Sensors and Actuators A 129 (2006) 75–79

Excitation efficiency of fluxgate sensors

Pavel Ripka a,∗, William G. Hurley b

a Czech Technical University, Faculty of Electrical Engineering, Department of Measurement,Technicka 2, 16627 Praha 6, Czech Republic

b National University of Ireland, Galway, Ireland

Received 4 July 2004; received in revised form 21 March 2005; accepted 19 September 2005Available online 18 January 2006

Abstract

Among ferromagnetic sensors, fluxgates are the most resistant to field shocks. In order to achieve low perming, the peak amplitude of thefluxgate excitation current must be high. The fluxgate excitation efficiency (Ip-p/Irms) can be increased by judicious tuning. This paper describesa simplified analytical solution for the non-linear fluxgate excitation circuit which is very different to the solution for a free-running tank circuit.The experimental results show a surprising effect: high excitation efficiency is achieved only at certain frequencies.© 2005 Elsevier B.V. All rights reserved.

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eywords: Fluxgate; Magnetic sensors; Tuning; Low-power sensors; Magnetometer

. Introduction

Every magnetic sensor containing ferromagnetic material hasemanence, causing “perming error” [1].

AMR sensors use “flipping” field pulses to restore their mag-etisation. It is difficult to reduce the perming of AMR below0 nT for 5 mT shock. The required flipping power is about0 mW for a 1 kHz flipping frequency [2]. The total poweronsumption of a high-precision analog AMR magnetometers about 30 mW, a level comparable to low-power fluxgate sen-ors (typically consuming 50–100 mW), which are physicallyigger, but have lower perming.

GMI sensors use AC measuring current, but this current can-ot demagnetize the sensor core, because it is too small tochieve saturation and the amplitude of the associated magneticeld is zero in the middle of the core cross-section. The typicalerming error is about 100 nT. The sensor can be demagnetisedsing a solenoid, but the circuitry is rather complex. Anotherossibility is to switch between two remanent states. The result-ng system is similar to a fluxgate.

Hall and GMR sensors with flux concentrators usually have

of low-remanence material and they have a suitable geometry,the resulting error is smaller than 1 �T (sometimes 100 nT), sothat it is masked by the temperature offset drift and hysteresisof the sensor itself (for the GMR) [3].

Fluxgate sensors use a high excitation current to achievelow perming (<1 nT) and low noise. The required peak valueof the excitation field should be typically 10-times to 100-timeshigher than the technical saturation value. A properly designedresonant excitation circuit can supply large current peaks usinglow power. Such a “ferroresonant circuit” was first described byBerkman [4]. Later the stability of the ferroresonant circuit wasanalyzed in [5] and performance of sensors working in this modewas reviewed in [6]. Parallel resonant excitation from a currentsource is commonly used (Fig. 1(a and b)) [7], but it is alsopossible to use a series resonance circuit powered by a voltagesource (Fig. 1(c)) [8]. The shape of the resonance current peakis practically independent of the voltage waveform. The mainadvantage of the series resonant circuit is that it can be excitedby switching a low voltage source—this is important especiallyfor 3-axis sensors, which are excited in series. Excitation powerof a typical untuned fluxgate sensor is 300–500 mW and it can

o demagnetisation coil. However, if the concentrators are made

∗ Corresponding author. Tel.: +4202 24353945; fax: +4202 33339929.

be reduced by a factor of 5–10. Perming is a particularly seri-ous problem in micro-fluxgate sensors incorporating flat coils,which cannot be effectively tuned.

The fluxgate tuned excitation circuit is highly non-linear, asthe sensor core is saturated for a large part of the excitationc

E-mail addresses: ripka@feld.cvut.cz (P. Ripka), ger.hurley@nuigalway.ieW.G. Hurley).

