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Sensors and Actuators A 182 (2012) 72– 81
Contents lists available at SciVerse ScienceDirect
Sensors and Actuators A: Physical
j ourna l h o me pa ge: www.elsev ier .com/ locate /sna
xperimental research on hysteresis effects in GMR sensors for analogeasurement applications
hen Liua,∗, Qi Huanga, Yong Lib, Wei Zhena
Sichuan Provincial Key Lab of Power System Wide-area Measurement and Control, University of Electronic Science and Technology of China (UESTC), Chengdu 611731, PR ChinaSchool of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
r t i c l e i n f o
rticle history:eceived 30 August 2011eceived in revised form 30 May 2012ccepted 30 May 2012vailable online 6 June 2012
eywords:
a b s t r a c t
A Wheatstone bridge GMR sensor can be used for analog magnetic field measurements. This paper dealswith hysteresis effects in GMR sensor, which is the major source of measurement error. Experiments areconducted by measuring hysteresis curves between applied magnetic field and sensor output voltagewith different typical initial magnetization states. GMR sensor has two operation modes: bipolar andunipolar. Bipolar operation means internal magnetization pattern of GMR sensor changes direction duringoperation range. This mode is inappropriate for direct measurement, as experimental results indicate that
MR sensoragnetic hysteresis
nalog measurementeasurement error
the shape of measured curves with the same range of applied magnetic field may be severely distorteddue to different initial magnetization states. Unipolar operation is an intermediate process of bipolaroperation with invariant magnetization direction. Its input–output relationship is almost linear that isespecially suitable for measurement. The principal measurement error within unipolar operation is DCoffset voltage, which is induced by remanence. It can be fixed by saturating GMR sensor before operation.
. Introduction
The Giant Magneto Resistive (GMR) effect, which indicates aarge change in resistance when ferromagnetic thin film materi-ls are exposed to external magnetic field, was first discovered in988 [1,2]. This begins a new paradigm of electronics based on thepin degree of freedom of the electron, hence named spintronics3,4]. It is widely used in hard disk read head for its extremely highensitivity that largely increases information storage density [5].ompared with preceded AMR sensors and Hall devices, it has sev-ral significant advantages, such as high sensitivity, high thermaltability, low cost and low power consumption [6–10].
Four such GMR resistors can be arranged into Wheatstoneridge configuration, which makes it appropriate for analog mea-urement applications [11–13], such as magnetometry, linearosition sensing and contactless current detection [14–18]. Therst commercial product for this was introduced in 1995 [19,20]. It
s a one-dimensional vector magnetic field sensor, with integratedux concentrator, produces differential voltage output when exter-al magnetic field applied along its sensitive axis (see Fig. 1) [21].
he flux concentrator is a thick layer of ferromagnetic material thatmplifies external magnetic field applied to the exposed two GMResistors (R1 and R4) to further increase the sensitivity of GMR∗ Corresponding author. Tel.: +86 152 1033 6559.E-mail address: [email protected] (S. Liu).
924-4247/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.sna.2012.05.048
© 2012 Elsevier B.V. All rights reserved.
sensor, and shields the other pair (R2 and R3) to keep their resis-tance invariant during normal operation.
One particular feature of ferromagnetic material is that ithas hysteresis. From physical point of view, magnetic hysteresismeans the internal magnetization pattern of the material does notuniquely depend on instantaneous applied magnetic field, but is acombined effect with magnetization history [22]. For GMR sensor,this exists in both GMR resistors and flux concentrator. Hysteresis isoften desirable in digital system applications because it can providelag effect to prevent error switch [20,23]. However, it is not appre-ciated in analog measurement applications for it may bring aboutlarge measurement error that severely influences the accuracy ofsensor output.
Magnetic hysteresis is characterized by hysteresis curve, therelationship between magnetization M and applied field H [22].A pair of closed reversal curves forms a hysteresis loop. Forone-dimensional vector magnetic field sensor, research is mainlyfocused on hysteresis along sensitive axis, by discussing suscep-tibility, remanence and coercivity of major hysteresis loop andminor hysteresis curves for both bipolar operation and unipolaroperation. Bipolar operation means internal magnetization pat-tern along sensitive axis changes direction in the range of externalapplied magnetic field, and unipolar operation means the direction
of magnetization pattern keeps invariant within operation range.The major hysteresis loop exists only in bipolar operation and isunique. It starts from negative saturation state to positive satu-ration (ascending major curve), and then goes back (descending
Actuators A 182 (2012) 72– 81 73
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have the same magnetization pattern with spin down electrons inmajority that increase the mean free path length of conduction elec-trons. This phenomenon is called magnetic modulation of electronspin in material and founds the basis for GMR effect [6].
