Instrumentation and MeasurementTechnology Conference - IMTC 2007Warsaw, Poland, May 1-3, 2007

Direct Interface for Magnetoresistive Sensors

E. Sifuentes"2, 0. Casas', and R. Pallas-Areny1 Instrumentation, Sensors and Interfaces Group

Castelldefels School of Technology, Technical University of Catalonia (UPC)Av. Canal Olimpic s/n 08860 Castelldefels (Barcelona), Spain

2 Autonomous University of Ciudad Juarez (UACJ), Computer and Electrical Engineering DepartmentAv. del Charro 450 nte., Juarez, Chihuahua, Mexico.

Abstract - AMR and GMR magnetoresistive sensors are typicallyconnected to form a Wheatstone bridge with four or two activesensing elements. The resistance change of each sensing elementis proportional to the external magnetic field over a limited fieldrangea The bridge output voltage is then linear for bridges withfour active sensors and nonlinearfor bridges with only two activesensors. This paper proposes an alternative method to directlyconnect magnetoresistive sensors to microcontrollers withoutplacing any active component between them. The sensor bridge isconsidered to be a resistive network with three inputs and oneoutput. Using one input in turn to measure the discharge time ofacapacitor connected to the bridge output, we obtain three differentdischarge times. We propose two equations that combine thosethree discharge times to obtain a digital output proportional to thefractional resistance change; one equation is usedfor sensors withfour active sensing elements and the other equation is used forsensors with only two active sensing elements. Measurements onan emulated sensor bridge yield a nonlinearity error below0.3 %FSR and a resolution of 12 bit. Measurements oncommercial AMR and GMR sensors yield nonlinearity errorsbelow 0.6 %FSR and 2.5 %FSR respectively, which are smallerthan the specified nonlinearity errorfor each sensor alonea

elements are connected in a half-bridge circuit (asymmetricalbridge circuit, Fig. 2), where only two arms are active and theother two arms are shielded from external magnetic fields.Then, the bridge output voltage is nonlinear. Whatever thenumber of active GMR elements, the common approach is tosupply the bridge a constant voltage or current and thenmeasure the output voltage, which is successively amplifiedand digitized by an ADC. Some industrial applications ofmagnetoresistive sensors are summarized in [3].

R +AR0

Vr

Ro -AR

Ro -AR

0vOo

Ro +AR

Fig. 1. AMR sensor built by connecting four magnetoresistive elements intoa Wheatstone bridge.

Keywords - Magnetoresistive sensors, sensor bridge, direct sensor-to- microcontroller interface, AMR sensor, GMR sensor.

I. INTRODUCTION Vr

The electrical resistance of magnetoresistive sensors

depends on the external magnetic field applied to them. Foranisotropic magnetoresistive (AMR) materials, the change inresistance is linear over a limited range of magnetic fieldstrengths [1]. To obtain a linear response, in a typicalconfiguration, four AMR films are connected to form a

Wheatstone bridge and a magnetic thin film is deposited on

them to supply a bias field that brings each bridge arm into itslinear region. The sensing films are so designed as to have theresistance of two of them increase and those of the two otherfilms decrease when subjected to an external field (Fig. 1). Ifthe bridge is supplied by a constant voltage, its output voltageis proportional to the fractional resistance change, hence tothe applied magnetic field.

The resistance of giant magnetoresistive materials (GMR)has also a nonlinear dependence on external magnetic fields[2]. Four GMR elements are either connected in a

Wheatstone bridge configuration, as in Fig. 1, or two GMR

Ro +AR Ro

Fig. 2. GMR sensor built from four magnetoresistive elements, two ofwhichare shielded from external magnetic fields.

It has been previously shown that resistive sensors can bedirectly connected to microcontrollers by measuring the timeneeded to discharge through them a capacitor previouslycharged through a reference resistor [4]. The method can alsobe applied to resistive sensor bridges [5], provided theequivalent impedance seen between any pair of bridgeterminals is resistive (i.e., there are not any internal activecircuits, for example for temperature compensation). Theresulting system is simple, compact, and low cost because no

integrated circuits other than the sensor and themicrocontroller are involved in the signal path.

The aim of this work is to apply that compact solution toconnecting AMR and GMR sensors to a (low-cost, low-

1-4244-0589-0/07/$20.00 ©2007 IEEE

Ro Ro +AR

V-- 01

1

power) MSP430 microcontroller (MCU), in such a way as toobtain a digital output proportional to the resistance variation,regardless of whether the sensor includes four (Fig. 1) or two(Fig. 2) active sensing elements.