924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2005.09.047

ycle. Nielsen et al. [9] used numerical iteration to solve the

76 P. Ripka, W.G. Hurley / Sensors and Actuators A 129 (2006) 75–79

Fig. 1. Fluxgate excitation circuits: parallel supplied from the current source (a); parallel supplied from the voltage source (b) (from [7]); serial supplied from thevoltage source (c) (from [8]).

equations of the tank circuit, with losses, fed by a sinewave cur-rent source. The authors have shown that it is possible to find aneffectively simplified analytical solution. The simplified analy-sis of the non-linear tank circuit in fluxgate excitation may besummarized as follows: in Fig. 2 the capacitor C is charged fromthe current source and the excitation current increases slowly dueto the presence of the large unsaturated inductance. At the onsetof saturation in the sensor core the reactance of the excitationcoil falls causing the capacitor to discharge, resulting in a largecurrent peak. The magnetic field energy of the saturated induc-tance (which is now effectively an air coil) is then returned tothe capacitor. A more detailed explanation is offered in the nextsection.

2. Simplified solution

The core of a high-performance fluxgate sensor is usuallyannealed so that it has a linear characteristic (constant perme-ability) up to the point of saturation. Thus, it may be stated thatthe excitation coil inductance L in Fig. 2 has two values: a highvalue of LN in the non-saturated state, corresponding to a low

resonance frequency ωN = 1/√

LNC, and a low value of induc-tance LS in saturation (air inductance), corresponding to a highresonance frequency ωS.

For the purposes of the analysis, we divide one half of theexcitation cycle T = 2π/ω into the three time intervals shown inFig. 3:

Interval 1: 0–t1In the first interval (0, t1) the core is not saturated and the

current increases from zero up to the saturation current IS.The capacitor current may be approximated to a sinewave

given by

Ic=̇I = I0 sin(ωt).

The solution for the inductor current is then (ignoring the sign):

ILn = I0

ω2LNCsin ωt = I0

(ωN

ω

)2sin ωt

Fig. 2. Parallel excitation tank supplied by sinewave current (from [4]).

Fig. 3. Idealized excitation current waveform (from [4]).

P. Ripka, W.G. Hurley / Sensors and Actuators A 129 (2006) 75–79 77

where ωN = 1/√

LNC is a natural resonance frequency of theloss-less parallel circuit with an unsaturated inductor (in ourcase, ω 〉〉 ωN). I0 is the generator current amplitude ω = 2π/Tand is the generator frequency.

Interval 2: t1–t2In the second time interval (t1, t2) the core is saturated.The excitation current rises to its maximum value IM and

decreases back to IS at t2.We can solve the circuit as a free-running tank.If we neglect the ohmic resistance, the solution for the exci-

tation current is

ILs = AS sin ωs(t − t1) + IS

where ωS = 1/√

LSC is a natural frequency for the tank circuitwith the saturated sensor inductor and the saturation current ISis the value of the inductor current at t1 (onset of saturation),given by

IS = I0

ω2LNCsin ωt1 = ω2

N

ω2 I0 sin ωt1

Interval 3: t2–T/2

Fig. 4. Fluxgate tuned by 1.1 �F capacitor at 15 kHz. Upper trace: excitationcurrent (250 mA/div), middle trace: generator current (100 mA/div), lower trace:excitation voltage (1 V/div).

3. The measurements

Validation measurements were performed on 30 mm longrace-track fluxgate field sensors. The sensor core is made of foursheets etched from 40-mm-thick amorphous Vitrovac 8116. Thecore is 30 mm long and 8 mm wide, the track width is 1.5 mm[11]. The excitation current amplitude sufficient to reduce theperming effect of this sensor below 1 nT was 600 mA p-p. Fig. 4shows the measured current waveforms: the tuned excitation cur-rent I is 750 mA p-p with rms level of 120 mA. The current peaksare delivered by the parallel tuning capacitor C = 1.1 �F so thatthe total current supplied from the generator is only 30 mA rms(middle trace). The measured waveform agrees well with themodel shown in Fig. 3. The saturation current can be estimatedfrom Fig. 5 as IS = 3.5 mA. Thus, IM in this case is very high:

In the third interval (t2, T/2) the core reverts to its unsaturatedstate and equations for interval 1 apply.

