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Sensors and Actuators A 147 (2008) 210–215

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

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irect interface circuit to linearise resistive sensor bridges

rnesto Sifuentesa,b,∗, Oscar Casasa, Ferran Revertera, Ramon Pallas-Arenya

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a Instrumentation, Sensors and Interfaces (ISI) Group, Castelldefels School of Technolog08860 Castelldefels, Barcelona, Spainb Computer and Electrical Engineering Department, Autonomous University of Ciudad J

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Article history:Received 16 November 2007Received in revised form 10 March 2008Accepted 4 May 2008Available online 23 May 2008

Keywords:MicrocontrollerResistive sensor bridgeSensor electronic interfaceMagnetoresistive sensor

a b s t r a c t

This paper proposes the dicontroller without any intthe discharging time of a Rand full-bridge circuits, wx of the bridge arms. Expenonlinearity error belowof 11 bit. Measurements o1.8%FSR for an AMR (Anisosensor, which are mainlyof the measurement is lialgorithm.

1. Introduction

Resistive sensors are often connected in a Wheatstone bridge

ecause placing several sensors (modelled by resistances R1, R2,3, and R4 in Fig. 1) in different bridge arms increases sensitiv-

ty and compensates for interference such as temperature [1]. Thiss the case, for example, for pressure and magnetoresistive sen-ors. The common approach to interface a resistive sensor bridgeo a microcontroller (MCU) is by supplying a constant voltage orurrent to the bridge. Then the output voltage is amplified and digi-ised with an analog-to-digital converter (ADC), either external ormbedded into the MCU. Table 1 shows some typical configura-ions of the Wheatstone bridge circuit in Fig. 1 and the resultingutput voltage (Vo) when a constant voltage (Vr) is applied [1];0 is the nominal resistance of the sensors and x is the fractionalesistance change (x = �R/R0). A quarter-bridge circuit (row 1 inable 1) has a single active arm and the output voltage is nonlin-ar with respect to x. A half-bridge circuit (rows 2–4 in Table 1)as two active arms, but the transfer characteristic is linear only

or case 4. A full-bridge circuit (row 5 in Table 1) has four activerms and a linear transfer characteristic [2]. The fractional resis-ance change x can be certainly estimated from any of the equationsn Table 1. However, the calculations are quite involved for the con-

∗ Corresponding author. Tel.: +34 934137089; fax: +34 934137007.E-mail addresses: sifuentes@eel.upc.edu, esifuent@uacj.mx (E. Sifuentes).

924-4247/$ – see front matter © 2008 Published by Elsevier B.V.oi:10.1016/j.sna.2008.05.023

C), Universitat Politecnica de Catalunya (UPC), Avda. del Canal Olımpic 15, Edifici C4,

(UACJ), Avda. del Charro 450 nte., Juarez, Chihuahua, Mexico

onnection of different configurations of resistive sensor bridges to a micro-diate active component. Such a direct interface circuit relies on measuringwork that includes the resistances of the sensor bridge. For quarter-, half-,bine the discharging times to estimate the fractional resistance change

ntal results for half- and full-bridge circuits emulated by resistors yield aSR (full-scale range) for x between 0 and 0.1 and an effective resolutiono commercial magnetoresistive sensors yield higher nonlinearity errors:c Magnetoresistive) sensor and 5.8%FSR for a GMR (Giant Magnetoresistive)o the nonlinearity of the sensors themselves. Therefore, the nonlinearityby the sensors, not by the proposed interface circuit and linearisation

© 2008 Published by Elsevier B.V.

figuration in row 3, and include divisions for those in rows 1 and 2[1].

Several circuits have been proposed to obtain a linear responsefrom bridges whose output voltage is nonlinear with x. One solutionis to include the bridge into a relaxation oscillator whose outputfrequency is proportional to the resistance unbalance in one of

the four bridge arms; the nonlinearity error achieved was smallerthan 0.5%FSR (full-scale range) for −0.005 < x < 0.005 [3]. The CMOSinterface circuit for resistive sensor bridges proposed in Ref. [4]compensates for offset and gain effects in the analog domain andprovides a linear digital output by a programmable amplifier and an8 bit ADC. The circuit proposed in Ref. [5] uses a feedback loop witha transadmittance amplifier to reduce the nonlinearity to about±0.4% for −0.2 < x < 0.2; however, minimal offset and nonlinearityerrors require matched bridge components, amplifiers, and gainsettings.

