Characterisation of magnetic wires for fluxgate cores

Characterisation of magnetic wires for fluxgate cores
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Available online at www.sciencedirect.com
Sensors and Actuators A xxx (2007) xxx–xxx
Characterisation of magnetic wires for fluxgate cores
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P. Ripka a,∗ , M. Butta a , M. Malatek a , S. Atalay b,1 , F.E. Atalay b
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a
Czech Technical University, Prague, Czech Republic
b Inonu University, Malatya, Turkey
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Received 15 July 2007; received in revised form 4 October 2007; accepted 5 October 2007
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Abstract
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Keywords: Fluxgate; Magnetic sensors; Magnetic wire
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Orthogonal fluxgate sensors need only a single core and they can be made very small. We show how to measure properties of composite Cu/Py
ferromagnetic wires to be used as cores for these sensors. Besides the well known axial loops we show how to measure the circumferential hysteresis
loop and gating curves, which can directly be used for sensor modeling.
It is generally believed that in composite wires the majority of the current flows through the copper core, thus reducing the possible perming
effect of poorly magnetized core sections. We will show that this is true only at very low frequencies and for low magnetic layer thickness. The
calculated values can be used as a starting point for FEM simulations.
© 2007 Elsevier B.V. All rights reserved.
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1. Introduction
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Orthogonal fluxgate sensors need only a single core and they
can be made very small [1,2]; recent types have cores made
of high quality amorphous soft magnetic wires [3–5]. Robbes
et al. have shown that orthogonal fluxgate mode brings higher
sensitivity and less noise compared to GMI mode of the same
core [5]. Fluxgate sensors in general are based on the nonlinearity of the ferromagnetic material and they have output at
even harmonics of the excitation frequency, usually at the second harmonics. “Fundamental-mode orthogonal fluxgate” [6,7]
is a device, which measures rotation of the core magnetization
due to the external field by applying small ac measuring field in
perpendicular direction. Thus, the output of this device is on the
first harmonics.
The operational principle of orthogonal fluxgates has not
been fully understood yet. Primdahl [8] gives only a basic
explanation based on rotational magnetization, which cannot
adequately describe the influence of hysteresis. For proper modeling of the sensor it is vital to measure its characteristics at real
operational conditions.
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Corresponding author. Tel.: +420 2 000 0000.
E-mail addresses: [email protected] (P. Ripka),
[email protected] (S. Atalay).
1 Tel.: +90 422 3410010/3890 3705.
The main drawback of using magnetic wire excited by ac
current through the wire is that the magnetic field in the central
part or the wire is small to saturate the material. By increasing
the excitation value this area is reduced, but it is still present and
creates a region causing unwanted perming effect.
Copper wires with electrodeposited magnetic layer [9,10]
were proposed to solve this problem: it was generally believed
that the excitation current flows mainly through the copper wire
due to its higher conductivity and that the magnetic layer is
uniformly magnetized. Similar structure attached to substrate
was also made by electroplating [11]. We will test this assumption: the current profile will be examined by comparing rough
estimates of circular permeability.
2. The sample core
The characteristics were measured on 50 ␮m Cu wire
covered by electrodeposited 10 ␮m layer of polycrystalline
Co18.97Ni49.60Fe31.43 alloy.
A three-electrode cell was used to carry out electrochemical experiments. The volume of the electrochemical bath was
approximately 85 ml. An Ag/AgCl electrode (BAS, 3 M NaCl,
and −35 mV vs. SCE at 25 ◦ C) was used as a reference
electrode. The high-density platinum gauze electrode, which
was approximately 500 times larger than the cathode, was
used as an auxiliary electrode. The bath contained a mixed
0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.sna.2007.10.008
Please cite this article in press as: P. Ripka, et al., Characterisation of magnetic wires for fluxgate cores, Sens. Actuators A: Phys. (2007),
doi:10.1016/j.sna.2007.10.008
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This is not the case of tangential hysteresis loop, which is vital
for understanding the transverse fluxgate.
