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Digital detection and feedback fluxgate magnetometer

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1996 Meas. Sci. Technol. 7 897

(http://iopscience.iop.org/0957-0233/7/6/006)

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Meas. Sci. Technol. 7 (1996) 897–903. Printed in the UK

Digital detection and feedbackfluxgate magnetometer

J Piil-Henriksen , J M G Merayo , O V Nielsen, H Petersen,J Raagaard Petersen and F Primdahl

Department of Automation, Bldg 322, Technical University of Denmark,DK-2800 Lyngby, Denmark

Received 4 January 1996, in final form 12 February 1996, accepted for publication5 March 1996

Abstract. A new full Earth’s field dynamic feedback fluxgate magnetometer isdescribed. It is based entirely on digital signal processing and digital feedbackcontrol, thereby replacing the classical second harmonic tuned analogueelectronics by processor algorithms. Discrete mathematical cross-correlationroutines and substantial oversampling reduce the noise to 71 pT root-mean-squarein a 0.25–10 Hz bandwidth for a full Earth’s field range instrument.

1. Introduction

In fluxgate magnetometry the amorphous metal ring coresensors developed at the Department of Electrophysics(Nielsen et al 1995) and other high-performance sensorsbased on crystalline milled materials are now believedto be so stable and low noise, that in full Earth’s fieldmagnetometers the analogue electronics rather than thesensor will limit the overall performance parameters.

The analogue fluxgate magnetometer traditionally usesthe filtered signal at the second harmonic of the sensor coreexcitation frequency. It is synchronously detected, low-passfiltered and used to control the feedback current flowingin the field compensation coil. The feedback current, ora voltage proportional to this current, is then digitized asa measure of the external magnetic field along the sensormagnetic axis. For a detailed description of the fluxgatemechanism the reader is referred to the review by Primdahl(1979).

All the even harmonic frequencies in the sensor outputsignal contain information about the magnetic field, andPrimdahlet al (1989b) demonstrated the use of the broadband sensor output signal rather than just the secondharmonic, thereby eliminating the need for narrow bandfiltering. This substantially simplified the analogue part ofthe electronics circuits and paved the way for introducinga digital signal processor (DSP) in the signal handlingpath. The broad band performance of the sensors came intofocus, and a re-examination of the fluxgate was undertaken(Primdahlet al 1989a, 1991, Petersenet al 1992).

Replacing the analogue signal processing by mathemat-ical algorithms in a modern high-speed DSP offers the pos-sibility of substantially enhancing the signal handling per-formance over that of the corresponding analogue circuits,and it opens the way for previously unseen flexibility in theoperational modes of the instrumentation. The feasibility ofdigitizing the short circuited fluxgate sensor output current

immediately after the input current-to-voltage amplifier andsubsequently obtaining a magnetic field dependent param-eter, well suited for field balancing and measurement, wasfirst demonstrated at the Department of Electrophysics asreported by Primdahlet al (1994).

The Max-Planck-Institut fur Extraterrestrische Physik,Berlin (Austeret al 1995) built the first real-time operatingFPGA-based feedback magnetometer, aiming at a planetarymission and performing favourably against their MARS-94and Equator-S analogue magnetometers.

The single-axis digital magnetometer described hereis a full Earth’s field instrument with effectively 20 bitssignificant output in the 10 Hz bandwidth, developed andtested around a PC processor board with an Analog DevicesADSP21020 CPU.

For applications on board satellites, and once a DSPis included in the circuits, then software can be made tocontrol a number of features, which previously could onlybe part of the instrument at the expense of added circuitcomplexity—if at all.

Reproducible nonlinearities and temperature changesmay be in-circuit compensated for. The instrumentautonomy may include self calibration and offsetadjustment, and it may be expanded to include failurediagnostics and error mode recovery.

The first experiments with this circuit indicate thatthe overall power consumption is comparable to that ofthe corresponding analogue circuits, which for the Ørstedinstrument is below 2 W. However, the trend in DSPdevelopment goes towards lower power and higher speed,so that a power reduction will probably result in the future.

The remainder of this paper first describes the analoguecircuitry needed to drive the fluxgate sensor, and tocondition the interfaces to the DSP. Next, the DSP board isbriefly described, and the mathematical routines for signaldetection and feedback control are discussed. Experimentalperformance parameters such as noise and frequency

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Figure 1. The excitation driver circuits. The balanced step-up and DC insulating transformer ensures symmetric drive currentin the long sensor drive cables with minimum overcoupling to the other cables. The tuning capacitor CT is placed close tothe sensor core in order to avoid large currents in the cable.

Figure 2. The core excitation current in the nonlinear tank circuit briefly saturates the core twice (in opposite directions)every excitation cycle at a very modest average current.

response are given, and finally, the overall properties ofthis new magnetometer is discussed.

