sensors
Review
Recent Progress of Fluxgate Magnetic Sensors: Basic Research
and Application
Songrui Wei 1 , Xiaoqi Liao 2,3 , Han Zhang 1 , Jianhua Pang 4 and Yan Zhou 5, *
1
2
3
4
5
*
Citation: Wei, S.; Liao, X.; Zhang, H.;
Pang, J.; Zhou, Y. Recent Progress of
Fluxgate Magnetic Sensors: Basic
Research and Application. Sensors
2021, 21, 1500. https://doi.org/
Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, China;
weisongrui@szu.edu.cn (S.W.); hzhang@szu.edu.cn (H.Z.)
College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China;
xiaoqiliao@szu.edu.cn
Ångström Laboratory, Department of Engineering Sciences, Uppsala University, 75121 Uppsala, Sweden
Shenzhen Institute of Guangdong Ocean University, International Biological Valley, Dapeng District,
Shenzhen 518060, China; njpjh@sina.com
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China
Correspondence: zhouyan@cuhk.edu.cn
Abstract: Fluxgate magnetic sensors are especially important in detecting weak magnetic fields. The
mechanism of a fluxgate magnetic sensor is based on Faraday’s law of electromagnetic induction.
The structure of a fluxgate magnetic sensor mainly consists of excitation windings, core and sensing
windings, similar to the structure of a transformer. To date, they have been applied to many fields
such as geophysics and astro-observations, wearable electronic devices and non-destructive testing.
In this review, we report the recent progress in both the basic research and applications of fluxgate
magnetic sensors, especially in the past two years. Regarding the basic research, we focus on the
progress in lowering the noise, better calibration methods and increasing the sensitivity. Concerning
applications, we introduce recent work about fluxgate magnetometers on spacecraft, unmanned
aerial vehicles, wearable electronic devices and defect detection in coiled tubing. Based on the above
work, we hope that we can have a clearer prospect about the future research direction of fluxgate
magnetic sensor.
Keywords: magnetic sensor; fluxgate; noise; sensitivity; calibration
10.3390/s21041500
Academic Editor: Guo-Hua Feng
1. Introduction
Received: 29 December 2020
Accepted: 5 February 2021
Published: 22 February 2021
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4.0/).
Sensors are devices for detecting, collecting and transmitting various kinds of information from the environment. It is the first step of most forms of artificial intelligence
and they play more and more important roles in many fields of industry and daily life.
Among them, magnetic sensors detect magnetic fields and currents and are widely used
in astro-observation, geophysics observation, non-destructive testing and wearable intelligent devices, etc. [1–5]. To date, many types of magnetic sensors based on different
mechanisms have been developed. The magnetic sensors based on fluxgate, Hall effect
and magnetoresistance effect are the most widely investigated [5]. In this review, we will
focus on the recent progress of fluxgate magnetic sensors regarding both basic research
and applications.
Compared with other magnetic sensors, fluxgate magnetic sensors have advantages
such as high sensitivity, high accuracy, high resolution, simple and compact structures, and
low noise [6–14]. What’s more, they can be used in different kinds of environment and
even hostile environments, and they have important applications in weak magnetic field
measurements. The basic structures of parallel and orthogonal fluxgate magnetometers
are schematically shown in Figure 1 [15]. They are mainly composed of three parts: the
magnetizing windings, the sensing windings and the core. The basic working principle
of a fluxgate sensor is about the periodic change of the magnetic permeability of the soft
Sensors 2021, 21, 1500. https://doi.org/10.3390/s21041500
https://www.mdpi.com/journal/sensors
s 2020, 20, x FOR PEER REVIEW
Sensors 2021, 21, 1500
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2 of 18
the magnetizing windings, the sensing windings and the core. The basic working principle of a fluxgate sensor is about the periodic change of the magnetic permeability of the
ferromagnetic
core
by a periodic
The periodic
current in
soft ferromagnetic
core which
is which
drivenisbydriven
a periodic
exciting exciting
current. current.
The periodic
curthe exciting
windings
will induce
a periodic
magnetic
field
the magnetic
rent in the exciting
windings
will induce
a periodic
magnetic
field in
theinmagnetic
core core and this
will
further
induce
a
periodic
current
in
the
sensing
windings.
When
there
and this will further induce a periodic current in the sensing windings. When there is nois no ambient
magnetic
the current
of exciting
the exciting
windings
the sensing
windings matches.
ambient magnetic
field,field,
the current
of the
windings
and and
the sensing
windings
However,
when
the
soft
core
is
exposed
to
an
ambient
magnetic
field,
the
soft core will be
matches. However, when the soft core is exposed to an ambient magnetic field, the soft
more
easily
saturated
in
the
ambient
magnetic
field’s
direction
and
less
easily
core will be more easily saturated in the ambient magnetic field’s direction and less easily saturated in
theopposite
oppositedirection.
direction.InInthis
thiscase,
case,the
thecurrents
currentsofofthe
theexciting
excitingwindings
windingsand
and the sensing
saturated in the
windings
do
not
match.
The
difference
between
the
current
of
exciting
the sensing windings do not match. The difference between the current of exciting wind-windings and
sensing windings are used to estimate the strength of the magnetic field and the output
ings and sensing windings are used to estimate the strength of the magnetic field and the
signal is usually integrated to the form of a voltage. For the orthogonal fluxgate sensor,
output signal is usually integrated to the form of a voltage. For the orthogonal fluxgate
the case is a little different. The noise of orthogonal fluxgate sensor is mainly originated
sensor, the case is a little different. The noise of orthogonal fluxgate sensor is mainly origfrom the domain walls movement. This is the so called Barkhausen noise. To reduce the
inated from the domain walls movement. This is the so called Barkhausen noise. To reduce
noise, a DC excitation current which is sufficiently larger than the AC excitation current is
the noise, a DC excitation current which is sufficiently larger than the AC excitation curapplied to reduce the movement of the domain walls. This describes fundamental mode
rent is applied to reduce the movement of the domain walls. This describes fundamental
orthogonal fluxgates (FM-OFG).
mode orthogonal fluxgates (FM-OFG).
1. Thediagram
schematical
diagram
(a) parallel
fluxgate
magnetic
sensor and fluxgate
(b) orthogonal
Figure 1. TheFigure
schematical
of: (a)
parallelof:
fluxgate
magnetic
sensor
and (b) orthogonal
magnetic sensor.
fluxgate
magnetic
sensor.
The
word
“parallel”
and
“orthogonal”
in
the
name
mean
orientation
The word “parallel” and “orthogonal” in the name mean the orientation between the excitationthe
magnetic
field and the
between the excitation magnetic field and the probed magnetic field. In (a), the excitation magnetic
probed magnetic field. In (a), the excitation magnetic field Hex is parallel to the probed magnetic field Hdc . In (b), the
field Hex is parallel to the probed magnetic field Hdc. In (b), the excitation current is along the axial
excitation current is along the axial direction. So, the excitation magnetic field is around the circle and orthogonal to the
direction. So, the excitation magnetic field is around the circle and orthogonal to the probed field
probed field Hdc . Only the orthogonal fluxgate sensor needs the DC exciting current which should be sufficiently larger
Hdc. Only the orthogonal fluxgate sensor needs the DC exciting current which should be sufficiently
than the AC larger
exciting
current.
than
the AC exciting current.
To date, many kinds of fluxgate sensors have been developed. According to the
To date, many kinds of fluxgate sensors have been developed. According to the oriorientation between the magnetic field of excitation current and target magnetic field,
entation between the magnetic field of excitation current and target magnetic field,
fluxgate sensors can be divided into parallel fluxgate sensors and orthogonal fluxgate
fluxgate sensors can be divided into parallel fluxgate sensors and orthogonal fluxgate sensensors, as shown in Figure 1. They are named after the orientation between the excitation
sors, as shown in Figure 1. They are named after the orientation between the excitation
magnetic field and the probed magnetic field. According to the measured signal, they can be
magnetic field and the probed magnetic field. According to the measured signal, they can
divided into voltage fluxgate sensors and time domain fluxgate sensors. In voltage fluxgate
be divided into voltage fluxgate sensors and time domain fluxgate sensors. In voltage
sensors, the voltage on the sensing windings is measured to estimate the ambient field. In
fluxgate sensors, the voltage on the sensing windings is measured to estimate the ambient
time domain fluxgate sensors, the time difference between the positive and negative signal
field. In time domain fluxgate sensors, the time difference between the positive and negwill be used to estimate the ambient field. The working principle of the voltage fluxgate
ative signal will be used to estimate the ambient field. The working principle of the voltage
sensor is described in the last paragraph. The working principle of the residence timefluxgate sensor
is described
in fluxgate
the last paragraph.
Theisworking
principle
of the
difference
(RTD)
magnetometer
schematically
shown
in residence
Figure 2 [16]. Figure 2a
time-difference
(RTD)
fluxgate
magnetometer
is
schematically
shown
in
Figure
2 [16].
Figis an ideal square hysteresis loop. When there is noexternal magnetic
field,
the relationship
ure 2a is an ideal
square
hysteresis
loop.
When
there
is
noexternal
magnetic
field,
the
re- in Figure 2b.
between the magnetic field and time will be shown as the solid black line
lationship between
theintervals
magneticbetween
field and
will be
as the
solid black
The time
thetime
positive
andshown
negative
saturation
statesline
arein
equal. Namely,
Figure 2b. TheRT
time
intervals
between
the
positive
and
negative
saturation
states
are
equal.
+
−
D = T − T = 0. When an external magnetic field in applied on the magnetic core, the
Namely, RT Dfigure
= T+ −will
T− =be0.lifted
When
magnetic
field
in appliedison
the magnetic
inan
theexternal
H direction
and the
equilibrium
broken
as shown in Figure 2c.
core, the figure
will
be
lifted
in
the
H
direction
and
the
equilibrium
is
broken
as
shown
in 2d.
Under this condition, the time difference is no longer zero as shown in Figure
Sensors 2021, 21, 1500
(more than 1500 prints per hour), fast drying of the motif, mass production, precise layerby-layer printing, and the option of printing on non-flat surfaces [17–19]. The structure of
this review is arranged as follows: Firstly, it is divided into two main parts, covering basic
investigations and applications. In the basic investigation part, recent works about the
noise, calibration method and the sensitivity are discussed. For the application part,
3 ofap18
plications in astro-observation, geographical observation, wearable electronic devices and
non-destructive testing are discussed.
Figure
Schematic diagram
diagramofofthe
theworking
workingprinciple
principle
RTD
fluxgate
magnetometer.
(a) Ideal
Figure 2.
2. Schematic
ofof
RTD
fluxgate
magnetometer.
(a) Ideal
squarehysteresis
hysteresisloop,
loop,(b)
(b)magnetic
magneticinduction
induction intensity
intensity corresponding
corresponding to
to the
the hysteresis
hysteresis loop
loop in
in (a),
square
(a),sinusoidal
(c) sinusoidal
excitation
signal
an RTD
fluxgate
and without
a target
magnetic
(c)
excitation
signal
of anofRTD
fluxgate
withwith
and without
a target
magnetic
field,field,
and (d)
and (d) induced
voltage
signal
from coil
sensing
and awithout
a target magnetic
field.
induced
voltage signal
from
sensing
withcoil
andwith
without
target magnetic
field.
2. Basic
Research
Their
high cost of fabrication has limited the application of fluxgate sensors in more
daily
necessity fields. The recent trend of fluxgate sensors in industry is to reduce the
2.1. Noise
fabrication cost. Many new fabrication methods have been proposed and the pad-printing
Butta et al. investigated the relationship between the noise of an orthogonal fluxgate
technique is one of them. The pad-printing technique is one of the micro-printing techand the composition of the wire-core [20]. The noise of a fundamental mode orthogonal