M M
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Fig. 2. Trilayer thin film structure of GMR resistor. The intermediate conductivelayer (denoted by Cu) is sandwiched by two ferromagnetic layers (denoted byFe). The dark arrows (denoted by M) indicate directions of magnetization in fer-
S. Liu et al. / Sensors and
ajor curve). Other hysteresis curves with applied field varyingetween two saturation fields are all minor hysteresis curves. Obvi-usly, there is infinite number of minor curves, the shape of whichepends on initial magnetization state of the material, the range ofpplied magnetic field and the direction of variation (ascendingr descending). The slope of hysteresis curve is called suscepti-ility, which reflects both sensitivity and linearity of GMR sensor.hen external field is removed, the magnetization pattern does not
anish thoroughly. This phenomenon is called remanence, whichroduces DC offset voltage output to the sensor. The critical appliedagnetic field in reverse direction with respect to original magne-
ization pattern that totally removes remanence is called coercivity,hich reflects the ability of magnetic material to resist demagneti-
ation [5]. Coercivity exists only in bipolar operation and is a marko distinguish it from unipolar operation.
This paper presents experimental results of hysteresis curves ofMR sensor with typical initial magnetization states. The inducedrror within each curve is analyzed and its applicability for practicaleasurement is discussed. Then, the most robust curve with readily
vailable initial magnetization state is selected for operation andhe procedure for its calibration is derived.
Thin film structure of GMR resistor and principle of GMR effectre briefly reviewed in Section 2, in order to enhance understandingf experimental results from microscopic explanation. The flux con-entrator contributes little to the shape of hysteresis curve becauset has much lower remanence and coercivity but greater saturationeld than GMR resistors [21,24]. Hence, it is only modeled as a lin-ar magnetic field amplifier and is not discussed in this section.ormally, internal magnetization pattern of GMR sensor cannot bebserved directly, but is reflected by output voltage of Wheatstoneridge. The experimental system for this is presented in Section, including conditioning circuit for GMR sensor, DC and AC mag-etic field generating system [9,25]. Experimental processes andnvironmental conditions are also mentioned there. Measurementesults are illustrated in Section 4. Hysteresis in bipolar opera-ion is shown in Section 4.1. The results indicate that susceptibilityf GMR thin film material is independent of specific magnetiza-ion state and remains almost constant during operation. But thehapes of minor hysteresis loops with the same range of appliedeld could be distorted a lot due to different initial magnetizationtates. The combined effect reveals the fact that bipolar operationf GMR sensor is not suitable for precise magnetic field measure-ent. The potential hazards are discussed in detail there. Then it
omes to unipolar operation. In Section 4.2, experimental resultsrove that unipolar operation is an intermediate process of bipo-
ar operation and can be used for analog measurement. Commonly,here exists a difference in remanence due to maximum applied
agnetic field. Hence, it is sensitive to external disturbance. Theost robust hysteresis curve is achieved by saturating the sensor
n positive direction (working direction) before operation [26]. Itsemanence (DC offset voltage) is stable and can be easily compen-ated by conditioning circuit. An automatic calibration procedureor this is depicted at last [27].
. Thin film structure and GMR effect
GMR resistor, in its simplest form, has a trilayer thin film struc-ure (Fig. 2). The sandwiching ferromagnetic layers are made ofoft magnetic materials (iron, nickel and cobalt alloy) and are typ-cally of 40–50 angstrom thickness (1 angstrom = 0.1 nm) [21,28].ompared with hard magnetic materials, it has much narrower
ysteresis loop with better linearity and smaller coercivity thatan be easily magnetized or demagnetized [9,29]. The intermedi-te conductive layer (typically 15 angstrom thick) is made of copperlloy and is much thinner than ferromagnetic layers. Its thickness isFig. 1. Schematic diagram of linear output GMR sensor. The two-way arrow denotesits sensitive axis. Terminals A and B are positive and negative outputs of Wheatstonebridge, respectively [11].
critical that determines the style of coupling, either antiferromag-netic (Fig. 2a) or ferromagnetic (Fig. 2b), between two sandwichinglayers [30,31]. For GMR material under research, the layers are nat-urally antiferromagnetically coupled to a very small degree that canbe overcome by external applied magnetic field. Their initial orien-tations of magnetization are determined by magnetic environmentduring fabrication process.