II. MEASUREMENT METHOD

The interface circuit for resistive sensor bridges analyzedin [5] relies on considering the bridge circuit to be a networkwith three input terminals and one output terminal (orconversely) (Fig. 3), instead of the usual two input terminalsand two output terminals considered in amplitude-basedinterfaces. In Fig. 3, first the capacitor C is charged throughRp, and then it is discharged through the equivalent resistancebetween node A and pin Al, by placing pins A2 and A3 inhigh impedance state; the time to discharge C to VTL (lowthreshold voltage of the internal Schmitt trigger in pin A4) ismeasured by the timer/counter embedded in the MCU. C ischarged again and discharged through the equivalentresistance between node A and pin A2, and the dischargetime measured; finally, C is charged once more anddischarged, this time through the equivalent resistancebetween node A and pin A3.

VDD

Req3 =R0(1- x)(3 + x) (4)

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where x is the fractional resistance change. If the internalresistances of the MCU pins, Rmin, are assumed to be muchsmaller than the equivalent resistances, Rm,- << Reqi, therespective discharge times through each equivalent resistanceare

(5)VDDt,=

~qiTL

To obtain a linear digital output and some interferencecompensation, we can calculate the ratio (to cancelmultiplicative interference) of a difference between measuredtimes (to cancel additive interference). The algorithmproposed for an AMR sensor (four active arms) is

tl -t3t2

(6)

which is the same algorithm used in [5] for piezoresistivepressure sensors. For a GMR sensor connected in a half-bridge circuit, the arm resistances in Fig. 3 are

RI=R4 =Ro(1+ x)= R3 =o

I/O A2

1/0 -Al

1/0 - A4 A

1/0 - A5

Fig. 3. Direct connection between a Wheatstone bridge and a

microcontroller.

The aim is to obtain a digital output proportional to theresistance variation by combining the three discharge timesmeasured. For a bridge with four AMR sensors (Fig. 3), therespective arm resistances are

R1 =R4 =Ro(1+x)

R2=R3 =Ro(1-x)(1)

and the equivalent resistances seen from pins Al, A2 and A3to node A respectively are

The equivalent resistances seen from pins Al, A2 and A3 tonode A are now

- R0(3+4x+x2)Reqi= A-i-±r

(6)EtmJb

Ro(4+4x+x2)

Req2 44+2x

R -Ro (3+2x)4+2x

The calculation method proposed to calculate the fractionalresistance change for such a GMR sensor is

2 t -t3 = Xt2 + t3 -tl

(1 1)

Therefore, it is possible to determine the fractionalresistance change for both sensor bridges.

III. MATERIALS AND METHODS

(9)(10)

Reql Ro (1+ x)(3 - x)4

Req2 = Ro

(2) The experimental work to assess the validity of the(2) proposed measurement method has been divided in two

(3) stages: a) Measurements on two emulated MR sensors, and b)measurements on two commercial sensors (AMR and GMR).

2

1/0 - A3 (7)

A. Measurements on emulatedMR sensors

First, an AMR sensor has been emulated by a completeWheatstone bridge built from 1000 Q (1 0/O) resistors.Changes in each bridge arm were induced by placing resistorsin parallel with R2 and R3 to produce RO(1 - x), and resistors inseries with R1 and R4 to produce Ro(1 + x). To emulate aGMR sensor, we built a half-bridge circuit with the sameresistors, but now only R1 and R4 were changed to produceRo(I + x). In both bridge circuits, the added resistors wereselected to obtain fractional resistance variations (x) from0.5 %otO 10o%.

Figure 4 shows the measurement circuit. An MSP430F123microcontroller running at 4 MIHz (quartz oscillator clock) issupplied at 3 V by a dedicated voltage regulator (LF30CV) toreduce power supply interference, which may result in triggernoise. The embedded 16-bit timer/counter counts thedischarge time by incrementing its value every 250 ns. Thefunction of pins Al, A2, A3, A4, and A5 in Fig. 3 wasimplemented by, respectively, pins P3.3, P3.6, P3.7, P1.3,and P1.2. The equations to calculate x from the measuredtimes were (6) and (11).