niques which have the advantages of being fast and simple. The micro-printing technique
fluxgate is usually ascribed to Barkhausen noise [21,22]. The origin of this noise is the moveprovides new features such as flexibility to fluxgate magnetic sensors. Compared with
ment of the domain wall in the alloy wires which make up the core of magnetic sensor. To
other micro-printing techniques, pad-printing has advantages such as high printing rates
date, most works are devoted to eliminating this kind of noise and much progress has been
(more than 1500 prints per hour), fast drying of the motif, mass production, precise layermade. Researchers have applied various methods such as optimizing the geometry to reby-layer printing, and the option of printing on non-flat surfaces [17–19]. The structure
duce the demagnetization and using multiple wires and the Barkhausen noise has thus been
of this review is arranged as follows: Firstly, it is divided into two main parts, covering
reduced to a very low level [23], but the total noise is still in a high level and the origin of
basic investigations and applications. In the basic investigation part, recent works about
the noise,
remaining
noise ismethod
unclear.and
In [20],
Butta et al.are
proposed
that For
the the
remaining
noisepart,
may
the
calibration
the sensitivity
discussed.
application
come
from
the
magnetostriction
of
the
wire.
According
to
the
definition
of
magnetostriction,
applications in astro-observation, geographical observation, wearable electronic devices
on one
hand, when an
external
magnetic field is applied on magnetic materials, there will
and
non-destructive
testing
are discussed.
be a deformation on the direction of the magnetic field. On the other hand, when stress is
applied
on the magnetic material, the magnetization of the material will also be changed. In
2.
Basic Research
2.1. Noise
Butta et al. investigated the relationship between the noise of an orthogonal fluxgate
and the composition of the wire-core [20]. The noise of a fundamental mode orthogonal
fluxgate is usually ascribed to Barkhausen noise [21,22]. The origin of this noise is the
movement of the domain wall in the alloy wires which make up the core of magnetic sensor.
To date, most works are devoted to eliminating this kind of noise and much progress has
been made. Researchers have applied various methods such as optimizing the geometry
to reduce the demagnetization and using multiple wires and the Barkhausen noise has
thus been reduced to a very low level [23], but the total noise is still in a high level and the
origin of the remaining noise is unclear. In [20], Butta et al. proposed that the remaining
noise may come from the magnetostriction of the wire. According to the definition of
magnetostriction, on one hand, when an external magnetic field is applied on magnetic
materials, there will be a deformation on the direction of the magnetic field. On the other
hand, when stress is applied on the magnetic material, the magnetization of the material
will also be changed. In the production process of alloy wires, many kinds of stress are
introduced. What’s more, when the magnetic sensor is working, stress can also be induced
because of the thermal expansion of the wire and the substrate. This means that for a certain
s 2020, 20, x FOR PEER REVIEW
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Sensors 2021, 21, 1500
the
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production process of alloy wires, many kinds of stress are introduced. What’s more,
when the magnetic sensor is working, stress can also be induced because of the thermal
expansion of the wire and the substrate. This means that for a certain magnetic field, there
will be different
magnetizations
in the
wire
to the stress
and magnetostriction.
magnetic
field, there
will
bedue
different
magnetizations
in the wireThe
dueflucto the stress and
tuation of the magnetostriction.
magnetization under
a
constant
external
field,
by
definition,
is
the
noise.
As
The fluctuation of the magnetization under a constant external
field, by
the magnetostriction
is
usually
dependent
on
the
composition
of
the
magnetic
materials,
definition, is the noise. As the magnetostriction is usually dependent on theincomposition of
this work different
compositions
of (Co
Fex)work
75Si15Bdifferent
10 systems
were investigated
which x
the magnetic
materials,
in1−xthis
compositions
of (Co1in
−x Fex )75 Si15 B10 systems
= 0.05, 0.055, 0.06,
0.062,
0.065, 0.07inand
0.08.xIt=is0.05,
found
that the
noise
is really
on It is found
were
investigated
which
0.055,
0.06,
0.062,
0.065,dependent
0.07 and 0.08.
the composition
and
the
noise
reaches
the
minimum
when
x
=
0.06.
At
the
same
time,
the
that the noise is really dependent on the composition and the noise reaches the minimum
magnetostriction
is also
thethe
other
hand, when x = is
0.06,
noise vanishing.
does
when
x = almost
0.06. Atvanishing.
the sameOn
time,
magnetostriction
alsothe
almost
On the
not depend onother
the stress
anymore.
It
means
that
this
part
of
noise
is
strongly
dependent
on
hand, when x = 0.06, the noise does not depend on the stress anymore.
It means
the magnetostriction.
the above
results,
they propose
when annealing,
the on the above
that thisBased
part ofonnoise
is strongly
dependent
on thethat
magnetostriction.
Based
materials should
not be
bend
and the
stress
should
be as the
small
as possible.
That
because
results,
they
propose
that
when
annealing,
materials
should
notisbe
bend and the stress
the magnetostriction
is dependent
the temperature.
Eventhe
materials
without obvious
should be
as small as on
possible.
That is because
magnetostriction
is dependent on the
magnetostriction
effects at room
may still
havemagnetostriction
strong magnetostriction
an- temperature,
temperature.
Eventemperature,
materials without
obvious
effects atatroom
nealing temperature.
may still have strong magnetostriction at annealing temperature.
Song et al. tried
to reduce
the noise
of the
fluxgate
systemsensor
by another
way.
Song
et al. tried
to reduce
the
noise ofsensor
the fluxgate
system
by As
another way. As
the noise on
is dependent
on the input
excitation
current, they
proposed
a method to easily
the noise is dependent
the input excitation
current,
they proposed
a method
to easily
theexcitation
most proper
excitation
current fluxgate
for a specific
fluxgate
sensor
[24]. The considered
find the most find
proper
current
for a specific
sensor
[24]. The
considered
of the
excitation
current
include
IDC and the
frequency.
parameters ofparameters
the excitation
current
include
IAC, IDC
andIAC,
the frequency.
The
excitationThe excitation
which
provides the
excitation
current
mainly
three
parts: the waveform
module whichmodule
provides
the excitation
current
mainly
includes
threeincludes
parts: the
waveform
generator,
the
signal
conditioning
electronics
and
the
voltage
controlled
current source, as
generator, the signal conditioning electronics and the voltage controlled current source,
shown
in
Figure
3.
With
such
a
module,
the
proper
parameters
of
the
excitation
as shown in Figure 3. With such a module, the proper parameters of the excitation current current with
thenoise
lowest
noise
can beobtained.
easily obtained.
they tested
the noise
the corresponding
with the lowest
can
be easily
Finally,Finally,
they tested
the noise
of theofcorresensor
in practical
application.
sponding sensor
in practical
application.
Figure 3.
The structure
of the excitation
modulemodule
which provides
the excitation
current current
in S.X. Song
et Song
al.’s work.
Figure
3. The structure
of the excitation
which provides
the excitation
in S.X.
et al.’s work.
Janosek et al. developed the lowest noise fundamental-mode, orthogonal fluxgate
magnetometer
far [25].
Low noise magnetometers
important in many
Janosek et
al. developedpublished
the lowestsonoise
fundamental-mode,
orthogonalare
fluxgate
fields
such
as
geomagnetic
observatories,
scientific
experiments
in
aerospace,
magnetometer published so far [25]. Low noise magnetometers are important in many nondestructive testing and
evaluation, and
nanoparticle
detection
[26–34]. According
to the structure,
fields such as geomagnetic
observatories,
scientific
experiments
in aerospace,
nondestrucfluxgate
magnetometers
can bedetection
classified[26–34].
into theAccording
parallel type
and
orthogonal type. For
tive testing and
evaluation,
and nanoparticle
to the
structure,
the parallel can
typebefluxgate
magnetometer,
the 1-pT
for 1 Hz cantype.
be only
fluxgate magnetometers
classified
into the parallel
typenoise
and orthogonal
Forobtained with
special
arrangements
and cross
correlation
measurements
[34–39].
On the
other hand, for
the parallel type
fluxgate
magnetometer,
the 1-pT
noise for
1 Hz can be only
obtained
with
the
orthogonal
type,
low
noise
can
be
only
obtained
with
the
fundamental-mode
operated
special arrangements and cross correlation measurements [34–39]. On the other hand, for
fluxgate.
Since
the
discovery
of
the
orthogonal
type
by
Sasada
in
2001
[40],
the
noise
of this
the orthogonal type, low noise can be only obtained with the fundamental-mode operated
kind
of
magnetometer
has
been
continuously
improved.
However,
a
widely
acknowledged
fluxgate. Since the discovery of the orthogonal type by Sasada in 2001 [40], the noise of
disadvantagehas
of orthogonal
type fluxgate
magnetometers
relatively
large offset drift.
this kind of magnetometer
been continuously
improved.
However,isa their
widely
acknowlAlthough
this offset drift
be reduced
in either digital
or relatively
analog domain,
edged disadvantage
of orthogonal
typecan
fluxgate
magnetometers
is their
large in Janosek’s
work,
this
method
is
not
applied
because
it
will
cause
an
increase
of
the
noise.
offset drift. Although this offset drift can be reduced in either digital or analog domain,
in
√
In
Janosek’s
work,
the
noise
for
1
Hz
is
0.75
and
1.5
pT
/
Hz
for
rms
Janosek’s work, this method is not applied because it will cause an increase of the noise. the open loop
andwork,
closedthe
loop,
respectively.
benefitting
from the annealing process of the
In Janosek’s
noise
for 1 Hz is Additionally,
0.75 and 1.5 pT
rms/√Hz for the open loop and
alloy
core,
the
offset
drift
is
also
very
small
(about
2.5
nT/K).
With
such
a good property,
closed loop, respectively. Additionally, benefitting from the annealing process
of the
alloy
the developed fluxgate magnetometer has many promising applications. For example,
core, the offset drift is also very small (about 2.5 nT/K). With such a good property, the
compared to a low-noise observatory magnetometer, it is found that it has good performance at mHz frequency and is suitable for the measurement such as magnetotellurics. It
can be also used in magnetocardiography (MCG) measurement. Benefitting from the low
noise and offset drift, MCG measurements can be performed under room temperature and
Sensors 2020, 20, x FOR PEER REVIEW
Sensors 2021, 21, 1500
5 of 18
developed fluxgate magnetometer has many promising applications. For example, compared to a low-noise observatory magnetometer, it is found that it has good performance
5 of 18
at mHz frequency and is suitable for the measurement such as magnetotellurics. It can be
also used in magnetocardiography (MCG) measurement. Benefitting from the low noise
and offset drift, MCG measurements can be performed under room temperature and
without
withoutshielding
shieldingand
andaveraging.
averaging.The
Thearrangement
arrangementofofthe
theMCG
MCGmeasurement
measurementisisshown
showninin
Figure
4
[25].
Figure 4 [25].
Figure4.4.The
Theschematic
schematicdiagram
diagramofofMCG
MCGmeasurements
measurementsbased
basedononfluxgate
fluxgatemagnetometers.
magnetometers.
Figure
2.2.
2.2.Errors
Errorsand
andCalibration
CalibrationMethods
Methods
For
tri-axis
orthogonal
For tri-axis orthogonalfluxgate
fluxgatemagnetometers,
magnetometers,there
thereare
arethree
threekinds
kindsofofinevitable
inevitable
errors
because
of
the
limitation
of
manufacture
technology:
zero
position
errors because of the limitation of manufacture technology: zero positionerror,
error,sensitivity
sensitivity
error
zero position
position error,
error, itit means
meansthe
theoutput
outputofofthe
themagnemagerrorand
andorthogonal
orthogonalerror.
error. For
For the
the zero
netometer
notzero
zero
under
a zero
magnetic
field.
If we
only
consider
effect
of core
tometer isisnot
under
a zero
magnetic
field.
If we
only
consider
the the
effect
of core
remremanence
circuit
drift,
relationship
between
the output
a real
magnetometer,
anence andand
circuit
drift,
the the
relationship
between
the output
of a of
real
magnetometer,
ideal
ideal
magnetometer
position
canwritten
be written
magnetometer
and and
zerozero
position
errorerror
termterm
can be
as: as:


