ux

Shechn

lingdeludinor a

uxgate SPICE model when the magnetic eld is notuniform in the core. Experiment of a micro-uxgate madeup of two separated permalloy (Fe20Ni80) parallelepipedcores [10] indicates that the model with demagnetisationfg

Sc

www.ietdl.org

2&actor is inaccurate and the numerical integral method has aood agreement with measurements.Realisation of the integral equation method directly in thePICE is not suitable. First problem is that enmeshmentannot be progressed in SPICE. Secondly, even the problem

thg

f14The Institution of Engineering and Technology 2014general, very easy.The total magnetic eld intensity H

Q

at any point can bedecomposed in three components: H

Q = HQe + HQ

mx + HQ

d,where H

Q

e and HQ

mx are the source elds, HQ

e is created bye excitation current, H

Q

mx is the external measuredeomagnetic eld, H

Q

d is curl free and is the demagnetisingeld created by the magnetised materials.With the integral equation method [1014], only the

erromagnetic core has to be discretised, assuming the corenot used; therefore, it is necessary to set up a more accurate the integral equation method, mesh generation is, inespecially when the magnetic eld in the core is veryinhomogeneous. For most uxgates, the ellipsoidal core iswith nite element analysis method, whereas the processingcircuits are designed with SPICE. It will save a lot of timeand improve the performance if the design of uxgate probeand processing circuits are both realised with the SPICE, soan accurate uxgate SPICE model is very necessary. Theparameters including magnetic performance of core, thegeometry of the uxgate should be regulated easily in orderto use it conveniently.On the aspect of the magnetic performance of core, the

previous reports [27] focus on the work to set up uxgateSPICE model using the accurate hysteresis loop of magneticmaterials. For the geometry of the sensor, it is usuallydescribed with the demagnetisation factor [8]. However, itis impossible to generalise the demagnetisation factorwithout some sort of averaging for non-ellipsoidal bodies[9]. Therefore using demagnetisation factor is inaccurate

With the new method, uxgate SPICE model was generatedautomatically. After entering the hysteresis loop and thegeometry of the uxgate, the accurate uxgate SPICEmodel can be built conveniently.

2 Fluxgate model based on integral equationmethod

Considering the following problem: the uxgate core isplaced in the external eld (earth magnetic eld and eldcreated by coils). The geometry and the ferromagneticbehaviour law of the core material are known. We areinterested in the calculus of the effect by the external eld.We analysed the uxgate with the numerical integralequation method [1014] which has been extensively usedin theoretical studies and in numerical analysis. Comparedwith nite element and nite difference methods of eldsolution, the air region does not have to be discretised withPublished in IET Science, Measurement and TechnologyReceived on 30th July 2013Revised on 26th November 2013Accepted on 16th December 2013doi: 10.1049/iet-smt.2013.0129

Method for modelling of flthe geometry influenceJuping Li, Shibin Liu, Bo Guo, Xiaowei Hou,School of Electronics and Information, Northwestern PolytE-mail: liushibin@nwpu.edu.cn

Abstract: This study proposes a new method of SPICE modelThe main advantage of the method, vis-a-vis the traditional momagnetisation is taken into consideration. The parameters inclcan be regulated easily. The proposed method was tested fexperiment results.

1 Introduction

Fluxgates are the most suitable vector magnetic eld sensors,which is applicable for measuring weak magnetic eld with aresolution up to 0.1 nT and absolute precision of 1 nT (forstation magnetometers) to 100 nT (for low-cost portableunits) [1]; however, the structure of the probe andprocessing circuits are relatively complicated. Theinconveniency is that the probe of uxgate is optimisedISSN 1751-8822

gate sensor including

anglin Yang, Songsong Qiuical University, Xian 710129, Peoples Republic of China

of uxgate sensor that considers the geometry of the uxgate.using demagnetisation factor, is that the inhomogeneity of theg magnetic performance of core, the geometry of the uxgaterod shape core uxgate, showing a good agreement with

