a weak magnetic field measurement system using micro-fluxgate sensors and delta-sigma interface

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO. 1, FEBRUARY 2003 103

A Weak Magnetic Field Measurement System UsingMicro-Fluxgate Sensors and Delta–Sigma Interface

Shoji Kawahito, Senior Member, IEEE, Ales Cerman, Keita Aramaki, and Yoshiaki Tadokoro, Member, IEEE

Abstract—This paper presents a weak magnetic field measure-ment system using micro-fluxgate (FG) sensors and a sensor signalprocessing technique using the delta–sigma modulation in the neg-ative feedback loop. The feedback of the lowpass filtered bitstreamoutput of a delta–sigma modulator to the magnetic field improvessystem linearity, hysteresis, and stability. In spite of the fact that thesecond-order delta–sigma modulator is used, the third-order noiseshaping can be obtained in the digital output bit-stream by the useof an integrator in the loop. This improves the SNR of the digitaloutput. The measured noise of the implemented system meets themeasured noise of the FG sensing element itself. The weak mag-netic field in the range of the Earth’s magnetic field is successfullymeasured. The nonlinearity error is less than 0.4% in the range of

100 T.

Index Terms—Delta–sigma modulation, fluxgate (FG) sensors,magnetometers, sensor interface.

I. INTRODUCTION

SMALL low-cost, high-sensitivity magnetic sensors are nowin demand for many applications such as portable navi-

gation systems. For a small and low-cost implementation ofthe system, a silicon-based integrated sensor is useful. How-ever, silicon-based magnetic sensors such as the Hall elementand the magneto-transistor are not compatible with the sensi-tivity required for magnetic compasses [1]. An micro-fluxgate(FG) sensor is a promising candidate for applications that re-quire high sensitivity and small size [2]–[6]. A FG is known asthe most sensitive magnetic sensor, which can be operated atroom temperature [7], [8]. The micro-FG is based on the sameworking principle as the traditional type of FG but is imple-mented in silicon micro technology. Using a CMOS-compatibleFG sensor process technology, the integration of the FG sensingelements with CMOS interface circuits is possible, resulting inthe small-size implementation [9]–[11].

Interface electronics of the FG sensors are divided into twocategories: analog output [9] [10] and digital output [11]. For ap-plications such as portable navigation systems, digital output isuseful. Oversampling digital interface techniques are becomingpopular for various types of sensors [12]–[15]. The digital FGinterface technique reported in [11] uses the first-order modu-lator, and the bitstream output is directly fed back to the mag-netic input. This technique is not always ideal for the good lin-

Manuscript received July 17, 2001; revised November 3, 2002.S. Kawahito is with the Research Institute of Electronic, Shizuoka University,

Hamamatsu, Japan.A. Cerman is with the Department of Measurement, Faculty of Electrical En-

gineering, Czech Technical University, Prague, Czech Republic.K. Aramaki and Y. Tadokoro are with the Toyohashi University of Tech-

nology, Toyohashi, Japan.Digital Object Identifier 10.1109/TIM.2003.809073

earity to the magnetic field because the negative feedback usingthe pulse signal does not meet the nulling of the total magneticfield, which is the measured magnetic field less the feedbackmagnetic field.

This paper presents a new method for the micro-FG magneticsensor interface using delta–sigma a modulation in the negativefeedback loop. In the proposed method, a continuous-timeintegrator and a second-order continuous-time lowpass filterare inserted in front of and at the output of the second-orderdelta–sigma modulator in the negative feedback loop, respec-tively. This method is effective for improving the linearitybecause the lowpass filter reduces the pulse amplitude ofthe bitstream output, and the large low-frequency gain of theintegrator enhances the total loop gain of the negative feedbackto meet the nulling of the magnetic field in the core. The zeroinput condition of the sensor also greatly reduces the sensornonlinearity and hysteresis. Another important property ofthis system is the fact that the third-order noise shaping isobtained in spite of the fact that the second-order sigma-deltamodulator is used. The third-order noise shaping improves thesignal-to-noise ratio (SNR) with a relatively smaller oversam-pling ratio.