 
 
𝐵Bx0
Bx1 𝐵
Bx 𝐵
 By1  𝐵
(1)
=  =By 𝐵 ++ 𝐵By0 , ,
(1)
𝐵Bz0
𝐵
Bz 𝐵
Bz1
in the above equation, Bx1, By1 and Bz1 are real output. Bx, By, and Bz are ideal output. Bx0,
in the above equation, Bx1 , By1 and Bz1 are real output. Bx , By , and Bz are ideal output. Bx0 ,
y0 and Bz0 are the zero position error terms and they can be obtained by the output of the
BB
y0 and Bz0 are the zero position error terms and they can be obtained by the output of the
magnetometer
whenthere
thereisisno
nomagnetic
magneticfield.
field.The
Thesensitivity
sensitivityerror
errorisisoriginated
originatedfrom
fromthe
the
magnetometer when
difference
between
the
sensitivity
of
the
three
coordinate
axes.
The
relationship
between
difference between the sensitivity of the three coordinate axes. The relationship between
thereal
realoutput,
output,ideal
idealoutput
outputand
andthe
thesensitivity
sensitivityofofthree
threeaxes
axescan
canbebewritten
writtenas:as:
the
𝐾
0
0 𝐵 

𝐵 
Bx1 𝐵
=Kx 0 0 𝐾 0 0 𝐵Bx ,
(2)
 By1  =  0 Ky 0  By ,
(2)
𝐵
0
0 𝐾 𝐵
0
0 Kz
Bz
Bz1
in the above equation, Bx1, By1 and Bz1 are the real output. Bx, By, and Bz are the ideal output.
inKxthe
Bx1 , By1 and
are
theyreal
Bx ,respectively.
By , and Bz are
, Kyabove
, and Kequation,
z are the sensitivities
of B
the
axis,
axisoutput.
and z axis,
In the
idealideal
case,
z1 x
output.
,K
and
Kzorthogonal
are the sensitivities
of the x axis,
y axis
and z axis,between
respectively.
In
Kx = Ky K=xK
z =
The
error is originated
from
the mismatch
the ideal
y , 1.
ideal
case,
K
=
K
=
K
=
1.
The
orthogonal
error
is
originated
from
the
mismatch
between
z
coordinate xand yreal coordinate
or the relationship between the real coordinates are not
the
idealorthogonal.
coordinate and
real coordinate
the relationship
the
real
coordinates
exactly
As above,
if the angleorbetween
the ideal between
coordinate
and
real
coordinate
are
not
exactly
orthogonal.
As
above,
if
the
angle
between
the
ideal
coordinate
and real
is as shown in Figure 5 [41], the relationship between the real output and ideal output
can
coordinate
as shown in Figure 5 [41], the relationship between the real output and ideal
be writtenisas:
output can be written as:
cos 𝛼 cos 𝛼 cos 𝛼 𝐵
𝐵

𝐵 


=coscos
(3)
Bx1
α x 𝛽 coscos
αy 𝛽 coscos
αz 𝛽 𝐵Bx ,
𝛾
cos
𝛾
cos
𝛾
𝐵
 By1  𝐵=  coscos



(3)
β x cos β y cos β z
By ,
cos
γ
cos
γ
cos
γ
B
B
x
y
z
z
z1
in ideal case, αx = βy = γz = 0, αy = αz = βx = βz = γx = γy = 90°. If we consider a fluxgate
gradiometer which is composed of two identical fluxgate magnetometers, an additional
in ideal case, αx = βy = γz = 0, αy = αz = βx = βz = γx = γy = 90◦ . If we consider a fluxgate
gradiometer which is composed of two identical fluxgate magnetometers, an additional
error term will occur which is originated from the inconsistent placement of two fluxgate
magnetometers. It is named the position error for the fluxgate gradiometer and the form of
the expression is same to the orthogonal error.
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error term will occur which is originated from the inconsistent placement of two fluxgate
magnetometers. It is named the position error for the fluxgate gradiometer and the form
of the expression is same to the orthogonal error.
Figure5.5.The
Thedifference
differencebetween
betweenideal
idealcoordinate
coordinate(a)
(a)and
andreal
realcoordinate
coordinate(b)
(b)about
aboutthe
theorthogonal
orthogonal
Figure
error.
The
a-b-c
coordinate
system
is
the
reference
coordinate.
Under
ideal
condition,
theoutput
output
error. The a-b-c coordinate system is the reference coordinate. Under ideal condition, the
coordinate
system
coincides
with
the
reference
coordinate,
as
shown
in
Figure
4a.
However,
under
coordinate system coincides with the reference coordinate, as shown in Figure 4a. However, under
real condition, there will be a deviation as shown in Figure 4b. For Equation (3), αx, βy and γz are the
real condition, there will be a deviation as shown in Figure 4b. For Equation (3), αx , βy and γz are the
angle between x and x1, y and y1, z and z1, respectively. Accordingly, αy, αz, βx, βz, γx, and γy are the
angle between x and x1 , y and y1 , z and z1 , respectively. Accordingly, αy , αz , βx , βz , γx , and γy are the
angle between x and y1, x and z1, y and x1, y and z1, z and x1, z and y1, respectively.
angle between x and y1 , x and z1 , y and x1 , y and z1 , z and x1 , z and y1 , respectively.
In Xu et al.’s work, the effect of sensitivity error, orthogonal error and position error
In Xu et al.’s work, the effect of sensitivity error, orthogonal error and position error
are considered together in one matrix A and the zero position error is considered in anare considered together in one matrix A and the zero position error is considered in another
other term B0. So, the total effect of these error terms can be written as:
term B0 . So, the total effect of these error terms can be written as:
𝑩𝟏 = 𝑨 ⋅ 𝑩 + 𝑩 𝟎 ,
(4)
B1 = A · B + B0 ,
(4)
𝑎
𝑎
𝑎
𝐵
𝐵
𝐵








