mechanic-optical
transducers have been presented for magnetic field sensing purposes. Therefore,
OCTs (
ransducers) are here defined as sensors that directly or
indirectly use optical sensing methods to measure electrical currents.
The advantage of direct magneto-optic transducers using opto-magnetic active
materials is the absence of additional disturbance variables caused by mechanical or
electrical sensor parts such as hysteresis, saturation, induction, temperature influence
and damping.
Over the last 30 years, numerous current measurement systems based on optical
devices have been developed. OCTs have numerous potential advantages over
conventional current transformers (CTs), depending on their sensor principle.
Potential advantages are:
- immunity to electromagnetic interference (EMI)
- high electrical insulation
- large bandwidth
- potentially high sensitivity
- ease in signal light transmission
- being compact and lightweight
- potentially low-cost
- no danger of explosion
- ease of integration into digital control systems
- no saturation
(dependent on the principle)
- hysteresis-free
- passive measurement
However, in most fields of application, OCTs have to compete with mature
technologies. Consequently, many customers simply desire sensor systems having
good performance with reasonable price (except for special uses) and choose
conventional technologies. Therefore, only few optical devices, mainly developed by
the customer itself, i.e. electric power companies and electric power distributors, or
major industrial companies, are field-tested and used.
Optical fibre sensors have been studied extensively over the last years. Fig. 9 and
Fig. 10 show the distribution of measurands and measurement technologies in
optical fibre technology based on the 15th Optical Fiber Sensors Conference 2002
Chapter 2
Investigation of applicable Techniques
Fig. 9: Distribution of papers according to measurands [Lee03]
Fig. 10: Distribution of papers according to used technologies [Lee03]
The diagrams shown above illustrate that there is a big interest in optical
current/voltage sensors. Fibre grating technologies have a great share of the
publications (Fig. 10) partly because this technology was at an intense research
phase at that time.
However, OCTs not only utilize fibre sensing elements. Also other geometries and
principles or hybrid devices have been proposed. Optical Current Transducers will
in the following be divided into five main groups:
- OCTs based on the Faraday effect
- Interferometric principles
- OCTs based on Bragg gratings
- Micromechanical sensors with optical readout
- Other optical current sensing principles
Chapter 2
Investigation of applicable Techniques
These main groups will be presented in the following chapters. This classification is
however, not accurately defined but rather used to give an overview over the
existing principles.
2.2.2. OCTs based on the Faraday Effect Explanation of the Faraday Effect
The Faraday effect is a magneto-optical effect that causes a change of the state of
polarization of light. Thus, the concepts of polarization and birefringence are briefly
explained to give a better understanding of the Faraday effect and the problems
arising in sensor applications.
Light can be regarded as a plane wave and, like all electromagnetic waves, has the
electric and magnetic fields perpendicular to the direction of propagation.
Conventionally, only the electric field vector
is described when speaking about
polarization, since the magnetic field vector is always perpendicular and
proportional to it. The two components of the electric field vector are defined as x
and y components. For a simple harmonic wave, these components vary sinusoidally
with the same frequency. However, their amplitude and phase might differ, compare
Fig. 11.
Fig. 11: Linear, circular and elliptic polarization [Wiki06]
Special cases of polarization are linear polarization, which only occurs when both
components have the same phase (Fig. 11 a)) and circular polarization which
supposes that the two components are exactly 90° out of phase and have exactly the
same amplitude, Fig. 11 b). The direction of rotation of the vector depends on
which of the two components is 90° ahead of the other one. These cases are called
right-hand circular polarization and left-hand circular polarization. All the other
Chapter 2
Investigation of applicable Techniques
cases, where the two components differ in amplitude or phase are called elliptical
polarization, Fig. 11 c).
Birefringence, or double refraction, is the decomposition of a ray of light into an
ordinary ray and an extraordinary ray when it passes through an optically anisotropic
material, depending on the state of polarization of the light. One can distinguish
between two different kinds of birefringence: linear birefringence and circular
Linear birefringence occurs in an optically anisotropic material with different speeds
of light propagation for different geometrical axes due to material anisotropy or
geometrical constraints in an optical waveguide. The difference of the
corresponding indexes of refraction fastslow nnn
is the linear birefringence.
Linear polarized light passing through a linear birefringence medium experiences a
phase difference in ° of
360 Equation (2)
where l is the length of the light path and λ0 is the wavelength of the light. This
phase difference causes a change of the polarization state and is for example used to
change the state of polarization (λ/4-plate). This effect may also occur in optically
isotropic materials due to mechanical stress and electric and magnetic fields.
Circular birefringence occurs in a material where the speed of propagation of the
light is different for left-hand polarized and right-hand polarized light. The material
is then called an optically active material. The difference of the two different indices
of refraction, nc, is the circular birefringence leftrightc nnn
Circular birefringence rotates the polarization of linearly polarized light by the angle
360 c
Equation (3).
In addition to the magnetic circular birefringence, a linear birefringence can be
induced by a magnetization perpendicular to the light propagation direction. This
effect is called Voigt or Cotton-Mouton effect, whereas the latter is often denoted
to a molecule orientation effects to a magnetic field in fluids. There may also be a
magnetic field dependent difference in optical absorption between the linear or the
circular polarization states: MLD (
ichroism) and MCD (
Chapter 2
Investigation of applicable Techniques
The Faraday effect
The Faraday effect is named after Michael Faraday who discovered this
phenomenon in 1845. It describes the rotation of polarisation of light propagating
in the direction of a magnetic field. When a beam of light is sent through a material
exhibiting the Faraday effect, the polarisation of the light will be rotated by the angle
θ in dependency of the magnetic field strength parallel to the light.
Fig. 12: The Faraday effect [Sohl93]
The Faraday effect is proportional to the magnetisation of the material,
= Equation (4)
where θ is the polarisation rotation, M is the magnetisation, l is the length of the
light path and k a constant dependent on the propagating material, the wavelength
and the temperature.
In paramagnetic and diamagnetic materials, the magnetisation and thus, also the
polarisation rotation is practically proportional to the magnetic field strength
[Sohl93]. The rotation can then be described in terms of the magnetic field strength
H and the Verdet constant V,
= LldHVθ
Equation (5)
The Verdet constant V is the specific rotation of a material and is defined as the
angle over the magnetic Field times the length (°/T·m).
= Equation (6)
V is determined by the magnetic properties of the material. B is the component of
the magnetic flux density parallel to the light propagation direction.
The Faraday effect arises from the interaction of the electron orbit and the electron
spin with the magnetic field. The general principle can be understood as right-
Chapter 2
Investigation of applicable Techniques
handed and left-handed circularly polarized light causing charges in a material to
rotate in opposite senses. Each polarization therefore produces a contribution to the
orbital angular momentum with opposite sign. A magnetic field gives rise to a spin-
polarization along the magnetic field direction and the spin-orbit interaction then
leads to an energy contribution for the two circular polarizations having the same
magnitude but with opposite sign [Blun01]. This leads to right-handed and left-
handed polarizations having different refractive indices in the material.
A linearly polarized wave can be seen as the sum of two circularly polarized waves
with equal amplitude but opposite direction of rotation. As these two waves
propagate with different speeds through the material, they will acquire a phase
difference proportional to the travelled distance. In terms of their sum, these two
beams, when they emerge, have a phase lag between them implying that the
emerging beam has a rotated plane of polarization by an angle which is equal to half
the phase change. The superposition of the left- and right-hand polarized
components can be seen in Fig. 13.
Fig. 13: Polarization before and after polarization rotation
This effect is non-reciprocal, meaning a light beam passing a medium twice in
opposite direction acquires a net rotation twice that of a single pass. It should be
noticed that according to the material, the Verdet constant is temperature- and
Faraday Materials and Geometry
A difference between on one hand diamagnetic and paramagnetic materials, and on
the other hand ferrimagnetic and ferromagnetic Faraday materials has to be made.
Diamagnetic (e.g. SF-57, SiO2, BK-7) and paramagnetic (e.g. TGG (
arnet), FR-5) Faraday materials have specific, but relatively low rotations. In
contrast, ferrimagnetic and ferromagnetic materials have Faraday rotations orders of
magnitude higher than diamagnetic and paramagnetic materials. The most
Chapter 2
Investigation of applicable Techniques
prominent ferrimagnetic materials are RIGs (
arnets). YIG (
arnet), Y3Fe5O12, and substituted YIGs are the most widely-used RIGs.
Strictly speaking, in all materials, the Faraday rotation is proportional to the
magnetization component along the direction of the optical propagation. For the
diamagnetic and paramagnetic materials, the shape of the modulator element is not
important in determining the magnetization. Also the magnetization is linearly
dependent on the applied field, and equation (5) can be used.
In ferri- and ferromagnetic materials the picture is more complex. In these materials,
volumes of equal direction of magnetization, the so-called magnetic domains, will
form. Thin transition regions, the Bloch walls, separate these domains of different
magnetization directions. The domain size is determined by the magnetostatic
energy balance that depends on the material properties and the sample geometry. In
thin bulk samples and epitaxially grown films with uniaxial anisotropy perpendicular
to the surface, the domains can form two-dimensional patterns extending through
the entire thickness of the film, Fig. 14.
Fig. 14: Two-dimensional domain pattern: schematic and measured (YIG film, no field)
These iron garnet films are sometimes also referred to as uniaxial garnet films.
Larger bulk iron garnet crystals however, exhibit a more complex three-dimensional
domain structure causing a higher non-linearity in the net Faraday effect and are less
interesting for magnetic field sensing purposes.
Hence, the definition of the Verdet constant V is not always suitable. Diamagnetic
and paramagnetic materials have a specific rotation in every point of their volume
and this rotation is independent of their geometry. The rotation for diamagnetic and
paramagnetic materials can therefore be described with the Verdet constant V.
Ferrimagnetic materials however, do not have a specific (constant) rotation, they
exhibit a domain structure where all domains are fully saturated in different
directions. Moreover, the rotation of those materials also depends on the geometry
of the medium. It is therefore actually wrong to speak of a Verdet constant for
those materials, many authors however do.
Chapter 2
Investigation of applicable Techniques
The ferri- and ferromagnetic materials, such as RIGs, exhibit a very high Faraday
rotation and are therefore interesting for sensor application. Iron garnets have
widely been used for “bubble memory” and displays. At present, the main
application is in optical isolators. These materials have therefore been studied
extensively and are commercially fabricated.
Bulk RIG crystals are grown similarly to silicon using the Czochralski technique. A
YIG seed crystal, for example, is dipped into the melt and is slowly pulled upwards
under constant rotation. Dopants can be added to the melt. These crystals normally
exhibit a cubic magnetic anisotropy.
Uniaxial anisotropy with stable direction of spontaneous magnetization, or easy axis,
can occur in thin bulk samples and epitaxially grown garnet films, compare Fig. 14.
Thin garnet films with a desired uniaxial anisotropy perpendicular to the film plane
are commonly grown epitaxially on a GGG (
arnet) substrate.
The common process is LPE (
pitaxy), but also SPE (
pitaxy) [Jang04] has been proposed recently.
An external magnetic field applied perpendicular to such a film causes the domains
with magnetization in direction of the field to grow at the expense of the other
domains, Fig. 15.
Fig. 15: Domain wall motion in thin films, schematic and recorded [Sohl93]
The resulting net polarization rotation can be approximated using the area ratio
between the two kinds of domains. The high frequency behaviour of these domains
depends on domain wall damping or domain wall resonance in the same way as the
magnetic susceptibility and is in the range of several hundred MHz for low damping
film materials [Wolf92].
A magnetic field applied in the plane of such a film rotates the magnetization of
both types of domains in direction of the applied field equally, Fig. 16. Thus,
magnetization rotation, as opposed to domain wall motion is the dominant
response. These films can be employed in an optical waveguide geometry
Chapter 2
Investigation of applicable Techniques
[Deet93/1]. Fig. 16 shows a possible planar waveguide geometry and the
magnetization rotation of the domains at an applied magnetic field.