To reduce the effect of the internal trigger noise, the MCUwas set in LPM0 mode (disabled CPU but enabled timer andinterruptions) while the discharge times where beingmeasured [4]. Pin P1.3 (external interrupt pin with a STbuffer) was set to interrupt the MCU (on the falling edge)every time the discharging C voltage reached VTL. The MCUprogram was written in assembler language. Rp was includedto improve the rejection of power supply interference whencharging capacitor C [4]. Because a large Rp lengthens themeasurement time, we selected Rp 120 Q, which results incharging times of 1 ms in each measurement.C was selected to obtain a suitable time constant (T=

ReqiC) for the discharge circuit. A large time constant impliesa slow slew rate of the exponentially decaying voltagewaveform at the trigger point, which makes the triggeringprocess more susceptible to noise, hence increasing the countdispersion and the standard deviation ofthe measurement. Onthe other hand, a too short time constant yields too fewcounts, hence a large quantization error. The optimal timeconstant for our circuit was experimentally determined to beabout 2-3 ms. Hence, we selected C = 2.2 tF, with +5 00tolerance and 100 x 1 0-6/C temperature coefficient.

The discharge times t1, t2 and t3 corresponding to,respectively, Reql, Req2, and Req3, were measured 100 timesand were sent to a PC via RS-232 by a control program inLabVIEW. The average value of each discharge time wascalculated. Then, the mean x was calculated by (6) for full-bridge sensors and by (11) for half-bridge sensors. The serialcommunication interface was implemented by a MAX3223supplied by a separate voltage regulator (LF30CV) to preventthat its functioning induced transients in the power supplyand affected the discharging process. Reqi, Req2, and Req3 weremeasured by a 6 1/2 digit multimeter (Agilent 34401A), whosereadings were taken as the actual resistance values, from

which the theoretical x value was calculated by using (6) and(11) again.

Voltage Regulator(LF30CV)

Cd =100 nF3V

MR sensorVDD P3.7 r -_,

P3.6

MSP430 p33 R

P1.3 A

P 1.2 WV

R/X R,, = 120 0 C

Voltage Regulator 3 V RS-232s;

Fig. 4. Measurement setup to evaluate different algorithms to calculatefractional resistance changes in a sensor bridge from time measurements.

B. Measurements onAMR and GMR sensors

The measurements on two commercial MR sensors wereimplemented by the setup in Fig. 4 and applying the samedesign solutions as in section III.A. The two sensors testedwere HMC1052 (Honeywell) (AMR type) and AAH002(NVE) (GMR type, two active arms). We build a 55 cm long(L) solenoid with 2 cm in radius (R) and 330 turns (N) ofAWG 20 enamel copper wire. For these dimensions, themagnetic flux density (B) along the z axis was uniform in thecenter ofthe solenoid (z = 0) and his value was

B=- ,NI

C4R2 + L2(12)

Near the ends of the solenoid, B deviated by less than i0.26 00 with respect to the value at the center of the solenoid[6]. (In an infinitely long solenoid, B would be constant alongits central axis.) The sensors were placed about the center ofthe solenoid with their sensitivity axis parallel to themagnetic field. By controlling the applied current, we couldchange B, whose values were selected from 0.75 G to 6 G forthe AMR sensor and from 0.75 G to 2.9 G for the GMRsensor.

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IV. EXPERIMENTAL RESULTS AND DISCUSSION

A. EmulatedMR sensors

For the full-bridge sensor circuit, x was calculated by (6)for each group of 100 time measurements (t1, t2, t3), in therange 0 < x < 0.1. The standard deviation s(x) = 7.4 x 10-,attributable to power supply interference, quantization noiseand CPU internal noise, was quite constant over themeasurement range. The nonlinearity error, calculated fromthe best straight line fitted to the data points, was 0.2 %FSRmaximum (Fig. 5).

In the half-bridge sensor circuit, x was calculated by (11).The standard deviation s(x) = 1.6 x 10-4 was also constantover the measurement range. The nonlinearity error obtainedfrom the best straight line fitted to the data points was0.3 %FSR maximum (Fig. 6). This error and the standarddeviation were a bit larger than those for a full-bridge circuit,probably because of error propagation in (11), which involvesfive time measurements, as compared to only three timemeasurements in (6).