𝑎 a12𝑎 a,13𝑩 = 𝐵 , 𝑩B𝟎 x= 𝐵 .
Bx0
where 𝑩𝟏 = 𝐵Bx1 , 𝑨 = 𝑎 a11
𝑎 a22𝑎 a23 , B𝐵=  By ,𝐵B0 =  By0 .
where B1 =  𝐵By1 , A =𝑎 a21
a31 a32 a33
Bz
Bz0
Bz1
With this method, the calibration is quick and accurate.
The coefficients
A and B0 can
With this method, the calibration is quick and accurate. The coefficients A and B0 can
be obtained by the method of undetermined coefficients after several measurements. At
be obtained by the method of undetermined coefficients after several measurements. At
the end of the paper, this calibration method is performed in experiments. For a single
the end of the paper, this calibration method is performed in experiments. For a single
three-component magnetometer, the maximum deviation can be reduced from 552.4 nT
three-component magnetometer, the maximum deviation can be reduced from 552.4 nT
to 15.0 nT with this calibration method. For the fluxgate gradiometer which is composed
to 15.0 nT with this calibration method. For the fluxgate gradiometer which is composed
of two similar magnetometers, the maximum deviation can be reduced from 3891.5 nT to
of two similar magnetometers, the maximum deviation can be reduced from 3891.5 nT to
37.2nT
nTwith
withthis
thiscalibration
calibrationmethod.
method.
37.2
Pan
et
al.
provided
a
new
calibrationmethod
methodfor
fortriaxial
triaxialfluxgate
fluxgatemagnetometers
magnetometers
Pan et al. provided a new calibration
(TFMs)
which
combines
a
magnetic
shielding
room
(MSR)
and
a
triaxial
uniform
magnetic
(TFMs) which combines a magnetic shielding room (MSR) and a triaxial uniform magnetic
fieldcoil
coil(TUMC)
(TUMC)[42].
[42]. As
As described
described above,
above, the
the TFM
TFM has
hasthree
threeintrinsic
intrinsicerrors.
errors. To
Todate,
date,
field
two
kinds
of
calibration
methods
are
proposed.
The
vector
calibration
method
uses
two kinds of calibration methods are proposed. The vector calibration method uses aa
knownvector
vectormagnetic
magneticfield
field
reference
its accuracy
is strongly
dependent
on
known
asas
thethe
reference
andand
its accuracy
is strongly
dependent
on the
the
accuracy
of
the
known
magnetic
field
[43].
However,
the
disturbance
of
the
environaccuracy of the known magnetic field [43]. However, the disturbance of the environmental
mental magnetic
and the inaccuracy
of thecannot
turntable
cannot
pursuit of
magnetic
field andfield
the inaccuracy
of the turntable
support
thesupport
pursuit the
of calibration
calibration
of fluxgate magnetometers,
so another
method,
the scalar
calibration
method
of
fluxgate magnetometers,
so another method,
the scalar
calibration
method
is proposed,
is proposed,
whose
accuracy
is noton
dependent
on information.
the attitude information.
concept
whose
accuracy
is not
dependent
the attitude
The conceptThe
of the
scalarof
the scalar calibration
wasasproposed
as early
the 1970s.
idealthe
conditions,
calibration
method wasmethod
proposed
early as the
1970s.asUnder
ideal Under
conditions,
form of
theTFM
formoutput
of the TFM
output
should besurface.
a spherical
surface.
due to of
thethe
existence
the
should
be a spherical
However,
dueHowever,
to the existence
above
of
the
above
three
errors,
the
form
of
the
TFM
output
will
change
from
a
sphere
to an
three errors, the form of the TFM output will change from a sphere to an ellipsoid. Based
ellipsoid.
Based
onellipsoid,
the shapethe
of the
ellipsoid, the
magnetometer
on
the shape
of the
magnetometer
can
be calibrated can
[44].be calibrated [44].
Inpractical
practicalcalibration,
calibration,the
theaccuracy
accuracymay
maybe
beaffected
affectedby
bythe
theenvironmental
environmentalmagnetic
magnetic
In
field[45,46]
[45,46]and
andthe
theintrinsic
intrinsicmagnetic
magnetic
impurities
turntable
[47,48]
if the
turntable
field
impurities
in in
thethe
turntable
[47,48]
if the
turntable
is
is used
to tune
attitude
of the
magnetic
problem
ofenvironmental
the environmental
magused
to tune
the the
attitude
of the
magnetic
field.field.
The The
problem
of the
magnetic
neticisfield
is more
and more
serious
widely
used
electronic
devices.ToTosolve
solvethis
this
field
more
and more
serious
withwith
the the
widely
used
electronic
devices.
problem,ininthis
thiswork,
work,the
theMSR
MSRisisused.
used.On
Onthe
theother
otherhand,
hand,in
insome
someearly
earlyworks,
works,to
toreduce
reduce
problem,
the
themagnetic
magneticfield
fieldwhich
whichisisoriginated
originatedfrom
fromthe
thepower
powersystem
systemofofthe
theturntable,
turntable,they
theyuse
useaa
manual method to rotate the turntable, but in this way, another problem about the time
evolution of the magnetic field emerges because it usually takes more time to tune the
turntable manually. To solve this problem, a standard TUMC is used. In Pan’s work,
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manual method to rotate the turntable, but in this way, another problem about the time
manual method to rotate the turntable, but in this way, another problem about the time
evolution of the magnetic field emerges because it usually takes more time to tune the
evolution of the magnetic field emerges because it usually takes more time to tune the
turntable manually. To solve this problem, a standard TUMC is used. In Pan’s work,
turntable
manually. To solve
this problem,
a standardand
TUMC isSecondly,
used. In Pan’s
work,
firstly,
firstly,they
theyconstructed
constructedthe
theerror
errormodel
modelofofthe
theTUMC
TUMC andTFM.
TFM. Secondly,the
themagnetic
magnetic
firstly,
they
constructed
the
error
model
of
the
TUMC
and
TFM.
Secondly,
the
magnetic
environmental
environmentalnoise
noisemodel
modelofofMSR
MSRisisadded.
added.The
Themost
mostimportant
importantpart
partofofthis
thiswork
workisisthe
the
environmental
noise model
ofdisturbance
MSR is added.
The and
mostthe
important
part
ofcharacteristics
this work is the
analysis
of
the
magnetic
field
in
MSR
magnetic
field
analysis of the magnetic field disturbance in MSR and the magnetic field characteristicsofof
analysis
ofMSR.
the magnetic field
disturbance performed
in MSR and the itmagnetic
field characteristics
of
TUMC
TUMCin
in MSR.Finally,
Finally,experiments
experimentsare
are performedand
and itisisproved
provedthat
thatthis
thiscalibration
calibration
TUMC
inhas
MSR.
Finally,
experiments
are performed
and itdiagram
is proved
that
this
calibration
method
high
sensitivity
and
accuracy.
The
schematic
and
the
experimental
method has high sensitivity and accuracy. The schematic diagram and the experimental
method
has high
sensitivity andinaccuracy.
The schematic
diagram and the experimental
picture
pictureofofthis
thismethod
methodisisshown
shown inFigures
Figures66and
and7,7,respectively
respectively[42].
[42].
picture of this method is shown in Figures 6 and 7, respectively [42].
Figure6.6.Schematic
Schematicdiagram
diagramofofthe
thecalibration
calibrationmethod
methodofofTFMs
TFMsbased
basedon
onMSR
MSRand
andTUMC.
TUMC.
Figure
Figure
6. Schematic diagram
of the calibration
method of
TFMs based
on MSR
and TUMC.
Figure 7. Experimental picture of the device for calibration of TFMs with MSR and TUMC: (a) Test platform; (b) CalibraFigure 7.
7. Experimental
Experimental picture
and
TUMC:
(a)(a)
Test
platform;
(b)(b)
Calibration
Figure
picture of
of the
thedevice
devicefor
forcalibration
calibrationofofTFMs
TFMswith
withMSR
MSR
and
TUMC:
Test
platform;
Calibration of TUMC; (c) Calibration of TFM.
of TUMC;
(c) Calibration
of TFM.
tion
of TUMC;
(c) Calibration
of TFM.
2.3.Sensitivity
Sensitivityand
andOther
OtherRelated
RelatedResearch
ResearchWorks
Works
2.3.
2.3.
Sensitivity and
Other Related
Research Works
Sensitivityisisaacore
coreproperty
propertyofofsensors.
sensors.For
Forfluxgate
fluxgatemagnetometers,
magnetometers,ititisisusually
usually
Sensitivity
Sensitivity is a core property of sensors. For fluxgate magnetometers, it is usually
expressed
as
the
change
of
an
output
such
as
voltage
or
time
difference
per
ambient
field.
expressed as the change of an output such as voltage or time difference per ambient field.
expressed as the change of an output such as voltage or time difference per ambient field.
Szewczyk et al. tried to increase the sensitivity of fluxgate sensors produced by the printed
circuit board method [15]. The printed circuit board method is proposed to solve the
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Szewczyk et al. tried to increase the sensitivity of fluxgate sensors produced by the printed
circuit board method [15]. The printed circuit board method is proposed to solve the probproblem
of the
high
traditional
fluxgatesensors.
sensors.The
Thehigh
highcost
cost of
of traditional
lem of the
high
costcost
of of
traditional
fluxgate
traditional fluxgate
fluxgate
sensors
is
due
to
the
large
amount
of
manual
work
involved
in
their
sensors is due to the large amount of manual work involved in theirproduction,
production,so
sothe
the
printed
circuit
board
method
can
reduce
the
cost
of
fluxgate
sensors
efficiently,
but
at
printed circuit board method can reduce the cost of fluxgate sensors efficiently, but atthe
the
same
same time,
time, the
the sensitivity
sensitivity of
of fluxgate
fluxgatemagnetometers
magnetometers based
based on
on printed
printed circuit
circuitboards
boardsisis
strongly
[49]. In
In[15],
[15],the
theauthors
authors
investigated
feasibility
of increasing
the
strongly reduced
reduced [49].
investigated
thethe
feasibility
of increasing
the sensensitivity
by lengthening
using
a magnetic
concentrator
based
onfinite
the
sitivity by lengthening
the the
corecore
andand
using
a magnetic
flux flux
concentrator
based
on the
finite element method and open-source software. The magnetic flux concentrator has
element method and open-source software. The magnetic flux concentrator has been apbeen applied in many other magnetic sensors to increase the sensitivity [50,51]. Generally
plied in many other magnetic sensors to increase the sensitivity [50,51]. Generally speakspeaking, it increases the sensitivity by decreasing the demagnetization field. However, the
ing, it increases the sensitivity by decreasing the demagnetization field. However, the perperformance of magnetic flux concentrators based on thin layer fluxgate sensors has never
formance of magnetic flux concentrators based on thin layer fluxgate sensors has never
been discussed. In this work, it is found that a longer core will effectively increase the sensibeen discussed. In this work, it is found that a longer core will effectively increase the
tivity but the effect of the magnetic flux concentrator is very weak, so it is not recommended
sensitivity but the effect of the magnetic flux concentrator is very weak, so it is not recomto use a magnetic flux concentrator in a printed circuit board-based fluxgate magnetometer.
mended to use a magnetic flux concentrator in a printed circuit board-based fluxgate magTo increase the sensitivity of a RTD fluxgate magnetometer, Chen et al. built a sennetometer.
sitivity model for RTD fluxgate magnetometers [16]. The model is clear and simple and
To increase the sensitivity of a RTD fluxgate magnetometer, Chen et al. built a sensican discuss the sensitivity of the RTD fluxgate and the coercivity of the magnetic core
tivity model for RTD fluxgate magnetometers [16]. The model is clear and simple and can
separately. When the excitation current is sinusoidal, the sensitivity of the RTD fluxgate
discusscan
thebesensitivity
RTD fluxgate
and the
coercivity
theas
magnetic
core sepasensor
written as of
thethe
function
of coercivity
of the
magneticofcore
well as amplitude
rately.
When
the
excitation
current
is
sinusoidal,
the
sensitivity
of
the
RTD
fluxgate
sensor
and frequency of the driving field, as shown in Equation (5) [52]:
can be written as the function of coercivity of the magnetic core as well as amplitude and