The electrical properties of thin film materials are somewhat dif-ferent from that of bulk counterparts. In bulk material, conductivityis proportional to mean free path length of conduction electronsbefore being scattered, as Matthiessen’s rule indicates [31]. The-oretical calculations suggest that this length can be as large ashundreds to thousands of angstroms. As for thin film, mean freepath length is severely constrained by its thickness that most con-duction electrons are scattered at the surface of thin film beforereaching full mean free path length of the material. This is evenmore complicated for ferromagnetic materials, which depend onpolarization of electron spin. From statistical point of view, the ratioof spin up to spin down electrons in non-ferromagnetic materials,such as conductive interlayer of GMR resistor, is equal. But the caseis no longer hold for ferromagnetic materials where the majority ofelectrons spin in one direction. In Fig. 2(a), the upward magnetizedlayer is primarily with spin down electrons, which scatter at inter-face with spin up layer (downward magnetized), and vice versa. Inthe presence of external field (Fig. 2b), both ferromagnetic layers
romagnetic layers. The dashed arrows indicate mean free path length of conductionelectrons. (a) In the absence of external field, the sandwiching layers are antiferro-magnetically coupled and mean free path length of electrons is short. (b) Externalfield H aligns sandwiching layers into ferromagnetic coupling and mean free pathlength of electrons is long.
74 S. Liu et al. / Sensors and Actuators A 182 (2012) 72– 81
Fig. 3. Three-dimensional representation of working principle of GMR resistor. Theshort arrows within ferromagnetic layers indicate magnetization pattern in eachdomain. (a) The current flows in the plane of thin film layers. (b) Low externalfi(s
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eld aligns magnetization patterns in some domains to be ferromagnetic coupling.c) Sufficiently high external field aligns all magnetization patterns in parallel andaturates GMR resistor.
For better understanding operational behaviors of GMR resistor, three-dimensional square-shaped thin film structure is con-tructed to illustrate magnetization patterns in sandwiching layers,s shown in Fig. 3. All ferromagnetic materials consist of smallegions called magnetic domains, where magnetization in each isniform [22,29,32]. These domains can be perfectly modeled aswo-dimensional in ferromagnetic thin films. GMR effect can bebserved when current flows both in the plane and perpendicularo the plane of the layers [5]. One advantage of in plane currentow is that its generated magnetic field can recover magnetization
atterns of both ferromagnetic layers to be antiferromagneticallyoupled (Fig. 3a). The sensitive axis of GMR sensor (see Fig. 1) isonstrained to be parallel with the direction of in plane currentow, as Fig. 3(b) and (c) indicate. When external applied magneticFig. 4. DC magnetic field generation system: A, solenoid; B, GMR sensor with con-ditioning circuit; C, precision resistor; D, DC power source; and E, voltage meter.
field is low, the GMR resistor works in its linear region, for theamount of ferromagnetically coupled domains is proportional toapplied field strength, so does the resistance vary. If applied fieldstrength is sufficiently high, the GMR resistor reaches its satura-tion state and is of minimum resistance. It should be noted thatboth ferromagnetic layers are unpinned and their magnetizationpatterns can be realigned by external magnetic field. This config-uration makes the sensor robust, which cannot be damaged evenexposed to extremely high magnetic fields [33]. Another issue isthat external field applied in both directions along sensitive axisaligns magnetic domains into ferromagnetic coupling, i.e. the resis-tance of GMR resistor always decreases, regardless of direction ofapplied field. Hence, the Wheatstone bridge of GMR sensor can onlyproduce positive voltage output (see Fig. 1).
The relative magnetoresistance of such trilayer structure isabout 10%. In real commercial products, GMR resistors have mul-tilayered structures that consist of alternating ferromagnetic andconductive layers, to achieve larger magnetoresistance with betterlinearity and lower hysteresis [11,19]. Each adjacent pair of ferro-magnetic layers are antiferromagnetically coupled, hence largelyincrease mean free path length when external field is applied.Besides, multilayer thin film resistors are designed into long,narrow stripe shapes to further improve magnetoresistance per-formances [21,34,35].
3. Experimental setup
To make GMR sensor work properly, additional conditioningcircuit should be added to adjust the output signal to appropri-ate level [36]. The Wheatstone bridge (Fig. 1) can be powered byboth current and voltage sources [6]. Here, a 2.048 V ultra-stablevoltage reference is selected. The differential output of Wheatstonebridge is proportional to voltage supply. This signal is further pre-amplified by an instrumentation amplifier with gain 10 throughdirect coupling.
Because hysteresis is a rate-independent phenomenon, i.e. thefinal magnetization pattern is the same no matter how fast externalmagnetic field is applied [22], hysteresis curves can be measured ina static way by plotting output voltage V versus applied field H atdiscrete points. An experimental system for this is set up, as shown
in Fig. 4. A solenoid is employed for providing reference magneticfield. GMR sensor is placed at central region of the solenoid wherethe generated field is uniform. To minimize disturbance inducedby earth magnetic field (typically 0.5 Oe), the solenoid is carefully
S. Liu et al. / Sensors and Actuators A 182 (2012) 72– 81 75
Fig. 5. AC magnetic field generation system: A, two-channel oscilloscope and B,f
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and descending major curves indicates magnetic hysteresis withinmajor hysteresis loop. For both curves, the upward moving segment
unction generator.
riented to make the sensitive axis of GMR sensor orthogonal to it.utput signal of GMR sensor is transmitted through co-axial cablend then measured by voltage meter. The solenoid is powered by aC voltage source that can saturate GMR sensor in both directionslong sensitive axis. The strength of generated reference magneticeld is proportional to the current flow within solenoid which cane accurately measured. In order to do this, a 1 � precision resistor
s connected in series with it. The voltage drop can be capturedy voltage meter. It should be noted that the precision resistor isf relatively large rated power. Consequently, its resistance variesittle due to thermal drift during experiment.