The circuit equations were solved separately for both modesin three time intervals, taking the boundary conditions intoaccount, i.e. continuity of excitation current and capacitor volt-age [7]. The resonant condition is

IS

I0ω2LNC = 1 or

IS

I0

ω2

ω2N

= 1 (1)

This simplified solution adequately describes the observedbehavior of tuned fluxgates: the resonance condition dependsnot only on C and ω, but also on generator amplitude I0. Adecrease in the number of excitation turns n should be com-pensated by a proportional increase in C, because LN ∼ n2 andIS ∼ 1/n.

Supposing that IM � IS, the maximum excitation current isgiven by

IM =√

I0ISLN

LS(2)

Thus, if the resonance condition is met, IM does not depend onC. The figure of merit for deep saturation is IM/IS, which doesnot depend on n. To increase this factor we need magnetic mate-rial with low saturation induction and high permeability, whichgives a high value of LN. We also should keep the excitationwinding close to the core, to achieve low LS—this is similar tothe requirements for a pick-up coil of a current-output fluxgate[10]. The ratio of inductances may be shown to be

LN

LS= 1 + µr Acore

Aair(3)

Fig. 5. Excitation current waveform enlarged to 5 mA/div (upper trace).

78 P. Ripka, W.G. Hurley / Sensors and Actuators A 129 (2006) 75–79

Fig. 6. Excitation power vs. excitation current p-p amplitude. Thick line high-lights the range of in Table 1.

Table 1Excitation power vs. frequency for 1 A p-p current

f (kHz) Vgo (V p-p) C (�F) A (�J) P (mW)

5 19 6.7 4 2010 15.4 2 1.78 17.815 15 1 1 1530 15 0.2 0.85 25.545 17 0.07 0.56 25.260 20 0.035 0.25 15

100 20 0.05 0.31 31

The sensor was always tuned by C for minimum power.

IM = 100IS and we can calculate from (1) and (2) that LS = 1.1 �Hand LN = 1.28 mH. This corresponds to the measured values andit was deduced from (3) that �r = 13000.

The complex behavior of the excitation tank circuit is causedby its substantial non-linearity. In our case, the largest currentamplitude achievable with a 20 V p-p output voltage genera-tor (having 50 � output resistance) was 1.6 A p-p at 45 kHz,while for 5 kHz it was only 1 A. High current amplitudes at highfrequency mean increased power consumption—this is true foreach fixed frequency. Fig. 6 shows the excitation power versuscurrent amplitude for frequencies between 15 and 100 kHz.

Excitation current of 1 A p-p was finally selected as it guar-antees high sensor stability at reasonable power consumption.Table 1 shows the excitation parameters achieved for this cur-rent at various frequencies. A is the energy required for oneexcitation cycle, while P is the excitation power. The favourableworking frequency is around 15 kHz, where the excitation powerconsumption has a local minimum of 15 mW. Another powerminimum appears at 60 kHz.

4. Conclusions

Fluxgate sensors have the lowest perming error of all fer-romagnetic sensors. It has been shown that their excitation

efficiency can be increased by proper tuning—1 nT permingfor 5 mT field shock can be achieved at 50 mW power con-sumption. The simplified model of the fluxgate excitation circuitexplains the observed properties of the non-linear circuit nearthe favourable operating point. The model provides guidelinesfor sensor designers. Experimental work shows that the powerconsumption is not monotonically increasing with frequency:local minima appear, which illustrate that simple design rulesbased on linear analysis cannot be used. The given analysis isbased on sinewave current excitation; the case of squarewavecurrent or voltage excitation is quite different and was analyzedin [8].

References

[1] P. Ripka, Magnetic Sensors and Magnetometers, Artech, Boston-London,2001.

[2] H. Hauser, et al., Flipping field and stability in anisotropic magnetore-sistive sensors, Sens. Actuators A 106 (34–37) (2003) 121–125.

[3] M. Vopalensky, P. Ripka, J. Kubik, M. Tondra, Improved GMR sensorbiasing design, Sens. Actuators A 110 (2004) 254–258.