Fig. 16: Wave guide structure
While the polar geometry with a wide area of light-material-interaction gives a good
average of the Faraday effect on the domain pattern in the film, the waveguide
geometry gives only a “one-dimensional” average of the few domains along the path
of light in the film. This geometry therefore gives a less linear signal. Thus, different
principles have been proposed to increase the interaction length or to linearize the
effect by using a bias field [Sohl91]. Also other problems, such as precise mode
coupling to the planar waveguide arise with this geometry. Only a few principles
have been proposed for sensor application.
The rotation of magnetisation of the domains however, is a faster process than
domain wall movement and therefore enables higher bandwidths of the planar
geometry up to at least 1GHz [Deet93/1] respectively to 600MHz for a low-
damping film exhibiting domain wall movement [Wolf92]. Domain wall rotation
also shows less hysteresis than domain wall motion [Deet93/1] and is not effected
by possible imperfections in the material such as lattice dislocations [Sohl93] since
no domain wall motion occurs.
The most commonly used Faraday materials are, on one hand diamagnetic and
paramagnetic glasses (e.g. SF-57 and FR-5) or TGG with relatively low Verdet
constants, and on the other hand rare earth iron garnets (RIGs) and ferromagnetic
materials with considerably higher Faraday rotations. Diamagnetic and paramagnetic
glasses are transparent over a wide range of wavelength and are used in bulk form
owing to their low Verdet constants. RIGs such as YIG have a limited transmission
spectrum in the near-infrared region, Fig. 17. They are transparent, i.e. exhibit no
noticeable loss in application, for wavelength of λ>1.1µm [Sohl93].
Chapter 2
Investigation of applicable Techniques
I – intensity of light
t – penetration depth
α – absorption coefficient
Fig. 17: Absorption of light in YIG depending on λ [Paro84]
However, due to their high Faraday rotation, they can be used in thin film geometry
and have therefore also been used at shorter wavelengths.
Table 1 gives an overview over the magnitude of Faraday rotation for the most
common Faraday materials.
Table 1: Faraday rotation for some common materials [Deet93/2]
Rare earth ions and other dopants can be added to improve the temperature
behaviour of YIG crystals. Also the Faraday rotation can be altered by adding
mainly rare earth ions. Numerous compositions with several substitutes have been
studied. Bi0.98Gd0.92La0.03Y1.07Fe4.72Ga0.28O12 films for example achieve a good
temperature linearity and high rotation in sensor application [Itoh99]. Bismuth is
commonly added to achieve higher rotations. The Faraday rotation of RIGs is thus
very much dependent on the substitutes and their concentration, but also the
temperature and the wavelength of the light, Fig. 18.
Chapter 2
Investigation of applicable Techniques
Fig. 18: Wavelength-dependency of the Faraday rotation for common materials [Dona88] Magnetic Field Sensing
The magnetic field in a Faraday medium can be measured by determining the
rotation of polarization θ, that occurs after a linearly polarized light beam passed the
Faraday medium. This can be done by measuring the intensity of the light beam
after passing a second polarizer (or analyzer). The intensity of this light beam is a
function of the angle of rotation and thus the magnetic field strength. (Fig. 19)
Fig. 19: General form of a Faraday current sensor [Sohl93]
Chapter 2
Investigation of applicable Techniques
Utilizing a folded design with a reflective surface at the end of the Faraday material
as shown in Fig. 20, leads to twice the polarization rotation for a given length of the
Faraday material.
Fig. 20: Schematic of a folded design giving twice the Faraday rotation
The characteristic of the sensor is determined by the orientation of the two
polarizers to each other. The angle between the transmission axes of the polarizers
determines by which value the transmitted intensity varies with a varying magnetic
field. The angles can be chosen anywhere between 0° and 90° giving the same
results for all other quadrants. The resulting intensities can be calculated employing
Malus’ law: considering a linearly polarized light beam incident on a polarizer, its
perpendicular component of the beam is blocked. Therefore, the amplitude of the
light transmitted by the polarizer is
Equation (7) )cos()( 0θEθE=
Hence, the intensity of the transmitted light is given by
Equation (8), )(cos)( 2
where E0 is the electric field vector, and I0 is the intensity of the incident beam
Three angles of orientation of the analyzer to the polarizer are especially interesting
for the sensor application, namely 0°, 45° and 90°. These three cases are shown and
discussed in Table 2 to Table 4.
Chapter 2
Investigation of applicable Techniques
Table 2: Characteristics of a “0°-Sensor”
This sensor gives the same signal for positive
and negative fields and has a quadratic
characteristic for small fields.
+This sensor is easy to fabricate since only
one polarizer is needed in a folded design
-It gives no indication of the direction of the
-Only small signal change for small fields
Table 3: Characteristics of a “45°-Sensor”
This sensor gives different signals for positive
and negative fields.
+This sensor is has a linear characteristic for
a wide range of field
+It detects the direction of the field
Chapter 2
Investigation of applicable Techniques
Table 4: Characteristics of a “90°-Sensor”
This sensor gives the same signal for positive
and negative fields.
+This sensor is relatively immune to drift
-It gives no indication of the direction of the
-It gives only a small and non-linear signal
for low fields
Another possibility to read out the state of polarization is to use a polarization
separating prism (Wollaston prism) and two detectors, as shown in Fig. 21. The two
orthogonal linearly polarized beams are detected separately. This technique has the
advantage that optical losses in the fibres and sensor material can be compensated.
The rotation of the polarization can directly be obtained by comparing the two
sensor signals.
Fig. 21: Polarization state detection with polarization splitter [Sohl93]
A similar loss compensation has been demonstrated using conventional polarizers,
but with light propagation in both directions through the sensor [Holm95]. All
Faraday detection principles are fundamentally based on intensity detection. The
structure, materials and the path of light of the different Faraday sensors however,
differ greatly.
The following overview is meant to give a brief and general idea of the major classes
of optical Faraday transducers. Some examples for each group are presented.
Chapter 2
Investigation of applicable Techniques Magnetic Concentrator with Optical Measurement
In this approach, a magnetic concentrator encloses the conductor, but instead of
this magnetic loop forming the core of a transformer, the field inside the
concentrator is measured optically in an air gap, Fig. 22. Due to the air gap, the field
in the core is limited and core saturation is avoided. With a larger air gap however,
the field in the gap becomes dependent on the position of the current conductor.
Fig. 22: Schematic of Faraday current sensor using a magnetic concentrator
Many sensors using this approach have been proposed. Using multiple-reflection in
a glass bulk mounted in a ferromagnetic field concentrator increases the total
effective optical path and therefore the sensitivity [Li97], [Yi00], [Yi02]. In order to
prevent reflection-induced phase shifts that interfere with the polarization rotation,
two methods have been proposed: critical angle reflection and dual-quadrature
reflection [Ning95].
One example [Yi00] for multiple critical angle reflections is shown in Fig. 23.
Fig. 23: Faraday glass element showing 7 critical angle reflections [Yi00]
Matsushita Electric Industry (Panasonic) developed a small optical magnetic field
sensor using a new garnet composition in 1999 [Itoh99], Fig. 24. This sensor is used
in a magnetic core flux concentrator and shows high linearity (1% for alternating
fields from 0.3 to 42mT) and temperature stability (2% from –20°C to +80°C).
Chapter 2
Investigation of applicable Techniques
According to Forrest et al. [Forr96], this sensor and earlier versions with less
linearity have been sold in thousands of units a year to a Japanese utility company
for use as a current fault sensor.
Fig. 24: Schematic of OCT probe [Itoh99]
A similar current sensor based on Bi-doped YIG is used for fault section
detection in Japanese underground transmission lines [Toya93]. This sensor is
mounted in a ring core of laminated silicon steel plates around the conductor in
order to measure the electric current.
Possible disadvantages of using magnetic core concentrators with an air gap are
sensitivities to currents in nearby conductors and dependency on the position of
the conductor owing to a not entirely closed concentrator as well as non-
uniformity of the magnetic field in the air gap.
To overcome these drawbacks, alternative configurations allowing the light to
pass through the Faraday material in a direction perpendicular to the magnetic
field have been proposed. Using such a structure enables a design with a smaller
air gap.
Toshihiko et al. proposed a sensor with a transverse configuration of the light
beam and the magnetic field in a small YIG bulk in 2001 [Yosh01], Fig. 25. The
magnetic field changes the 3D local magnetization according to the domain
characteristics in the crystal. The Faraday rotation of the light beam passing in z-
direction is direct proportional to the integration of the magnetisation in z-
direction over the 3D zone within the YIG crystal.
Chapter 2
Investigation of applicable Techniques
Fig. 25: Measuring set-up for a transverse configuration in YIG [Yosh01]
In 2003, the same group proposed a similar scheme where a uniaxial garnet film was
obliquely inserted in a narrow core gap and the light beam passes through the film
in the transverse direction to the core [Yosh03], Fig. 26. The authors claim that in
film form, the incident light beam undergoes an equal amount of Faraday rotation
independent of the incident angle to the film plane.
Fig. 26: Scheme of a current sensor in transverse configuration [Yosh03]
These transverse schemes [Yosh01], [Yosh03] allow a very high sensitivity and a
better insulation from surrounding currents due to a considerably smaller air gap
width. Moreover, this transverse scheme is easier to construct than a longitudinal
one. Bulk Optics
This type of OCT is analogous to an optical implementation of a conventional CT.
It consists of a Faraday material completely enclosing the conductor, Fig. 27.
Numerous designs have been proposed with light beams encircling the current-
carrying conductor exactly once or several times. These sensors are fabricated from
diamagnetic or paramagnetic single-glass blocks with relatively low Verdet constants
and do not suffer from problems such as intrinsic birefringence and bending-
induced linear birefringence occurring in optical fibre sensing elements (compare
Chapter 2
Investigation of applicable Techniques
Fig. 27: Schematic of a Faraday OCT using bulk optics
The first proposed geometry by Takahachi et al. [Taka83] shows a square-shaped
sensing element closing the optical path via three reflection corners, Fig. 28. In this
sensor, the reflection-induced phase-differences cancel each other through double-
quadrature reflections.
Fig. 28: Square-shaped OCT [Taka83]
A triangular-shaped sensing element has been introduced by Chu et al. [Chu92] using
critical angle reflections to preserve the state of polarisation, Fig. 29. This design is
easier to manufacture but the demand on the angular tolerance is very high (angles
for internal critical angle reflection θC are within ±0.01°).
Fig. 29: Triangular sensing element [Chu92]
Chapter 2
Investigation of applicable Techniques
Later, an openable form emulating a conventional current clamp has been
developed [Ning93].
Further designs have been published, including a circular ring using multiple critical-
angle reflections of a light beam encircling the conductor five times [Ning91/1] and
therefore increasing the current sensitivity by the same factor, Fig. 30.
Fig. 30: Circular geometry with optical path [Ning91/1]
Several bulk OCTs have been developed for commercial application, especially in
Japanese power systems. This design however, is sensitive to shock and vibration. Optical Fibre Sensing Elements
This kind of current sensor basically consists of an optic fibre wound a number of
times around the current-carrying conductor forming a coil, Fig. 31. The fibre itself
exhibits a Faraday effect and acts as the sensing material.
Fig. 31: Schematic of an optical fibre sensing element
Although the Verdet constant of a fibre is not very high, a measurable rotation can
be achieved with a long fibre wound around the conductor many times. A good
approximation of the closed line integral of the field is achieved. These fibres are
typically single-mode silica fibres and do not require a precision matching or
alignment. The sensitivity can be adjusted by adding dopants to the core or by
varying the number of turns. In order to remain the state of polarization in the fibre
between the sensing region and the light source/detectors, polarization-maintaining
Chapter 2
Investigation of applicable Techniques
single-mode fibres are used. These fibres have a core of elliptical cross-section or
index of refraction anisotropy introduced by dopants or uniaxial stress.