Resistive sensors can be directly connected to a MCU by mea-suring the time needed to discharge a capacitor through them [6].This approach is simple, compact, and low-cost because only thesensor and a MCU are required. This method has been applied to(full-bridge) piezoresistive pressure sensors [7] by considering thebridge as a circuit with one input terminal and three output ter-minals, instead of the usual two input terminals and two outputterminals considered in amplitude-based interface circuits. How-ever, there is not any known proposal to apply this method toquarter- and half-bridge resistive sensors; neither is there any sys-tematic analysis aimed to estimate the fractional resistance change

E. Sifuentes et al. / Sensors and Actu

Fig. 1. Wheatstone bridge circuit built from four resistive sensors supplied by aconstant voltage.

Table 1Output voltage for quarter-, half-, and full-bridge circuits (Fig. 1) when supplied bya constant voltage Vr [1]

R1 R2 R3 R4 Output voltage (Vo)

(1) R0 R0 R0 R0 (1 + x) Vrx

2(2 + x)(2) R0 (1 + x) R0 R0 R0 (1 + x) Vr

x

2 + x

(3) R0 (1 − x) R0 R0 R0 (1 + x) Vr−x2

4 − x2x

(4) R0 R0 (1 − x) R0 R0 (1 + x) Vr 2(5) R0 (1 + x) R0 (1 − x) R0 (1 − x) R0 (1 + x) Vrx

x whatever the number and position of active arms. This workextends the method described in Ref. [7] and proposes a generalequation to estimate x in either quarter-, half-, and full-bridge resis-tive sensors. The proposed method is then applied to commercialmagnetoresistive (MR) sensors based on bridge circuits.

2. Measurement method

Fig. 2 shows the proposed direct interface circuit for a resistivesensor bridge, which is considered to have one input terminal andthree output terminals. This circuit relies on measuring the dis-charging time of a RC network [6] that includes the resistances ofthe sensor bridge. The measurement involves two stages: (a) charg-ing and (b) discharging and time measurement. During the chargingstage, pin A4 is set as an output providing a digital “1”, whereas pinsA1, A2, and A3 are set as an input, offering high impedance. There-fore, capacitor C is charged towards VDD (positive supply voltage

Fig. 2. Direct connection between a Wheatstone bridge circuit and a microcon-troller.

ators A 147 (2008) 210–215 211

Fig. 3. Voltage waveform across C in Fig. 2 during the measurement sequence.

for I/O pins) through the internal resistance of the MCU pin and theresistor Rp for a time longer than 5RpC; Rp improves the rejectionof power supply interference [8]. During the second stage, pin A4 isset as a high-impedance input, pin A1 is set as an output providinga digital “0”, and pins A2 and A3 do not change their state. At thisinstant, C is discharged towards VSS (ground reference for I/O pins)through the equivalent resistance (Req1) between node A and pin A1,and the embedded timer starts the measurement of the dischargingtime. When the voltage across C reaches the low-threshold voltage(VTL) of the Schmitt-trigger (ST) buffer embedded into A4, the timerstops. Fig. 3 shows the waveform of the voltage across C during themeasurement sequence [6]. Afterwards, C is charged again and thendischarged through the equivalent resistance (Req2) between nodeA and pin A2. Finally, C is charged once more and then dischargedthrough the equivalent resistance (Req3) between node A and pinA3. Table 2 shows the resulting values of the three equivalent resis-tances (Req1, Req2 and Req3) for different bridge configurations. Ifthe internal resistance (Rini) of the MCU pins is assumed to bemuch smaller than those equivalent resistances (i.e., Rini < < Reqi),the discharging time equals

ti = ReqiC lnVDD − VSS

VTL − VSS. (1)

If VDD, VTL, VSS and C remain constant during each measurement,then ti is proportional to Reqi.

The goal is to have an interface circuit able to estimate the frac-tional resistance change x of the bridge. Because none of the times

ti are proportional to x, we propose to use a linearisation algo-rithm that combines the three discharging times measured andthat should be simple enough to be applied by any common micro-controller. To compensate some errors, we can calculate a ratio (tocancel multiplicative errors) of a difference between measured dis-charging times (to cancel additive errors). Hence, a general equationto estimate x for any bridge configuration is

x∗ = at1 + bt2 + ct3

dt1 + et2 + ft3= aReq1 + bReq2 + cReq3

dReq1 + eReq2 + fReq3, (2)

where t1, t2, t3 are the respective discharging times through Req1,Req2, Req3, and a, b, c, d, e, and f are the coefficients of the time-based equation. Because Reqi is a parallel and series combination ofR0, R0(1 + x), and R0(1 − x), its general value can be written as

