Sensors and Actuators A 123–124 (2005) 258–266

Silicon resonant accelerometer with electronic compensationof input-output cross-talk

V. Ferrari∗, A. Ghisla, D. Marioli, A. TaroniDipartimento di Elettronica per l’Automazione and INFM, Universita di Brescia, Via Branze 38, 25123 Brescia, Italy

Received 7 October 2004; received in revised form 17 March 2005; accepted 28 March 2005Available online 31 May 2005

Abstract

A resonant accelerometer manufactured in silicon bulk micromachining with electrothermal excitation and piezoresistive detection ispresented. The structure is a seismic mass supported by two parallel flexure hinges as a doubly-sustained cantilever, with a resonatingmicrobeam located between the hinges. The acceleration normal to the chip plane induces an axial stress in the microbeam and, in turn, aproportional change in the microbeam resonant frequency. Beam resonant frequency of around 70 kHz and acceleration sensitivity of 35 Hz/gover the range 0–3 kHz were measured on prototypes, in accordance with analytical calculations and simulations. The microbeam operatesu e effect oft ensation isp show that thes©

K

1

ootsTraFsafc

m

entntrol

withods

n of

ctric,n bes ofds.nant

aturencetiveationarditedhethe

0d

nsealed at atmospheric pressure, therefore a comparatively low quality factor results due to air damping. In this condition, thhe input-output cross-talk was found to be significant. The cross-talk is analyzed and modeled, and an electronic active comproposed. The compensated sensor was inserted into a phase-locked loop oscillator and tested. Reported experimental resultsensor performs in excellent agreement with the theoretical predictions.2005 Elsevier B.V. All rights reserved.

eywords: Accelerometer; Resonant sensor; Cross-talk; Oscillator; MEMS

. Introduction

In resonant sensors the oscillation frequency at resonancef a mechanical microstructure is changed by a physicalr chemical quantity to be measured, in such a way that

he value of the measurand quantity can be derived by thehift in the resonant frequency of the microstructure[1–4].he principle can be applied to several measurands, andesonance parameters other than the frequency, such asmplitude or phase, can also be used in the sensing process.requency-output resonant sensors typically offer highensitivity and stability, potentially leading to good accuracynd resolution. In addition, the “quasi-digital” nature of the

requency signal eases interfacing to readout and processingircuitry and improves noise immunity.

The fabrication of resonant sensors by means of siliconicromachining allows the use of the well-established

∗ Corresponding author. Tel.: +39 030 3715444; fax: +39 030 380014.E-mail address: vittorio.ferrari@unibs.it (V. Ferrari).

silicon technology to obtain microdevices with excellmechanical and elastic properties and a very precise coof the geometry and dimensions of the microstructure[5–7].Moreover, silicon sensors can be more easily integratedmicroelectronic or optical-fibre systems. Several methfor the actuation of the microresonator and detectiothe oscillations are reported in the literature[8–13]. Forthe actuation, the electrostatic, magnetic, piezoeleacoustic, electrothermal and optothermal methods caused. The sensing is typically accomplished by meanpiezoresistive, capacitive, optical or piezoelectric metho

As a particular case of resonant sensors, resomicroaccelerometers have been reported in the liter[14–18] in response to the demand for high-performaall-silicon accelerometers, for instance in the automoindustry. Several examples use the electrothermal excitand piezoresistive detection, which are straightforwto realize on silicon by means of implanted or deposresistors[19–20]. As with other operating methods, telectrical nature of the input and output signals allows

924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2005.03.067

V. Ferrari et al. / Sensors and Actuators A 123–124 (2005) 258–266 259

detection and tracking of the resonant frequency by meansof closed-loop circuits that, in this case, feed the amplifiedsignal from the piezoresistors back into the excitation stageof the heater resistor. The whole sensor works as a two-portdevice with electrical input and output.

An important issue with two-port resonant sensors is thatwhen the acoustic-mechanical path through the resonator hasa comparatively high attenuation, i.e. when the quality fac-tor Q is low, any causes of parasitic cross-talk between inputand output become increasingly important, because they in-troduce stray parallel paths that can swamp the resonancebehaviour of the sensor.

The electrical cross-talk is discussed in[21,22], andtechniques for cross-talk mitigation have been recently re-ported for microresonators with electrostatic[23,24] andelectrothermal[14] actuation.

In this paper, the design, operation and characterizationof a micromechanical uniaxial accelerometer are described,based on a resonant microbeam with electrothermal actua-tion and piezoresistive detection. The microbeam operatesunsealed at atmospheric pressure, therefore a comparativelylow quality factor results due to air damping. In thiscondition, the effect of the input-output cross-talk was foundto be significant.