3. The instrumentation
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4. Circumferential hysteresis loops
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Circumferential (tangential) hysteresis loop is measured for
core excited by current flowing through the core wire: exactly
as for the real operation. The circular flux is derived from the
voltage V, which appears between the wire terminals. In order to
calculate the induced voltage Vi , correction should be made for
voltage drop Ri on the wire resistance R. We found that the dc
resistance value can be used for this correction in wide frequency
range rather than real part of the impedance. Clear artifacts indicate the wrong correction: in Fig. 3 the overcompensated curve
has two intersections close to the loop ends. The circumferen-
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solution of 5 mM Co(SO4 )2.6H2 O, 0.1 M Ni(SO4 )2.6H2 O,
10 mM Fe(SO4 )2.6H2 O, 0.2 M H3 BO3 , 35 mM NaCl, 7 mM
C7 H4 NNaO3 S.2H2O and 0.01 g/l C12 H25 NaO4 S. All solutions
were prepared by dissolving reagent grade chemicals in distilled
water. The bath pH was adjusted to 2.6 by adding 0.1 mM HCl
and 0.1 mM NaOH up to the required value using a Jenway 3520
pH meter. The plating was carried out at 25 ◦ C in stirred solution
and at a constant potential of −1 V versus Ag/AgCl (BAS, 3 M
NaCl, and –35 mV vs. SCE at 25 ◦ C) for 180 min.
The sample geometry is shown in Fig. 1.
The length of the Py-covered part of the wire was 36 mm. The
wire was inserted into the ceramic tube with only slightly higher
internal diameter and outer diameter of 1 mm. The sensing (pickup) winding was later wound around this tube. We have used
26 mm long coil wound by 450 turns of 0.09 mm thick copper
wire. Another 300 turns of auxiliary coil of the same length was
wound around the inner coil.
The core B-H loops should be measured for both tangential
and longitudinal directions, as these loops may be very different
due to the anisotropy.
Although the measurement of the longitudinal hysteresis loop
is challenging due to the small amount of ferromagnetic material,
the measuring procedures are well described in the literature.
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Fig. 1. Geometry of the composite wire.
The current flowing in the wire and the voltage drop on it
have been sampled with NI 5911 digitizer which provides 5 MHz
sampling frequency and 14 bits resolution. The setup is shown
in Fig. 2a.
Since the card has only one channel a multiplexer was used,
so that V and Iexc cannot be sampled simultaneously. We use
equivalent-time sampling, so that V and Iexc samples are taken
in subsequent period. External synchronization is used in order
to avoid any phase delay between the corresponding sample
pairs.
A similar measurement setup has been used to measure longitudinal curves. In this case we obtained the flux in longitudinal
direction, integrating the voltage induced in the pick up coil
wounded around the wire (Fig. 2b).
Fig. 2. (a) Setup for measuring the circumferential hysteresis loop. (b) Modification to the setup for measuring the longitudinal properties.
Please cite this article in press as: P. Ripka, et al., Characterisation of magnetic wires for fluxgate cores, Sens. Actuators A: Phys. (2007),
doi:10.1016/j.sna.2007.10.008
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The sensor characteristics may be different from the core
wire material characteristics: the sensor is characterized by
the total flux through the pick-up coil, which contains only a
small core area and large area of air. At higher excitation intensities the core permeability is low and the air flux becomes
important. It should be noted that numerical correction is only
possible because of high-resolution A/D converter we use.
Older systems use analog compensation by subtracting voltage
from the compensation coil; this requires nulling before each
measurement.
The sensor axial loops are shown together with gating curves
in the next section.
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where A is the circular area: A = l, t = l(r2 − r1 ), t is the thickness
of the ferromagnetic layer, r1 is the copper wire diameter and r2
is the external diameter of the core.
The corrected set of hysteresis loops is shown in Fig. 4:
each curve belongs to a certain amplitude of the excitation
current.
From Fig. 4 one can see that a minimum rms current of 40 mA
is required to fully saturate the core. This minimum current is
increasing with frequency due to the eddy currents and other
losses. This is clearly demonstrated in Fig. 5, which shows the
sensor characteristics: second harmonics output voltage versus
dc measured field. For 30 mA excitation current this characteristics has gross hysteresis and the sensor is useless. This is
dramatically improved for 40 mA excitation.
5. Longitudinal curves
Axial (longitudinal) hysteresis loops were measured by using
similar setup as in Fig. 2. The excitation field of 10 kHz frequency was created by the Helmholtz coil. The core field B
was measured by numerically integrating the voltage induced in
26 mm long pick-up coil wound by 450 turns of 0.09 mm thick
copper wire. The air flux was numerically subtracted.
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Fig. 5. Second harmonic of induced voltage (V) vs. Bext (␮T); Iexc = 30 and
40 mA, 10 kHz.