This paper is organized as follows. The operation and thestructure of the micro magnetic sensor are described in Sec-tion II. Section III treats the principle of the proposed FG sensorinterface circuits. The experimental results are given in Sec-tion IV.

II. M ICRO-FG SENSOR

Fig. 1 shows the basic FG sensor and its working principle.The basic FG sensor consists of a core of ferromagnetic mate-rial, an excitation coil, and a pick-up coil. The core is excitedby a triangular-wave magnetic field generated by the ex-citation coil. The amplitude has to be large enough to saturatethe magnetic core. At the pick-up coil output, a pulse wave ap-pears due to the induction through the magnetic core. Withoutany external magnetic field, the pulse wave of the pick-up coiloutput is symmetrical, and it contains only odd harmonics ofthe excitation frequency. If an external magnetic field tobe measured is applied, the total magnetic field ,the magnetic induction, and the pick-up coil output become asshown by dashed lines in Fig. 1. This results in the pulse-phaseshifting of the pick-up coil output, and the generation of evenharmonics due to the asymmetry of the pulse. The second har-monic has the largest amplitude among even harmonics, and thereadout electronics usually tune to the second harmonic for thesignal extraction. The amplitude of the second harmonic is pro-portional to the external magnetic field if the external magnetic

0018-9456/03$17.00 © 2003 IEEE

104 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO. 1, FEBRUARY 2003

(a)

(b)

Fig. 1. Basic FG sensor and its working principle. (a) Basic FG sensor.(b) Working principle.

field is sufficiently smaller than the saturation magnetic field ofthe core. The amplitude of the second harmonic is also propor-tional to the excitation frequency in the frequency range wherethe frequency response of the ferromagnetic core is flat [16].This property is based on the fact that the induced voltage at thepick-up coil output is proportional to the derivative of the mag-netic induction.

The configuration of the micro-FG sensor used is shown inFig. 2. The sensor has flat excitation and pick-up coils and adouble-sided symmetrical core [5]. This sensor configurationcomes from an older version with asymmetrical single-sidedcore [9]. The excitation coil is located such that a magneticfield of equal magnitude but opposite sign is applied to the twoferromagnetic cores of the micro-FG sensor. The two pickupcoils are connected in series. Their relative orientation is suchthat the induced voltages of the two coils cancel in the absenceof an external magnetic field. When an external magnetic fieldis present, the magnetic induction in the cores becomes asym-metric, and voltage pulses appear at the series-connected pickupcoils. The coil pitch is 20 m with the wire width of 15 mand the spacing of 5m. The total number of pickup coil turnsand excitation coil turns is 80 and 40, respectively. The size ofthe ferromagnetic (NiFe) core is 1280 640 m. The mea-sured sensitivity of the sensor is 22.5 V/T with the excitationfrequency of 1 MHz. The peak-to-peak noise level is 120 nT inthe frequency range of 10 mH to 10 Hz, and the noise powerspectrum density is 124 nT/Hz @ 1 Hz. More details aboutthe sensor are published in [5].

III. SENSORREAD-OUT ELECTRONIC SYSTEM USING

SIGMA–DELTA MODULATION PRINCIPLE

A. Basic Principle of Readout Electronics

The basic principle of the FG sensor read-out electronics to-gether with the spectrum presentations is shown in Fig. 3. An

ac excitation current generated by the driver excites the sensor.The signal in the sensor output, which is proportional to the mea-sured magnetic field, appears on even harmonics of the excita-tion frequency, and the largest amplitude is held in the second-order harmonic. The phase-sensitive detector (PSD) is tuned tothe second harmonic of the sensor output voltage. The outputof the PSD contains harmonic components other than the de-modulated baseband component. The lowpass filter extracts thebaseband component.