[4] R.Ja. Berkman, B.L. Bondaruk, Feroresonansnyj rezhim vozbuzhdeniamagni nych modulatorov i ferozondov (Ferroresonance mode of exci-tation of magnetic modulators and fluxgate sensors), Geofiziczeskayaapparatura 50 (1972) 20.

[5] R. Berkman, B. Bondaruk, V. Korepanov, Advanced flux-gate magne-tometers with low drift, in: Proceedings of the MEKO 1997 World

[

[

B

MmEmSf

Congress, pp. 121–126.[6] V. Korepanov, R. Berkman, L. Rakhlin, Ye. Klymovych, A. Prystai, A.

Marussenkov, M. Afanassenko, Advanced field magnetometers compar-ative study, Measurement 29 (2001) 137–146.

[7] P. Ripka, W.G. Hurley, Excitation tuning of fluxgate sensors, in: Pro-ceedings of the IMTC 2002, pp. 677–680.

[8] P. Ripka, W.G. Hurley, Switching-mode fluxgate, in: Proceedings of theTransducers Conference, Boston, 2003, pp. 1283–1286.

[9] O.V. Nielsen, et al., Development, construction and analysis ofthe ’Orsted’ fluxgate magnetometer, Meas. Sci. Technol. 6 (1995)1099–1115.

10] F. Primdahl, et al., The sensitivity parameters of the short-circuited flux-gate, Meas. Sci. Technol. 2 (1991) 1039–1045.

11] P. Ripka, Race-track fluxgate with adjustable feedthrough, Sens. Actua-tors A 85 (2000) 22.

iographies

Pavel Ripka received an Engineering degree in 1984,a CSc (equivalent to PhD) in 1989, Docent degreein 1996 and in 2002 Professor degree at the CzechTechnical University, Prague, Czech Republic. Dur-ing 1991–1993, he was a visiting researcher at theDanish Technical University and during 2001 he heldMarie Curie Experienced Researcher’s Fellowship atthe National University of Ireland, Galway. He worksat the Department of Measurement, Faculty of Elec-trical Engineering, Czech Technical University as aprofessor, lecturing in Measurements, Engineering

agnetism and Sensors. His main research interests are Magnetic Measure-ents and Magnetic Sensors, especially Fluxgate. He is a member of IEEE,lektra society, Czech Metrological Society, Czech National IMEKO Com-ittee, Eurosensors Steering Committee and Associated Editor of the IEEEensors Journal. He was a General Chairman of the Eurosensors XVI con-erence held in Prague in 2002.

P. Ripka, W.G. Hurley / Sensors and Actuators A 129 (2006) 75–79 79

William Gerard Hurley (M’77, SM’90) was bornin Cork, Ireland. He received the BE degree with1st class honors in Electrical Engineering from theNational University of Ireland, Cork in 1974. TheMS degree in Electrical Engineering from the Mas-sachusetts Institute of Technology, Cambridge MA,in 1976 and the PhD degree at the National Uni-versity of Ireland, Galway in 1988. He worked forHoneywell Controls in Canada as a Product Engi-neer from 1977 to 1979. He worked as a Develop-ment Engineer in transmission lines at Ontario Hydro

from 1979 to 1983. He lectured in electronic engineering at the University

of Limerick, Ireland from 1983 to 1991 and is currently Vice Presidentand Professor of Electrical Engineering at the National University of Ire-land, Galway. He was a visiting professor at the Massachusetts Instituteof Technology in 1997/1998. He is the Director of the Power ElectronicsResearch Center in Galway. Research interests include high frequency mag-netics, power quality, automotive electronics and alternative energy systems.He received a Best Paper Prize for the IEEE Transactions on Power Elec-tronics in 2000. Prof. Hurley is a Fellow of the Institution of Engineers ofIreland and a member of Sigma Xi. He has served as a member of theAdministrative Committee of the Power Electronics Society of the IEEEand was General Chair of the Power Electronics Specialists Conference in2000.