frequency of the driving field, as shown in Equation (5) [52]:
1
1

∂RTD
2
Hem
Hem

r
r
S=
+
(5)
= 

2
2 ,
∂Hx 𝑆 =ω
=1 − Hc + Hx
+ 1 − Hc − ,Hx
(5)
Hem
Hem
as the
thecoercivity
coercivityofofthe
thecore
coreisisdependent
dependent
driving
condition
However, as
onon
thethe
driving
condition
andand
the
the
relationship
between
them
is
unknown,
it
is
difficult
to
calculate
the
sensitivity
with
relationship between them is unknown, it is difficult to calculate the sensitivity with EquaEquation
(5). What’s
more,
sensitivity
also
dependenton
onthe
thetarget
target magnetic
magnetic field
tion (5). What’s
more,
thethe
sensitivity
is is
also
dependent
field as
as
shown
in
Figure
8
[16].
It
can
be
seen
that
only
under
low
target
magnetic
field
conditions,
shown in Figure 8 [16]. It can be seen that only under low target magnetic field conditions,
the
the sensitivity
sensitivity isis nearly
nearly uniform
uniform (within
(within ±± 1000
1000 nT),
nT), so
so the
the sensor
sensor can
can only
onlyaccurately
accurately
measure
measure low
lowfields
fields[53].
[53].In
InSzewczyk’s
Szewczyk’swork,
work,they
theydeduced
deducedthe
theexpression
expressionof
ofsensitivity
sensitivity
under
under sinusoidal
sinusoidal excitation
excitation from
from the
theexpression
expressionof
ofsensitivity
sensitivityunder
undertrilinear
trilinearexcitation
excitation
and
tried
to
calculate
the
differential
permeability
µd
more
accurately.
Finally,
and tried to calculate the differential permeability µd more accurately. Finally,the
themodel
model
isis verified
verified by
byexperiments.
experiments. This
This work
work separates
separates the
the investigation
investigation of
of sensitivity
sensitivity of
of RTD
RTD
fluxgates
fluxgatesand
andcoercivity
coercivityof
ofthe
themagnetic
magneticcore.
core.ItItalso
alsooffers
offersaaplatform
platformto
tofurther
furtherinvestigate
investigate
the
thestructure
structureof
ofRTD
RTDfluxgate
fluxgatemagnetic
magneticsensors.
sensors.
Figure8.8.Relationship
Relationshipbetween
betweensensitivity
sensitivityof
ofRTD
RTDfluxgate
fluxgatemagnetometer
magnetometerand
andtarget
targetmagnetic
magneticfield.
Figure
field. Because
this relationship,
thefluxgate
RTD fluxgate
magnetometer
canbeonly
be applied
in detectBecause
of thisof
relationship,
the RTD
magnetometer
can only
applied
in detecting
weak
ing
weak
magnetic
field.
magnetic field.
Yang et al. proposed a time domain method to measure current [54]. It is a bidirectionally saturated fluxgate based on open-loop self-oscillating technology. The advantage
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Yang et al. proposed a time domain method to measure current [54]. It is a bidirectionally saturated fluxgate based on open-loop self-oscillating technology. The advantage
of this method is that there is no time delay because the current is estimated by the time
of
this method
is that
no time and
delay
currentofisthe
estimated
by To
theobtain
time
difference
between
thethere
first is
half-cycle
thebecause
second the
half-cycle
excitation.
difference
between
the
first
half-cycle
and
the
second
half-cycle
of
the
excitation.
To
obtain
a better temperature stability, the authors used a nanocrystalline alloy core. Finally, the
aperformance
better temperature
stability,
authorsby
used
a nanocrystalline
alloy core. such
Finally,
the
of the method
is the
confirmed
experiments
and the properties
as lineperformance
of
the
method
is
confirmed
by
experiments
and
the
properties
such
as
linearity
arity and sensitivity are discussed. Ramasamy et al. characterized the superconducting
and
sensitivity
are discussed.
Ramasamy et al.
characterized
the superconducting
quantum
quantum
interfere
device (SQUID)-based
time
domain electromagnetic
(TDEM)
system
interfere
(SQUID)-based
time
domain
electromagnetic
(TDEM)
system
It is
[55]. It is device
found that
the early time
of the
fluxgate
magnetometer
behaves
like a [55].
combinafound
that
the
early
time
of
the
fluxgate
magnetometer
behaves
like
a
combination
tion of induction coil and magnetic field sensor. However, at later times, it behaves likeofa
induction
coil and
pure magnetic
fieldmagnetic
sensor. field sensor. However, at later times, it behaves like a pure
magnetic field sensor.
3. Applications
3. Applications
Because of their high sensitivity and resolution, fluxgate magnetic sensors are widely
Because of their high sensitivity and resolution, fluxgate magnetic sensors are widely
used in geophysics and astro-observations. Recently, China’s first Mars mission Tianwen-1
used in geophysics and astro-observations. Recently, China’s first Mars mission Tianwen-1
and NASA’s spacecraft Juno both used fluxgate sensors to detect the magnetic field on Mars
and NASA’s spacecraft Juno both used fluxgate sensors to detect the magnetic field on
and Jupiter.
The unmanned
aerialaerial
vehicles
are also
as theasnew
carrier
to perform
such
Mars
and Jupiter.
The unmanned
vehicles
are used
also used
the new
carrier
to perform
detections
about
Earth’s
magnetic
field
apart
from
the
traditional
carriers
such
as
a
helicopsuch detections about Earth’s magnetic field apart from the traditional carriers such as a
ter aeromagnetic
surveyssurveys
or a ground
magnetic
surveys.surveys.
helicopter
aeromagnetic
or a ground
magnetic
3.1. Astro
Astro Observation
Observation
3.1.
Recently,China’s
China’sfirst
firstMars
Marsmission
missionTianwen-1
Tianwen-1was
waslunched
lunched and
and Mars
Mars Orbiter
Orbiter MagneMagneRecently,
tometer
(MOMAG)
is
one
of
the
seven
scientific
payloads
on
it.
The
project
is
performed
by
tometer
one of the seven scientific payloads on it. The project is performed
a team
from
Chinese
Environment of
of
by
a team
from
ChineseAcademy
AcademyofofSciences
SciencesKey
Key Laboratory
Laboratory of Geospace Environment
University of
of Science
Science and
and Technology
Technologyof
ofChina
China[56].
[56].The
TheMOMAG
MOMAGincludes
includestwo
twoseparate
separate
University
fluxgate sensors which
inin
Figure
9 [56].
TheThe
dual
magnetomfluxgate
whichare
arefixed
fixedon
onaaboom
boomasasshown
shown
Figure
9 [56].
dual
magneeter structure
is designed
to eliminate
the the
interference
of the
magnetic
field
induced
by the
tometer
structure
is designed
to eliminate
interference
of the
magnetic
field
induced
by
orbiter.
Considering
thatthat
the distance
between
the two
(about
0.9 m)0.9
is much
the
orbiter.
Considering
the distance
between
the magnetometers
two magnetometers
(about
m) is
much
smaller
compared
with
theofsize
of Mars’s
magnetosphere,
the difference
of the
smaller
compared
with the
size
Mars’s
magnetosphere,
so the so
difference
of the results
results
between
themagnetometers
two magnetometers
be assumed
be solely
to the
orbiter
between
the two
can becan
assumed
to betosolely
due due
to the
orbiter
andand
the
the
corresponding
noise.
In this
the magnetic
the orbiter
canseparated
be separated
corresponding
noise.
In this
way,way,
the magnetic
fieldfield
fromfrom
the orbiter
can be
from
from
the total
magnetic
method
is firstly
developed
in the
Venus
Express
project
the total
magnetic
field.field.
ThisThis
method
is firstly
developed
in the
Venus
Express
project
in
in
2006.
2006.
Figure 9.
9. The
The schematic
Orbiter
Figure
schematic diagram
diagram of
ofTianwen-1
Tianwen-1Mars
Marsorbiter
orbiterand
andthe
thedual-structure
dual-structureMars
Mars
Orbiter
Magnetometer
on
it.
Magnetometer on it.
has been
been found
found that
that there
there isisno
noglobal
globalmagnetic
magnetic field
fieldon
onMars
Marsby
bythe
theMars
MarsGlobal
Global
ItIt has
Surveyor (MGS)
(MGS) Mission
Mission in
in1998,
1998,but
buttwo
twoother
otherkinds
kindsof
ofmagnetic
magneticfield
fieldstill
stillexist.
exist.They
Theyare
are
Surveyor
the magnetosphere
magnetosphere produced
produced by
bythe
thesolar
solarwind
windand
andthe
thelocal
localstrong
strongmagnetic
magneticcrustal
crustalfield
field
the
near the southern highlands of Mars. The most important mission of MOMAG is to measure
the vector magnetic field of the two sources and the interaction between them. The solar
Sensors 2021, 21, 1500
the vector magnetic field of the two sources and the interaction between them. The solar
wind is a cluster of plasmas running under supersonic speed. It carries the interplanetary
magnetic field (IMF) with it. As it cannot pass through Mars, it leaves a magnetosphere
around the Mars with the frozen-in IMF. The structure of the magnetosphere is shown in
Figure 10 [56]. It mainly includes the bow shock, magnetosheath, magnetic pileup boundary
10 of 18
(MPB) and the ionosphere or photoelectron boundary (PEB). The bow shock is the outermost part of magnetosphere. The solar wind transitions from supersonic to subsonic when
it passes through the bow shock. The layer inside the bow shock is the hotter, denser, more
turbulent
magnetosheath
and
the MPB
is the
lower boundary
magnetosheath.
The layer
wind
is a cluster
of plasmas
running
under
supersonic
speed. of
It carries
the interplanetary
magnetic
(IMF) with is
it.the
AsPEB.
it cannot
pass
through
it leaves a magnetosphere
inside thefield
magnetosheath
It is the
critical
partMars,
of magnetosphere
of Mars which
around
thethe
Mars
thefrom
frozen-in
IMF.
Theand
structure
ofmostly
the magnetosphere
shown
separates
ionswith
mostly
the solar
wind
the ions
from Mars. Onisthe
night
in
Figure
It mainly
includes
bow shock,
magnetic
pileup
side,
there10
is [56].
a magnetic
tail. About
thethe
magnetic
crustalmagnetosheath,
field near the southern
highlands,
boundary
(MPB)
thestronger
ionosphere
(PEB).
The abow
shock
we know that
it isand
much
than or
thephotoelectron
magnetic fieldboundary
of the Earth.
It forms
small
local
ismagnetosphere
the outermostand
partstrongly
of magnetosphere.
The solar
wind
transitions
from
supersonic
to
affects the magnetic
field
from
solar winds
at lower
altitude.
subsonic
whenit itcan
passes
through
the bow
shock.
layer inside
the bow shock
is parthe
On one hand,
protect
the planet
surface
fromThe
the damage
of electrically
charged
hotter,
more
magnetosheath
and the
is theflux
lower
of
ticles indenser,
universe.
On turbulent
the other hand,
it can also shield
the MPB
ion escape
nearboundary
the southern
magnetosheath.
The layer inside the magnetosheath is the PEB. It is the critical part of
highlands.
magnetosphere
of Mars
which separates
theperform
ions mostly
frommeasurement,
the solar wind
andneed
the ions
As the fluxgate
magnetometers
do not
absolute
they
to be
mostly
from
Mars.
On
the
night
side,
there
is
a
magnetic
tail.
About
the
magnetic
calibrated both on Earth and in-flight. After the measurement, the results need to becrustal
further
field
near the
southern
we know that
it is To
much
stronger
thanpower
the magnetic
field
corrected
to exclude
thehighlands,
various influencing
factors.
save
the limited
of the spaceof
the the
Earth.
It forms aplan
small
localcarefully
magnetosphere
and
strongly
affects the
field
craft,
observation
is also
designed.
Near
the periareon
andmagnetic
apoareon,
the
from
solar
winds
at
lower
altitude.
On
one
hand,
it
can
protect
the
planet
surface
from
the
magnetometer will work at the sampling frequency of 32 Hz. In other positions, the magnedamage
electrically
charged
particles
in universe.
other hand,
it can also shield
tometer of
will
work at the
sampling
frequency
of 1 Hz.On
Onthe
average,
the magnetometer
will
the
ion
escape
flux
near
the
southern
highlands.
detect the magnetic field of Mars’s magnetosphere 1.89 kilobits per second.
Figure10.
10.Schematic
Schematicdiagram
diagramof
ofthe
themagnetosphere
magnetosphereproduced
producedby
bysolar
solarwind
windon
onMars.
Mars.
Figure
As
the fluxgate
do not perform
absolute
measurement,
to
Kotsiaros
et al. magnetometers
reported the measurement
of Jupiter’s
magnetic
field bythey
the need
fluxgate
be
calibrated both
on Earth
and
in-flight.
After the
measurement,
results needdesign,
to be
magnetometer
installed
on the
spinning
spacecraft
Juno
[57]. Similarthe
to Tianwen-1′s
further
corrected
to excludeonthe
various
influencing
factors. To
save the limited
power
the fluxgate
magnetometer
Juno
also uses
two independent
magnetometers
placed
on a
of
the
theto
observation
plan
is also
carefullyfield
designed.
Near
thespacecraft
periareonitself.
and
bar
of spacecraft,
the spacecraft
eliminate the
effect
of magnetic
induced
by the
apoareon,
magnetometer
will
work
at two
the sampling
frequency
of 32 Hz.
In other
Differently,the
Juno
spins every 30
s, or
about
turns per minute.
According
to Faraday’s
positions,
the magnetometer
willorwork
at law,
the sampling
Hz. On average,
law of electromagnetic
induction
Lenz’s