Reqi = �i + �ix + �ix2

Den(x), (3)

where ˛i, ˇi, and ıi are known coefficients, and the denomina-tor Den(x) is common to the three equivalent resistances for eachbridge configuration, as shown in Table 2. Replacing (3) in (2) and

d Actu

ange f

+ x)

+ x)

+ x)

+ x)

212 E. Sifuentes et al. / Sensors an

Table 2Equivalent bridge resistances and equations to estimate the fractional resistance ch

Bridge configuration (Fig. 2) Req1

(1)R1 = R2 = R3 = R0 R0(3 + 3x)

4 + xR4 = R0 = (1 + x)

(2)R1 = R4 = R0 (1 + x) R0(3 + x)(1

4 + 2xR2 = R3 = R0

(3)R1 = R0 (1−x)

R0(3 − x)(14

R4 = R0 (1 + x)R2 = R3 = R0

(4)R1 = R3 = R0

R0(3 − x)(14

R4 = R0 (1 + x)R2 = R0 (1 − x)

(5)R1 = R4 = R0 (1 + x) R0(3 − x)(1

4R2 = R3 = R0 (1 − x)

rearranging yields

x∗ = A + Bx + Cx2

D + Ex + Fx2, (4)

where

A = a�1 + b�2 + c�3,B = a�1 + b�2 + c�3,C = a�1 + b�2 + c�3,D = d�1 + e�2 + f �3,E = d�1 + e�2 + f �3,F = d�1 + e�2 + f �3.

(5)

To achieve x* = x, we first need A = F = 0 in (4) to have

x∗ = Bx + Cx2

D + Ex= x(B + Cx)

D + Ex. (6)

Then, from (6), we also need B = kD and C = kE. For k = 1, we have

a�1 + b�2 + c�3 = 0,d�1 + e�2 + f �3 = 0,a�1 + b�2 + c�3 = d�1 + e�2 + f �3,a�1 + b�2 + c�3 = d�1 + e�2 + f �3.

(7)

Because we have six unknowns but only four equations, there areseveral possible solutions to solve (7) for a, b, c, d, e, and f foreach bridge configuration. Therefore, different equations based on(2) can estimate x in each bridge circuit. Table 2 shows the sim-plest equations to estimate x for quarter-, half-, and full-bridge

circuits. The operations involved in such equations are the samerequired to estimate x from the voltage outputs in rows 1 and2 in Table 1, which in addition need voltage amplification anddigitisation.

3. Materials and method

The circuit in Fig. 2 was implemented using a MSP430F123microcontroller (Texas Instruments) running at 4 MHz (quartzoscillator clock). The embedded 16 bit timer counted the discharg-ing time by incrementing its value every 250 ns. Pins P3.3, P3.6,P3.7 and P1.2 implemented the function of pins A1, A2, A3 and A4in Fig. 2, respectively. To reduce the effect of the internal triggernoise, the MCU was set in LPM0 mode (disabled CPU but enabledtimer and interruptions) when the discharging times were beingmeasured [6]. Pin P1.2 (external interrupt pin with an internal STbuffer) was set to interrupt the MCU on the falling edge. The valueof C was selected to obtain a suitable time constant (� = ReqiC) forthe discharge circuit. The optimal time constant in terms of speed-resolution trade-off for our circuit when measuring 1 k� resistorswas experimentally determined to be about 2–3 ms. Hence we

ators A 147 (2008) 210–215

or quarter-, half- and full-bridge circuits directly connected to a MCU (Fig. 2)

Req2 Req3 Time-based equation

R0(4 + 2x)4 + x

R0(3 + x)4 + x

x∗ = 2(t1 − t3)t2 + t3 − t1

R0(2 + x)2

4 + 2x

R0(3 + 2x)4 + 2x

x∗ = 2(t1 − t3)t2 + t3 − t1

R0(4 − x2)4

3R0

4x∗ = 2(t1 − t3)

t2 + t3 − t1

R0(4 − x2)4

R0(3 + x)(1 − x)4

x∗ = t3 − t1

2(t1 + t3 − 2t2)

4R0

4R0(3 + x)(1 − x)

4x∗ = t1 − t3

t2

selected C = 2.2 �F (±5% tolerance and 100 × 10−6/◦C temperaturecoefficient). The resistor Rp was 120 �.