Our interface configuration is derived from this basicprinciple, while negative feedback and delta–sigma modu-lation techniques are used in order to obtain a stable digitaloutput. The block diagram is shown in Fig. 4. The systemconsists of a sensor, a front-end amplifier, a PSD, an in-tegrator, a second-order delta–sigma modulator, a one-bitdigital-to-analog converter, a continuous-time analog lowpassfilter, and a driver. Because of the use of the integrator in theloop, the system has the third-order noise-shaping property inspite of using the second-order delta–sigma modulator.

The sensor is excited by an excitation coil, and its outputsignal is read by the pair of the anti-serially connected pick-upcoils. A feedback coil is coupled to the sensor core. This outputsignal is preamplified by the front-end amplifier with the gainof and the PSD detects the second-order harmonic. Thecontrol signal of the PSD is deduced from the excitation signalby using a frequency doubler and a phase shifter.

For the calculation of the system transfer function as a simpleform, we assume that the FG sensing element, the front-endamplifier, one-bit DAC, and the driver have a flat frequencyresponse in the frequency range of interest. The high-frequencydegradation of the FG sensing element is mainly caused bythe ferromagnetic core. Since the FG sensing elements use athin-film permalloy whose excitation and pick-up magneticfield direction is parallel to the hard axis of the ferromagneticcore, the frequency response is flat up to the order of tens ofmegahertz [4]. The front-end amplifier and the driver can bedesigned to be sufficiently wideband compared to the samplingfrequency. The one-bit DAC is a switch with a reference voltagesource, and it can be assumed to have a flat frequency response.

The detected signal component at the output of the PSD canbe modeled as

(1)

where is the measured external magnetic field, is themagnetic field generated by the feedback coil, andis thesensitivity of the sensing element.

The integrator is implemented with a standard contin-uous-time active integrator. The function of this integrator isthe extraction of the baseband component, an amplification toassure sufficiently large loop gain in the frequency range of thesensor signal, and stabilization of the negative feedback system.Furthermore, the lowpass filtering capability of the integratoracts as an anti-aliasing filter. This is obvious if the excitationfrequency of the FG sensor is chosen to be much higher thanthe sampling frequency of the delta–sigma modulator. Thetransfer function of the integrator is given by

(2)

KAWAHITO et al.: WEAK MAGNETIC FIELD MEASUREMENT SYSTEM 105

Fig. 2. Structure of the micro-FG sensor.

Fig. 3. Frequency domain behavior of the FG sensor signal processing.

where is the open-loop dc gain of the amplifier used inthe integrator. The integrator output is fed to the second-orderdelta–sigma modulator. The block diagram of the modulator isshown in Fig. 5. The transfer function in thedomain is givenby

(3)

where is the quantization noise and the termcharacterizes the second-order noise shaping of the quantizationnoise [17]. The input signal is transferred with two-stepdelay, but without any change of the frequency spectrum. Inthe delta–sigma modulator with a reference voltage of , theinput voltage of the range [ , ] is converted into thedimensionless digital value of the range [1,1]. Therefore, thedelta–sigma modulator is considered to have a gain of

for the signal component. The one-bit DAC with the voltagereference has a gain of . The continuous-time lowpassfilter (LPF) is used in the negative feedback path in order toimprove the linearity. The transfer function of this filter is givenby

(4)

where is the cut-off frequency. The cut-off frequency definesa frequency band of the baseband signal. This cut-off frequencyhas to be chosen to meet the stability condition, which is dis-cussed later. The driver is used to supply a large drive currentto the feedback coil. The feedback coil generates the magneticfield, which compensates the measured external field. Withoutthis LPF, a pulse magnetic signal of large amplitude is appliedto the ferromagnetic core [11]. Though this still works as a neg-ative feedback system, the large pulse influences the systemlinearity due to the large nonlinearity and the hysteresis of theferromagnetic core. For a proper choice of the LPF cut-off fre-quency, the pulse amplitude of the feedback magnetic field in-side the sensor is reduced. It compensates the external magneticfield and, in fact, the sensor works as a zero indicator, whilefeeding a quantization noise to the sensor input for third-ordernoise shaping. This principle of the negative feedback from thefiltered bit-stream of the - modulator very efficiently sup-presses the sensor nonlinearity and hysteresis and enables high-resolution digital detection. The feedback magnetic fieldis generated by a wound feedback coil with the pitch. Thefeedback current is regulated with a resistor . Therefore,

is given by

(5)