of enmeshment is resolved, there are still many variablesused in the magnetic eld equation formation that the netlist compilation work becomes very problematic andcomplex. Moreover, it is required to start the net listcompilation work again, if the geometry of the coil andcore is changed. This is a problematic and time consumingtask.This paper presents a new method of SPICE modelling of

uxgate sensor that considers the geometry of the uxgate.IET Sci. Meas. Technol., 2014, Vol. 8, Iss. 4, pp. 214219doi: 10.1049/iet-smt.2013.0129

is meshed into n elements. The conditions used in thisanalysis are as follows: (i) the magnetisation is assumed asuniform in each element and (ii) the magnetic charge isassumed to occur only at surface of the element.Considering the core we analysed is very thin and theexcitation magnetic eld is parallel to the plane of the core,magnetisation in the direction of the thickness is ignored. Ineach element, the internal magnetic eld change with thesource eld

hix = heix + hmx + hdix (mQ

i(hix, hiy))

hiy = he + hmy + hd (mQ

i(hix, hiy))i = 1, 2, . . . , n

2.2 Demagnetisation eld

The equations for the demagnetisation eld are

HQ d = 0 m0HQ

d = rm = m0mQ

Considering the demagnetising eld is curl free, we know thatit exists a scalar potential corresponding to the demagnetisingeld such that h

Q

d = w. Scalar potential satises thefollowing equation

2w = rm/m0 rm = m0mQ

Man (

p((

(M

a

www.ietdl.orggQ

i =1

4p

v

nQ

J ( rQ

i rQ)

rQ

i rQ 3

dV (3)

where nQ

J is the direction of the excitation current, and JQ

is theexcitation current density. r

Qis the coordinate of the eld

point in the ith element and rQ

is the coordinate of thesource point. V is the volume of the excitation coil.

Hs = H NB

td Mirr (Hs)

dHs= Man (Hs)

kd/(1 c) a(MHs + aM =

(Man/Ms)

Ru+ H0 ex

[

+H1 exp(Man/Ms)

a1

( ) exp

([

M = c Man + (1 c) MirrB = m0(Hs +M )

iy iy

(1)

where hi is the internal total magnetic eld in the ith element.hm is the geomagnetic eld to be measured and hei is theexcitation eld in the ith element. hdi is the demagnetisationeld in the ith element. m

Q

i is the magnetisation in the ithelement. Excitation eld and demagnetisation eld in eachelement will be given in Sections 2.1 and 2.2.

2.1 Excitation eld

The excitation eld generated by the excitation coil isdescribed by the following equations

HQ e = JQ m0 HQ

e = 0

The excitation eld is divergence free. According to the BiotSavart formula, the magnetic eld in the ith element inducedby the excitation current is

hQ

ei = 14p

vJQ

( rQ) r

Q

i rQ

rQ

i rQ 3

dV = gQi JQ (2)IET Sci. Meas. Technol., 2014, Vol. 8, Iss. 4, pp. 214219doi: 10.1049/iet-smt.2013.0129The magnetic eld because of all elements is calculated as

hQ

d = nj=1

wj = 1

4p

nj=1

Sj

(mQ

j d sQ

j)

r(4)

where jj is the magnetic scalar potential because of the jthelement, r is the distance between the source point and theeld point, Sj is the surface area of element j.Substituting (2)(4) into (1), the uxgate is described with

the following equations

hix= gix J| |+hmx+nj=1

(wijxxmjx+wijxymjy)

hiy= giy J| |+hmy+nj=1

(wijyxmjx+wijyymjy)i= 1, 2, . . . , n

(5)

Calculation of matrix elements wij is given in [12].

