+Model ARTICLE IN PRESS SNA 6051 1–6 Available online at www.sciencedirect.com Sensors and Actuators A xxx (2007) xxx–xxx Characterisation of magnetic wires for fluxgate cores 3 P. Ripka a,∗ , M. Butta a , M. Malatek a , S. Atalay b,1 , F.E. Atalay b 4 a Czech Technical University, Prague, Czech Republic b Inonu University, Malatya, Turkey OF 5 6 Received 15 July 2007; received in revised form 4 October 2007; accepted 5 October 2007 7 RO Abstract 8 16 Keywords: Fluxgate; Magnetic sensors; Magnetic wire 11 12 13 14 DP 15 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. 9 10 17 TE 1. Introduction 1 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. 2 3 EC 4 5 6 7 8 RR 9 10 11 12 13 15 16 17 18 19 20 Q1 1 2 ∗ UN CO 14 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 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 +Model SNA 6051 1–6 ARTICLE IN PRESS 2 P. Ripka et al. / Sensors and Actuators A xxx (2007) xxx–xxx This is not the case of tangential hysteresis loop, which is vital for understanding the transverse fluxgate. 3. The instrumentation 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 OF 51 4. Circumferential hysteresis loops DP 50 TE 49 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- EC 48 RR 47 CO 46 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. UN 45 RO 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 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 +Model ARTICLE IN PRESS SNA 6051 1–6 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 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. DP 102 TE 101 EC 100 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. RR 99 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. CO 98 tial field B is calculated by numerical integration of the induced voltage: 1 Φ 1 = Vi dt = (V − Ri ) dt B= (1) A A A UN 96 97 RO Fig. 3. Overcompensated circumferential hysteresis loop. 3 OF P. Ripka et al. / Sensors and Actuators A xxx (2007) xxx–xxx 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.2007.10.008 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 +Model SNA 6051 1–6 ARTICLE IN PRESS 4 P. Ripka et al. / Sensors and Actuators A xxx (2007) xxx–xxx 7.2. Estimation from Ls measurements 168 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: I , 2πr for r ≥ a OF 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. 143 7. Circular permeability 141 153 7.1. Estimation from GMI measurements 147 148 149 150 151 EC 145 146 TE 152 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). 144 158 Z = Rdc ka 159 160 161 162 163 164 165 166 167 J0 (ka) 2J1 (ka) 1+i δ 2ρ δ= ωμ0 μ∅ k= CO 156 UN 155 RR 157 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]: 154 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 DP 142 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) RO UIN = 1 μI 2 μH 2 = 2 8π2 r 2 170 171 172 173 174 175 176 177 178 179 180 (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 = 169 (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) 181 182 183 184 185 186 187 188 189 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) 190 191 192 193 194 195 196 197 198 199 200 201 (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.2007.10.008 202 +Model ARTICLE IN PRESS SNA 6051 1–6 P. Ripka et al. / Sensors and Actuators A xxx (2007) xxx–xxx 5 Table 1 Estimates of circular permeability Measured values 206 207 208 209 210 211 212 213 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 215 (16) 219 H= UIN 1 μI 2 (r − a1 )2 = μH 2 = 2 8π2 (a2 − a1 )2 223 225 WIN = 228 229 8π2 (a2 − a1 )2 a2 a1 (18) (r − a1 )2 2πr dr μI 2 (3a22 − a12 − 2a1 a2 ) = 48πa22 226 227 μI 2 UN 224 (17) and hence the interior’s energy density and total magnetic energy integrated in between a1 and a2 are CO 222 I(r − a1 ) 2πa2 (a2 − a1 )|a1 ≤r≤a2 RR 218 7.2.3. Case III: the current density is homogenous in ferromagnetic shell In this case, we should write for the field H: 221 6703 3761 3206 2249 1709 547 (14) (8πLs a24 /μ0 l) − a14 μ∅ = a24 − a14 220 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: 217 II μø And the inductance of the air is neglected. Expressing the relative permeability μø from Eq. (13) we finally obtain for Case 1: 214 216 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. DP 205 0.524 0.916 1.145 1.667 2.186 6.498 μø TE 204 8.91 5 4.13 2.99 2.272 0.727 EC 203 |Z| () OF 1 10 20 50 100 1000 LS (H) Estimated from LS RO 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]. 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 (19) References Circular permeability in Case 3 is then 24πLs a22 μ0 l(3a22 − 2a1 a2 8. Conclusions 230 (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.2007.10.008 263 264 265 266 267 268 269 +Model 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 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. 314 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. 320 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. 326 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. 331 OF 277 303 RO 276 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. DP 275 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 TE 274 [4] Z.J. Zhao, X.P. Li, H.L. Seet, X.B. Qian, P. Ripka, Comparative study 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. EC 273 P. Ripka et al. / Sensors and Actuators A xxx (2007) xxx–xxx RR 272 Q2 6 CO 271 ARTICLE IN PRESS UN 270 SNA 6051 1–6 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.2007.10.008 304 305 306 307 308 309 310 311 312 313 315 316 317 318 319 321 322 323 324 325 327 328 329 330 332 333 334 335

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