B. Stability Condition

To analyze the stability condition of the system, let us con-sider the loop transfer function in thedomain. From (2), thedelta–sigma modulator has a transfer function of for the


Fig. 4. Block diagram of the FG interface using�-� modulator.

Fig. 5. Block diagram of the second-order delta–sigma modulator.

input signal. This term has the gain of 1 and the phase delay ofrad, where is the sampling frequency. Therefore, for

the frequency range , the phase delay is negligible. Fromthe above equations, the loop transfer function in thedomainfor the signal component is given by

(6)

where

(7)

is the dc loop gain. The loop transfer function has three poles.The analysis of the stability condition is simple if we can choose

. In this case, the pole of the integrator becomes thedominant pole. The stability condition of the feedback systemis given by at the phase delay of180 . Since

(8)

and

(9)

the stability condition is given by

(10)

The stability condition is easily met by the choice of the cut-offfrequency of the lowpass filter.

C. Noise Shaping

The negative feedback with the second-order delta–sigmamodulator and the continuous-time integrator has thethird-order noise-shaping characteristic. To analyze thesystem transfer function as a discrete-time system, the transfer

function of the continuous-time integrator is converted todiscrete time using

(11)

This approximation is valid if the frequency range of interestis much smaller than the sampling frequency. The resultingtransfer function of the integrator in thedomain is given by

(12)

where is a constant determined by the ratio ofintegrator cut-off frequency to sampling frequency.

The total loop behavior of the system is characterized by(1)–(5). Equation (2) is replaced by (12). Equation (4), thetransfer function of the lowpass filter, can also be expressedas the -domain function by using (11), and the total systemfunction in the domain can be derived. However, becauseof the complexity of the equation, the derived equation doesnot help in understanding the system behavior. Therefore, twospecial cases are considered here.

First, for the frequency much lower than the LPF cut-off fre-quency, the LPF is assumed to have unity gain and no phasedelay. In this case, (5) is simplified as

(13)

where is the gain of the feedback. The totalsystem function with closed feedback in this case is given by

(14)

where is the total loop gain factor.The actual total dc loop gain is given by . The param-eters and are important for the system behavior. Forand , (14) is simplified to

(15)


Fig. 6. Power spectrum density of the proposed system with third-order noise shaping (MATLAB simulation).

Fig. 7. System output PSD for� < 1 (MATLAB simulation).

where the term stands for the third-order noiseshaping of the quantization noise. Therefore, the third-ordernoise shaping is obtained for the frequency much lower thanthe cut-off frequency of the LPF.

For , the noise superimposed at the input is intensified.In this case, the system transfer function is given by

(16)

where is the noise referred to the magnetic field. The signaland the noise are influenced by the integrator transfer function,and the quantization noise is transferred with the second-ordernoise shaping only.

Next, let us consider the system behavior with the frequencymuch higher than the cut-off frequency of the LPF. In this re-

Fig. 8. Signal processing of the output bitstream.

Fig. 9. Comparison of the proposed system SNR and second-order noiseshaping SNR.

gion, there is no negative feedback effect, and the system hasthe second-order noise shaping property by the second-orderdelta–sigma modulator itself.