6. Gating curves
Gating curves are the most important internal characteristics
of fluxgate sensors. They show pick-up coil flux Φa versus the
excitation field H [8,10]. Gating curve has two peaks which
distance is equal to the coercivity of the longitudinal hysteresis
curve. The height of the peaks depends on the axial (measured)
external dc field Bmeas .
An example of gating curves for two values of the measured
field is shown together with axial sensor curve in Figs. 6 and 7.
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tial field B is calculated by numerical integration of the induced
voltage:
1
Φ
1
=
Vi dt =
(V − Ri ) dt
B=
(1)
A
A
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Fig. 3. Overcompensated circumferential hysteresis loop.
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Fig. 4. Set of B (T)–H (A/m) circumferential loops at 10 kHz for current amplitude from 10 to 50 mA (span 5 mA).
Fig. 6. Axial sensor curve and gating curve for Bmeas = 370 ␮T.
Please cite this article in press as: P. Ripka, et al., Characterisation of magnetic wires for fluxgate cores, Sens. Actuators A: Phys. (2007),
doi:10.1016/j.sna.2007.10.008
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7.2. Estimation from Ls measurements
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The following estimations have origins in the calculation of
self-inductance Ls of the straight conductor of diameter a and
infinite length. The field inside the conductor is increasing with
the distance r from the center:
Ir
H=
,
2πa2
for r ≤ a
(5)
And outside the conductor the field is decreasing with distance r:
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2πr
for r ≥ a
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H=
(6)
Inside the conductor the energy density U of the field H is
Fig. 7. Axial sensor curve and gating curve for Bmeas = 1 mT.
Odd harmonics caused by crosstalk were removed by calculation
to make the figures more clear.
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7. Circular permeability
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7.1. Estimation from GMI measurements
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In order to estimate the current profile by finite element
method, the conductivity and permeability of both wire regions
should be known [12]. We calculated the permeability using
four different formulas: either from giant magneto-impedance
(GMI) data or from the wire induction assuming that all the
current flows through the copper only (Case I) or the current
is uniformly distributed uniformly in both, the copper wire and
magnetic layer (Case II), or finally for all current flowing through
the ferromagnetic layer (Case III).
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Z = Rdc ka
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J0 (ka)
2J1 (ka)
1+i
δ
2ρ
δ=
ωμ0 μ∅
k=
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As GMI effect is measurable only at higher frequencies, we
consider only the case that most of the current flows in ferromagnetic shell. Thus, we can use linearized Landau–Lifshitz for
homogeneous cylindrical conductor [13]:
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And total energy in the conductor interior is
R2
μI 2
WIN =
UIN dV =
r 2 2πr dr
8π2 R42 R1
V
μI 2 R42 − R41
=
16π
R42
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1
μI 2 2
μH 2 =
r
2
8π2 a4
(2)
(3)
(4)
J0 and J1 are the Bessel functions of first kind and a is the wire
outer radius (a2 in the figure above)
The values of Rdc and |Z(f)| were measured by RLC analyzer. The material resistivity of 5.4 × 10−8 was calculated from
known dimensions and Rdc value.
The permeability values were calculated iteratively by using
Eqs. (2)–(4).
(7)
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UIN =
1
μI 2
μH 2 =
2
8π2 r 2
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(8)
The limits of integration R1 and R2 are the inner and outer
radiuses of the annulus (circle), respectively.
Outside the conductor the energy density UEXT is
UEXT =
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(9)
And total energy in the exterior is
μI 2
R2
μI 2 R2 1
dr =
ln
WEXT =
UEXT dV =
4π R1 r
4π
R2
V
(10)
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Similar equations may be used for more annular sub-areas.
The self-inductance LS can be then calculated from the total
energy:
1 LS
I2
WTOT = WIN + WEXT =
(11)
2
l
7.2.1. Case I: current density is distributed only in the
bulky copper core
The contribution of Cu core comes from Eq. (8) for R1 = 0
and R2 = a1 . The final formula for unit length inductance is in
Ref. (12). The Cu core has negligible internal self-inductance Ls
(up to 10 nH), which contributes to Ls .