The experimental work to assess the validity of the proposedmeasurement method was divided in two stages: (a) measure-ments on half- and full-bridge circuits emulated by resistors, and(b) measurements on two commercial MR sensors based on bridgecircuits. For each value of x applied, the discharging times t1, t2and t3 were measured 100 times and were sent to a personal com-puter (PC) via RS-232. Then, x* was calculated by the equation ofrow 5 in Table 2 for full-bridge circuits, and by the equation of row2 for half-bridge circuits. We selected these two bridge configura-tions because they are the same as those of the MR sensors laterused.

To allow for a flexible use of computing and memory resources,and graphical representation, the equations to estimate x in Table 2were computed using a PC. Nevertheless, for the MSP430 it is pos-sible to define floating-point variables, which results in a precisionof around seven decimal digits for the basic arithmetic operations(−, +, /, and *) when using C-library routines. Consequently, we alsocalculated x* using the MCU to asses whether or not the proposedmethod requires any capabilities beyond those of a common MCU,or an excessive computation time.

3.1. Bridge circuits emulated by resistors

We built a full-bridge circuit (row 5 in Table 2) by using resis-tors R0 = 1 k� (1%). Changes in each bridge arm were introducedby placing resistors in parallel with R2 and R3 to produce R0(1 − x),and resistors in series with R1 and R4 to produce R0(1 + x). We alsobuilt a half-bridge circuit (row 2 in Table 2) with the same resistors,but only R1 and R4 were changed to produce R0(1 + x). In both bridgecircuits, the added resistors were selected to obtain fractional resis-tance variations (x) from 0.5% to 10%. The actual value of x appliedwas determined in voltage mode using the equations in Table 1.

3.2. AMR and GMR sensors

The two MR sensors tested were: HMC1052 (Honeywell), whichis an AMR (Anisotropic Magnetoresistive) sensor with full-bridgetopology and a typical resistance R0 = 1 k�, and AAH002 (NVE),which is a GMR (Giant Magnetoresistive) sensor with half-bridgetopology and R0 = 2 k�. To create a known magnetic field to beapplied to the sensors, we build a 55 cm long (L) solenoid with2 cm in radius (R) and 330 turns (N) of AWG 20 enamel copper wire(Fig. 4). The magnetic flux density (B) along the z-axis is uniform in

E. Sifuentes et al. / Sensors and Actuators A 147 (2008) 210–215 213

measuring time is 100 times longer.

4.2. AMR and GMR sensors

Figs. 7 and 8 show the nonlinearity error (calculated from thebest-fit straight line) of the estimated x* versus B for the AMRand GMR commercial sensors, respectively. The maximal nonlin-earity error equals 1.8%FSR (Fig. 7) for the AMR sensor and 5.8%FSR(Fig. 8) for the GMR sensor. These errors and their dependence onB, hence on x, are very similar to those obtained when the sen-sors were measured in voltage mode, which are also shown inFigs. 7 and 8. Therefore, the nonlinearity error of the completesystem can be attributed to the nonlinear characteristic of the sen-sor, rather than to the interface circuit and linearisation algorithmsproposed. This error can be reduced by dividing the measurementrange in subranges. For example, for the GMR sensor, limiting themeasurement range to 75 �T < B < 195 �T, yields a maximal nonlin-earity of 2.2%FSR.

The standard deviation of x* remained constant over the mea-−5

Fig. 4. Solenoid to create a known magnetic field.

the center of the solenoid (z = 0) and its value is [9]

B = �oIN/L√1 + 4R2/L2

, (8)

where �o is the permeability of the air and I is the applied current.In an infinitely long solenoid, B would be constant along its centralaxis, but for the L and R values in our case, B values deviated byless than ±0.3% from that constant value. The sensors were placedabout the center of the solenoid with their sensitivity axis parallelto the magnetic field (Fig. 4). By controlling the current applied, weset B whose values were selected from 75 �T to 600 �T for the AMRsensor and from 75 �T to 290 �T for the GMR sensor, which are theirrespective linear measurement ranges. The actual response of theAMR and GMR sensors available was determined in voltage mode:a 3 V supply voltage was applied to each sensor and its differentialoutput voltage was measured by a multimeter (Agilent 34401A).