However, the sensitivity of the sensing part of the fibre is influenced by intrinsic and
stress-induced linear birefringence due to bending of the sensing fibre or vibrations.
Furthermore, since linear birefringence is temperature-dependent, the sensor will be
sensitive to external temperature perturbations. In order to overcome the induced
linear birefringence, a number of solutions have been presented [Ning95]. For
example can the linear birefringence be removed by annealing the fibre coil
[Rose96]. Another possibility is to suppress the influence of the bending-induced
birefringence by using a fibre with a large degree of circular birefringence. A twisted
fibre or a SEB (
irefringence) fibre is used so that the Faraday rotation
is superimposed onto this circular birefringence.
Optical current sensors using optical fibres as sensing elements have been produced
by ABB for AC currents [Bohn02] (Fig. 32) and DC currents [Bohn05].
Fig. 32: Principle and picture of a fibre-optic AC-current sensor [Bohn02]
Siemens developed a similar AC current transducer [Will02].
Toshiba has developed a silica fibre OCT [Taka97] with a reflecting arrangement.
This type has the double sensing length and can be used to suppress the influence of
vibration-induced birefringence since the influence on the clockwise-propagating
beam will be in anti-phase to the effect on the counterclockwise-propagating beam,
Fig. 33.
Chapter 2
Investigation of applicable Techniques
Fig. 33: Reflective-type wound-fibre OCT [Yu02]
NxtPhase Corp. has developed a commercial current sensor [Blak03], [Sand02]
using the Faraday effect in a different architecture than the polarimetric
technique. This sensor uses the Sagnac interferometer design and is based on the
changes of the velocities of right- and left-hand polarized light waves
propagating in the magnetic field around the conductor, Fig. 34. These two light
waves travel with different velocities through a coil of a polarization-maintaining
sensing fibre and the time-difference is measured. It is easier to accurately
measure changes in light velocity than changes in polarization state. Since this is
a velocity measurement scheme, there is no need to anneal the fibre. First field
tests of this sensor started in 2000.
Fig. 34: NxtPhase sensor “NXTC” principle [Blak03]
Also Takahashi et al. developed a Sagnac interferometer-type fibre-optic current
sensor [Taka04].
Faraday sensor techniques using fibres as sensing elements made great progress
during the last few years. Some of the proposed sensors exhibit sensitivities of the
highest standards and are produced for precise current metering.
Chapter 2
Investigation of applicable Techniques Unlinked Type
This type of sensor, also referred to as witness sensor, is based on magnetic field
sensing techniques. Instead of forming a closed loop around the conductor, this
sensor only measures the magnetic field at a point near the conductor making it
rather a magnetic field sensor than a current sensor, Fig. 35. However, this sensor
can be used as a current sensor if the system is calibrated. Other applications are
condition monitoring and fault-detection in electric power systems.
Fig. 35: Schematic of a Faraday-effect sensor, unlinked type geometry
In order to achieve a sufficient sensitivity for measuring magnetic fields at a “point”,
the Faraday material needs to have a very high Faraday rotation. Therefore
predominantly materials with high rotations such as YIG and substituted YIG are
One example for such kind of sensor is proposed by Sohlström [Sohl93] using a Bi-
substituted YIG film as Faraday material in a sensor head to measure magnetic
fields, Fig. 36. The polarized light beam passes twice through a YIG crystal of
130µm thickness being reflected at a mirror. This sensor can, after calibration, also
be applied to measure electric currents.
Fig. 36: Principle of a magnetic field sensor head [Sohl93]
Unlinked type OCTs have been commercially produced by NGK Insulators, Ltd. in
Japan [Imae92]. This sensor is based on a YIG crystal and is used as a ground fault
current detector. The principle is shown in the picture below.
Chapter 2
Investigation of applicable Techniques
Fig. 37: Principle of an optical magnetic field sensor [Imae92]
A current sensor using a TGG crystal to measure an electric current has been
presented by Cruden et al. [Crud95]. In 1998, the same group proposed an unlinked
type OCT made of a FR-5 glass piece [Crud98] (dimensions 2·25·25mm3), Fig. 38.
Fig. 38: Reflective type OCT [Crud98]
In order to enhance the sensitivity of a YIG crystal-based magnetic field sensor,
ferrite flux concentrators are used in [Deet96], [Roch00] and [Robl02]. The
bandwidth of the sensor by Deeter [Deet96] is in the order of 10MHz and a noise
equivalent field of 6pT/Hz, Fig. 39.
Fig. 39: Sensor head with flux concentrators [Deet96]
In 2003, Bai et al. proposed an OCT for integrated power electronic modules [Bai03]
using Bi-doped YIG. A scheme of this “point-sensor” is shown in Fig. 40.
Chapter 2
Investigation of applicable Techniques
Fig. 40: Sensing tip [Bai03]
An enhanced version [Inou95] of the current sensor presented earlier in the
magnetic concentrator section [Toya93] is used as a magnetic field sensor in the
vicinity of the conductor to detect the section of a fault current.
Also the sensor head of the current transducer previously presented in the magnetic
concentrator section [Itoh99] (Fig. 24) is used as a witness sensor with inferior
characteristics. This device, produced by Matsushita, uses a Bi-substituted RIG-film
as Faraday material, Fig. 41.
Fig. 41: Schematic of the opto-magnetic field sensor probe [Itoh99]
A different principle related to the Faraday effect is presented in [Dido00]. This
principle is the same as in other conventional Faraday effect sensors but instead of
measuring the average area of the up and down magnetized domains, the position of
the domain wall is measured. A yttrium iron garnet crystal is mounted between two
small magnets with opposite magnetisation directions. This special material forms
two domains only (characterized by mutually opposite magnetisation direction) with
opposite Faraday rotations, Fig. 42.
Fig. 42: Principle of a two-domain sensor principle [Dido00]
Chapter 2
Investigation of applicable Techniques
A polarized light beam coming from the source (1) illuminates the crystal plate (2).
This plate, closely located to the current-carrying conductor (3), forms a two-
domain structure by means of two permanent magnets (not shown). The light,
propagating through the analyzer (4), is detected by a position-sensitive photo
receiver (5).
For calibration the analyzer has to be rotated to a position where the light passing
through the lower domain is extinguished for zero magnetic field. Measurements of
the magnetic field (electric current) can now be made by detection of the position of
the domain wall, Fig. 43.
Fig. 43: Dark and bright zones indicating opposite Faraday rotation
The boundary between “bright” and “dark” domains changes in accordance to the
value of the magnetic field. Also ac currents can be measured evaluating the zone of
intermediary brightness as shown below, Fig. 44.
Fig. 44: Intermediate zone at 100kHz
This relatively new sensor principle is able to measure high currents from dc up to
hundreds of kHz and is relatively temperature-independent.
2.2.3. Interferometric Principles
In an interferometer, the difference in length between two optical paths is
measured. In order to use this principle to measure a current or a magnetic field, it
must be transferred into a path length variation. In most cases, this change is
accomplished through magnetostriction. This principle was first proposed by Yariv
et al. [Yari80] in 1980: a magnetostrictive material is mechanically coupled to a fibre.
When this material is exposed to a magnetic field, a change in shape occurs, which
induces strain in the fibre resulting in a change of length of the fibre. This change in
Chapter 2
Investigation of applicable Techniques
optical path length can be measured by bringing the fibre into one arm of a Mach-
Zehnder-Interferometer. Numerous different designs have been realized. A sensor
exploiting the magnetostriction of a ferromagnetic core with a single-mode fibre
coiled onto it is presented in [Pere02], Fig. 45.
Fig. 45: Fibre-optic current sensor [Pere02]
The best principle has been proven to be an optical fibre coated with
magnetostrictive materials such as nickel, metallic glasses or ceramic
magnetostrictive materials[Jarz80], [Sedl96], Fig. 46.
Fig. 46: Fibre coated with magnetostrictive material in an interferometer [Sedl96]
However, this sensor also reacts to all other kinds of parameters that can cause a
change in optical path length, e.g. temperature. Many of these problems have
however been solved, but still, the remaining non-linearity, hysteresis and saturation
of magnetostrictive materials limit the applicability of this technique.
Other sensor principles using interferometric detection have also been studied. For
example by Ning et al. [Ning91/2], the optical path length change is caused by the
strain of a piezoelectric element driven by the output-voltage of an ordinary current
transformer around the current-carrying conductor ,Fig. 47.
Chapter 2
Investigation of applicable Techniques
Fig. 47: Piezoelectric-optic current sensor [Ning91/2]
Another approach to change the optical path length is by creating a strain in the
fibre caused by the Lorentzian force. This sensor utilizes a conductor-coated sensing
fibre in one arm of a Mach-Zehnder interferometer [Okam90]. The DC or AC
current flowing through the coating causes the metal-coated fibre to extend or
vibrate elastically, which can be sensed in terms of an optical-phase change (Fig. 48).
Fig. 48: Lorentzian force current sensor [Okam90]
2.2.4. OCTs based on Bragg Gratings
This principle is actually an interferometric one, but is grouped separately due to
differences in detection mechanisms and structure.
In recent years, several sensors that measure the mechanical strain of a material in a
magnetic field with a Bragg grating have been proposed. A Bragg grating is an
optical grating that works as an optical filter. A FBG (
rating) is a
periodic or aperiodic perturbation of the effective refractive index and/or the
effective absorption coefficient in the core of an optical fibre.
Light propagating in the core will be reflected by the interfaces between regions
having different refractive indexes. But the reflected light is generally out of phase
and is extinct. However, for a certain wavelength, the Bragg wavelength
Bragg, the
light reflected by the periodically varying index of refraction will be in equal phase
and added constructively. This leads to the reflection of light in a very narrow range
of wavelength. Other wavelengths are nearly not affected and pass the fibre. When
such a fibre is strained, the grating constant changes and consequently the reflected
wavelength changes. That can be detected as a function of strain and thus the
magnetic field.
Chapter 2
Investigation of applicable Techniques
Many different types of FBG current sensors have been developed. A simple
example is proposed by Feng et al. [Feng00] using a magnetostrictive rod with a
FBG fibre mounted on it to measure the change in Bragg-wavelength, caused by the
lengthened rod, Fig. 49.
Fig. 49: FBG sensor scheme, redrawn after [Feng00]
A different approach to measure a current is chosen by Fisher et al. [Fish97] using
the output signal of a conventional current transformer to actuate a piezoelectric
cylinder on which a FBG fibre is bonded, Fig. 50.
Fig. 50: Scheme of a FBG sensor [Fish97]
The output voltage of the current transformer is proportionally translated into the
variation of diameter of the cylinder causing a linear current-frequency shift
Cavaleiro et al. [Cava98] use a different approach. Their sensor is based on the
temperature sensitivity of a fibre Bragg grating. A current passing through a thin
conductive coating on the surface of the FBG causes the temperature change. This
current is the secondary current of a Rogowski coil measuring the electrical current
of the current-carrying conductor, Fig. 51.
Fig. 51: Bragg sensor with temperature induced phase shift [Cava98]
Chapter 2
Investigation of applicable Techniques
By monitoring the temperature-induced Bragg wavelength shift, the value of the
electrical current can be recovered.
All these principles require a rather expensive wavelength-detection technique and
suffer from temperature interference.
However, a sophisticated fibre Bragg sensor has been introduced by Chiang et al.
[Chia03], overcoming the temperature sensitivity and using a simple and cheap
detection technique. This sensor consists of a fibre Bragg grating bonded on two
joined metal alloys (Terfenol-D and MONEL 400). At zero magnetic fields, the
sensor shows a single reflection peak. But when a magnetic field is applied, the
Terfenol-D is stretched due to huge magnetostriction, while the dimensions of the
MONEL 400 remain unchanged resulting in two separated reflection peaks, Fig. 52.