In both bridge circuits, the nonlinearity error can belargely attributed to the non-ideal characteristics of the MCUports [4]. In particular, each pin has a non-negligible internalresistance (Rmin) of about tens of ohms that adds to Reqi. Thisresistance lengthens the discharge times and result in anonlinear relationship between the bridge resistance and themeasured time.

Nonlinearity error (%FSR)

the CPU activity during the measurement process. Hence, wedo not need an external Schmitt trigger as used in [5].

The novel algorithm (11) yields a digital outputproportional to fractional resistance change for asymmetricalbridge sensors (Fig. 2). Such a linear relationship can also beobtained in voltage-based interfaces, that in addition canprovide faster responses, but at the cost of adding severalcircuits between the bridge and the MCU [7].

The effective resolution was 12 bits for both bridgecircuits, when calculated from the standard deviation of themean x estimated with 100 observations and a coveragefactor k = 2. We used a 4 MHz quartz oscillator clock insteadof the 20 MHz clock used in [5]. This is because the PICMCU used in [5] had an effective clock of only 5 MHz due toits internal timing for instruction execution; the 20 MiHzresulted in a higher internal noise, without the benefit of ahigh effective clock frequency for time measurement. Theresolution could be improved increasing the MSP430 clockfrequency, but a faster stable clock would be more expensiveand consume more power.

B. AMR and GMR sensors

For the HMC1052 AMR sensor, x was calculated by (6)for each group of 100 time measurements (t1, t2, t3). Thestandard deviation s(x) = 7.75 x 10-5 was similar to thatobtained for an emulated AMR sensor, and it was alsoconstant over the measurement range 0.75 G < B < 6 G (Fig.7). The best straight line fit to the data points was

B (G)= 1032x- 0.0196 (13)0.25

0.20

0.15

0.10

0.05

0.002 3 4 5 6 7 8 9 10 11

x (%)

Fig. 5. Nonlinearity error obtained from the best straight line fittedto the data points in a full- bridge sensor circuit.

The measurement circuit here designed for a full bridgeoutperforms that in [5], in spite of the same algorithm (6)being used in both circuits. The circuit here was supplied at3 V, which is more common in portable battery poweredapplications than the 5 V supply used in [5]. Further, theMSP430123 has five power-saving programmable modes,which reduce power consumption. The LPMO mode usedhere is similar to the idle mode available in othermicrocontrollers, where the CPU is also disabled; thisoperating mode eliminates the internal trigger noise due to

The nonlinearity error was 0.6 %FSR maximum, hencesmaller than the typical nonlinearity error specified by thesensor alone when the bridge output voltage is measured(+1.8 %FSR). The resolution was 7.5 mG, and it was limitedby laboratory instruments used to generate small changes ofmagnetic flux density.

Nonlinearity error (%FSR)

0 35 r r rF r r F r r r r

0.30

0.25

0.20

0.15

0.10

0.05

0.005 6

x (%)

8 9 10 11

Fig. 6. Nonlinearity error obtained from the best straight line fittedto the data points in an asymmetrical, half- bridge, sensor circuit (Fig.2).

4

x experimental (/o)o 65

o. 55

o 45

o. 35

o 25

o 15

o 050.7 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7 5.2 5.7 6.2

B (G)

Fig. 7. Experimental fractional resistance change x calculated by (6)vs. magnetic flux density applied to a HMC 1052 AM\R sensor.

0.70-

0.60-

0.50-

0.40-

0.30-

0.20-

0.10

0.00

Nonlinearity error (%FSR)

0.7 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7 5.2 5.7 6.2B (G)

Fig. 8. Experimental nonlinearity error obtained for the magneticflux density applied to a HMC 1052 AM\R sensor.

x (%)

Nonlinearity error (%FSR)

4

2

0.7 0.9 II 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9

B (G)

Fig. 10. Experimental nonlinearity error obtained for the magneticflux density applied to an AAH002 GMR sensor.

The nonlinearity error was 6.0 0OFSR maximum, muchlarger than the 0.3 00 obtained for an emulated sensor bridge(Fig. 6). If we approximated the sensor response by aquadratic curve instead, the maximal difference was 2.600FSR~, hence smaller than that obtained with the linearapproximation in (14). This suggests that the actual GNMRsensor response is almost quadratic. Hence, we applied theLimited Maximal Error (LME) calibration criterion proposedin [8] to linearize measurement systems with quadraticresponse. If the error at the ends of the measurement rangewas accepted to be equal to the error at the center of themeasurement range, the two optimal calibration points were1.06 G and 2.58 G. The two calibration points used inpractice were 1.05 G and 2.55 G, quite close to those optimalpoints. The best straight-line fit to the data points was then

B (G) =62.298x -0.9647 (15)

4

2

B (G)

Fig. 9. Experimental fractional resistance change x calculated by (I11)vs. magnetic flux density applied to an AAH002 GMR sensor.