2.3 Magnetisation law model

The magnetic device can be simulated by solving (5) with thenon-linear behaviour of the material M(H ). A rod shape coreuxgate was analysed in this paper. Neglecting the transversemagnetisation, the uxgate core material is described with thefollowing frequency-dependent hysteresis model, and thecircuit realisation of the curve is given in [15, 16].In an external excitation magnetic eld H, the relation

between the internal magnetic eld Hs and themagnetisation is (see (6))where Ms is the saturation magnetisation of the core material.Mirr is the irreversible part of magnetisation. Man is theanhysteretic magnetisation. Ru, H0, H1, a0 and a1 are theparameters determining the shape of the anhystereticmagnetisation. The linear region is modelled by theparameter Ru and the saturation by H0, H1, a0 and a1. Theparameter describes the coupling of ferromagnetic

irr (Hs)

Hs)Mirr (Hs))Man/Ms)

a0

) exp (Man/Ms)

a0

( )]

an/Ms)

1

)] (6)215& The Institution of Engineering and Technology 2014

domains. The coefcient k is the pinning parameter whichdetermines the amount of energy dissipated, and is adirectional parameter which ensures that energy is alwayslost through dissipation. is equal to 1. = 1 for dHs/dt> 0 and = 1 for dHs/dt < 0. The coefcient c is a measureof the amount of reversible change in magnetisation. N isthe parameter [16] related with the geometry and theconductivity of the core.

3 Automatic generation of the SPICE model

We have given the uxgate model described with (5) and (6)in Section 2. However, realisation of (5) directly in the SPICEis not suitable. Firstly, the build and the enmeshment of thegeometric model cannot be realised directly in the SPICE.Another problem is that (5) includes 2n sub-equations.Every element needs a circuit to describe itself. All thesecircuits are interrelated. If the traditional method is appliedto generate the net list, a large circuit needs to be drawn inWorkview. This is a problematic and time consuming task.And it is required to start the net list compilation workagain, if the geometry of the coil and core is changed.If the value of the coefcient matrices g and w in (5) was

calculated, the circuit for (5) can be achieved by ordinary

value across the resistor in Fig. 1 is the internal magneticeld of the core at the ith element. The voltage value of thevoltage-controlled voltage source Exi is the demagnetisingeld along the X-axis at the ith element. The voltage valueat node inxi is the sum of the excitation magnetic eld andthe geomagnetic eld to be measured along the X-axis atthe ith element.The net list for sub-circuit a in Fig. 1 generated by the

programme is shown in Fig. 3. The input of this sub-circuitis the external magnetic eld and the demagnetisation eldat every element. The output is the internal magnetic eldat every element. nhdx is the node corresponding to the

Fig. 3 Net list for sub-circuit a in Fig. 1

www.ietdl.orgFig. 1 Circuit for one sub-equation in (5)components (Fig. 1). The circuit in Fig. 1 will be describedin detail below. In this section, a method for generating theuxgate SPICE model automatically through programmingis proposed. Fig. 2 shows the programme procedure for thegeneration of the uxgate SPICE model. The input ofthe programme is the geometry of the uxgate, includingthe geometry model of the uxgate core and the coil. From(5), it is observed that all sub-equations have the samemathematical form, and the difference among thesesub-equations is only the coefcient. After the completionof the calculations of coefcient matrices g and w in (5),using loop statement and ofstream head le, circuits of allsub-equations in (5) were written to the output le.Once the calculations of coefcient matrices g and w in (5)

have been performed, the circuit for (5) can be realised withresistors and controlled sources. Fig. 1 shows the circuit216& The Institution of Engineering and Technology 2014realisation of the sub-equation in (5). Source eld heix + hmx,heiy + hmy(i = 1, , n) was realised by 2n current-controlledvoltage source. The bias of every current-controlled voltagesource is the geomagnetic eld to be measured. Themagnetisation intensity is obtained by calling the circuit ofthe non-linear MH curve of the core material. The voltage

Fig. 2 Programme used to generate the uxgate SPICE modelIET Sci. Meas. Technol., 2014, Vol. 8, Iss. 4, pp. 214219doi: 10.1049/iet-smt.2013.0129

demagnetisation eld at every element. From Fig. 1 and (5),we observed that by calling the sub-circuit in Fig. 3 2ntimes and the circuit for the MH curve of the core materialn times using loop statement, net list corresponding to (5) isobtained with the programme.From Fig. 2, it is observed that the problem that the build

and the enmeshment of geometric model cannot be realiseddirectly in the SPICE was solved. Compared with thetraditional method, generation of the net list throughprogramming is much more easy and quick. Taking thecircuit for the demagnetisation eld at the ith element asexample, the values of demagnetisation matrices wi1xxwi2xxwinxx and wi1xy wi2xywinxy have to be set manuallywith the traditional method. However, with our method,parameter settings are controlled by the programme.Cumbersome manual settings with the Workview wereavoided. Another advantage is that the large circuit wasavoided to be drawn. If the geometry of the sensor ischanged, it is required to draw a large circuit and set the

resistance of the excitation coil R = 13.3. The circuit forthe core is described in Section 3.