The absolute measurement error of digital voltage meter is oneast digit of its operation range. Hence the relative error is signifi-ant when measuring small quantities, including solenoid currentow around remanence, which corresponds to zero applied mag-etic field, and sensor output voltage around coercivity, where theeasured value approaches zero. The missing information about
etail performance can be partially recovered from time-domainaveforms obtained in AC magnetic field system, as seen in Section
.1.2.To evaluate hysteresis influences on dynamic signal measure-
ents, an AC magnetic field generation system is set up, as shownn Fig. 5. The DC power source is replaced by a function genera-or with programmable voltage output. A two-channel oscilloscopes used to observe synchronized time-domain waveforms of botholenoid current flow (applied magnetic field) and GMR sensoroltage output. Another application of AC system is to demagne-ize GMR sensor to its equilibrium state, i.e. natural magnetizationtate with antiferromagnetic coupling between ferromagnetic lay-rs (Fig. 3a), by applying a slowly damped AC magnetic field withufficiently large initial magnitude until zero. This process is calledC demagnetization [22] to distinguish it from DC counterpart. Theesulting magnetization state is used to investigate minor hystere-is curves (Section 4.1.2).
All ferromagnetic materials are sensitive to thermal influences37–39]. The susceptibility has a minus temperature coefficient, i.e.
temperature raise will cause ferromagnetic layers harder to beagnetized. Although Wheatstone bridge configuration has a good
ompensation for this, sensitivity and saturation magnetic field ofMR sensor still suffer from it to some extent, which cannot beeglected in practical applications [6,13]. This issue is beyond the
cope of following investigations and the ambient temperature isestricted to 27 ◦C during experimental processes.Fig. 6. Major hysteresis loop of GMR sensor: A, ascending major curve; B, descendingmajor curve; C, remanence; and D, coercivity.
4. Results and discussion
The experiments conducted in this section examine basic prop-erties of hysteresis curves of GMR sensor. Bipolar operation modeis more fundamental than unipolar operation and is introducedat first. It should be noted that both operation modes are definedaccording to direction of magnetization along sensitive axis (Sec-tion 1), rather than direction of applied magnetic field. Indeed,bipolar operation exists when applied field does not changedirection, while unipolar operation exists when applied field isbidirectional, as seen in Section 4.2.2. To investigate the applica-bility of both operation modes for analog measurement, the rangeof applied magnetic field is confined to be even symmetrical withrespect to zero field for bipolar operation and to be one directionalin unipolar operation.
4.1. Hysteresis in bipolar operation
4.1.1. Major hysteresis loopThe major hysteresis loop (Fig. 6) provides an overall perspective
of output behaviors of GMR sensor, which founds a good basis foranalyzing and evaluating the shapes of mass minor curves. Here,“positive” and “negative” applied magnetic fields along sensitiveaxis are relative concepts, and the direction for investigating hys-teresis in unipolar operation (Section 4.2) is chosen as positive.The major hysteresis loop of GMR sensor is even symmetrical withrespect to applied magnetic field. This is determined by thin filmstructure of GMR resistors (Section 2), and is distinct from thoseof common ferromagnetic materials (odd symmetrical). Conse-quently, the ascending and descending major curves are no longermonotonic. Each can be decomposed into two segments: one goesdownward, indicates a demagnetizing process; and the other goesupward, that corresponds to a magnetizing process. The two seg-ments join at the point of coercivity. Hence, the terms “ascending”and “descending” only indicate directions of variation for appliedmagnetic field.