4. Experimental results and discussion

4.1. Bridge circuits emulated by resistors

Figs. 5 and 6 show the nonlinearity error (calculated from thebest-fit straight line) of the estimated x* versus actual x for thefull- and half-bridge circuits, respectively. The maximal nonlin-earity error was 0.2%FSR (Fig. 5) for the full-bridge circuit and0.3%FSR (Fig. 6) for the half-bridge circuit, which are probably due tothe quantization error in the discharging-time measurement. Theresults were similar when x was estimated by the MCU, and thecomputation time was smaller than 1 ms. High Rini values couldyield offset and gain errors but they do would not increase thenonlinearity [10]. The interface circuit herein proposed has non-linearity errors similar to those in Ref. [3,5] but it is more compact,economic and simple to design.

The standard deviation of x* remained constant over the mea-surement range for both bridge configurations. It was equal to7.4 × 10−5 for the full-bridge circuit and 1.3 × 10−4 for the half-bridge circuit. This variability is mainly due to power supply noiseand noise resulting from CPU activity [6]. If we define the resolu-tion as the amplitude of the uncertainty interval and use a coveragefactor of two, then the resolution equals four times the standard

Fig. 5. Nonlinearity error of the estimated x* vs. x for a full-bridge circuit.

deviation. Accordingly, the measurement of x has an effective res-olution of 8 bit for a measuring time of about 10 ms. If we usethe mean of one hundred values of x* as an estimate of the mea-surement, then the resolution increases to 11 bit, but of course the

surement range for both sensors. It was equal to 7.7 × 10 for the

Fig. 6. Nonlinearity error of the estimated x* vs. x for a half-bridge circuit.

214 E. Sifuentes et al. / Sensors and Actu

Fig. 7. Nonlinearity error of (a) the estimated x* vs. B, and (b) the differential voltagevs. B for the HMC1052 AMR (full-bridge) sensor.

[

Fig. 8. Nonlinearity error of (a) the estimated x* vs. B, and (b) the differential voltagevs. B for the AAH002 GMR (half-bridge) sensor.

AMR sensor and 1.4 × 10−4 for the GMR sensor, which are closeto the values obtained when the bridge circuit was emulated byresistors. If x was estimated by averaging one hundred values ofx*, then the effective resolution would be 7 bit for the AMR sensorfor 0.001 < x < 0.006 (which correspond to 75 �T < B < 600 �T) and10 bit for the GMR sensor for 0.02 < x < 0.06 (which correspond to75 �T < B < 290 �T).

5. Conclusions

Quarter-, half-, and full-bridge sensor circuits can be directlyconnected to a microcontroller without using any analogue inte-grated circuit in the signal path, thus resulting in a compact, simpleand low-cost design solution. The fractional resistance change ofthe resistive sensor bridge can easily be estimated by a time-basedequation (Table 2) that combines three discharging-time measure-ments. These equations in Table 2 involve operations that can beperformed by a microcontroller. The maximal nonlinearity errorof the proposed interface circuit is 0.3%FSR for half-bridge circuitsand 0.2%FSR for full-bridge circuits for 0 < x < 0.1 and an effective

ators A 147 (2008) 210–215

resolution of 11 bit, which are acceptable for many industrial appli-cations.

Acknowledgments

This work has been funded in part by the Spanish Min-istry of Education and Science, projects TEC2004–05520 andDPI2006–04017; and by the European Regional Development Fund.Ernesto Sifuentes has been funded by PROMEP and UACJ Mex-ico. The authors also acknowledge the technical support of FrancisLopez.

References

[1] R. Pallas-Areny, J.G. Webster, Sensors and Signal Conditioning, second ed., JohnWiley & Sons, New York, 2001.

[2] Wheatstone Bridge Nonlinearity, Technical Note 507, Vishay MeasurementsGroup, 1999.

[3] V. Ferrari, C. Ghidini, D. Marioli, A. Taroni, Oscillator-based signal conditioningwith improved linearity for resistive sensors, IEEE Trans. Instrum. Meas. 47 (1)(1998) 293–298.

[4] A.J. Lopez-Martin, J.I. Osa, M. Zuza, A. Carlosena, A CMOS interface for resistivebridge transducers, in: IEEE International Symposium on Circuits and SystemsISCAS, vol. 2, 2002, pp. 153–156.

[5] G. De Graaf, R.F. Wolffenbuttel, Systematic approach for the linearization andreadout of nonsymmetric impedance bridges, IEEE Trans. Instrum. Meas. 55 (5)(2006) 1566–1572.

[6] F. Reverter, J. Jordana, M. Gasulla, R. Pallas-Areny, Accuracy and resolutionof direct resistive sensor-to-microcontroller interfaces, Sens. Actuators A 121(2005) 78–87.