Fig. 52: Reflection peak separation [Chia03]
The reflection peak of that part of the grating on Terfenol-D shifts to a longer
wavelength, while that of the other half on MONEL 400 remains on its original
position. The magnetic field thus causes a split in the reflection spectrum making it
easy to measure, using a simple photo detector to detect its intensity. Moreover, the
almost identical thermal expansion coefficients of the Terfenol-D and MONEL 400
make the peaks shift in the same direction by the same amount keeping the overlap
of the two reflection spectra constant and therefore the sensor insensitive to
temperature changes. However, Terfenol-D-based sensors are limited in their
bandwidth to only a few kHz [Gree90].
A potential advantage of a Bragg grating based system is the relative ease of
multiplexing, which can potentially reduce the costs of the source and electronics
when multiple devices are to be used. [Culs04]
Chapter 2
Investigation of applicable Techniques
2.2.5. Micromechanical Sensors with Optical Readout
With the rise in MEMS industry in the 1990’s many well-known and widely
understood principles have been applied in order to measure magnetic fields and
thus, electric currents. Most principles use mechanical deformation basing on
standard silicon-technology and optical readout to ensure electromagnetic immunity.
However, no commercialisation of this technology has been seen yet. Some of the
principles are presented below.
Heredero et al. [Hede99] proposed a micromachined optical fibre current sensor
measuring the magnetic field around a conductor. The sensing element consists of a
square silicon membrane that has a cylindrical permanent magnet fixed on its central
region. The vibration of this structure at the presence of the magnetic field gradient
generated by an AC current is measured with white-light interferometry. There is a
great advantage in feasibility and price for LEDs and detectors since there is no
limitation for a central wavelength and standard single-mode optical fibres can be
used. The actuator design is a simple one-mask process. The principle is shown in
Fig. 53.
Fig. 53: Micromachined optical fibre current sensor [Hede99]
This sensor is mechanically limited by dynamic range and bandwidth and is not able
to detect homogenous magnetic fields.
The same group proposed a DC and AC sensor with a similar structure using a
dual-wavelength fibre Bragg grating technique working in quadrature in order to
interrogate the microcavity [Hede03].
Another micromechanical magnetometer has been introduced by Yang et al.
[Yang02]. This sensor optically detects the deflection of a ferromagnetic-coated
beam in a magnetic field, Fig. 54.
Chapter 2
Investigation of applicable Techniques
Fig. 54: Principle and SEM image of the magnetometer [Yang02]
This principle is subjected to effects like squeeze-film damping, which considerably
limits its performance.
A similar sensor was proposed by Goedeke et al. [Goed04]. Here, the deflection of a
cobalt-coated cantilever is measured optically.
In [Kepl04], the sensing element is a U-shaped cantilever that bears a thin film lead.
The magnetic field strength is converted into a movement of the cantilever when a
current flows through the film, the resonant frequency of the cantilever being 5kHz,
Fig. 55.
Fig. 55: Schematic of the sensor with optical readout of the cantilever position [Kepl04]
The front plane of the bended cantilever acts as a deflecting mirror enabling an
optic readout system. The dynamic range of this sensor can be tuned by altering the
current in the film.
Another intensity type principle has been tested for fault detection on electric power
transmission lines by Carome et al. [Caro91]. It consists of a pair of multimode
optical fibres directly mounted end-to-end. One fibre is fixed while the other is
deflected by a magnetic field. The miss-alignment results in change in intensity
transferred from one core to the other and can be measured as function of the
magnetic field.
Chapter 2
Investigation of applicable Techniques
2.2.6. Other Optical Current Sensing Principles
Following, some principles that allow to measure electric currents are briefly
presented. These principles are rather unusual and might not be commercially used
for current sensing.
- A new type of OCT based on a new physical effect, the thermal lens coupled
magneto-optical effect in ferrofluid, is presented in [Chen98], [Ning91/1].
When a laser beam is focused on an absorptive ferrofluid thin film, an
effective concave lens is resulted, which diverges rays in the beam and makes
them interfere. A consequently appearing pattern of diffraction rings can be
detected by two fibres, which detect the current-corresponding variation of
light intensity of the diffraction rings.
- An OCT using liquid crystals and chromatic modulation has been presented
by Pilling et al. [Pill93], Fig. 56. The CT attenuates a certain portion of the
optical spectrum incident upon it by an amount dependent on the current
flowing in the power line. The spectrum is analysed by a double-layer
photodiode and the current in the power line can thus be indirectly measured
by evaluating the ratio of the photodiode shortcut currents.
Fig. 56: LC modulator based on chromatic modulation [Pill93]
This principle however, suffers from temperature dependency and a very
high response time.
2.2.7. Conclusion Optical Current Transformers
Concluding the development in optical current sensing, one can say that OCTs are
on the way to commercialisation and many have already been field-tested and
commercially installed.
There is an industrial need for two kinds of current sensors. One sensor with high
accuracy for revenue metering of high currents and one fast, high dynamic sensor
with a wide bandwidth for protecting the installation in case of overload currents
For revenue metering, there are already numerous companies field-testing or
commercially installing high-accuracy current metering systems. Most major electric
Chapter 2
Investigation of applicable Techniques
companies like ABB, Siemens and GE show efforts in developing optical current
metering systems. Great efforts are especially made in Japan but optical current
sensors are still far from being widely used. It can be seen that during the last years
there has been a shift from bulk-glass sensors to all-fibre sensors reflecting the
progress in temperature- and birefringence-compensation techniques.
For fault detection sensors, there has not been a steady commercial development.
Most principles for fault detection fall into the group “unlinked type” (chapter since those sensors are simpler, potentially cheaper and sufficiently precise.
These devices are commonly based on magnetic field sensing and primarily use iron
garnets with high Faraday rotation as sensing medium. Many technologies have
been proposed, predominantly in the first half of the 1990’s, but only few are
commercially installed. Again, Japanese companies seem to have made the greatest
effort in developing these technologies. Several thousands of optical current fault
sensors are reported to have been produced and sold within Japan since the late
1990s. Panasonic (Matsushita) alone reported the shipment of several thousand
optical sensor heads for fault detection [Yu02]. However, there has not been an
open market for optical current fault sensors.
Noteworthy is the recent development of hybrid opto-mechanic systems, many of
which are based on reflective intensity modulation. These devices have, however,
not been industrialized yet, but are potentially cheap owing to standard optic
components and batch processing production techniques.
2.3. Conclusion of the Technology Investigation
Considering all presented techniques, it can be concluded that none of the non-
optical current or magnetic field sensors exhibits the demanded reliability in high-
EMI environments without additional shielding and isolation and/or fulfils the
required bandwidth, dynamic range and size.
Optical current measurement systems are favourable for that purpose because of
their inherent insensitivity to EMI and galvanic isolation. Most of the indirect OCTs
however, suffer from inherent problems such as bandwidth limitation, saturation
and hysteresis due to their mechanical components or other interferences associated
with energy conversions. Some examples for limitations are the low resonance
frequencies of most MEMS sensors or saturation, hysteresis and actuation
frequency limits of magnetostrictive components in Bragg sensors.
The most suitable sensor principle for this application are OCTs with intrinsic opto-
magnetic effects, i.e. the Faraday effect. Considering the purpose of current fault
detection, a simple and cheap “unlinked type” sensor in the vicinity of the
conductors is sufficient since no precise current measurement using fibre-coils or
magnetic concentrators is necessary.
Chapter 2
Investigation of applicable Techniques
The best solution for that seems to be a Faraday sensor with “point measurement”
of the magnetic field employing high-rotation materials such as RIGs.
Two such sensors are available at the Microsystem technology department of KTH
and will be used for some first measurements and fault detection tests in this work.
The Faraday materials and properties of these sensors however, are unknown, but
will be determined in chapter 4.2.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
3. FEM Simulation of the Magnetic Field
3.1. Introduction
The chosen technique using Faraday “point”-sensors to detect a fault in the
described system with parallel IGBTs gives the possibility to use a single sensor to
detect a fault in each of the current lines. This is possible when the sensor is
brought into the exact middle between the two conductors (Fig. 57) and the sensor
has a “45°-characteristic” (compare chapter with polarizer and analyzer
having a 45° rotation to each other. The magnetic field around an infinitely long,
thin and straight conductor can be calculated using
=2 Equation (9)
where I is the current in the conductor and r is the distance from the conductor.
The case for the application with two conductors with rectangular cross-section is
more complex.
Fig. 57: Magnetic field between parallel conductors
The magnetic fields caused by both conductors in the exact middle will cancel each
other when the current in both conductors flows in the same direction due to the
symmetry of the geometry, Fig. 57. When one of the IGBTs fails, only one of the
lines will be conducting, resulting in a positive or negative field at the sensor
depending on which of the IGBTs failed. This can be detected with a “45°-sensor”.
In order to reliably detect the current or in this case a current fault in the
conductors, the magnetic field and its pattern around the conductors has to be
Chapter 3 FEM Simulation of the Magnetic Field Pattern
The conductors in the actual application will have a non-circular cross section and
will be placed in proximity to each other. The current in the conductors might
change with a frequency of tens of kHz. That makes it difficult to calculate the
magnetic field and its distribution, since eddy currents and skin effect will occur and
significantly influence the magnetic field.
Therefore, a FEM (
ethod) simulation of the two conductors and the
surrounding magnetic field was made. From this we can get some essential
Firstly, it is essential to know the expected magnitude of the field between the two
conductors in order to conclude the necessary sensitivity of the sensor to detect a
Secondly, the distribution of the field between the conductors is important to know
in order to determine the best location of the sensor.
Lastly, the frequency behaviour of the magnetic field is very important. The
frequency response has to be flat up to hundreds of kHz in order to detect faults
with minimum delay.
The simulation has to be done for two cases: The case when both conductors are
carrying the same current in the same direction and the case of a fault where only of
the conductors is conducting. Since at higher frequencies, skin effect and induction
are expected to have a very large influence on the current density distribution in the
conductor and thus the magnetic field, the field has to be investigated for a range of
The FEM software COMSOL Multiphysics (formerly Femlab) was used to simulate
the two conductors and the magnetic field around them. The simulation can be
done in 2D with a cross-section of the conductors perpendicular to the direction of
the currents as the 2D plane. A 2D model implies that the length of the conductors
is infinite which is not strictly true in application. In principle, for a correct
simulation with finite conductor lengths a much more complicated 3D simulation
would be necessary, but since the 2D simulation is expected to give a sufficiently
good indication of the resulting magnetic fields, a 2D model has been used.
In order to model the two copper conductors and the resulting field around them,
the Femlab model “Quasi-Statics, Magnetic, Perpendicular Induction Currents,
Vector Potential” from the Electromagnetics Module is used. To set and maintain
the correct currents in the conductors, an additional “Weak Form, Point” model
had to be added that integrates the actual current density over the conductor and re-
calculates the input potential for each conductor.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
Geometry and dimensions for the simulation are chosen in the order of the
presumable actual application. The cross section of the conductors carrying a
current perpendicular to the simulation plane (z-direction) is 100·10mm2, Fig. 58.
Fig. 58: Sketch and dimensions of the two conductors
In normal operating condition, both conductors carry the same current I0. In order
to simulate the case of fault in one of the conductors, the current in the right
conductor was simply set to I=0A and the current in the left conductor was set to
twice the initial value 2I0.
The y-component of the magnetic field strength between the conductors is the
determinant one representing currents in both conductors and will therefore be
investigated as the measurand. The sensor also will be able to measure the magnetic
field in only one axis and will be placed between the two conductors in a way to
detect the magnetic field in y-direction (Hy).