The major hysteresis loop consists of two portions: linear regionand saturation region. Only linear region is suitable for analogmeasurement applications. The large deviation between ascending
has a larger slope (in absolute value) than downward moving seg-ment, i.e. the susceptibility for magnetizing process is larger than
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6 S. Liu et al. / Sensors and
hat for demagnetizing process. In addition, during both processes,he susceptibilities are not absolutely invariant. In other words,here exist nonlinearities within the measurement range of GMRensor. This issue is more obvious for unipolar minor hysteresisoop and will be discussed in Section 4.2.1. Compared with the rangef linear region, the amount of remanence is large enough that itsnduced DC offset voltage output cannot be neglected during oper-tion. For GMR sensor with linear output, coercivity (in absolutealue) is proportional to remanence. But it should be noted thatespite remanence is minimized at the presence of coercivity field,
t still exists for a small portion after the coercivity field is removedo zero. In other words, the coercivity field cannot demagnetizeMR sensor thoroughly, but is smaller than DC demagnetizingeld, as seen in Section 4.2.2. Hysteresis curves in linear regionave somewhat different shapes with major curves, as presented
n subsequent sections.A distinct feature of major hysteresis loop is that it does not
ccommodate. The accommodation process can be observed wheninor hysteresis loops are cycled between two magnetic fields, as
hey gradually drift toward an equilibrium loop [22]. In practicaleasurement applications, this phenomenon can be regarded as
ransient response behavior of GMR sensor with respect to appliedagnetic field and brings about measurement error to some extent.ence, the major hysteresis loop provides a good quantitative ref-rence for analyzing dynamic effects in minor hysteresis loops.
.1.2. Bipolar minor hysteresis loopsTo investigate hysteresis in bipolar operation, experiments
rimarily focus on steady-state linear response behaviors (afterccommodation) of GMR sensor with respect to applied peri-dic magnetic fields. The measured hysteresis curves are closedhat form bipolar minor hysteresis loops. For analog measure-
ent applications, the initial magnetization state of GMR sensor isefined in the absence of external applied field, i.e. the initial state isniquely characterized by remanence and can be partially reflectedrom DC offset voltage output (different remanences may producehe same offset voltage). Obviously, remanence is minimized afterC demagnetization (see Section 3), and the corresponding magne-
ization state is called equilibrium. On the other hand, remanencen negative direction is maximized after negative saturation mag-etic field is removed. These two initial magnetization states arehosen for analyzing hysteresis in bipolar minor loops. The rangef applied magnetic field is selected as −3 Oe to 3 Oe. It is relativelymall with respect to the whole linear range of GMR sensor. Hence,emanence and coercivity are dominant.
The measured loops are shown in Fig. 7(a) and (c). Duringxperimental processes, accommodation phenomena are indeedbserved as the final steady-state hysteresis loops deviate from ini-ial magnetizing curves with applied magnetic field ranging from
to 3 Oe (not plotted). Bipolar minor hysteresis loop with equilib-ium initial state (Fig. 7a) is not exactly even symmetrical, becauseMR sensor cannot be demagnetized thoroughly. Here, the ini-
ial state has a small portion of remanence in negative direction,ue to a larger output voltage at −3 Oe than that at 3 Oe, and amaller coercivity field (in absolute value) in negative directionhan that in positive direction. Like major hysteresis loop, the sus-eptibility during magnetizing process (upward moving) in bothscending and descending minor curves is larger than that duringemagnetizing process (downward moving). This leads to sensitiv-
ty error with GMR sensor. The joint points between two adjacentalf sine waves (waveform D in Fig. 7b) correspond to coercivities inig. 7(a). It can be seen that sensor output voltage in time-domain
aveform changes abruptly at coercivity, which indicates a sud-en change in susceptibility. Hence, the shape of minor hysteresisoop around coercivity (Fig. 7a) is not smooth. This inaccuracy isnduced by experimental system (see Section 3). In Fig. 7(b), there
tors A 182 (2012) 72– 81
exits a lag phase shift between waveforms of applied magnetic fieldand sensor output voltage, the amount of which is determined bycoercivity.
Bipolar minor hysteresis loop with after negative saturation ini-tial magnetization state (Fig. 7c) is no longer symmetrical, but isseverely distorted. The output voltage at −3 Oe is 50% larger thanthat at 3 Oe, and coercivities of both ascending and descendingminor curves lie in the positive region of applied magnetic field.Consequently, the corresponding time-domain output waveform(Fig. 7d) for negative applied field appears to have a higher peakvalue and a larger time span than that for positive applied field,from which the original sine wave applied magnetic field can hardlybe recognized.
To investigate common properties among these hysteresisloops, the ascending and descending curves are plotted separately(Fig. 8). It can be seen that the minor hysteresis curves (curvesB and C) are parallel with each other, which indicate that thesusceptibilities of both magnetizing and demagnetizing processesare independent of initial magnetization state and remain almostconstant. It is the slight nonlinearities of these curves that makeminor hysteresis loops closed. The susceptibilities of major curves(curve A) are slightly larger than those of minor curves. But thesedeviations are sufficiently small when compared with the abso-lute magnitudes of susceptibilities and the difference betweenmagnetizing and demagnetizing susceptibilities. Hence, both sus-ceptibilities can be treated as invariant during bipolar operation,regardless of any specific range of applied magnetic field. This ishelpful for developing a mathematical model to estimate outputbehaviors of GMR sensor [40].