4.1 Reduction of computation time usingsymmetry

To reduce the nodes in the net list and the computation time,symmetry of the sensor is analysed. When symmetry exists,half, quarter or eighth models can be solved to savecomputation time because the number of elements wasreduced. The core is meshed using 8-node hexahedralelement. Fig. 5 is the top view of the core. The excitationmagnetic eld and the external measured eld are alongX-axis. Owing to symmetry of the magnetic eld, therelationship among the magnetisation at the jth element andthe magnetisations at other elements is

mjx = mj+15x = mj+30x = mj+45x, j = 1, . . . , 15

Therefore, the mathematic model for the core is

15

www.ietdl.org4 Validation of the model

A rod shape core uxgate (Fig. 4a) taken as an example wasanalysed using this method. The excitation winding andsearch winding are implemented uniformly. The number ofturns of the excitation coil is 330, and the number of turnsof the pick up coil is 1100. The core material is 0.1 mmthick, 30 mm length and 1 mm width permalloy. The ttingparameters of MH curve for the core were: = 1.0694 106, c = 0.3, k = 1.7143, Ms = 5.98 10

5, Ru = 0.3997,h0 = 0.0001, h1 = 1.1263 10

20, a0 = 0.0827, a1 = 0.0201and N = 0.0014. Fig. 4b shows the circuit of the rod shapecore sensor with a sinusoidal excitation voltage. R is the

Fig. 4 Fluxgate sensor with rod shape core and its circuitsa Rod shape core uxgateb Circuit of the rod shape core sensorvalues of the circuit elements again with the traditionalmethod. However, with our method, the programme is stilluseful by inputting the new geometry of the sensor, and thenew net list can be obtained automatically and quickly.To sum up, the model consists merely of resistor, linear

dependent sources which are built-in models of thewidespread simulator SPICE. With the programme inFig. 2, if the knowledge of the geometry of the sensor isknown, the uxgate SPICE model described with (5) and(6) was generated automatically and quickly. The input ofthe SPICE model is excitation current. The internalmagnetic eld intensity and magnetisation intensity on eachelement can be calculated accurately with SPICE.IET Sci. Meas. Technol., 2014, Vol. 8, Iss. 4, pp. 214219doi: 10.1049/iet-smt.2013.0129hix = gixJ + hmx+j=1

wdijxxm jx (7)

where

wdijxx = wijxx + wi(j+15)xx + wi(j+30)xx + wi(j+45)xx

4.2 Results with proposed SPICE model andexperiment

The testing system includes a function generator (Agilent33220A), a power amplier (NF HSA4011), a multimeter(Agilent 34401A), an oscilloscope (Agilent inniium54830D), a power supply (Agilent E3610A), a solenoid(length 30 cm, diameter 3 cm and 2300 turns) and amagnetometer (CMT-6 W). The schematic diagram of thetesting system is showed in Fig. 6. The signal used toderive the sensor was generated by the function generatorand amplied by the power amplier. The output voltage

Fig. 5 Meshes of the core

Fig. 6 Schematic diagram of the testing system217& The Institution of Engineering and Technology 2014

signal generated by the detection coil of the sensor wasdetected and showed in channel 2 of the oscilloscope. Andthe Channel 1 was used to detect and display the excitationcurrent waveform. The measured magnetic eld wasgenerated using the power supply and the solenoids. Thestrength of the external magnetic eld was calibrated by thecurrent value measured by the multimeter. To eliminateinterference, the system was placed away from theferromagnetic materials and before each test the zero eldswas calibrated using the magnetometer.From the circuit of the uxgate sensor in Fig. 4b, we

obtained the mathematical model

U (t) = ieR+ 2 Ldiedt U1(t)+ U2(t)