a spinningfrequency
conductorofin1magnetic
field will
the
magnetometer
will in
detect
the magnetic
field
of Mars’s
1.89 kilobits
induce
an edge current
the conductor
and the
edge
currentmagnetosphere
will in turn generate
an addiper
second.
tional magnetic field. This additional magnetic field can be seen as the background noise
Kotsiaros et al. reported the measurement of Jupiter’s magnetic field by the fluxgate
magnetometer installed on the spinning spacecraft Juno [57]. Similar to Tianwen-1’s design,
the fluxgate magnetometer on Juno also uses two independent magnetometers placed on
a bar of the spacecraft to eliminate the effect of magnetic field induced by the spacecraft
itself. Differently, Juno spins every 30 s, or about two turns per minute. According
to Faraday’s law of electromagnetic induction or Lenz’s law, a spinning conductor in
magnetic field will induce an edge current in the conductor and the edge current will in
turn generate an additional magnetic field. This additional magnetic field can be seen as
the background noise and it will affect the measurement of the Jupiter’s intrinsic magnetic
field. According to author’s estimations, the additional magnetic field is about 0.001 Gauss
Sensors
2020,
20, x FOR PEER REVIEW
2020, 20, x FOR
PEER
REVIEW
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11 of 18
11 of 18
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it will affect the
of the Jupiter’s
intrinsic
magnetic field.
and it will affectand
the measurement
ofmeasurement
the Jupiter’s intrinsic
magnetic
field. According
to au-According to author’s
the additional
field
is about
0.001
Gaussfield
in an
thor’s estimations,
the estimations,
additional magnetic
field ismagnetic
about 0.001
Gauss
in an
intrinsic
of intrinsic field of
about
3
Gauss.
For
fluxgate
sensors,
this
value
is
pretty
large
and
should
not be
ignored.
about 3 Gauss.in
For
fluxgate
sensors,
this
value
is
pretty
large
and
should
not
be
ignored.
an intrinsic field of about 3 Gauss. For fluxgate sensors, this value is pretty
large
and
The
authors
applied
the
finite
element
method
and
the
Maxwell
equations
to
quantitatively
The authors applied
thenot
finite
element method
and the
Maxwell
to quantitatively
should
be ignored.
The authors
applied
theequations
finite element
method and the Maxwell
calculate
the
spinning
induced
magnetic
field.upThey
also put
up
a method
eliminate
this
calculate the spinning
induced
magnetic
field.
They
also
put
a method
tomagnetic
eliminate
thistoThey
equations
to quantitatively
calculate
the spinning
induced
field.
also put
additional
field.
Theresults
corresponding
results
are shown
in12
Figures
11the
and
12 [57].
At the end
additional field.up
The
corresponding
are additional
shown
in Figures
11 and
[57]. At
end
a method
to eliminate
this
field.
The
corresponding
results
are shown
in
of also
the paper,
also At
provide
another
which
similar
to
the “thin
shell”which
method
of the paper, they
provide
another
method
which
similar
to the
“thin
shell”
method
Figures
11 andthey
12
[57].
the end
of theismethod
paper,
they
alsois
provide
another
method
is
to evaluate
the
induced
field.
to evaluate the similar
induced
field.
to the “thin shell” method to evaluate the induced field.
Figure
11.
The results
of different
times
of the
finiteused
element
method used
in analyzing the magFigure
11. The
results
of
different
the finite
element
method
in analyzing
the field
magFigure 11. The
results
of different
times
of thetimes
finiteofelement
method
used
in analyzing
the magnetic
caused by the
netic
field
causedspace
by the
spinning space craft.
netic
field
caused
by
the
spinning
craft.
spinning space craft.
Figure12.
12.
Two
different
casesofofthe
themodulation
modulation
results.
The
blue
one
the
case
with
a
Figure 12. Two different
cases
ofdifferent
the modulation
results.
The blueresults.
one
is for
the
case
with
afor
Figure
Two
cases
The
blue
one
is is
for
the
case
with
a stronger
stronger
magnetic
field
in
z
direction
while
the
yellow
one
is
for
the
case
with
a
stronger
magnetic
stronger magnetic
field
in
z
direction
while
the
yellow
one
is
for
the
case
with
a
stronger
magnetic
magnetic field in z direction while the yellow one is for the case with a stronger magnetic field in
field in x-y direction.
field in x-y direction.
x-y direction.
3.2.Geophysics
GeophysicsObservation
Observation
3.2.
3.2. Geophysics Observation
LeMaire
Maireaetet
al.applied
applied
fluxgate
sensor
which
ismounted
mounted
onan
anunmanned
unmannedaerial
aerial
al.
aafluxgate
which
on
Le Maire et al. Le
applied
fluxgate
sensor
which issensor
mounted
onisan
unmanned
aerial
vehicle
(UAV)
mapping
[58].
Compared
with
other
geophysical
methvehicle
(UAV)
in magnetic
magnetic
mappingwith
[58].
Compared
with
other
geophysical
mapping
vehicle (UAV) in
magnetic
mapping
[58]. Compared
other
geophysical
mapping
meth- mapping
ods, magnetic
has of
the
advantages
mapping
both
large
scale
objects
and smallmethods,
magnetic
mapping
has
the advantages
ofscale
mapping
both
scale
objects
and
ods, magnetic mapping
has
themapping
advantages
mapping
bothoflarge
objects
andlarge
smallscale
with with
the same
instrument.
Traditionally,
magnetic
mapping
persmall-scale
the
same
instrument.
Traditionally,
magnetic
mapping
is usually
scale objects with
theobjects
sameobjects
instrument.
Traditionally,
magnetic
mapping
is
usually
per- is usually
formed
by
the
ground
or
airborne
magnetic
surveying.
However,
there
a
gap
of
height
performed
by
the
ground
or
airborne
magnetic
surveying.
However,
is
a
gap
of
height
formed by the ground or airborne magnetic surveying. However, there is a gap of height
between
ground
and
magnetic
surveying
because
between
the
ground
andairborne
airborne
magnetic
surveying
becausethe
thefixed-wing
fixed-wing
aircraftand
and
between the ground
andthe
airborne
magnetic
surveying
because
the fixed-wing
aircraft
and aircraft
helicopters cannot fly too low for safety reasons. For ground magnetic surveying, its result
can be easily affected by the noise from the anthropogenic origin which will affect the
Sensors 2020, 20, x FOR PEER REVIEW
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12 of 18
helicopters cannot fly too low for safety reasons. For ground magnetic surveying, its result
can be easily affected by the noise from the anthropogenic origin which will affect the results
of airborne magnetic surveying, so the results of ground and airborne magnetic surveying
results of airborne magnetic surveying, so the results of ground and airborne magnetic
are not easy to relate. However, the demand for continuously measuring the magnetic field
surveying are not easy to relate. However, the demand for continuously measuring the
of different heights is strong. It is well known that the map obtained by magnetic method
magnetic field of different heights is strong. It is well known that the map obtained by
can vary by several orders of magnitude according to different distances to the magnetic
magnetic method can vary by several orders of magnitude according to different distances
origin or different spacing between magnetic profiles.
to the magnetic origin or different spacing between magnetic profiles.
The recently
recently emerging
UAVs
can
flyfly
at
The
emerging UAV
UAV is
is an
anideal
idealsolution
solutionfor
forthis
thisproblem.
problem.AsAs
UAVs
can
thethe
height
between
ground
andand
100100
m, m,
it effectively
fillsfills
the the
gapgap
of traditional
ground
and
at
height
between
ground
it effectively
of traditional
ground
airborne
magnetic
surveying.
Generally,
the
UAV
can
be
divided
into
two
types:
fixed
wing
and airborne magnetic surveying. Generally, the UAV can be divided into two types: fixed
and rotary
wing. wing.
The fixed
higher
and
larger
range.
Butrange.
they need
wing
and rotary
Thewing
fixedUAVs
winghave
UAVs
havespeed
higher
speed
and
larger
But
larger
plate
to
take
off
and
land.
On
the
other
hand,
the
rotary
wing
UAVs
is
a
new
member
they need larger plate to take off and land. On the other hand, the rotary wing UAVs
is a
of themember
family of
usedoffor
airborne
is smaller and
more
maneuverable
new
of UAVs
the family
UAVs
usedmagnetism.
for airborneIt magnetism.
It is
smaller
and more
comparing withcomparing
the fixed wing
UAVs.
It wing
only requires
veryrequires
small plate
to take
offplate
and
maneuverable
with the
fixed
UAVs. Itaonly
a very
small
land.
But
at
the
same
time,
the
spatial
range
of
rotary
wing
UAV
is
also
smaller
(several
to take off and land. But at the same time, the spatial range of rotary wing UAV is also
kilometers)
and the
speed is and
lower
m/s).
In this work,
as the
wingasUAV
smaller
(several
kilometers)
the(typically
speed is 10
lower
(typically
10 m/s).
Inrotary
this work,
the
is
used,
the
smaller
and
lighter
fluxgate
vector
magnetometer
is
more
preferrable.
the
rotary wing UAV is used, the smaller and lighter fluxgate vector magnetometer isAs
more
fluxgate
vector
magnetometer
does
not
measure
the
absolute
magnetic
field,
it
needs
to
be
preferrable. As the fluxgate vector magnetometer does not measure the absolute magnetic
calibrated
before
using.
In this before
work, the
noise
mainly
the intrinsic
andfrom
induced
field,
it needs
to be
calibrated
using.
In isthis
work,from
the noise
is mainly
the
magneticand
fieldinduced
of UAV.magnetic field of UAV.
intrinsic
work is
is performed
performed in
in the
the Northern
Northern Vosges
VosgesMountains.
Mountains. The
The geological
geological context
context is
is
The work
asas
houses,
pipelines
andand
various
buried
fercomplex and
and many
manyanthropogenic
anthropogenicobjects,
objects,such
such
houses,
pipelines
various
buried
rous objects,
may
affect
investigated
ferrous
objects,
may
affectthe
thelocal
localmagnetic
magneticfield.
field.This
Thisplace
place has
has been widely investigated
deep drilling
drilling project
project for
for geothermal
geothermal resource
resource prospecting.
prospecting. In
In this
this work,
work, the
the
because it is the deep
anomaly map
map of
of ground
ground (0.8
(0.8 m),
m), 1.2
1.2 m,
m, 30
30 m
m and
and 100
100 m
m are
are drawn.
drawn. The
The results
results of
of
magnetic anomaly
100 m
m after
after reduction
reduction to the pole of ground survey in the south is shown in Figure 13 [58].
100
It is superimposed
superimposedon
ona asatellite
satellite
image.
A Matrice
quadcopter
designed
Da
image.
A Matrice
210210
RTKRTK
quadcopter
designed
by DabyJiang
Jiang
Innovation
(DJI, Shenzhen,
as shown
in Figure
[58].
The of
results
of
Innovation
(DJI, Shenzhen,
China)China)
is usedisasused
shown
in Figure
14 [58].14
The
results
ground
ground
survey
and
UAVs
are
compared
and
the
comparison
with
upward
continuation
survey and UAVs are compared and the comparison with upward continuation is also peris
also performed.
It is both
found
both the and
wavelength
and
amplitude
ofanomaly
the magnetic
formed.
It is found that
thethat
wavelength
amplitude
of the
magnetic
maps
anomaly
maps
different
for different
altitudes.
The results
are
consistent
with
former
are different
forare
different
altitudes.
The results
are consistent
with
former
studies
both
in the
studies
both (e.g.,
in theidentification
crustal scale of
(e.g.,
identification
of major contacts)
faults or geological
contacts)
crustal scale
major
faults or geological
and local scale
(e.g.,
and
local scaleof(e.g.,
identification
anthropic pipes
or archaeological remains).
identification
anthropic
pipes orof
archaeological
remains).
onon
a UAV
at at
thethe
height
of of
Figure 13. The
The magnetic
magneticmap
mapobtained
obtainedby
bythe
thefluxgate
fluxgatemagnetometer
magnetometer
a UAV
height
100 m
m with
with aa satellite
satellite image
image as
as the
the background.
background.
100
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21, 1500
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Sensors 2020, 20, x FOR PEER REVIEW
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Figure 14. (a) The Matrice 210 RTK quadcopter designed by Da Jiang Innovation (b) and the BarFigure 14. (a)
210
RTK
quadcopter
designed
by Da
Innovation
(b) and
BarFigure
(a)The
TheMatrice
Matrice
210
RTK
quadcopter
designed
by Jiang
Da Jiang
Innovation
(b)the
and
the
tington MAG03-MC fluxgate magnetometer (c). The overall weight of the magnetic equipment is
tington
MAG03-MC
fluxgate
magnetometer
(c).
The
overall
weight
of
the
magnetic
equipment
isis
Bartington
MAG03-MC
fluxgate
magnetometer
(c).
The
overall
weight
of
the
magnetic
equipment
484 g.
484
g.
484 g.
3.3. Other Related
3.3.
Other
3.3.Applications
Other Related
Related Applications
Applications
Schoinas et al.Schoinas
fabricated
characterized