3.2. Normal Working Condition
The picture below shows a surface plot of the simulation with two copper bars,
both carrying a current of 1000A in the same direction at a frequency of 1Hz. This
state represents the normal working condition at a very low frequency to show the
field distribution without any considerable skin effect or induction influences.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
Fig. 59: Hy between conductors carrying 1000A each, f=1Hz
It can be seen, that the y-component of the magnetic field in the middle between the
two conductors is about zero and increasing, respectively decreasing, in direction of
the conductors. The field in equidistance to both conductors is, as expected, zero
because the magnetic fields around each conductor cancel each other when both
carry the same current in the same direction.
To examine the distribution of the magnetic field between the conductors in
dependency on the frequency, the simulation was run for a variety of frequencies
from 1Hz to 1MHz. A plot of the magnetic field (y-component) in dependency on
the x-coordinate between the conductors for a wide frequency range is shown in
Fig. 60. The values of the field are taken along the x-axis for y=0.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
Fig. 60: Hy in dependency on x coordinate, both conductors carrying 1000A
The graph shows that the magnetic field in equidistance to both conductors has
zero magnitude for all frequencies. It can be seen that the field shows almost no
dependency on the x-location for higher frequencies.
This behaviour is due to the current being diverted to the corners of the conductor
resulting in a inhomogeneous current density. This phenomenon is called skin effect
and can for circular conductors be described with the skin depth d:
= Equation (10)
where d is the depth below the surface of a circular conductor at which the current
density is 1/e the current density at the surface. ρ is the resistivity of the conductor,
ω is the angular frequency of the current and µ is the absolute magnetic permeability
of the conductor. This description for the skin depth however, does not hold for
non-circular conductors. The behaviour is similar but more complex. The same
effect of deflection of the current density occurs. An uneven distribution of the
current density for different frequencies in the conductor halves can be seen in Fig.
61, obtained by FEM simulation.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
1Hz 20Hz 50Hz 200Hz 1000Hz
Fig. 61: Distribution of the current density due to the skin effect for different frequencies
From the asymmetry of the current density can be seen that the magnetic field
caused by the parallel conductor (carrying the same current) also influences the
current density distribution. It has to be noticed, that similar colours in the images
for different frequencies correspond to different current densities. The
homogeneous current density in the very left image (f=1Hz) is J1·106A/m2,
whereas the current density in the corner of the very right image (f=1000Hz) is
Fig. 62 shows the magnetic field (y-component) around both conductors at a
frequency of 100Hz.
Fig. 62: Magnetic field (y-component), both conducting 1000A, f=100Hz
Fig. 62 shows a large area of relatively homogeneous field between the two
conductors. This behaviour is very distinctive for frequencies greater than about
100Hz, compare to Fig. 60. In the vicinity of the corners of the conductors
however, a greater field gradient can be seen.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
3.3. Case of Failure
In order to investigate the field in the case of failure of one of the conductors, the
simulation is run for only one conductor additionally carrying the current of the
faulty conductor. The resulting magnetic field is the indication for a fault of one of
the conductors and has to be reliably detected by the sensor. Fig. 63 shows the field
distribution for the case of fault in the right conductor at f=100Hz.
Fig. 63: Left conductor carrying 2000A, right conductor 0A, f=100Hz
The resulting field distribution between the two copper bars from Fig. 63 appears to
be relatively homogeneous. Fig. 64 shows the distribution of the y-component of
the magnetic field in dependency of the x-coordinate between the two conductors
for different frequencies.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
Fig. 64: Hy in dependency on x coordinate, only one conductor carrying 2000A
Fig. 64 clearly shows that for frequencies greater than about 100Hz, the field is fairly
independent of the location in x. This behaviour can be explained with the
additional influence of eddy currents circulating in the right conductor.
In Fig. 65, it can be seen that the induced eddy currents that circulate in the right
conductor also show skin effect behaviour for higher frequencies. The resulting
distribution of positive current density in the corners of the conductor and negative
current density in the middle of the faulty conductor contribute to a relatively
homogenous field between the conductors.
Induced currents and skin effect are thus the major reasons for the resulting
homogeneity of the magnetic field pattern between the conductors.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
Fig. 65: Total current density (z-component) at 200Hz, only left conductor carrying 2000A
In order to estimate the equalizing influence of the faulty conductor, a simulation of
a single copper conductor of the same geometry was carried out, Fig. 66.
Fig. 66: Magnetic field around a single conductor (100Hz, 2000A)
To compare the equalizing effect of the second conductor, Hy is plotted similarly to
Fig. 64 for a range of frequencies. The result is shown in Fig. 67.
Chapter 3 FEM Simulation of the Magnetic Field Pattern
Fig. 67: Hy in dependency on x coordinate, single conductor carrying 2000A
The comparison of Fig. 64 and Fig. 67 clearly shows that the second conductor
greatly homogenizes the magnetic field between the two bars.
Following, also the magnetic field distribution along the y-axis (x=0) is investigated.
Therefore, the magnetic field (y-component) is plotted for:
a) the case of failure, when only the left conductor is conducting. (Hy along the y-
axis for x=0, distance to both conductors is 15mm)
Fig. 68: Hy along the y-axis for x=0, two conductors (I1=2000A)
Chapter 3 FEM Simulation of the Magnetic Field Pattern
b) the single conductor at a distance equal to above (15mm) :
Fig. 69: Hy along the y-axis at 15mm from the single conductor (2000A)
Comparing Fig. 68 and Fig. 69, it can clearly be seen that the presence of the second
conductor also significantly equalizes the magnetic field along the y-axis for higher
frequencies. For frequencies above 100Hz the magnetic field is practically
independent of the location of the sensor.
3.4. Conclusion
Concluding the results of the simulation, one can say that the design with two
parallel conductors of rectangular cross-section relatively close to each other greatly
equalizes the magnetic field between them. This effect is noticeable when both
conductors are conducting, as well as for the case of failure, when only one
conductor carries the current. The magnetic field equalizes in magnitude at higher
frequencies for a wide area (in x-and y-direction) between the conductors resulting a
large area of relatively homogeneous field. This “induced homogeneity” makes the
correct placement of the magnetic field sensor uncritical. The resulting field per
current in the centre position of the conductors is about
23. for frequencies
higher than 100Hz, compare Fig. 68.
Fig. 64 and Fig. 68 also show that the resulting magnetic field for frequencies greater
than 100Hz is almost frequency-independent. This frequency-independence of the
magnetic field together with the relative homogeneity of the magnetic field makes
this build-up favourable to detect a fault with great safety. The magnetic field is
Chapter 3 FEM Simulation of the Magnetic Field Pattern
virtually frequency- and location-independent only representing the currents
running in both conductors.
The simulation also shows that the definitely best point to place the sensor is right
in the middle and at equidistance to the conductors. A placement between the edges
of the conductors exposes the sensor to a much greater field gradient and a higher
frequency-dependence and is therefore not favourable.
Another result of the simulation is, that the field gives a very flat frequency response
into the MHz range, which is important to detect a failure within microseconds.
That also means, that non-sinusoidal currents, as they are expected in the actual
application with fast switching IGBTs, can equally be measured.
Everything mentioned makes the proposed geometry favourable for the detection
of current faults in both conductors.
It has to be noticed that the described favourable behaviour is geometry-dependent.
Different cross-sections and distances exhibit different equalization characteristics.
Chapter 4 Experiments
4. Experiments
4.1. The Sensors
The chosen technique to measure the magnetic field and thus the current is to use a
magnetic field sensor exploiting the Faraday effect. Two such sensors are available
in the department of Electrical Engineering at KTH. These sensors have been
developed by Hans Sohlström in 1990 within a project at KTH [Svan90].
Fig. 70: Faraday sensor head
These sensors use a folded design with two multimode fibres (ØCladding=140µm,
ØCore=100µm) fixed in a plastic jacket. The polarizers are fixed at the ends of the
fibres. A gradient index lens collimates the polarized light to a reflective gold layer
on the backside of the Faraday film. The reflected light beam again transverses the
Faraday film and the second polarizer and is focused into the second multimode
fibre, compare Fig. 71. The two available sensors have a similar physical appearance
and will following be named Sensor I and Sensor II.
Fig. 71: Schematic of the used Faraday sensor
Chapter 4 Experiments
Also the appendant electronic circuitry with a light source (InGaAs diode,
λ=1300nm), a photo detector and an amplifier is available. All components are
mounted in a box with two optical connectors for the sensor fibres, three
connectors for the power supply (U=±15V, ground) and a BNC connector for the
signal output. This device will following be called amplifier box.
The fibre-optic connectors on the sensors were of an obsolete kind and had to be
replaced with SMA fibre-optic connectors to match the amplifier box. By
connecting the fibres with the connectors to the amplifier box, a big difference in
the output signal level was found every time the connectors are screwed to the
connection threads of the box. This could be explained with alignment errors in the
connectors or problems with the optic quality on the fibre end. The zero-field
output voltage (U0) is therefore always different when the fibres are reconnected.
The connection to the detector is uncritical because the sensitive area of the
detector is much bigger than the emitting area of the LED.
All sensor characteristics, even the used Faraday materials of the two available
sensors were completely unknown. Hence the sensor characteristics had to be
4.2. Characterization of the Sensors
In order to use the sensors as reliable magnetic field sensors, or in this case as
current fault sensors, their properties have to be known. But, since the available
sensors are only used to make first tests in order to prove that the proposed
technique to detect current faults is applicable in praxis, not all sensor characteristics
have to be precisely determined.
The most important properties of the sensor are its sensitivity, linearity and
temperature dependency.
4.2.1. Sensitivity
The sensitivity of a sensor is the ratio of output signal or response of the instrument
to a change of input or measured variable [Copp85]. Here, the input variable is the
magnetic field strength or magnetic flux density and the output signal is the
corresponding change of the output voltage.
In order to correlate the input measurand to the output signal, the output voltage
has to be related to the change of a known magnetic field. Therefore, an alterable,
homogeneous magnetic field has to be generated.
Such a field can easily be produced in a coil. The magnetic field in a coil can be
directly modified by changing the current in the coil. For that purpose a coil with
properties as in Fig. 72 was used.
Chapter 4 Experiments
r1=30mm - inside radius of the coil
r2=52mm - outside radius of the coil
l=51mm - length of the coil
N=1100 - number of windings of the coil
I - current in the coil in amperes
x1, x2- distances, on axis, from the ends
of the solenoid to the magnetic
field measurement point
Fig. 72: Schematic cross section of a solenoid of finite length and radial thickness
The axial magnetic field in a finite solenoid can be calculated for any point along the
axis of the solenoid using the following formula [Denn06]:
B Equation (11)
where n is the number of turns of wire per unit length in the solenoid.
(21569== l
For the magnetic field measurement point at the centre of the solenoid, x1=(-x2),
the formula reduces to:
= Equation (12)
This point is used for the calibration measurements. Inserting the data of the coil
into equation (12) at a current of I=1A gives magnetic field-current relation of
4514.B = or A
11505=H Equation (13)
All following sensitivity calibration measurements were done in the centre of the
coil. The change of output voltage of the sensor will subsequently be related to the
change of the magnetic field using the relation above.
In order to validate the theoretical field in the coil, a test measurement with a Hall
sensor element was done in the field of the coil. Due to geometrical reasons the
sensor could not be placed in the centre of the coil, hence the field had to be
measured at the end of the coil (x2=l and x1=0). Using equation (11) for x2=l and
x1=0 gives a value of B=10,56mT/A. This value coincides with the measured values
Chapter 4 Experiments
within the relatively large uncertainty of the instrument and therefore the previously
done calculations and relations can be considered to be correct.
All calibration measurements were made with the set-up shown in Fig. 73.
Fig. 73: Measurement set-up for sensitivity determination
In order to determine the sensor sensitivity, linearity and the rotation of the two
polarizers to each other, B-U curves for high magnetic fields were recorded. The
magnetic field was generated by a direct current (Imax=4A), supplied by a DC current
source, running through the above described coil. The sensing element was placed
in the exact centre of the coil. Fig. 74 and Fig. 75 show the B-U characteristic
curves of sensor I and sensor II for a large range of field. The maximal field
generated by the current source (Imax=4A) is corresponds to B=57.8mT using
equation (13). Both measurements were made for a field cycle starting at 0mT Æ -
57.8mT Æ +57.8mT Æ 0mT.