The experimental results indicate that bipolar operation modeof GMR sensor cannot be used directly for analog magnetic fieldmeasurement. Firstly, it is unable to discriminate between positiveand negative applied fields due to the absence of negative volt-age output. Secondly, the output is not unique with respect to thesame applied field, because the initial magnetization states are infi-nite. Despite some initial states can be known before measurement,large disturbance magnetic field applied in both directions alongsensitive axis may distort the original shape of hysteresis loop dur-ing operation and induce a change in remanence (DC offset voltage)and coercivity (time delay). Finally, for a particular bipolar minorhysteresis loop, its time delay of coercivity is not fixed, but is magni-tude dependent. For example, in Fig. 7(b) and (d), if the frequency ofapplied magnetic field is chosen as 5 Hz with amplitude invariant,its time delay is 10 times larger than that for 50 Hz applied field. Toeliminate these drawbacks and make bipolar operation mode pos-sible for analog measurement, a mathematical model for bipolarminor hysteresis loops with different initial magnetization statesshould be built and the parameters within this model should beidentified. It is a rather complex issue and is difficult for hardwarerealization, which is beyond the scope of research in this paper.
4.2. Hysteresis in unipolar operation
4.2.1. Unipolar minor hysteresis loopIn Section 1, unipolar operation is defined as the total magne-
tization pattern of GMR sensor does not change direction duringoperation. Actually, it is only a necessary condition for this. Exper-iments should be conducted to reveal some unique features ofunipolar operation before reaching its complete definition. For ana-log measurement purpose, the external magnetic field is alwaysapplied in positive direction along sensitive axis. Consequently, theremanence is also positive. Hence, the equilibrium initial magneti-
zation state is less powerful for investigating hysteresis in unipolaroperation and is not chosen here. To present the whole outputbehavior of GMR sensor in positive direction, applied magnetic fieldranges from positive saturation to zero and then goes back. The
S. Liu et al. / Sensors and Actuators A 182 (2012) 72– 81 77
Fig. 7. Bipolar minor hysteresis loops: (a) with equilibrium initial magnetization state; (c) with after negative saturation initial magnetization state. In both (a) and (c), curvesA and B are ascending minor curve and descending minor curve, respectively. (b) and (d) are time-domain responses of GMR sensor when 50 Hz sine wave magnetic fieldi (b) ao
mF
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s applied, which correspond to hysteresis loops in (a) and (c), respectively. In bothutput voltage.
easured curves form unipolar minor hysteresis loop, shown inig. 9.
In unipolar operation, the susceptibility during magnetizingrocess (curve A) is nearly equal to that in demagnetizing processcurve B). The slight deviation between these two curves indi-ates magnetic hysteresis, which is rather small compared withhat in bipolar operation. According to manufacturer’s report, forach curve, its nonlinearity within measurement region of GMRensor is less than 1.5%, the extent of which depends on range ofpplied magnetic field [41]. Commonly, smaller operation rangeeads to less deviation. Hence, this error contributes little to sen-or’s accuracy that can be neglected in most analog measurementpplications. In crucial situations, it can be fixed through unipolarysteresis modeling [42,43]. For ascending minor curve in Fig. 9,
f applied magnetic field decreases at some point in linear regionefore reaching positive saturation, the corresponding demagne-izing curve (not plotted) lies within unipolar minor hysteresis loop
nd meets the ascending curve at zero magnetic field. The obtainedinear unipolar minor hysteresis loop with after positive saturationnitial magnetization state is especially suitable for analog mea-urement, for its remanence is robust that cannot be changed bynd (d), waveform C indicates applied magnetic field; waveform D indicates sensor
any positive applied magnetic field. The induced DC offset voltageoutput can be easily compensated by external conditioning circuit.There exists accommodation process in this linear minor loop asapplied field cycles between zero and its maximum. The demag-netizing curve ultimately approaches descending minor curve inFig. 9. This transient process brings about dynamic nonlinearityerror (within 1.5%), which can also be neglected.
In unipolar operation, any negative applied magnetic field istreated as disturbance, which may change original operation modeand bring about additional error. A detailed research for this is givenin Section 4.2.2. It should be noted that hysteresis loop in Fig. 9 doesnot represent the full range of unipolar operation. Compared withmajor hysteresis loop (Fig. 6), the exact lower limit of applied mag-netic field is negative coercivity field, rather than zero. The negativeapplied magnetic field in positive unipolar operation is useless foranalog measurement, but can provide a criterion for disturbancedetection, as seen in Section 4.2.3.