flexible fluxgate
sensorfluxgate
with pad-printed
et
al.
and
aa flexible
sensor
Schoinas
etand
al. fabricated
fabricated
andacharacterized
characterized
flexible
fluxgate
sensorwith
withpad-printed
pad-printed
solenoid coils [59].
Recently,
wearable
intelligent
devices
are
a
new
trend
in
daily
solenoid
new
in
solenoidcoils
coils[59].
[59]. Recently,
Recently,wearable
wearableintelligent
intelligentdevices
devicesare
areaaconsumer
newtrend
trend
inconsumer
consumerdaily
daily
electronic devices.
In
this
trend,
the
flexible
sensor
is
the
indispensable
component.
The
electronic
devices.
In
this
trend,
the
flexible
sensor
is
the
indispensable
component.
electronic devices. In this trend, the flexible sensor is the indispensable component.The
The
fluxgate magnetic
sensor
is well sensor
knownis
its known
high
sensitivity
andsensitivity
resolutionand
for resolution
the
low for
fluxgate
magnetic
well
for
fluxgate
magnetic
sensor
isfor
well
known
for its
its high
high
sensitivity
and
resolution
for the
thelow
low
magnetic field.magnetic
However,
in consumer
electronic
devices,
the high
sensitivity
andsensitivity
resolutionand
field.
However,
in
electronic
devices,
the
magnetic
field.
However,
inconsumer
consumer
electronic
devices,
thehigh
high
sensitivity
andresolution
resolution
are not necessary,
so it
is replaced
other
kindsby
ofother
magnetic
sensors
such as
anisotropic
are
necessary,
so
ititisis
replaced
kinds
ofofmagnetic
sensors
such
are not
not
necessary,
soby
replaced
by
other
kinds
magnetic
sensors
suchas
asanisotropic
anisotropic
magnetoresistance
(AMR)
sensors.
The
main
obstacle
for
wider
application
of
fluxgate
sen-of fluxgate
magnetoresistance
(AMR)sensors.
sensors.The
Themain
main
obstacle
wider
application
of fluxgate
magnetoresistance (AMR)
obstacle
forfor
wider
application
sensor is their complex
and
expensive
fabrication
method,
so
a
method
that
can
easily
fabricate
sensor
is
their
complex
and
expensive
fabrication
method,
so
a
method
that
can
easily
sor is their complex and expensive fabrication method, so a method that can easily fabricate
fluxgate sensors
in largesensors
numbers
is urgently
needed,
evenisthough
this process
the
sensifabricate
fluxgate
in large
numbers
urgently
needed,
evenin
though
in thisthe
process
fluxgate
insensors
large
numbers
is urgently
needed,ineven
though
this
process
sensitivity and resolution
may
be
lowered.
In
this
work,
a
pad-printing
technique
is
applied
to
the
sensitivity
and
resolution
may
be
lowered.
In
this
work,
a
pad-printing
technique
tivity and resolution may be lowered. In this work, a pad-printing technique is applied is
to
fabricate the solenoid
coil
of
the the
sensor
[60–63].
The
schematic
diagram
and
the
photoapplied
fabricate
solenoid
of the
sensor [60–63].
The
schematic
diagram
the
fabricateto
the
solenoid
coil
of thecoil
sensor
[60–63].
The
schematic
diagram
and theand
photographic view photographic
of
the printed
sensor
are printed
shown
in Figure
15
[59].
The
synthesis
process
is
the
sensor
shown
in
Figure
[59].
The
synthesis
processis
graphic
view view
of
theofprinted
sensor
are are
shown
in Figure
15 15
[59].
The
synthesis
process
schematically shown
in
Figure
16
[59].
After
synthesis,
the
performance
of
the
sensor
is
charis
schematically
shown
in
Figure
16
[59].
After
synthesis,
the
performance
of
the
sensor
is
schematically shown in Figure 16 [59]. After synthesis, the performance of the sensor is characterized. The characterized.
corresponding
results
include
the
waveform
of
the
output
voltage
of
the
sensThe
corresponding
results
include
the
waveform
of
the
output
voltage
of
acterized. The corresponding results include the waveform of the output voltage of the sensing coil, the magnitude
of the
sensor’s
second
harmonic
response
and the
sensor and
sensitivity.
the
coil,
the magnitude
of the second
sensor’s
second
harmonic
response
and the
sensor
ing sensing
coil, the
magnitude
of
the sensor’s
harmonic
response
the sensor
sensitivity.
All the above sensitivity.
results
are
measured
under
different
excitation
currents.
It
is
worth
noting
All
the
above
results
are
measured
under
different
excitation
currents.
It is
All the above results are measured under different excitation currents. It is worth noting
worth
noting
that
the
noise
of
the
sensor
is
at
a
high
level.
This
is
due
to
the
shape
of
the
that the noise of
the
sensor
is
at
a
high
level.
This
is
due
to
the
shape
of
the
bar
sensor
which
that the noise of the sensor is at a high level. This is due to the shape of the bar sensor which
sensor
which
is similar Additionally,
to the case of linear
transformer.
Additionally,
the temperature
is similar to thebar
case
of
linear
transformer.
the
temperature
of
the
sensor
is
also
is similar to the case of linear transformer. Additionally, the temperature of the sensor is also
the sensor
is temperature
also measured.
It is found
that
the temperature
is dependent
on the
measured. It isof
found
thatItthe
dependent
on
the strength
of frequency
measured.
is found
that theistemperature
is dependent
onand
thefrequency
strength and
of
◦
strengthThe
andhighest
frequency
of the excitation
current.
The
highest
temperature
is 67.2 C which
the excitation current.
temperature
istemperature
67.2 °C
which
appears
near
the
excitation
the excitation
current.
The highest
is 67.2
°C which
appears
near the excitation
appearsp-p
near the excitation
coils
a 700-mA
p-p excitationofcurrent
at 100 kHz and the
coils under a 700-mA
at under
100 kHz
andatthe
the sensing
coils under excitation
a 700-mA current
p-p excitation
current
100temperature
kHz and the temperature
of the sensing
◦ C under
of the
sensing coil
is 32.6
the
same
condition.
It can beisconcluded that
coil is 32.6 °C temperature
under
the
same
condition.
It
can
be
concluded
that
the
printing
technique
coil is 32.6 °C under the same condition. It can be concluded that the printing technique is
the printing
technique
is imperfect
because the temperature
distribution
is unsymmetric
imperfect because
the temperature
distribution
is unsymmetric
the same
current.
imperfect
because the
temperature
distribution isunder
unsymmetric
under
theThe
same current. The
under
the
same
current.
The
corresponding
results
are
shown
in
Figure
17
[59].
correspondingcorresponding
results are shown
in Figure
17 [59].
results
are shown
in Figure 17 [59].
Figure 15.
offluxgate
the printed
fluxgate magnetometer
wearable
intelligent
device
(a) and
Figure 15. Structure
of Structure
the printed
magnetometer
on wearable on
intelligent
device
(a) and
the experimental
picture
Figure 15. Structure of the printed fluxgate magnetometer on wearable intelligent device (a) and
the
experimental
picture
(b).
(b).
the experimental picture (b).
Sensors 2020, 20, x FOR PEER REVIEW
Sensors 2020, 20, x FOR PEER REVIEW
Sensors 2021, 21, 1500
14 of 18
14 of 18
14 of 18
Figure 16.
printed
fluxgate
magnetometer.
(a) Printing
the bottom
Figure
Theproducing
the
printed
fluxgate
magnetometer.
Printing
the bottom
bottom
16. The
producingprocess
processofofthe
the
printed
fluxgate
magnetometer.
(a) Printing
the
conductive layer;
vias;
(c) (c)
Printing
thethe
bottom
insulating
layer;
(d) The
conductive
layer;(b)
(b)Printing
The
Printingthe
theconductive
conductive
vias;
Printing
bottom
insulating
layer;
(d) The
mounting
and
attachment
of
magnetic
core;
(e)
Printing
the
insulating
walls;
(f)
Printing
the
top
mounting
and
attachment
of
magnetic
core;
(e)
Printing
the
insulating
walls;
(f)
Printing
the
top
mounting and attachment of magnetic core; (e) Printing the insulating walls; (f) Printing the top
insulating layer;
(g)
Printing
the
top
conductive
layer.
insulating
layer;
(g)
Printing
the
top
conductive
layer.
insulating layer; (g) Printing the top conductive layer.
Figure 17. The temperature distribution of the printed fluxgate magnetometer under a certain
working17.
condition.
Figure
The
of of
thethe
printed
fluxgate
magnetometer
under
a certain
17.
Thetemperature
temperaturedistribution
distribution
printed
fluxgate
magnetometer
under
a certain
working condition.
Apart from the fluxgate magnetometer which needs the AC or DC excitation current,
Zhou et al. applied a fluxgate magnetometer based on weak magnetic detection technology
Sensors 2020, 20, x FOR PEER REVIEW
Sensors 2021, 21, 1500
15 of 18
15 of 18
Apart from the fluxgate magnetometer which needs the AC or DC excitation current,
Zhou et al. applied a fluxgate magnetometer based on weak magnetic detection technology
to
the defects
defectsofofarbitrary
arbitraryorientations
orientations
in coiled
tubing
Traditionally,
to probe
probe the
in coiled
tubing
(CT)(CT)
[64].[64].
Traditionally,
magmagnetic
flux
leakage
(MFL)
testing
is
one
of
the
non-destructive
testing
(NDT)
methods
netic flux leakage (MFL) testing is one of the non-destructive testing (NDT) methods used
used
for detection
CT failures
[65–67].
However,
it issensitive
only sensitive
to circumferentially
for detection
CT failures
[65–67].
However,
it is only
to circumferentially
distribdistributed
defects
and
cannot
detect
axially
distributed
defects.
The
method
proposed
uted defects and cannot detect axially distributed defects. The method
proposed
in this
in
thiscan
work
can effectively
detect
theindefects
in any direction.
It can also between
distinguish
work
effectively
detect the
defects
any direction.
It can also distinguish
difbetween
different
types
of
defects
such
as
axial,
circumferential
and
pore
type
defects.
ferent types of defects such as axial, circumferential and pore type defects. Additionally, as
Additionally,
as it does
require
rotationfields,
of magnetic
fields,
theequipment
size of the is
equipment
it does not require
thenot
rotation
ofthe
magnetic
the size
of the
relatively
issmall.
relatively small.
The
mechanism of
ofthe
theweak
weakmagnetic
magneticfield
fielddetection
detection
technology
in defect
The working
working mechanism
technology
in defect
dedetection
is
schematically
shown
in
Figure
18
[64].
The
mechanism
of
the
technology
is
tection is schematically shown in Figure 18 [64]. The mechanism
of
the
technology
is
that
that the permeabilities of the workpiece (µ) and the defect (µ0 ) are usually different. If the
the permeabilities of the workpiece (µ) and the defect (µ′) are usually different. If the perpermeability of the defect is higher (µ0 > µ), the curve of magnetic induction intensity B will
meability of the defect is higher (µ′ > µ), the curve of magnetic induction intensity B will be
be concave as shown on the left bottom panel of Figure 18. If the permeability of the defect
concave as shown on the left bottom panel of Figure 18. If the permeability of the defect is
is lower (µ0 < µ), the curve of magnetic induction intensity B will be upward as shown on
lower (µ′ < µ), the curve of magnetic induction intensity B will be upward as shown on the
the right bottom panel of Figure 18. The magnetic induction intensity of every position
right bottom panel of Figure 18. The magnetic induction intensity of every position around
around the workpiece can be measured by passing a three-dimensional magnetic sensor
the workpiece can be measured by passing a three-dimensional magnetic sensor above the
above the workpiece. Then, the gradient of magnetic induction intensity with space can be
workpiece. Then, Bthe
intensity with space can be obtained
∆x )− B( x ) of magnetic induction
( x +gradient
obtained by ∂B
. As ∆x is a constant, ∂B
and B( x + ∆x ) − B( x ) should have
∆ ≈
∆x
∂x
∂x
by
. As ∆𝑥 is a constant,
and 𝐵 𝑥 + ∆𝑥
𝐵 𝑥 should have the same
∆ but different amplitudes, so the interference between adjacent magnetic
the same shape
shape
but
different
amplitudes,
so
the
interference
between
adjacent
magnetic magnetic
anomalies
anomalies will be reduced and this is helpful to distinguish the superimposed
will
be
reduced
and
this
is
helpful
to
distinguish
the
superimposed
magnetic
anomalies.
In
anomalies. In addition, comparing with the gradient of magnetic induction intensity of the
addition, comparing
withofthe
of magnetic
induction
intensity
the
workpiece,
the gradient
thegradient
geomagnetic
field is
much smaller,
soof
it the
canworkpiece,
suppress the
gradient
of the geomagnetic
fieldIfiswe
much
smaller,
it can suppress
the components
local background
local
background
gradient field.
calculate
the so
gradient
of the three
of B
gradient
field. If we calculate the gradient of the three components of B (Bx, By, Bz) in three
(B
x , By , Bz ) in three directions (x, y, z), then the magnetic gradient tensor G can be obtained
directions
y, z), then the magnetic gradient tensor G can be obtained as Equation (6):
as Equation(x,(6):
  ∂⎡2 ϕm ∂2 ϕm ∂2 ϕm 
 ∂B
⎤