2. Analogue circuitry

The ring–core fluxgate sensor has the same geometry anduses the same type of stress annealed amorphous magneticmetal alloy as the cores for the Danish Ørsted satellitemagnetometer described by Nielsenet al (1995). Thering–core has 11 wraps of amorphous ribbon in a Macor

bobbin supporting about 200 turns of excitation coil. Thesecondary pickup coil has two sections of 295 turns each,as shown in figure 10(a) of Nielsenet al (1995).

The excitation driver circuit (figure 1) is similar to thetank circuit of Acuna (1974). The symmetric 2.1875 kHzexcitation square waves are controlled by the DSP board,and the power switches drive the step-up transformerfollowed by the symmetric 4 mH series inductors, whichconvert the constant voltage output of the transformer intoa constant current drive of the tuned tank circuit formed

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Figure 3. Short-circuited fluxgate secondary input circuit.The coil maintains the enclosed flux 8ext , so that a currentimpulse proportional to the external field is generated everytime the core is saturated and looses its permeability(Primdahl et al 1989b).

by CT (9 µF) and the excitation winding.C0 is a large DCblocking capacitor. The excitation current flowing in thenonlinear ring–core inductor is shown in figure 2. Shortcurrent impulses of 890 mAp−p saturate the core deeply ata very modest average power consumption level.

The input circuit for adapting the sensor secondaryoutput signal to the needs of the input analogue-to-digitalconverter (ADC) is shown in figure 3. The sensor outputcoil is short circuited via the capacitorCinput (3 µF) tothe inverting input of the operational amplifier, and theshort circuit current continues to flow through the feedbackresistor, which determines the current-to-voltage conversionof the sensor current. The operational amplifier is acurrent feedback circuit (AD846) which is inherently stablein this configuration as opposed to the voltage feedbacktypes. This broad band input stage eliminates the need forfurther analogue signal conditioning, and the short circuitoutput mode of the fluxgate sensor has other advantagesas discussed by Primdahlet al (1989b). The feedbackresistorRback (39 k�) is chosen to give the amplified sensornull feedthrough signal an output range of less than the±3.0 Vp−p input of the ADC.

About one excitation period of the output signal is

Figure 4. The fluxgate sensor short-circuit output current. The two lower traces show the actual output current waveformswith the sensor exposed to ±50 000 µT along the sensor axis. The top trace shows the difference between the two lowertraces, and it represents the pure B field generated signal corresponding to 100 000 µT.

shown in the two lower traces of figure 4 (the excitationfrequency here is 6.25 kHz at variance with that of figure 2,and the input stage gain is reduced compared to that offigure 3 in order to accomodate the larger signal). Thetwo lower traces are recorded with the Earth’s field (about50 000 nT) along and antiparallel to the sensor axis, and thedifference signal corresponding to an effectiveB field of100 000 nT is shown at the top. The top trace represents theshape of the pureB field generated signal, and the bottomtraces show the combinedB field and feedthrough signalfrom the sensor. The combined gain of the input path infigure 5 from a DC or slowly varyingB field parallel to thesensor axis and to bits out of the DSP ADC is approximately0.1 nT per bit peak-to-peak amplitude of the signal.

Nulling of the field along the sensor is accomplishedby a separate feedback coil placed coaxially around thefluxgate sensor secondary coil, as indicated in figure 5.The 16-bit digital-to-analogue converter (DAC) on theDSP board controls the feedback current via the resistorRf eedback. The DAC output range is±3.0 V, and it hassufficient current driving capability to generate±50 000 nTvia the 1.49 k� combined feedback and coil copperresistance. The feedback coil has a constant of 27 mT A−1

with 50 000 nT corresponding to a current of 1.85 mA.The DAC 16-bit converter update rate may be as high as500 kHz. It is, however, controlled by the DSP to give oneupdate per excitation period equalling about 457µs. Thisconstitutes a considerable oversampling compared to thefinal 10 Hz bandwidth of the magnetometer, and it accountsfor the more than 16-bit resolution of the instrument. Theresolution of the 16-bit DAC settings corresponds to about1.66 nT bit−1.

3. Digital signal processor board

The DSP PC board (PC/21K-040) is based on theAnalog Devices ADSP21020 processor, procured fromLoughborough Sound Images, UK.

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The complete single-axis magnetometer layout is shownin figure 5 with the±3.0 V 16-bit input ADC, the output16-bit ±3.0 V DAC, and the driver lines for the excitationcircuit. The magnetometer output consists of the 16 bits tothe DAC updated at 2.1875 kHz, and interfaced to the PCvia the DSP–board connector.