Fig. 6 shows the result of a computer simulation usingMATLAB, where the sampling frequency of 1 MHz and cut-offfrequency of the feedback lowpass filter of 20 kHz are used.The third-order noise shaping is obtained in the frequencyrange up to about 10 kHz. The sharp peak presents the magneticsignal of 25 Hz. Fig. 7 shows a simulation result for the case of

. In this case, a small error during the simulation acts asa white noise, and the noise is intensified in the low-frequencyrange by the transfer function for the input noise in (16).


Fig. 10. Circuit schematic of the second-order delta–sigma modulator.

This means that the design of the parameters, and is veryimportant for the low-noise interface.

The effect of the third-order noise shaping is examined bycalculating the SNR. The output of the sensor interface is a bit-stream, and the high-resolution digital data are obtained usinga digital filter. Fig. 8 shows a block diagram of the digital filterused for calculating the SNR. The 64th-order three-stage combfilter section coarsely filters the shaped quantization noise torelax the steep cut-off design of the successive lowpass FIRfilter. In the first decimator, the frequency is down sampledby a factor of 1/64. Then, the cut-off frequency of the 21st-order lowpass FIR filter and the second decimator determinethe bandwidth of the baseband signal and the final samplingfrequency. For instance, a factor of the second decimator ischosen as , where is the oversampling frequency ofthe delta–sigma modulator, and is the cut-off frequency ofthe FIR filter. Fig. 9 shows a simulation result of the achiev-able SNR as a function of the cut-off frequency of the digitalfilter. The oversampling frequency in this case is 1 MHz. Com-pared with the system with the second-order delta–sigma mod-ulator without negative feedback, the proposed system with thesecond-order delta–sigma modulator with the integrator and thenegative feedback enhances the SNR by 11 and 17 dB, respec-tively, for the cut-off frequency of 5 and 1 kHz. Note that thecalculated SNR is only for the quantization noise, and the actualtotal SNR is determined by the total noise due to the sensor, thecircuit components, and the quantization.

IV. EXPERIMENTAL

A real magnetic field measurement system has been imple-mented. Since the micro-FG sensor used does not have a feed-

Fig. 11. Measured power spectrum density of the second-order delta–sigmamodulator implemented with 0.8-�m CMOS.

back coil on the sensor chip, the feedback coil is wound ex-ternally using copper wire with the diameter of 0.1 mm. Thesecond-order delta–sigma modulator is implemented with theindustrial 0.8 m double-poly double-metal CMOS technology.The circuit schematic is shown in Fig. 10. The power spectrumdensity of this modulator output is shown in Fig. 11. The capac-itance used in the modulator is 2 pF. A sufficiently low noisefloor ( 110 dB) and a low harmonic distortion are obtained.The other components are commercially available.

In the experiment, the sensor is excited by 200 mA-sine-wave current at the frequency of 1 MHz using the exci-tation coil. Thus, the PSD is tuned to 2 MHz to extract thebaseband signal components from the second-order harmonic.


Fig. 12. Measured power spectrum density of the proposed magnetometeroutput signal.

(a)

(b)

Fig. 13. Linearity of the digital magnetic detection. (a) Linearity to the appliedmagnetic induction. (b) Nonlinearity error.

The oversampling frequency of the delta–sigma modulator ischosen as 125 kHz in this case to meet the condition andto suppress sufficiently the harmonics of the excitation signal.

The power spectrum density of the system output signal isshown in Fig. 12. The sharp peak shows the input magnetic

signal. The amplitude of the input magnetic field is 150T - ,and the frequency is 25.4 Hz. The third-order noise shaping isobtained in the range from 5 to 10 kHz. In the frequency rangefrom 1 to 5 kHz, the slope of the noise shaping is limited to thesecond order. In the frequency range up to 1 kHz, thenoisedominates the noise level. The noise spectrum density at 1 Hzis about 150 nT/ Hz. This noise level roughly corresponds tothat of the micro-FG sensor itself. The noise of the FG sensoris dominated by the Barkhausen noise, which has anoisecharacteristic [5]. The system linearity and its error in the rangeof the measured magnetic field of100 T are shown in Fig. 13.The hysteresis is less than 0.25T, and the nonlinearity error isless than 0.4%. In the digital FG sensor system using the pulsefeedback reported in [11], the nonlinearity error is about 3%.