[7] J. Jordana, R. Pallas-Areny, A simple efficient interface circuit for piezoresistivepressure sensors, Sens. Actuators A 127 (1) (2006) 69–73.

[8] F. Reverter, M. Gasulla, R. Pallas-Areny, Analysis of power-supply interfer-ence effects on direct sensor-to-microcontroller interfaces, IEEE Trans. Instrum.Meas. 56 (1) (2007) 171–177.

[9] P. Lorrain, D.R. Corson, Electromagnetism: Principles and Applications, W.H.Freeman and Company, New York, 1990.

10] E. Sifuentes, O. Casas, F. Reverter, R. Pallas-Areny, Improved direct interfacecircuit for resistive full- and half-bridge sensors, in: Fourth International Con-ference on Electrical and Electronics Engineering ICEEE, Mexico, September,2007, pp. 197–200.

Biographies

Ernesto Sifuentes received his BSc degree in electronic engineering from Techno-logical Institute of Durango (ITD), Durango, Mexico in January 1999; he receivedhis MSc degree in electronic engineering from Technological Institute of Chihuahua(ITCH), Chihuahua, Mexico in May 2002. Since August 2002, he has been as a titu-lar professor (PTA) in the UACJ (Autonomous University of Ciudad Juarez), Mexico.Since September 2005, he has been in the Castelldefels School of Technology, which

belongs to the Technical University of Catalonia (UPC) Barcelona, Spain, where heis actually working in his PhD thesis research funded in part by PROMEP and UACJ,Mexico. His research interests are electronic instrumentation, embedded systems,direct sensor-to-microcontroller interfaces, and sensor networks.

Oscar Casas was born in Barcelona, Spain, on April 15, 1970. He received the Inge-niero de Telecomunicacion and Doctor Ingeniero de Telecomunicacion degrees fromthe Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, in 1994 and 1998,respectively. He is an associate professor of Electronic Engineering at the UPCand teaches courses in several areas of electronic instrumentation. His researchincludes sensor interfaces, autonomous sensors, electronic instrumentation, non-invasive physiological measurements and sensors based on electrical impedancemeasurements.

Ferran Reverter was born in Llagostera, Spain, on January 4, 1976. He receivedthe BSc degree in Industrial Electronic Engineering from the University of Girona,Girona, Spain, in 1998, the MSc degree in Electronic Engineering from the Uni-versity of Barcelona, Barcelona, Spain, in 2001, and the PhD degree in ElectronicEngineering from the Technical University of Catalonia (UPC), Barcelona, in 2004.Since 2001, he has been an assistant professor in Analogue Electronics and Digi-tal Systems with the UPC. From 2005 to 2007, he was a Visiting Postdoctoral Fellowwith the Delft University of Technology, Delft, The Netherlands. He is coauthor (withRamon Pallas-Areny) of the book Direct sensor-to-microcontroller interface circuits(Barcelona: Marcombo, 2005). His research interests are in the field of electronicinstrumentation, in particular, the design and characterisation of interface circuitsfor sensors.

E. Sifuentes et al. / Sensors and Actu

Ramon Pallas-Areny received the Ingeniero Industrial and Doctor Ingeniero Indus-trial degrees from the Technical University of Catalonia (UPC), Barcelona, Spain,in 1975 and 1982, respectively. He is a professor of electronic engineering at thesame University, and teaches courses in electronic instrumentation. In 1989 and1990 he was a visiting Fulbright Scholar and, in 1997 and 1998 he was an HonoraryFellow at the University of Wisconsin, Madison. In 2001 he was nominated Pro-fessor Honoris Causa by the Faculty of Electrical Engineering of the University ofCluj-Napoca (Romania). His research includes instrumentation methods and sen-sors based on electrical impedance measurements, autonomous sensors, sensorinterfaces, noninvasive physiological measurements and electromagnetic compat-

ators A 147 (2008) 210–215 215

ibility in electronic systems. He is the author of six books, the leading author offive books and coauthor of two books on instrumentation in Spanish and Cata-lan. He is also coauthor (with John G. Webster) of Sensors and Signal Conditioning,2nd ed. (New York: Wiley, 2001), and Analog Signal Processing (New York: Wiley,1999). He was a recipient, with John G. Webster, of the 1991 Andrew R. Chi PrizePaper Award from the Instrumentation and Measurement Society (IEEE). In 2000 hereceived the Award for Quality in Teaching granted by the Board of Trustees of theUPC, and in 2002 the Narcıs Monturiol Medal from the Autonomous Government ofCatalonia.