4.2.2. Unipolar operation with negative initial remanenceThe influence of negative remanence for unipolar operation
is maximized when initial magnetization state is chosen as after
78 S. Liu et al. / Sensors and Actuators A 182 (2012) 72– 81
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Fig. 10. Unipolar operation with after negative saturation initial magnetizationstate. The applied magnetic field ranges from 0 to 5 Oe in (a), and 0 to 15 Oe in
(b). In both subfigures, curve A indicates initial magnetizing curve; B and C indicatedescending and ascending curves of unipolar minor hysteresis loop in linear region,respectively; D indicates final magnetizing curve.negative saturation. The output behaviors of GMR sensor withapplied magnetic fields ranging from 0 to 5 Oe and 0 to 15 Oeare plotted in Fig. 10(a) and (b), respectively. For the former case,its initial magnetizing curve follows the path of ascending majorhysteresis curve. Then, the subsequent descending and ascendingcurves form a unipolar minor hysteresis loop. This loop accommo-dates upwards as applied field cycles, i.e. an increase in positiveremanence, which is stronger than that with after positive satura-tion initial state (Section 4.2.1). If applied magnetic field continuesto increase, the output voltage exactly goes on to follow the path ofascending major curve until reaching positive saturation, as curveD indicates. During this magnetizing process, the susceptibilitychanges abruptly at the joint point (5 Oe) of curve C and curveD, from that of unipolar operation to bipolar operation. This phe-nomenon is independent of accommodation process for it alwaysoccurs no matter how many times the applied magnetic field cyclesbetween 0 and 5 Oe. The sensor output performance with 0–15 Oe
unipolar operation range (Fig. 10b) is almost the same with 0–5 Oe,except an increase in remanence.These experimental results indicate that unipolar operation ofGMR sensor is only an intermediate process of bipolar operation,
S. Liu et al. / Sensors and Actuators A 182 (2012) 72– 81 79
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hose existence does not influence original bipolar magnetizationattern. Consequently, the unipolar minor hysteresis loop in Fig. 9an be treated as such process that corresponds to major hysteresisoop. Hence, the complete definition of unipolar operation is givens follows: firstly, it always begins with a demagnetizing process;econdly, the total magnetization pattern does not change direc-ion; thirdly, the susceptibility of magnetizing hysteresis curve isqual to that of demagnetizing hysteresis curve.
Since unipolar operation mode is appropriate for analog mea-urement applications, its measurement error is primarily causedy remanence, which is a combined effect of initial magnetizationtate and maximum applied magnetic field that produces DC offsetoltage output. This offset voltage is not monotonic with respecto maximum applied field, as shown in Fig. 11 (with after neg-tive saturation initial state). Its descending portion correspondso a decrease in negative remanence, and the ascending portionorresponds to an increase in positive remanence. The joint pointetween these two portions relates to DC demagnetizing field,here the remanence is minimized. At this point, the offset volt-
ge is less than zero, which is caused by mismatch of GMR resistorsn Wheatstone bridge configuration (Fig. 1). This phenomenon isalled bridge offset [44]. Its induced error is invariant during oper-tion.
If the lower limit of range of applied magnetic field is assumedo be zero, it should be noted that in Fig. 11, GMR sensor works innipolar operation mode in positive direction only for maximumpplied magnetic field that is larger than DC demagnetizing fieldaround 5 Oe), i.e. the remanence is positive. This portion can beivided into two regions. If maximum applied field lies in region, the achieved unipolar minor hysteresis loop is linear. Indeed,he output behaviors illustrated in Fig. 10(a) and (b) correspond toower and upper limits of region C, respectively. In practical sit-ations, transient positive disturbance field may lead maximumeld into region D, where the increase in remanence is consider-bly large that contributes a lot to measurement error. If maximumpplied field lies in region A, i.e. between zero and coercivity fieldaround 1 Oe), the sensor still works in its unipolar operation modeut in negative direction. The initial magnetizing curve followshe ascending major curve (see Fig. 6) toward coercivity which is
ndeed a demagnetizing process and then goes back. In this case, theensitivity of GMR sensor is negative, and a slight decrease in rema-ence (Fig. 11) indicates magnetic hysteresis in negative unipolarperation. If maximum applied field lies in region B, i.e. betweenFig. 12. Flowchart of automatic calibration procedure of GMR sensor in unipolaroperation.
coercivity and DC demagnetizing field, the operation mode is actu-ally bipolar. For example, assuming that maximum applied fieldis 3 Oe, then the descending minor curve follows the path withthat in Fig. 7(c) between 0 and 3 Oe (neglect of accommodationprocess). The above analysis indicates that measurement results ofGMR sensor are unreliable if its initial magnetization state is totallyunknown. This is particularly true when maximum applied mag-netic field is small. Hence, one major function of calibration systemis to guide internal magnetization pattern of GMR sensor to someknown state before measurement applications.