U1(2)(t) = 15i=1

Fixd (hix + mix)dt

( )

Fix = 4m0(Ne/l li)S = 4m0(Ne/l)Vi

(8)

where U(t) is the excitation voltage, R is the resistance of theexcitation coil with value of 13.3, ie is the current in the

Fig. 8 Comparison between simulation and experimenta Simulated (dashed curve) and experiment (solid curve) currents inthe excitation coil with 1 V peak amplitude sinusoidal voltage excitation at1 kHz and an external measured eld 40 Tb Simulated (dashed curve) and experiment (solid curve) output waveformswith 1 V peak amplitude sinusoidal voltage excitation at 1 kHz and anexternal measured eld 40 Tc Amplitude of the second harmonic at 40 T against excitation voltageamplitude, ( ) experiment result and () SPICE model result

www.ietdl.orgexcitation coil. In Section 2, the excitation magnetic eldwas expressed with the excitation current density J. Here,the current is also expressed by the excitation currentdensity ie = JSc/Ne, where Sc is the cross-section of theexcitation solenoid (Fig. 4a) which is made up of theexcitation coils. The cross-section is parallel with the majoraxis of the rod core. Ne is the number of the excitation coil.L is the hollow inductance of the excitation coil with valueof 6.1 105 H. Coefcient 2 appears because there are twoexcitation coils. U1(t) and U2(t) are the induction voltage ofthe excitation coil. With different inputs ie and ie, U1(t)and U2(t) are obtained, respectively, by calling the circuitfor the core two times. Coefcient 4 appears because aquarter of the model was used. l is the length of the core, liis the length of the ith element, S is the cross-section of thecore and Vi is the volume of the ith element.Observing Figs. 1 and 4a, it is found that if the excitation

voltage, MH law of the core material and the external

Fig. 7 Simulated (dashed curve) and experiment (solid curve)hysteresis loop of the rod core with 2 V peak amplitude sinusoidalvoltage excitation at 1 kHz218& The Institution of Engineering and Technology 2014

IET Sci. Meas. Technol., 2014, Vol. 8, Iss. 4, pp. 214219doi: 10.1049/iet-smt.2013.0129

measured eld were given, the current in the excitation coil,the magnetic eld and the magnetisation of every elementcan be solved at every moment from (6)(8).In absence of external measured eld, the measured and

computed hysteresis loops of the rod core driven by 2 Vpeak amplitude sinusoidal voltage excitation at 1 kHz wereshown in Fig. 7. The measured hysteresis loop of the rodcore can be obtained using

B(t) = 1NpS

V (t) dt

uxgate has conrmed this approach. The model obtainedthrough the new method was suitable for system design ofuxgate. The analysis design of probe and processingcircuits could both be completed. Hence, a time-savingmethod with better effect was achieved. The method canalso be applied to other magnetic devices.

6 Acknowledgments

This work was supported by the Natural Science Foundationof China. (no. 60874101), Higher School Specialized

www.ietdl.orgH(t) = Nelie(t)

where Np is the number of turns of the pick up coil, V(t) is thevoltage across the pick up coil. The core is inserted into onlyone coil, and the other coil is used to compensate for themagnetic eld and any common-mode interference.With 1 V peak amplitude sinusoidal voltage excitation at 1

kHz and an external measured eld 40 T, comparisonbetween the experiment and the simulation result are shownin Figs. 8a and b. Dashed curve (solid curve) in Fig. 8a isthe simulation (experiment) current in the excitation coil.Dashed curve (solid curve) in Fig. 8b is the simulation(experiment) output voltage. Sensitivity of the secondharmonic against excitation voltage amplitude is given inFig. 8c. It can be observed that the simulation results withour SPICE model agree well with the experiment results.The computation time for the dashed curves in Figs. 8a andb is about 8.89 s. We have measured the central processingunit time taken for the generation of the net list. The timeneeded to generating the net list was 0.0103 s.With the traditional SPICE model, the core is described

with one macroscopic magnetisation using demagnetisationfactor. The distribution of the magnetisation was notconsidered. If the actual magnetic eld is inhomogeneous,one macroscopic magnetisation is inaccurate. With ourSPICE model, the magnetisation in each element can beconsidered accurately. In reality, the magnetic eld varieswith the position in the core. Saturation occurs rst in themiddle region of the core, and then the two sides.Demagnetisation factor cannot include this informationcorrectly.