Chapter 4 Experiments
Characteristic curve sensor I
-60 -40 -20 0 20 40 60
B [ m T]
U [mV]
Fig. 74: Characteristic curve of Sensor I, large fields (0mTÆ-57.8mTÆ+57.8mTÆ0mT)
Sensor I shows a relatively linear curve and neglectable hysteresis. However, a drift
due to temperature increase during the measurement can be seen.
Charcteristic curve sensor II
-60,00 -40, 00 -20,00 0,00 20,00 40,00 60,00
B [ m T]
U [mV]
Fig. 75: Characteristic curve of Sensor II, large fields (0mTÆ-57.8mTÆ+57.8mTÆ0mT)
Sensor II exhibits a more non-linear characteristic for larger fields and a hysteresis
for small fields.
Sensor I shows the more linear behaviour and is free of hysteresis. Both sensors
exhibit similar sensitivities. From the slope and shape of the characteristic curves, it
can also be concluded that in both sensors polarizer and analyzer have an
orientation of 45° to each other. This feature is advantageous because also the
Chapter 4 Experiments
direction of the field and therefore the information about which of the parallel
IGBTs in test set-up failed can be determined from the sensor signal.
The resulting sensitivity for sensor I and an average sensitivity for sensor II for high
fields are given in Table 5. Because of the fact that the zero-field output (U0) of the
sensor differs each time the fibres are reconnected to the amplifier box, the
sensitivity is rather given in % per field than in signal voltage per field.
Table 5:Sensitivities for large fields
Sensor I (U0=1.011V) Sensor II (U0=0.858V)
Sensitivity [%/mT] 0.250 0.228
Sensitivity [mV/mT] 2.52*1.96*
* is different for different U0, here given for certain U0
The magnetic field of the test set-up in chapter 3 is expected to be smaller than
shown in Fig. 74 and Fig. 75. Therefore sensitivity measurements of a lower field
range of ±7000A/m or ±8.7mT (corresponding to about ±600mA in the coil) were
made. The results of the measured sensitivities are shown in Table 6.
Table 6: Sensitivities for small fields
Sensor I (U0=0.795V) Sensor II (U0=0.693V)
Sensitivity [%/mT] 0.212 0.147
Sensitivity [mV/mT] 1.69*1.02*
* is different for different U0, here given for certain U0
It can be seen that the sensitivities of both sensors are smaller for low magnetic
fields. Especially sensor II exhibits a lower sensitivity due to its stronger non-linear
characteristic, compare Fig. 75.
Fig. 76 shows the characteristic curve of an undoped YIG sensor that was presented
in a work conducted at KTH [Svan90].
Chapter 4 Experiments
Fig. 76: Characteristic curve of an undoped YIG sensor [Svan90]
The sensitivity of this sensor was re-calculated from the graph to be S=0.267
%/mT. This sensitivity is similar to the sensitivity measured for sensor I (S1=0.250
%/mT) for a similar range of field. Furthermore, the two curves have a similar
linearity and the dimensions of the Faraday film of the sensor (area of 2mm·2mm
and 300µm thickness) coincide with those of sensor I. It can therefore be assumed
that sensor I is the in [Svan90] described undoped YIG sensor. This sensor has two
plastic polarizers (Polaroid) with a 45°-orientation and a structure as described in
Fig. 71.
Sensor II, however, can not be clearly matched to one of the sensors that were
developed at KTH. The sensitivity of sensor II is close to that of the mentioned
pure YIG sensor but its characteristic curve and the dimensions of the Faraday film
(area of 1mm·1mm) do not match one of the earlier presented sensors. Sensor II
might be one of the substituted YIG sensors that were developed at KTH but can
not be assigned to one of them.
4.2.2. Temperature Behaviour
In order to determine the influence of the temperature on the sensor signal, the
output signal for both sensors was measured at different ambient temperatures.
Therefore the sensor was placed in a temperature-controlled chamber. The output
voltage of both sensors was measured for a temperature range from T=10°C to
T=60°C at zero field. For the actual application a wider temperature range has to be
covered but this is only to give some indication of the temperature influence. The
resulting temperature curves are shown in Fig. 77 and Fig. 78 below.
Chapter 4 Experiments
Temperature response Sensor I
10 15 20 25 30 35 40 45 50 55 60
Tem perature [°C]
U [V]
Fig. 77: Temperature response Sensor I
Temperature response Sensor II
10 15 20 25 30 35 40 45 50 55 60
Tem perature [°C]
U [V]
Fig. 78: Temperature response Sensor II
From the graphs can be concluded that the temperature has a large influence on the
output signal of both sensors. Sensor I exhibits a strong non-linear, somewhat
chaotic temperature dependency. The same holds for sensor II but with a more
linear temperature dependency. The maximal temperature drift for sensor I is about
U=0.25%/K and the average temperature drift for sensor II is around
U=0.28%/K. That means that even small temperature changes result in a larger
voltage change than the signal from a weak magnetic field would be.
In order to reliably and precisely measure magnetic fields with these sensors, they
either have to be held at a constant temperature or some kind of temperature
compensation has to be done.
Chapter 4 Experiments
A possible change of sensitivity with temperature was not determined. This
probable effect can only be neglected when the temperature is kept constant.
4.2.3. Modification of the Electronics
Concluding the results of the sensor sensitivity measurements and the temperature
behaviour, the response of the sensor system has to be changed in order to get a
reliable signal for small magnetic fields. Significant sensor parameters such as
amplification and bandwidth can be altered by tuning the amplifier circuitry of the
amplifier box. A schematic of the electronic circuit in the amplifier box is shown in
Fig. 79.
Fig. 79:Schematic of the amplifier box
The first amplifier stage acts as a transimpedance amplifier converting the current
from the light detection diode into a voltage. The second amplifier stage is an
inverting operational amplifier amplifying the voltage level from the first stage.
The signal response of the sensor can be increased by increasing the total
amplification of the circuitry. The voltage amplification of the second stage can be
calculated using the following equation:
V= Equation (14)
In order to reduce the influence of the temperature drift, the second amplifier stage
can be AC-coupled. That can be done by inserting a capacitor CS between RS and
the operational amplifier stage, Fig. 79. RS and CS behave like a high pass with a cut-
off frequency of
Chapter 4 Experiments
f= Equation (15)
To reduce the influence of the high frequency noise, the upper bandwidth can be
limited by altering the relation C1 to R1 and C2 to R2. Both RC links behave like a
low pass:
f= and
f= Equation (16)
The initial values for the bandwidth and amplification are calculated from the values
in Fig. 79 using equation (15) and equation (16): V=1.45
In order to get a better signal from the electronics, some changes in the circuitry are
made. A useful new value for the amplification would be V15, which results in an
about tenfold zero-field voltage of the initial output level U0 but without exceeding
the supply voltage level of 15V.
In order to suppress the slow parameter changes, i.e. the temperature drift, a high
pass is introduced into the circuit by AC-coupling the circuit, i.e. introducing a
capacity CS. A suitable value for the lower limit of the bandwidth would be
The upper bandwidth limit is to minimize high frequency noise and eliminate any
risk for instability in the amplifier. The design parameter for the upper bandwidth is
the maximal time delay of the sensor to the signal. A fault in one of the current lines
should be detected in less than 3µs. The two upper bandwidth limiting first order
links in the circuitry are C1,R1 and C2,R2. Both act as low pass filters, but only the
one with the lower cut-off frequency will significantly influence the bandwidth limit.
Both RC links can be treated as first-order low pass circuits. The rise time (tr) is the
time for the leading edge of a pulse to rise from 10% to 90% of its final value (Fig.
80) and is the limiting factor for resolving the demanded 3µs.
Fig. 80: Rise time
Chapter 4 Experiments
The rise time is related to the bandwidth by the following approximate equation
Equation (17) 350
r.tBW =
Not only the rise time, but also the time delay of the amplifiers and following signal
processing electronic has to be regarded. Therefore a rise time of about 2µs is
acceptable, leaving a delay of 1µs for appending electronic circuitry. Thus, the
minimal upper bandwidth to resolve 2µs is
=== .
fBW Equation (18)
The desired properties of the sensor electronics (V15, f310Hz, fup175000Hz)
were attained by altering the capacities and resistances according to equation (15) to
equation (18).
Table 7: Resistors, capacitors and properties of the tuned electronic box
As a compromise, values for the
resistors and capacitors were chosen
as below
resulting in new properties for the
sensor electronics as below
R1=100k (unchanged) V=15
C1=6.8pF (unchanged) f1=fup=234051Hz
RS=2k (unchanged) f3=flow=7.96Hz
CS=10µF f2=353677Hz
C2=15pF. tr=1.5µs
These properties promise a tenfold sensitivity and a negligible temperature influence
on the signal. The rise time allows to detect a fault within 1.5µs, the response time
of the Faraday material to a magnetic field is in the high MHz range and is therefore
negligible. A response of the sensor in the range of a few microseconds should
therefore be possible. A complete sensitivity analysis and phase delay measurement
with the changed electronics is done in the following chapters.
Chapter 4 Experiments
4.2.4. Noise
The sensor output has a noise level in the range of about 3mV. This noise arises
from the shot noise of the detector and noise in the detection amplifiers (probably
dominant). The level of noise can be minimized by using low-noise photo detectors
and high-quality operational amplifiers. The noise level however, is not a big
problem for the current fault detection, whereas precise field measurement is only
possible using the averaged waveform measurement function of the oscilloscope.
4.2.5. Characterization of the Sensor Sensitivity
The expected field for the actual application and the following measurements is
much smaller than the previously measured field range of ±57.8mT. Therefore, a
more precise measurement with the tuned circuitry was done for small fields. The
simulation in chapter 3 predicts a field of around 6400A/m for currents of 2000A,
that corresponds to B=8.04mT, which is created in the coil at a current of only
556mA. Fig. 81 and Fig. 82 show the characteristic curves of sensor I and sensor II
for the range of the expected field with the tuned electronic circuitry. In order to get
a signal for the DC characterization of the curve, the AC-coupling capacitor CS was
Characteristic Curve Sensor I
-9,0 -7,0 -5,0 -3,0 -1,0 1,0 3,0 5,0 7,0 9,0
B [m T]
U [mV]
Fig. 81: Characteristic curve Sensor I, small fields
Chapter 4 Experiments
Characteristic Curve Sensor II
-9,0 -7,0 -5,0 -3,0 -1,0 1,0 3,0 5,0 7,0 9,0
B [m T]
U [mV]
Fig. 82: Characteristic curve Sensor II, small fields
The characteristic curve of sensor I shows an almost linear dependency of the
output voltage to the current in the magnetic field. Sensor II exhibits a linear
behaviour in one direction of the magnetic field but a non-linear dependency in the
other direction. This behaviour might be caused by effects related to domain wall
For this smaller range of field, sensitivities as below are measured.
Table 8: Sensitivities measured for small fields
Sensor I (U0=8.231V) Sensor II (U0=4.849V)
Sensitivity [%/mT] 0.212 0.152
Sensitivity [mV/mT] 17.46*7.3517*
* is different for different U0, here given for certain U0
The following sensitivity and validation measurements (chapter 4.3) however, were
made for changing magnetic fields caused by alternating currents. The rms (
quare) value of the AC-coupled signal is measured with an oscilloscope. It is
therefore more accurate to measure the sensitivity of the sensors the same way by
relating the acquired rms signal of the oscilloscope to the rms value of the coil
current. By doing that, influences of hysteresis effects and not perfect sinusoidal
waveforms are reduced. Also the zero-level drift due to the temperature change, that
occurred during the DC measurements, is eliminated. Fig. 83 shows a plot for the
measured points of Sensor I. Each point in the graph resembles the waveform, the
sensor signal gives for a whole cycle.