The /DATABIT from the DSPLINK output istransferred to the Q input of the first D-flip-flop undertiming control of /IOE, and again transferred to the secondD-flip-flop under precise timing control by the latch to theADC sampling clock. Thereby the ADC sampling is lockedto be exactly an integer 64 times per period of the excitationand with a negligible timing jitter.

An analogue output used for the noise spectral analysisdescribed below is derived directly from the voltage acrossthe Rf eedback resistor. The feedback resistor and thecompensation coil were interchanged in order to have oneside of the resistor grounded, and for filtering it was shuntedby 0.22 µF giving the combined circuit a low pass cut-offat about 100 Hz, which is comfortably larger than the 10 Hznoise bandwidth used below.

4. The detection and control algorithms

In this project two different approaches have been used inimplementing the input filter algorithm—one with a verysimple box-shaped cross-correlation reference, and anotherwhere the filter coefficients (mirroring the reference curve)are obtained from one excitation period of the sensor signalshown in figure 4 (top), by removing the DC componentand by making the two half-periods identical, as suggestedby Primdahlet al (1994). The box-shaped reference wasincluded because the implementation is extremely simple,and by matching the width of the boxes to maximum cross-correlation with theB field signal it performed excellently.

The cross-correlation functionRxr(k) between twodigital signalsx(n) andr(n) is defined as:

Rxr(k) = 1

N

N−1∑n=0

r(n)x(k + n) (1)

whereN is the length of the considered window and equalto one excitation period. If the input signal is periodic,then the correlation is also a periodic function of time, andif the windowN exactly matches the period, then the cross-correlation estimatorsRxr(k) approaches the actual integrallimit values for the continuous functions sampled byx(k)

andr(k).In the time domain equation (1) is seen to be a series

of multiplications followed by a summation. This isgenerally known as a time-convolution or filtering, and itmay be implemented as a finite impulse response (FIR) filterwithout feedback (no zeros), which is always stable. Thefilter coefficientsap must then match theB field sensitivepart of the signal in figure 4 (top) (or the box-shapedreference), and the filter is then implemented according tothe following expression:

y(n) =N−1∑p=0

apx(n − p) (2)

wherex(n) is the input to the filter, and each output valuey(n) represents a weighted average of the precedingN

samples of the input. As indicated aboveN = 64 isused here. Expression (2) is normally realized as a ‘DirectForm 2’ representation (reduced number of stored valuescompared to ‘Direct Form 1’) solely working with: (a) unitdelay, (b) multiplication, (c) addition and (d) simple branch(cf the processor board manuals).

Some characteristic differences exist between the filtersbased on the simple box-reference and on the actualB

field signal. Fourier spectra of both show zeros at theexcitation frequency and at all its odd harmonics. Thechosen box-reference has slightly different even harmonicspectral weights from those of theB signal reference, andit has additional zeros at the 8th, 16th, etc, harmonics.However, this seems not to have any great influence on theperformance but will be the subject of a future investigation.

Figure 6 shows a graphical representation of the filteroutput or the cross-correlation function for two excitationperiods numbered (i) and (i-1). Every single one of the 64points of the cross-correlation function represents a cross-correlation by equation (2) between the filter coefficientsand the 64 preceding input signal samples, and assuminga constant external field the periodic change is caused bythe periodic phase change of the input signal relative to thereference. The average externalB field is supposed to havechanged from period (i) to period (i-1), as reflected by thedifferent amplitudes of the cross-correlation functions.

Figure 6 also explains the detection pattern. Theextremum value of the cross-correlation function occursevery time the input signal and the reference function arein phase, which happens twice every excitation period atprecisely predictable times. The two extreme values aresampled once every excitation period, added, multiplied byan amplification factorAm, and carried as an update tothe summing integrator register, which in turn controls theDAC feedback output. The situation in figure 6 illustratesthe response to aB field in one direction along the fluxgatesensor axis. Inverting the externalB field results in amirroring of the filter output about the time axis.

Being only 32 samples apart, the two averages have astatistical overlap of about 50%.

The integrator in the traditional analogue circuit isreplaced by a summing register being updated once perexcitation period by the selected samples from the cross-correlation function and multiplied by the amplificationfactor Am, as explained above. The final upper 3 dBfrequency of the magnetometer feedback loop transferfunction (100 Hz) is so much smaller than the excitationfrequency that the delay and the discrete steps of theintegrator can be ignored. The basic digital integratortime constant is equal to the update interval, which is theexcitation period of 457µs.

5. Overall magnetometer frequency response

The digital feedback loop is equivalent to a first-order inherently stable analogue loop, and the overallmagnetometer frequency response is determined by thetotal loop gain. The integrator time constant and the

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Digital detection and feedback fluxgate magnetometer

Figure 5. Block diagram of the total digital magnetometer. See text for more information.