L
μ0
=
l
8π
Inductance of FM shell is then
L
μ
a2
=
ln
l
2π
a1
(12)
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(13)
Please cite this article in press as: P. Ripka, et al., Characterisation of magnetic wires for fluxgate cores, Sens. Actuators A: Phys. (2007),
doi:10.1016/j.sna.2007.10.008
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Table 1
Estimates of circular permeability
Measured values
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μ∅ =
7.2.2. Case II: the current density is homogenous in both
copper core and ferromagnetic shell
For this case we assume WIN WEXT . The total interior magnetic energy can be calculated using Eq. (8) over two integral
areas; Cu (R1 = 0 and R2 = a1 , μ0 ) and FM (R1 = a1 and R2 = a2 ,
μø μ0 ) resulting in
μ0 I 2 4
1 LS
4
4
WIN =
(a
+
μ
(a
−
a
))
=
(15)
I2
∅
1
2
1
2
l
16πa24
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(16)
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H=
UIN
1
μI 2 (r − a1 )2
= μH 2 =
2
8π2 (a2 − a1 )2
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WIN =
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8π2 (a2 − a1 )2
a2
a1
(18)
(r − a1 )2 2πr dr
μI 2 (3a22 − a12 − 2a1 a2 )
=
48πa22
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μI 2
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(17)
and hence the interior’s energy density and total magnetic energy
integrated in between a1 and a2 are
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I(r − a1 )
2πa2 (a2 − a1 )|a1 ≤r≤a2
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7.2.3. Case III: the current density is homogenous in
ferromagnetic shell
In this case, we should write for the field H:
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3761
3206
2249
1709
547
(14)
(8πLs a24 /μ0 l) − a14
μ∅ =
a24 − a14
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3571
2004
1655
1198
910
290
(16,420)
6,880
5,430
4,840
4,260
3,970
2πLs
μ0 l ln(a2 /a1 )
and consequently for Case 2:
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II
μø
And the inductance of the air is neglected.
Expressing the relative permeability μø from Eq. (13) we
finally obtain for Case 1:
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I
μø
III
μø
(13,722)
7,728
6,383
4,621
3,511
1,123
It is evident that at 1 kHz the GMI formula cannot be used:
the GMI ratio is very small, which leads to large uncertainties,
and the current in the copper core is not negligible. Similarly
also (17) for Case III cannot be used for low frequencies. Even
though the resistivity of copper is lower than permalloy, formula
13 evidently cannot be used for frequencies above 1 kHz. Thus,
Case I and Case II is not applicable for fluxgate analysis. GMI
formula gives more reliable results at higher frequencies, as it
takes into an account the eddy currents.
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0.524
0.916
1.145
1.667
2.186
6.498
μø
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8.91
5
4.13
2.99
2.272
0.727
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|Z| ()
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50
100
1000
LS (␮H)
Estimated from LS
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Frequency (kHz)
Estimated from GMI
μ∅ =
− a12 )
For the estimation of circular permeability in the frequency
range of 10–100 kHz which is relevant for transverse fluxgate,
either GMI formula or Case 3 formula can be used with similar
results. In the lower frequency range (10–50 kHz) Case III formulae is more precise, while for higher frequencies (50 kHz to
1 MHz) GMI formula is preferable. The exact current distribution can be then calculated by FEM [12]. Our results confirmed
that the commonly accepted myth of composite wires is wrong.
It is not true that the majority of the current flows in the copper
core. The possible solution of this problem is an insulation layer
between copper and ferromagnetic layer—unfortunately this is
technological challenge.
The permeability values we calculated are rough estimates,
because we highly simplified the current profiles. However, they
can serve as starting points for future finite element simulations.
The measured axial hysteresis loop can be regarded as a material property because the core has very little demagnetization in
axial direction. Contrary to that the circumferential loops are
only effective loops for the given geometry, even though the
demagnetization in this direction is zero. The reason is that the
H field in this case is far from being homogenous. The measured
gating curves can be directly used for sensor modeling using the
approaches shown for parallel fluxgates in Refs. [14,15].
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References
Circular permeability in Case 3 is then
24πLs a22
μ0 l(3a22 − 2a1 a2
8. Conclusions
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(20)
The measured and calculated results are shown in Table 1.
[1] P. Ripka (Ed.), Magnetic Sensors and Magnetometers, Artech House, 2001,
pp. 40–41.
[2] D. Robbes, Highly sensitive magnetometers—a review, Sens. Actuators A:
Phys. 129 (1–2) (2006) 86–93.
[3] I. Sasada, Orthogonal fluxgate mechanism operated with dc biased excitation, J. Appl. Phys. 91 (2002) 7789–7791.
Please cite this article in press as: P. Ripka, et al., Characterisation of magnetic wires for fluxgate cores, Sens. Actuators A: Phys. (2007),
doi:10.1016/j.sna.2007.10.008
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Mattia Butta born in Lecco in 1980. He received the “Laurea” degree (Bc
equivalent) from the “Politecnico di Milano” in electrical engineering in 2003.