For the AAHOO02 GNMR sensor, x was calculated by ( 1)fur each group of 100 time measurements (t1, t2, t3). Thestandard deviation s(x)= 1.8 X 10-4 was similar to thatobtained for an emulated GNMR sensor, and it was alsoconstant over the measurement range 0.75 G < B < 2.9 G.The resolution obtained for B was 7.5 mG. Applying the leastsquares method to the actual response of the sensor, the beststraight-line fit to the data points (Fig. 9) was

B (G) =63.567x -1.064 (14)

The maximal nonlinearity error in this case (Fig. 10) was6.8 0OFSR maximum, which is a bit larger than that obtainedby (14), probably because of the actual values of the twocalibration points used, which did not were the optimal pointscalculated. Fig. 10 shows the typical shape for thenonlinearity error of a quadratic response approximated by astraight line drawn through two calibration points other thanthe end points [8].

The typical nonlinearity error specified for the sensorbridge alone when supplied at constant voltage and its outputvoltage is measured, is 4 00. In order to know the actualsensor response when used in this "voltage mode", wesupplied it at 3 V and its output voltage was measured by a6 1/2 digit multimeter (Agilent 34401lA) for 0.75 G < B <

2.9 G. The nonlinearity error obtained from the best straightline fitted to the data points was 6.5 0OFSR maximum, whichis similar to that obtained by (14) and (15). The errorobtained for a quadratic approximation to the sensor outputvoltage was 3.5 0OFSR maximum. This confirms that theGNMR sensor response (in the measurement range tested) isalso almost quadratic. Therefore, the dependence of thenonlinearity error on B (Fig. 10) is probably due to thenonlinear characteristic of the sensor, rather than to the

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interface circuit proposed (Fig. 3). This error could bereduced by dividing the measurement range in subranges. Ifthe measurement range was limited to 0.75 G < B < 2 G, andLME criterion [8] applied, the nonlinearity error obtainedfrom the best straight-line fitted to the data points was2.5 %FSR maximum.

V. CONCLUSION

Magnetoresistive sensors consisting of four or two activeelements, connected into a Wheatstone bridge configuration,can be directly connected to a microcontroller by using thedirect interface circuits in Fig. 3, and applying equations (6)and (11). This method can be used for AMR and GMRsensors in full-bridge circuits and asymmetrical half-bridgecircuits. Measurements on an emulated sensor bridge yield anonlinearity error below 0.3 %FSR. Measurements on anHVMC1052 AMR sensor result in a nonlinearity error lowerthan 0.6 %FSR, which is three times smaller than the typicalnonlinearity error for the sensor alone when the bridge outputvoltage is measured in the conventional way. Measurementswith an AAH002 GMR sensor have a nonlinearity error of6.8 %FSR maximum, which is similar than the nonlinearityerror for the sensor bridge alone operated in the voltagemode. The higher nonlinearity for GMR half-bridges can beattributed to the nonlinearity of each bridge arm ofthe sensor.This nonlinearity error can be reduced by dividing themeasurement range in subranges.

The interface circuit proposed is compact, simple andinexpensive because it does not need any analog integratedcircuit in the signal path, and can be applied to other resistivebridge sensors. The improved results with respect to thoseobtained in [5] for a different microcontroller, and a differentcircuit layout, show that direct interface circuits can achieve a

resolution and accuracy comparable or better than voltage-based interfaces that use the A-to-D converter embedded insome microcontrollers.

ACKNOWLEDGMENT

This work has been funded in part by the Spanish Ministryof Education and Science, projects TEC2004-05520 andDPI2006-04017; and by the European Regional DevelopmentFund. Ernesto Sifuentes has been funded by PROMEP andUACJ Mexico. The authors also acknowledge the technicalsupport of Francis Lopez.

REFERENCES

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[4] F. Reverter and R. Pallas-Areny, Direct Sensor-to-MicrocontrollerInterface Circuits: Design and Characterisation. Barcelona (Spain):Marcombo, 2005.

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