Chapter 4 Experiments
AC -Sensitivity Senso r I
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00
Brms [mT]
Urms [mV]
Fig. 83: AC Sensitivity for Sensor I
This graph has a linear characteristic. The resulting “AC-sensitivity” is shown in
Table 9.
Table 9: “AC-sensitivities” measured for small fields
Sensor I (U0=7.73V)
Sensitivity [%/mT] 0.209
Sensitivity [mV/mT] 16.14*
* is different for different U0, here given for certain U0
Further tests however, showed that both sensors are not only sensitive to magnetic
fields in the axis of propagation of the light but also in one axis perpendicular to the
axis of light in the plane of the YIG crystal.
Fig. 84: Sensitive axes of the sensor
Chapter 4 Experiments
That is surprising since this behaviour was not expected. In order to characterize
this behaviour, the sensor signal was investigated at different angles to a
homogeneous magnetic field which was created by the coil. First, the sensor was
brought into the magnetic field with its sensitive y-axis perpendicular to the field and
then was rotated around its y-axis with the angle β, Fig. 85.
Fig. 85: Sensitivity test in plane of the film
The resulting curve in a static field of about 2.5mT is shown in Fig. 86.
beta [°]
U [V]
Fig. 86: Measured in-plane sensitivity U(β)
This curve has a sinusoidal characteristic. A small voltage drop with increasing β is
caused by the temperature increase of the coil during the measurement. The
sinusoidal behaviour has similarities to the polarization rotation, a simplified
longitudinal Kerr effect would cause. This effect occurs in reflection of linearly
polarized light on a magnetized surface with the magnetization in the plane of
incidence. The in-plane magnetization results from the rotation of the magnetization
domains in direction of the applied field, compare Fig. 16. The direction of the
rotation changes when the magnetization direction is opposed. This effect is zero at
incident angles of 0° and 90° but the magnitude of the rotational angle of the Kerr
effect for a ferromagnetic material is generally between 10-4 to 10-3 degrees with a
Chapter 4 Experiments
maximum circular rotation at incident angles of about 65° [Mans02]. The transverse
Kerr effect however, does not rotate the polarization, but changes the reflectivity of
the sample and is of lower magnitude.
For comparison, a theoretical calculation of the longitudinal Kerr effect is shown
together with the measured data in Fig. 87.
U(beta) measured and calculated
beta [°]
U [V]
Fig. 87: In-plane sensitivity compared to theoretical longitudinal Kerr effect
The following equation was used to represent the theoretic behaviour of the
longitudinal Kerr effect:
)45)(cos(cos Kerr
= θβII Equation (19)
Where θKerr is the polarization rotation caused by the Kerr effect. The variables
intensity I0, Kerr rotation θKerr and the axis of β have been altered to match the
measured curve. The resulting Kerr rotation θKerr is 0.0029°, which is in the range of
the rotation a longitudinal Kerr effect would have. Higher fields exceeding about
5mT however, result in a more complex non-sinusoidal curve. From this we can say
that a Kerr effect occurring in the interface between the YIG crystal and the gold
layer or, more probably on the “lens side” of the crystal (compare Fig. 71) could be
the cause of these results. A delamination of the epoxy bond, creating a YIG-to-air
interface could also have contributed. Other explanations are possible. Further
investigation of this however, fall outside this work.
This sensitive direction is defined as the z-axis. When the sensor is now fixed in the
orientation Hz
and is rotated around the z-axis with the angle α (Fig. 88), the
sensor only responds to the field part in y-direction exhibiting a sinusoidal graph
with a maximum at y ||
Chapter 4 Experiments
Fig. 88: Rotation with α in a homogenous field
That indicates that the sensor is sensitive in two directions. For the use of these
sensors, it is important to know if both sensitivities superimpose and if the sensitive
axes are perpendicular to each other. That can be done by comparing a theoretical
superimposition of both sensitive axis with experimental measurements.
Therefore the sensitivities in the y-axis (Sy) and in the z-axis (Sz) are measured. Now
a theoretical rotation of the sensor with the angle α from 0° to 180° around the x-
axis (compare Fig. 88) is calculated with following function:
=α zy SSf Equation (20)
This function sums up both components in dependency of α. All measurements
were made at the end of the coil with an alternating current of 50Hz and
Ir.m.s.=300mA corresponding to a field of about 3mT. This proceeding is feasible
since both sensitivities shown sinusoidal characteristics. The measured values for Sy
and Sz are presented in Table 10.
Table 10: Perpendicular sensitivities in sensor I and sensor II (B3mT)
Sy [mV] Sz [mV]
Sensor I 52 70
Sensor II 23 82
Fig. 89 shows the theoretical calculations of sensor I and sensor II with the values
from the table above.
Chapter 4 Experiments
Fig. 89: Theoretical sensitivity curve in dependency on alpha, Sensor I and Sensor II
This theoretical experiment was repeated in praxis rotating the sensor around its x-
axis and measuring marked values such as the maximum response voltage Umax, the
angle for the maximum response αmax, and the angle for zero response α0. It has to
be noted, that these measurements were not very precise because no mechanical
fixation was used.
The theoretical and experimental results in Table 11 however, indicate that both
sensitivities superimpose and the two sensitive axes are perpendicular to each other.
Table 11: Comparison theoretical and experimental results
Sensor I Sensor II
theoretical experimental theoretical experimental
αmax 36,6° 38° 15,7° 18°
α0126,6° 127° 105,7° 105°
Umax 87,2mV 88mV 85,2mV 86mV
Although the sensitivity in the z-axis is greater than the desirable sensitivity in the y-
axis, it will not be used for field measurement since the occurring effect is unknown
and non-linear for fields above around 5mT.
From the characterization results of both sensors it can be concluded that it is
definitely favourable to use sensor I for further experiments and measurements.
Sensor I shows a 40% higher sensitivity in the y-direction and a lower sensitivity in
the z-direction than sensor II. Sensor I also has a more linear characteristic curve
and exhibits less hysteresis and will therefore be used for the following
Chapter 4 Experiments
4.3. Validation of the Simulation Results
The fact that the sensors are sensitive in two perpendicular directions does not
make them unusable as current fault sensors in the proposed geometry between two
parallel conductors.
The geometry of the proposed application with two parallel conductors (compare
chapter 3.) exhibits only magnetic field components in the x- and y-direction, Fig.
90. Only very low fields in the direction of the current (z-axis) are expected between
the two conductor bars. That enables a measurement of only the y-component if the
sensor is oriented in a way so that its sensitive z-axis is parallel to the direction of
the current.
Fig. 90: Sensor and conductor coordinate systems
Proper alignment of the sensor’s z-axis parallel to the direction of the current
enables measurement of the y-component only.
4.3.1. Measurement Set-up
For validation of the simulation results and to confirm the predicted behaviour of
the magnetic field, a measurement set-up similar to a possible industrial application
was built, Fig. 91. A current source with the frequency of 50Hz can be connected to
the ends of both conductors. A non-conducting medium separates the two
conductors by 30mm.
Fig. 91: Set-up with two separated conductors
Chapter 4 Experiments
Instead of two copper bars as simulated in chapter 3, two aluminium bars with the
same cross sectional area of 10·100mm2 and a length of 620mm were used. Because
copper and aluminium have different electrical conductivities, the FEM simulation
was re-run with aluminium as the conductor material. The resulting magnetic field
pattern predicts a similar behaviour to the simulation results with copper as the
conductor material. However, the equalizing effect with the aluminium occurs at
higher frequencies and can be seen in the simulation results in Fig. 92. The lower
electrical conductivity of the aluminium (σAl=3.774·107S/m compared to
σCu=5.998·107S/m) results in smaller eddy currents and a less distinct skin effect that
causes the current concentration in the corners of the conductor. Consequently, the
equalisation effect between the aluminium bars occurs at higher frequencies than for
copper as the conductor material.
Fig. 92: Comparison of the field pattern (Cu vs. Al) obtained by FEM simulation, f=50Hz
Because of its more linear behaviour and greater sensitivity in the y-direction, sensor
I is used to measure the magnetic field pattern. In order to only measure the y-
component of the magnetic field, the second sensitive direction (z-direction) has to
be determined and aligned parallel to the conductors in direction of the current
flow, compare Fig. 90. The magnetic field was measured along the y-axis over the
entire width of the conductor from one side to the other side (from y=-0.5 to y=0.5,
resembling the coordinate system of the simulation). The measured output voltage
of the sensing unit was transferred into a value for the magnetic field strength
according to equation (13).
Chapter 4 Experiments
These conditions of the experimental set-up are similar to those in the simulation,
except that the length of the conductor is not infinite and potential secondary fields
might also influence the current in the conductor or superimpose the field pattern.
Furthermore, the signal will not only be the response to the y-component of the
field and the y-sensitivity of the sensor. There will also be a contribution of fields
and sensitivities in other directions due to a not-perfect alignment.
The so measured magnetic field pattern between two conductors, whereof only one
is carrying a net current, and the simulated magnetic field pattern of two aluminium
conductors is shown in Fig. 93. The current in the conductor is Irms=20A and the
measured voltage Urms is directly translated to a field Hrms. The sensor signal was
measured with an oscilloscope using an averaged cycle-rms value. That was
necessary because the maximum signal (U=1.83V) was within the noise level. The
measured values correspond to the amplitude of the magnetic field strength caused
by a sinusoidal current of Imax=20A.
Fig. 93: Comparison simulated and measured field, two conductors
Fig. 93 clearly shows a similarity of the simulated field pattern and the measured
values. The measured curve indicates an equalizing behaviour in the middle position
as indicated by the simulation. With copper as conductor material or at higher
frequencies, this behaviour would be more distinct, compare Fig. 92.
In order to give the simulation results more significance, a second magnetic field
pattern measurement for the case of a single aluminium conductor (compare Fig.
69) was performed. The measured magnetic field pattern and the simulated field
distribution are shown in Fig. 94.
Chapter 4 Experiments
Fig. 94: Comparison simulated and measured field, one conductor
Again, the measured field pattern reflects the predicted field distribution. A slide
asymmetry in the field pattern can be seen which is due to the not perfectly aligned
z-axis of the sensor to the direction of the current and hence, resulting sensitivity
contributions in opposite directions (positive and negative) at the two edges of the
Fig. 95 shows the magnetic field in the centre position between the conductors
(x=0, y=0) in dependency of the current (fault condition).
Magnetic field between the conductors
10 15 20 25 30 35 40
I [m A]
U [mV]
Fig. 95: Magnetic field dependency on current in one conductor
Chapter 4 Experiments
The field linearly increases with the current in the conductor as predicted by the
The magnitude of the simulated field however, is about 15% lower than that of the
measured field. The reason for this discrepancy has not been determined. A
difference of the calculated and actual field in the coil for sensitivity determination
as well as a temperature difference between the measurements and inaccuracies in
the used measurement devices might have contributed to the difference.
4.3.2. Conclusion of the Simulation and Measured Results
The experiments proved that the simulation is applicable for designing the
conductors an their arrangement, as well as to predict the magnetic field pattern.
The equalizing effect of the magnetic field between the conductors has been
demonstrated. The simulated magnetic field strength is about 15% lower than the
measured values but still gives a good indication of the expected field strength.
The equalization of the field in terms of magnitude, the predicted independency of
the field of frequencies f>100Hz as well as the expected flat frequency response
make the proposed geometry with two parallel conductors advantageous for current
fault measurements.
4.4. Phase Shift Measurements
The time delay of the sensor signal to a change of the current in a conductor is an
essential parameter for this application. Therefore, the phase shift of the sensor
signal to the current in the conductor was measured.
The phase shift measurements were done by comparing the two signals at the
oscilloscope. Channel one shows the sensor signal from the amplifier box. Channel
two is the voltage from a coaxial shunt resistor which is in series with a load (200)
and a low-inductance coil which generates the magnetic field for the sensor. A high-
frequency power source (fmax=10kHz) was used to generate a measurable current.