V. CONCLUSION

A digital FG magnetic sensor system using a new type ofinterface with delta–sigma modulation and negative feedbackfrom the digital domain has been presented. Low hysteresis andhigh linearity in the digital magnetic detection are obtained.The third-order noise-shaping property of the system has beenconfirmed by an experiment. In the present noise level of themicro-FG sensor used, the quantization noise suppression ef-fect due to the third-order noise shaping is not always usefulfor the totally low-noise design. However, this will be impor-tant for the high-resolution digital magnetic sensor system if alow-noise micro-FG sensor is developed in the near future. Theimplementation of the one-chip CMOS interface is straightfor-ward based on the prototype circuits tested.

ACKNOWLEDGMENT

The authors would like to thank Prof. Dr. P. Ripka of CzechTechnical University for his helpful comments.

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Shoji Kawahito (SM’00) received B.E. and M.E.degrees in electrical and electronic engineering fromToyohashi University of Technology, Toyohashi,Japan, in 1983 and 1985, respectively, and the D.E.degree from Tohoku University, Sendai, Japan, in1988.

In 1988, he joined the Faculty of Electrical En-gineering, Tohoku University, Sendai, Japan. From1989 to 1999, he was with Toyohashi Universityof Technology. He is currently a Professor withthe Research Institute of Electronics, Shizuoka

University, Hamamatsu, Japan. From 1996 to 1997, he was a Visiting Professorat the Swiss Federal Institute of Technology, Zurich, Switzerland. His researchinterests include high-sensitivity magnetic sensors, integrated smart sensors,integrated imaging devices, high-speed and high-sensitivity image sensors, andmixed analog/digital LSI circuits.

Dr. Kawahito is a member of the Institute of Electronics, Information, andCommunication Engineers of Japan and the Institute of Image Information andTelevision Engineers of Japan. He received the Outstanding Paper Award at the1987 IEEE International Symposium on Multiple-Valued Logic and the SpecialFeature Award in LSI Design Contest at the 1998 Asia and South Pacific DesignAutomation Conference.

Ales Cerman received the degree in electrical engi-neering from the Faculty of Electrical Engineering,Czech Technical University, Prague, Czech Republic,in 2000. He is currently pursuing the Ph.D. degreeat the Department of Measurement, Czech TechnicalUniversity.

From September 2000 to April 2001, he was a Re-search Associate of Prof. Kawahito at the ResearchInstitute of Electronics, Shizuoka University, Hama-mastu, Japan. His research interests are FG magne-tometers and design of analog and digital signal pro-

cessing systems and their applications for the sensors.

Keita Aramaki received the B.E. and M.E. degrees in information and com-puter science from Toyohashi University of Technology, Toyohashi, Japan, in1998 and 2001, respectively.

He is currently with the Toyohashi University of Technology as well as AstecCo., Tokyo, Japan. His research topics include magnetic sensor interfaces.

Yoshiaki Tadokoro (M’78) received the B.E., M. E.,and D.E. degrees in electronics engineering from To-hoku University, Sendai, Japan, in 1967, 1969, and1976, respectively.

He is presently with the Toyohashi University ofTechnology, Toyohashi, Japan. His current researchinterests cover one- and two-dimensional signal pro-cessing, multirate signals processing, and navigationsystems for the blind.

Dr. Tadokoro is a member of the Institute of Elec-trical Engineering of Japan, the Electronics, Informa-

tion, and Communication Engineering of Japan, the Society of Instrument andControl Engineering of Japan, and the Institute of Image Information and Tele-vision Engineering of Japan.

a weak magnetic field measurement system using micro-fluxgate sensors and delta-sigma interface

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