4.2.3. Calibration procedureAs mentioned in Section 4.2.1, unipolar minor hysteresis loop is
most robust when its initial magnetization state is chosen as afterpositive saturation. Then the principal source of disturbance comesfrom negative applied magnetic field. In unipolar operation, theinput–output relationship is monotonic. Since small applied neg-ative field does not change operation mode, a threshold voltagebetween zero and DC offset voltage induced by remanence can beset for its detection. If output voltage is less than threshold volt-age, the sensor should start calibration procedure to re-saturate itin positive direction before large negative disturbance changes itsoriginal remanence. In practical cases, the actuator for this is anexternal coil, which should be much smaller than the solenoid inFig. 4. A flowchart for automatic calibration is illustrated in Fig. 12.
For individual GMR sensor component, the offset voltage afterpositive saturation may be different with each other. The two stepsin dashed block are designed for getting this and are executed onlyat the first time when GMR sensor is powered on. In a completemeasurement system, the measured analog quantities are sampledand converted to digital counterparts through an A/D converterfor storage and further processing. Typically, a microcontroller isused for controlling the sequence of these commands. The calibra-tion system is integrated in controller. When the sampled quantityis smaller than threshold voltage, the controller sends a stimulat-ing signal to saturate GMR sensor through external coil and thenremoves it. During such process, the sampled quantities are invaliddata. One advantage of this system is that it can provide calibrationservice at the presence of measured magnetic field. After comparedwith threshold voltage, the offset voltage should be subtracted fromsampled quantities to obtain final measurement result.
There exists aftereffect in ferromagnetic materials as theamount of remanence decays with time when applied magneticfield is small. For GMR sensor, such effect is not serious. Whenapplied magnetic field is removed, its internal magnetization state
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an be held for more than one day. In practical situations, the sensorhould be re-saturated regularly, in order to minimize such effect.
. Conclusion
This paper investigates measurement errors of Wheatstoneridge GMR sensor induced by magnetic hysteresis in analogagnetic field measurement applications. Bipolar and unipolar
peration modes are discussed separately. Experimental resultsndicate that the bipolar operation is not suitable for measurement,ue to its unreliable internal magnetization states. On the otherand, unipolar operation is capable of doing such work, but thepplied magnetic field is constrained one directional. In practicalituations, the applied magnetic field is much random and unpre-ictable. Consequently, the two operation modes may be coupledogether. A direct mathematical modeling of such process is ratheromplex. Hence, the true value can hardly be recovered from sen-or output voltage. This problem can be resolved through magneticiasing [45–48], to make the total field in one direction, which cane executed by external coil.
cknowledgment
The research in this paper is partially supported by Nationalatural Science Foundation of China (NSFC, Grant No. 50977007).
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Biographies
Shen Liu was born in 1988, in Shenyang, PR China. He received his B.S. degree inMeasurement Control and Instrumentation in 2010, from University of ElectronicScience and Technology of China (UESTC), Chengdu, PR China. Since December 2010,he has been a research intern at Institute of Mechanics, Chinese Academy of Science,Beijing, PR China, where his research primarily focuses on drag-free control andformation flying of scientific spacecrafts. His research interests also include multi-physics coupling, system dynamics and complex network control.
Qi Huang was born in Guizhou Province, PR China. He received his B.S. degree in
Electrical Engineering from Fuzhou University, Fuzhou, China, in 1996, M.S. degreefrom Tsinghua University, Beijing, China in 1999, and Ph.D. degree from ArizonaState University, Tempe, AZ, USA, in 2003. He is currently a Professor at Univer-sity of Electronic Science and Technology of China (UESTC) and the Deputy Deanof School of Energy Science and Engineering, UESTC, and the Founding Director of
Actua
SHmci
YvH
S. Liu et al. / Sensors and
ichuan Provincial Key Lab of Power System Wide-area Measurement and Control.is current research and academic interests include power system high perfor-ance computing, power system instrumentation, power system monitoring and
ontrol, and integration of distributed generation into the existing power systemnfrastructure.
ong Li received his B.S. degree in 2009, and M.S. degree in 2012, both from Uni-ersity of Electronic Science and Technology of China (UESTC), Chengdu, PR China.e is currently a Ph.D. candidate in Mechanical Engineering at School of Mechanical
tors A 182 (2012) 72– 81 81
and Aerospace Engineering, Nanyang Technological University, Singapore. His cur-rent research interests include design and modeling of MEMS/NEMS sensors andsystems, micro solid oxide fuel cell, and atomic simulation of nanomaterials.
Wei Zhen was born in 1957, in Hebei Province, PR China. He received his B.S. degree
in Power System Automation in 1982, from Xi’an Jiaotong University (XJTU), Xi’an,China. After that, he works in Sichuan Electric Power Test & Research Institute asa Senior Engineer, and the Director of Power System Engineering Research Center.His researching fields include power system relay protection, power system analysisand state-of-the-art technology development.