Due to the high pass that was necessary to AC-couple the signal, a phase shift
occurs at low frequencies. The phase shift measurements were therefore made for
higher frequencies. Fig. 96 shows that the value of the phase shift does not change
with increasing the frequencies higher than 8kHz, thus this value is the time delay of
the sensor to a current fault.
Chapter 4 Experiments
Phase shift
3000 5000 8000 10000
f [Hz]
phase shift [µs]
Fig. 96: Phase shift
Fig. 97 shows the measured curves of the sensor signal and the shunt voltage
imported from the oscilloscope.
Fig. 97: Screen shot of the phase shift (f=10kHz)
The phase delay between the current and the sensor signal was measured to be
tdelay=2.06µs. This agrees reasonably well with the calculated rise time of the
amplifier box of tr=1.5µs. The additional delay may be caused by the photo detector
and the second low pass that was neglected in the bandwidth calculation in chapter
4.2.3. A faster response can be achieved by using faster amplifiers and changing the
Chapter 4 Experiments
4.5. Current Fault Measurements
In this chapter, a provisional parallel conductor geometry is investigated in terms of
magnetic field pattern and applicability for current fault tests. Electronic circuitry is
designed to detect a fault in one of the lines from the analogue sensor signal and
output a digital flag for the corresponding fault. The sensor with appending
evaluation electronics is tested in an IGBT-switched set-up to examine the capability
of the sensor to immediately detect occurring current faults.
4.5.1. Test Conductor Set-up
In order to test the sensors under conditions as close to the actual application as
possible, a set-up for high currents and fast switching IGBTs is build at the electrical
engineering department of KTH within the thesis work of Martin Skoglund
[Skog06]. This set-up will provide currents of up to 180A and will be able to switch
them at frequencies of 200Hz.
In order to test the sensors in this set-up, a different conductor geometry was built
by Martin Skoglund. Two thin copper plates with a half-circular profile are
separated by a thin insulator foil, Fig. 98. This geometry is smaller in dimensions
and promises higher fields.
Fig. 98: Dimensions and arrangement of the conductors
For fault measuring, the sensor is placed in the centre of the circular conductor
4.5.2. Magnetic Field Measurement Results
Since the above mentioned conductor geometry is used in the set-up to detect the
current faults, it has to be investigated in terms of the magnetic field at the sensor
The magnetic field in the middle of the two conductor half-circles can
approximately be calculated by assuming that the field caused in the centre of a half-
circle of one conductor roughly equals half the field in a solenoid with the same
dimensions. The influence of the second conductor is neglected.
Chapter 4 Experiments
The magnetic field in the centre of a finite solenoid with zero winding thickness
calculates as:
µB 0
= Equation (21)
In this case, the number of the windings is N=1, the length of the solenoid is
l=0.02m and I is the current in the solenoid (conductor). That results in a magnetic
field strength in the centre of the half-circle conductor of
= Equation (22)
This value resembles the expected field in the case of failure. In normal working
condition, the field in the centre should be zero due to the axial symmetry of the
The following graph shows the measured values for “fault” and “no fault” as well as
the calculated field for a “fault” using equation (22).
Magnetic field, test set-up
5 10152025303
I [A]
H [A/m]
One conducting
Both conducting
Fig. 99: Magnetic field in test set-up
The results show that the magnetic field for the case of failure is much higher than
for the “no fault” case. The no-failure-field can be even smaller when the sensor is
precisely placed in the centre of the conductors and no second sensitivity axis would
influence the results. It should also be noticed that in the case of a fault, the fault
current will be twice the current of normal working condition. It should therefore
easily be possible to detect a fault by setting the detection threshold between the
expected values. The calculated curve (Fig. 99) gives a good indication of the
expected field.
Chapter 4 Experiments
The placing of the sensor, however, is expected to be more crucial for this
geometry. Fig. 100 shows the magnetic field pattern for an infinitely long straight
copper bar with the cross-section of the actual conductor (1·20mm2).
Fig. 100: Plot and image of Hy of the test-geometry, I=20A
Fig. 100 shows that induced currents and skin effect in this geometry are much
smaller, especially due to the small thickness of the conductor (1mm). These effects
are only significant at frequencies greater than about 1000Hz. It can be concluded
that equation (22) holds to calculate fields up to about 1000Hz since no change in
the magnetic field can be seen for lower frequencies.
4.5.3. Design of the Detection Electronics
In order to interface the sensor signal to the test set-up, the analogue output signal
from the sensor has to be edited. The fault handling logic of the test set-up requires
CMOS level signals of 15V. A digital “high” is to be fed to the logic in each case of
a fault to immediately switch the corresponding IGBT.
Therefore, an electronic circuit was built, Fig. 101. The sensor signal passes through
an amplifier and is then fed to two comparators. This first amplifier was introduced
as an attempt to isolate the input voltage from possible transients caused by
feedback from the comparator output. The used open breadboard construction
however, still caused signal oscillations when the comparators switched. Both
comparators compare the signal to a changeable reference signal. Comparator 1
gives a high output if the signal exceeds a positive reference signal and the output of
comparator 2 goes into the high-state if the signal is lower than the negative
reference signal. Both outputs are fed into an RS flip-flop after passing an necessary
Chapter 4 Experiments
inverter. The RS latch is necessary for the set-up logic to indicate that a failure has
occurred. The latch can be mechanically reset by switch S1 and switch S2.
Fig. 101: Comparator and latch circuit for failure indication
Chapter 4 Experiments
Both comparators have a positive feedback (feedback resistor R2=1M) to limit the
disturbing influence of the noise at reference level. The resulting hysteresis for
comparator 1 (non-inverting hysteresis) is
= Equation (23)
The resulting inverting hysteresis for comparator 2 is
= Equation (24)
These values are well below the expected signal of about U91mV (calculated using
equation (22) Æ H=4500A/m and the sensitivities from Table 9 Æ U91mV) for
the maximal current in the set-up of I=180A .
A screen shot of the output signal of comparator 1 can be seen in Fig. 102.
Fig. 102: Comparator 1 signal with hysteresis (positive feedback)
The reference level was set to U45mV. The measured hysteresis of about
=1.6mV is in the same scale of the calculated hysteresis of 1.5mV.
Chapter 4 Experiments Delay measurement of the detection electronics
The comparator and latching circuit causes an additional time delay to the phase
delay of the sensor with the electronic box (tdelay=2.06µs), compare chapter 4.4. This
additional delay was measured with the oscilloscope giving a step signal to the input
of the circuit and comparing it to the latched output O0, Fig. 103.
Fig. 103: Time delay for comparator and latch circuit (=280ns)
The resulting time delay of the circuit was tcircuit=280ns. The resulting overall delay
of the sensor and appendant comparator and latching circuit is approximately
ttotal=tdelay+tcircuit=2.34µs. That enables the sensor to detect an occurring fault in less
than the demanded 3µs.
Chapter 4 Experiments
4.5.4. Current fault detection
In order to test the sensor in an application-like set-up, the sensor was installed in a
simplified early version of the set-up built by Martin Skoglund. The half-circular
conductor pair with the sensor in the centre was installed in the set-up, Fig. 104.
Fig. 104: Sensor installed in the set-up
This simplified set-up is capable of switching currents of 70A (2·35A in the “no-
fault” condition) at a frequency of 1kHz. Failure handling and triggering from the
fault signal to the IGBT drivers was not possible at the time of the test. Therefore,
only the sensor signal and the latched fault signal can be displayed and investigated.
A simplified schematic of the set-up is shown in Fig. 105.
Fig. 105: Simplified schematic of the set-up
In normal-working condition, both IGBT simultaneously switch 35A each. In case
of a fault, only one IGBT continues switching 70A. The magnetic field at the sensor
in normal-working condition should be close to zero. In case of a fault (one IGBT
is switched off at a random point of time of the switching cycle), the sensor signal is
Chapter 4 Experiments
proportional to the current in the IGBT that continues switching. Fig. 106 shows an
oscilloscope plot of the sensor signal and the latched fault after an induced fault of
one of the IGBTs. The expected sensor signal for a fault current of I=70A with the
sensor between the half-circular conductors is U37.2mV (calculated using equation
(22) Æ H=1750A/m and the measured sensitivity of the sensor). The reference
level for fault detection was therefore set to Uref=±30mV.
Fig. 106: Sensor signal and latch signal in case of current fault (Uref=-30mV)
It can be seen that the sensor signal increases with the magnetic field (current) after
the fault occurs, and latches the fault when the reference voltage is reached. The
time delay of the comparator and latching circuit between the signal reaching the
reference voltage (Uref=-30mV) and the latched signal is, as measured before, 280ns.
Also the rise time of the electronic box seems to agree with the designed value
(designed to be tr=1.5µs).
Only a few test runs were possible, but the sensor with the appending electronics
reliably indicated a fault each time it occurred. Normal-working condition with both
IGBTs switching simultaneously did not trigger the fault latch.
Further tests however, will have to be made with the set-up fully working to
compare the fault signal to the IGBT drivers and the current-signals in both IGBTs
with the sensor signal. Further experiments with a complete set-up however, could
not be made due to time limitations.
Chapter 5 Conclusion
5. Conclusion
It has been shown that the proposed technique employing a high-Faraday rotation
“point sensor” using YIG as sensing material is suitable to detect current faults in a
parallel conductor geometry. The proposed geometry and detection scheme enables
the detection of a current fault in two parallel lines with a single sensor only.
Measurements demonstrate that a fast detection of a fault in under 3µs is possible.
The sensor electronics have been adapted to indicate a fault in either of the lines
and interface a CMOS-level protection circuit.
A FEM simulation showed the favourable influence of the proposed parallel
conductor geometry with intermediate field detection. An equalization of the field in
frequency and distribution was predicted by the simulation and proved by magnetic
field pattern measurements.
First tests with the sensor in an application-similar set-up showed promising results
for fast and reliable current fault detection, even for low fields.
The proposed optical sensor technique is insensitive to electromagnetic interference
and is inherently galvanically insulated. A reliable detection of current faults in high-
EMI and high-voltage environments should therefore be possible using this
6. Outlook
The proposed technique for fault detection has been proved to be applicable in
high-voltage and high-EMI environments. The performance of the tested sensor
however, can be considerably increased.
Different Faraday materials, for example substituted YIGs, can be used to obtain
higher sensitivities and lower temperature dependencies. Hence, the sensor can also
be used in DC-coupling and for static fields. The sensitivity of the device can be
further increased using a magnetic concentrator in the form of a partial iron core.
The sensor can also be used as a “true” current sensor in a small air gap of a
magnetic concentrator completely encircling the conductor.
Optimised electronic amplification circuitry integrated in a printed circuit board and
high-quality light sources and detectors can considerably lower the noise level of the
device. Faster response to the input signal is possible using faster amplifiers and
CMOS logic and a further optimised configuration.
The proposed technique for current fault detection is easily integratable, reliable,
virtually maintenance-free and potentially “low-cost” for high-quantity production.
The presented work was carried out from October 2005 to March 2006 at the
Microsystem Technology (KTH) research group at the Royal Institute of
Technology in Stockholm.
I want especially thank my supervisor at KTH, Ass.-Prof. H. Sohlström, for the
skilled support and fruitful discussions during my work here. Beyond, I want to
thank Kjell Noren for technical support and the entire research group of
Microsystem Technology for making the time in Sweden enjoyable.
I further want to thank Prof. Dr.-Ing. Dr. h.c. H. Wurmus and Dr.-Ing. S. Hecht of
the Technical University of Ilmenau for supervision and for giving me the
possibility to write my thesis at KTH.
I also want to thank Martin Skoglund for the great cooperation during the project as
well as ABB AB, especially Lennart Ängquist, who made the whole project possible.
Special thanks go to my family, who greatly supported me during my entire studies.
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