From the same University he obtained a “Laurea specialistica” degree (MSc
equivalent) with honours in 2005. He is currently PhD student at the Czech
Technical University in Prague and his main field of interest is the development
of coil-less fluxgate.
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Michal Malátek (Ing) was born in Ustı́ nad Orlicı́, Czech republic, in 1978.
He received the Master degree in electrical engineering from Czech Technical University in Prague (CTU) in 2003. He is presently PhD student at the
Faculty of Electrical Engineering of the CTU. Main topics of his research are:
giant magnetoimpedance in amorphous structures, magnetic measurements and
development of magnetic sensors.
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Selcuk Atalay was born in Turkey in 1964. He got his PhD in the magnetoelastic properties of amorphous alloys in 1992 from Bath University. His interests
are oriented to magnetocaloric and magnetoimpedance effect in some magnetic materials. He has been head of physics department since 2000 at Inonu
University.
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Funda Atalay was born in Turkey in 1971. She graduated in physics. She
received her PhD from Inonu University in 2000, and she has been working
as a lecturer at Physics department. Her research interests deals with magnetic nanowire, electrodeposition of magnetic materials and magnetoimpedance
effect.
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Engineering, Czech Technical University as a full professor, teaching courses
in electrical measurements and instrumentation, engineering magnetism and
sensors. He also worked as visiting scientist at Danish Technical University
(1990–1993), National University of Ireland (2001) and in the Institute for the
Protection and the Security of the Citizen, European Commission Joint Research
Centre in Italy (2005/6). His main research interests are magnetic measurements
and magnetic sensors, especially fluxgate. He is a member of IEEE, Elektra
society, Czech Metrological Society, Czech National IMEKO Committee and
Steering Committees of Eurosensors and SMM conferences. He served as an
associate editor of the IEEE Sensors Journal. He was a General Chairman of
Eurosensors 2002 conference.
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Biographies
Pavel Ripka received an Ing degree in 1984, a CSc (equivalent to PhD) in
1989 and Prof. degree in 2001 at the Czech Technical University, Prague, Czech
Republic. He works at the Department of Measurement, Faculty of Electrical
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of the sensing performance of orthogonal fluxgate sensors with different
amorphous sensing elements, Sens. Actuators A, in press.
[5] D. Robbes, C. Dolabdjian, Y. Monfort, Performances and place of
magnetometers based on amorphous wires compared to conventional magnetometers, J. Magn. Magn. Mater. 249 (1–2) (2002) 393–397.
[6] I. Sasada, Symmetric response obtained with an orthogonal fluxgate operating in fundamental mode, IEEE Trans. Magn. 38 (2002) 3377–3379.
[7] E. Paperno, Suppression of magnetic noise in the fundamental-mode
orthogonal fluxgate, Sens. Actuators A 116 (2004) 405–409.
[8] F. Primdahl, The fluxgate mechanism. Part I. The gating curves of parallel
and orthogonal fluxgates, IEEE Trans. Magn. 6 (1970) 376–383.
[9] C. Petridis, A. Ktena, E. Laskaris, et al., Ni–Fe thin film coated Cu wires
for field sensing applications, Sens. Lett. 5 (2007) 93–97.
[10] J. Fan, X.P. Li, P. Ripka, Low power orthogonal fluxgate sensor with
electroplated Ni80Fe20/Cu wire, J. Appl. Phys. 99 (8) (2006), Art. no.
08B311.
[11] O. Zorlu, P. Kejik, R.S. Popovic, An orthogonal fluxgate-type magnetic
microsensor with electroplated permalloy core, Sens. Actuators A 135
(2007) 43–49.
[12] J.P. Sinnecker, et al., AC magnetic transport on heterogeneous ferromagnetic wires and tubes, J Magn. Magn. Mater. 249 (2002) 16–21.
[13] L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1975.
[14] L. Perez, I. Lucas, C. Aroca, et al., Analytical model for the sensitivity of
a toroidal fluxgate sensor, Sens. Actuators A 130 (2006) 142–146.
[15] A.L. Geiler, V.G. Harris, C. Vittoria, N.X. Sun, A quantitative model for
the nonlinear response of fluxgate magnetometers, J. Appl. Phys. 22 (2006)
08B316–08B316-3, doi:10.1063/1.2170061.
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