Figure 6. Graphical representation of the correlation FIR filter output. Shown are 2 12 excitation periods; each period with

constant B field, but different periods with different B fields. The peaks of maximum signal correlation within each period aresampled, averaged and added to the integrator summing register.

gains from the input magnetic field to the ADC outputbits, and from the output bits to the DAC and to thecompensation magnetic field of the feedback coil are givenabove. The loop gain also contains the fixed FIR filtergain and the amplification factorAm, which is used toadjust the overall instrument response to 100 Hz during the10 Hz noise bandwidth measurements reported below. Theopen loop response of the magnetometer approaches halfthe excitation frequency according to the Nyqvist theorem,

when the FIR filter coefficients correspond to one excitationperiod. The broad band noise will of course in this case belarger than the 10 Hz bandwidth noise.

6. Noise spectral density

The noise of the amorphous metal 17 mm diameter ringcores developed for the Earth’s field mapping Ørstedmagnetometer, and used here for the digital magnetometer,

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J Piil-Henriksen et al

Figure 7. Output noise spectral density (top), and noise signal time series (bottom). The vertical dotted line (top panel)indicates the 0.25 Hz to 10 Hz frequency band having an integrated noise of 71.1 pTrms. The lower panel covers (almost)32 s on the horizontal axis, and the minor divisions of the vertical axis correspond to 100 pT.

is generally found to be in the proximity of 10–20 pTrms in10 Hz bandwidth (Nielsenet al 1995). With the sensorinside a six-layer mu-metal magnetic shield the Ørstedinstrument shows about 50–60 pTrms noise in about 10 Hzbandwidth.

The digital feedback loop fluxgate output noise wasmeasured by connecting the (100 Hz) filtered analogueoutput voltage across the feedback resistor, as describedabove, to the input of a digital 1 mHz–100 kHz averagingFFT analyser. The noise ranged from 70 pTrms to 80 pTrms

depending on the feedback resistor in the band 0.25 Hzto 10 Hz. Figure 7 shows one example of the noise ofa ±52 µT full scale range instrument giving 71 pTrms in0.25–10 Hz bandwidth.

As for the analogue Ørsted instrument the noise of thedigital instrument seems limited by the electronic circuitsrather than by the sensor noise proper. Generally a ratioof about−123 dB for the digital instrument exists betweenthe rms noise and the full scale range, which indicates thatthe DAC and the feedback circuit should be investigatedfor future improvements.

7. Discussion and conclusions

The feasibility of constructing a full Earth’s field digitalfeedback loop fluxgate magnetometer has been successfullydemonstrated. The frequency response and the outputnoise compare well with those of the Earth’s field mappingØrsted analogue magnetometer, but the output noise is still

larger than the open loop sensor noise. The existence ofa constant ratio between output full scale range and noiselevel points to the DAC and the feedback circuit as thedominant limiting factors. Other circuit noise sources notyet seen may of course exist, and these are the subject offuture investigations.

Of equal importance to a full Earth’s field magneto-meter is the stability of the zero level over time andover a temperature range. Here the introduction ofdigital algorithms replacing analogue circuits certainly willdecrease error sources such as offset in the integrator circuitand the odd harmonics sensitivity of the even harmonicsphase detector. Other shortcomings of the analogue circuitsexist, which may be removed or minimized by digitaltechniques.

The implementation of extensive instrument autonomyis important for space instruments and for remoteinstrumentation. A digital instrument is far more adaptableto redundancy, autonomous response to external changes,and to fault detection and corrective actions. Selfcalibration and automatic correction for linearity errorsand temperature changes are obvious new features forimplementation.

In conclusion we believe that the success of thisinstrument, and of that of Austeret al (1995), has openeda new promising route for the development of the classicalfluxgate principle into a still more reliable instrumentapproaching the absolute accuracy and resolution of scalarinstruments.

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Digital detection and feedback fluxgate magnetometer

Acknowledgments

The digital feedback loop fluxgate magnetometer is beingdeveloped as a tri-axial instrument for the Swedishmicrosatellite Astrid-2, and the principle will be tested in1997 on board the planned NASA sounding rocket ‘AuroralTurbulence II’ funded in part by the Danish Technical-Scientific Research Council. The development is made inclose collaboration with the Finnish Sodankyla GeophysicalObservatory, the Alfven Laboratory at the Royal Instituteof Technology, Stockholm, Sweden, and with the Danishcompany Terma Electronics A/S in part funded by theDanish Academy of the Technical Sciences. We wish tothank these institutions for their support.

One of us (JP-H) wishes to thank the Department ofElectrophysics at the Technical University of Denmark forsupport during his work described above as part of thefulfilment of the requirements for a masters degree.

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