x
⎡∂Bx ∂Bx
⎤
𝐵 B 𝐵 B 𝐵 B 
∂x∂y
∂x∂z 
∂x
∂y
∂z
∂x2
⎢
⎥

xx
xy
xz
⎢
⎥
 ∂By ∂By ∂By   ∂2 ϕm ∂2 ϕm ∂2 ϕm 
𝐵 Byx𝐵 Byy𝐵 Byz
⎥ == 
 = ⎥= ⎢
𝐺=⎢
, ,
(6)
(6)
G=

2
 ∂x
∂y∂x
∂y∂z 
∂y
∂z 
∂y
⎢
⎥

𝐵
𝐵
𝐵
2
2
2
∂Bz
⎢∂Bz ∂Bz
⎥ ∂⎢ ϕm ∂ ϕm ∂ ϕm ⎥
Bzx Bzy Bzz
∂x
∂z
∂z∂y
⎣∂y
⎦ ∂z∂x
∂z2 ⎦
⎣
is the
themagnetic
magneticscalar
scalarpotential
potentialand
andits
itsdifferential
differentialwith
withspace
spaceisisthe
thecorresponding
corresponding
whereϕφmm is
where
magnetic
induction
intensity
in
that
direction.
B
ij
(i,
j
=
x,
y,
z)
are
the
components
of the
magnetic
intensity in that direction. Bij (i, j = x, y, z) are the components
of
tensor
in the
j direction
along
the ithe
axis.
The magnetic
gradient
tensor
contains
the inforthe
tensor
in the
j direction
along
i axis.
The magnetic
gradient
tensor
contains
the
mation of theofdefects.
In Zhou’s
work,work,
three magnetometers
which which
are responsible
for one
information
the defects.
In Zhou’s
three magnetometers
are responsible
for
one direction
(x,z),
y and
z), respectively,
are composed
orthogonally
together
andthe
form
direction
(x, y and
respectively,
are composed
orthogonally
together
and form
trithe
triaxial
fluxgate
to Section
2.2review,
of thisthey
review,
also the
calibrate
the
axial
fluxgate
sensor.sensor.
SimilarSimilar
to Section
2.2 of this
also they
calibrate
zero error,
zero
error and orthogonal
of the
triaxial
last, they
scaleerror,
error scale
and orthogonal
error of theerror
triaxial
system.
At system.
last, theyAt
applied
thisapplied
method
this
method
in
experiment
and
found
that
different
forms
and
directions
of
defects
be
in experiment and found that different forms and directions of defects can be can
distindistinguished
effectively.
guished effectively.
Figure 18. The working principle of the weak magnetic detection technology.
Sensors 2021, 21, 1500
16 of 18
4. Summary and Outlook
In the past two years, much progress has been made about lowering the noise, new
calibration methods and increasing the sensitivity of fluxgate magnetometers. Fluxgate
magnetic sensors have been applied in many new fields and many practical problems
solved. In the future, we believe that the following research fields will be productive.
Firstly, the work about lowering the noise should focus on the type of noise apart from
the Barkhausen noise because after years of effort, the Barkhausen noise has been reduced
to a low level. More attention should be paid to the quality of the alloy core because the
remanent noise may be due to the magnetostrictive effect of the alloy core. Additionally, the
offset drift is also dependent on it. Secondly, due to the lower noise and wider bandwidth,
the fundamental mode is a more popular trend comparing with the second harmonic
mode. Thirdly, time domain magnetometers such as residence time difference fluxgate
magnetometers are a new trend of this field. Fourthly, the most important problem of
fluxgate magnetometers in consumption applications is their high cost, so the main target
of this field is to reduce the production cost, even though in this process, the sensitivity
may be reduced and the noise may be increased to some extent.
Author Contributions: Conceptualization and methodology, Y.Z. and J.P.; writing—original draft
preparation, S.W. and X.L.; writing—review and editing, Y.Z., J.P. and H.Z. All authors have read
and agreed to the published version of the manuscript.
Funding: Y.Z. acknowledged the support by Guangdong Special Support Project (2019BT02X030),
Shenzhen Peacock Group Plan (Grant No. KQTD20180413181702403), Pearl River Recruitment
Program of Talents (2017GC010293) and National Natural Science Foundation of China (Grant No.
11974298, 61961136006). This work is supported by National Natural Science Foundation of China
(No. 61961136001); Innovation Team Project of Department of Education of Guangdong Province (No.
2018KCXTD026). Natural Science Basic Research Program of Shaanxi (No. 2020JQ-344); Fundamental
Research Funds for the Central Universities, CHD (No. 300102129302).
Data Availability Statement: No new data were created as it is a review paper.
Conflicts of Interest: The authors declare no conflict of interest.
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