5 Conclusion

To incorporate the geometry of the uxgate into the uxgateSPICE model, a method of SPICE modelling of uxgatesensor was proposed. If the knowledge of the geometry ofthe sensor is known, net lists can be obtained with ourmethod quickly. The parameters including magneticperformance of core, the geometry of the uxgate can beregulated easily. Experiment result of a rod shape coreIET Sci. Meas. Technol., 2014, Vol. 8, Iss. 4, pp. 214219doi: 10.1049/iet-smt.2013.012920126102110031) and Graduate Students EntrepreneurialSeed Fund of Northwest Polytechnical University (nos.Z2013074 and Z2013075).

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2 And, B., Baglio, S., La Malfa, S., Bulsara, A.: SPICE simulation ofcoupled core uxgate magnetometers pp. 15

3 Zhao, Y., Hu, J.L., Lou, W.Z., Zhang, L.F.: The study of a uxgateSPICE model based on schmitt trigger, Key Eng. Mater., 2011, 483,pp. 212218

4 And, B., Baglio, S., La Malfa, S., Bulsara, A.: Adaptive modeling ofhysteretic magnetometers, IEEE Trans. Instrum. Meas., 2012, 61, (5),pp. 13611367

5 Trujillo, H., Cruz, J., Rivero, M., Barrios, M.: Analysis of the uxgateresponse through a simple spice model, Sens. Actuators A, Phys., 1999,75, (1), pp. 17

6 Gupta, S., Ahn, C.H., Park, J.: Electromagnetic modeling and harmonicanalysis of micro-machined ring-type magnetic uxgate sensor usingSPICE pp. 622625

7 And, B., Baglio, S., Bulsara, A., La Malfa, S.: RTD uxgatebehavioral model for circuit simulation, Procedia Eng., 2010, 5,pp. 12881291

8 Aharoni, A.: Local demagnetization in a rectangular ferromagneticprism, Phys. Status Solidi (b), 2002, 229, (3), pp. 14131416

9 Kubk, J., Ripka, P.: Racetrack uxgate sensor core demagnetizationfactor, Sens. Actuators A, Phys., 2008, 143, (2), pp. 237244

10 Vuillermet, Y., Audoin, M., Cuchet, R.: Application of a non-linearmethod of moments to predict microuxgates output. 2010 14thBiennial IEEE Conf. Electromagnetic Field Computation (CEFC), 2010

11 Rakotoarison, H.L., Ardon, V., Chadebec, O., Delinchant, B., Guerin,S., Coulomb, J.L.: Formal sensitivity computation of magneticmoment method, IEEE Trans. Magn., 2008, 44, (6), pp. 10141017

12 Szabo, Z., Ivanyi, A.: Demagnetizing eld in ferromagnetic sheet,Physica B, 2001, 306, pp. 172177

13 Kukrea, O., Bulent Ertan, H.: An integral equation approach to thecomputation of nonlinear elds in electrical machines, IEEE Trans.Magn., 1988, 24, (4), pp. 21182124

14 Canova, A., Repetto, M.: Integral solution of nonlinear magnetostaticeld problems, IEEE Trans. Magn., 2001, 37, (3), pp. 10701077

15 Brachtendorf, H.G., Eck, C., Laur, R.: Macromodeling of hysteresisphenomena with SPICE, IEEE Trans. Circuits Syst. II: Analog Digit.Signal Process., 1997, 44, (5), pp. 378388

16 Mandache, L., Topan, D.: Managing eddy current losses andferromagnetic material nonlinearities in distorting regimes, ElectricMachines and Drives Conference, 2009. IEMDC 09. IEEEInternational, 36 May 2009, pp. 14491454Research Fund for Doctoral Program (no.219& The Institution of Engineering and Technology 2014