The work presents an analysis of the electrical and ther-mal cross-talk paths between the sensor driving and detections tronicc

2

micM Eu-r amo ionsi

s ileverc twop ed-cw -l

arema lkp em-i ed byf

eache andd thep ithn

Fig. 1. Schematic view of the sensor structure (a); top view (b).

The microbeam is put into its first flexural resonance byelectrothermal actuation via the heater, and the correspond-ing fundamental frequency is detected by the piezoresistor[25,26,8]. The neutral axes of the supporting hinges and thethinner microbeam are not collinear, so the microbeam under-goes tensile/compressive axial stress induced by the bendingof the lateral hinges when the seismic mass oscillates in thepositive/negative direction of thez-axis. The microbeam res-onant frequency is proportional to the axial stress and, in turn,to the acceleration alongz.

A picture of the microsensor is shown inFig. 2. A top glassprotects the chip, which also includes other microstructuresirrelevant to this work, though the resonator operates unsealedat ambient pressure.

Flexural vibrations of a clamped-clamped beam, underthe hypothesis of high aspect ratio (length/thickness� 1)

F largedv

ignals, and proposes a purposely designed active elecompensation circuit.

. Sensor description and operating principle

The device was fabricated in the SensoNor Norultimems bulk micromachining process, offered as a

opractice MPW service for MEMS. A schematic diagrf the accelerometer structure with the relevant dimens

s shown inFig. 1(a) and (b).The structure was realized starting from a (1 0 0)p-type Si

ubstrate and is formed by a doubly-suspended cantonfiguration, where a seismic mass is supported byarallel flexure hinges which include a central clamplamped microbeam. The microbeam has lengthl = 600�m,idth w = 120�m, and thicknessh = 3�m with a rectangu

ar shaped cross section.The seismic mass with the hinges, and the microbeam

ade respectively by an implanted 23-�m thick n-well and3-�m thickn-type epitaxial layer, after removal of the bu-type Si by anisotropic backside etching with electrochcal etch stop. The suspended structures were releasrontside dry etching through then-epi layer.

A resistive heater and a piezoresistor are placed atnd of the microbeam, in locations where the excitationetection efficiency is maximized. Both the heater andiezoresistor are made byp-doped surface resistors, wominal sheet resistance of 800�/square.

ig. 2. Picture of the sensor chip with the resonant accelerometer in eniew.

260 V. Ferrari et al. / Sensors and Actuators A 123–124 (2005) 258–266

and small deflections, can be treated by the theory ofEuler–Bernoulli[27–29].

When an axial loading forceF is applied to the beam,the resonant frequenciesfn for the various modes can be ex-pressed as[30,31,6]:

fn(F ) = 1

2π

α2n

l2

√EI

ρA

√1 + γn

Fl2

12EI(1)

whereρ andE are the beam density and Young’s modulus,lis the beam length,A = wh is the cross section area, wherew andh are the width and thickness, respectively, andI =wh3/12 is the moment of inertia.

In Eq. (1) the beam is assumed narrow enough that anylateral stress is negligible, therefore the Young’s modulusE is considered instead of the effective Young’s modulusE/(1− ν2), whereν is the Poisson’s ratio[32].

The coefficientsαn andγn depend on mode number. Forthe first mode, leading to the fundamental natural frequencyf1, it is α1 = 4.730 andγ1 = 0.295[31].

By inserting into Eq.(1) the dimensions of the microbeamand the material parameters of Si (E = 1.69× 1011 N/m2;ρ = 2.33× 103 kg/m3), the resonant frequencyf1 in the un-loaded case, i.e. forF = 0, can be calculated, resulting inf1 = 72.9 kHz. The same value within few percents was ob-tained by finite-element simulations.

a thef la-t t.A ert tions itiv-i medb lieda outu

firstn d tob f thea

ventf d di-m ith am

3

t theo rmala

p terr of

Fig. 3. Sensor excitation–detection circuit.

the total voltage:

p(t)= 1

Rh

[V 2

bias+V 2

iM

2− V 2

iM

2cos(2ωt)+2VbiasViM sin(ωt)

]

(2)

Therefore, the generated thermal power and, in turn, theinduced stress include a static term and two dynamic har-monic components atω and 2ω.

The detection piezoresistorRp is connected as the feed-back resistor of an operational amplifier forming an activebridge, whose output is AC-coupled by a high-pass filterand further amplified by a factorG1 = 1000. As reported inFig. 1a), the resistance of the heater and piezoresistor areRh = 3.8 k� andRp = 6.5 k�, respectively.

The frequency response function betweenvi andvo wasmeasured with a gain-phase analyzer (HP4194A) over the60–75 kHz range, withViM = 2 V andVbias= 2.4 V. Such volt-age values result in a static power to the heater of about 2 mW.

The results are shown inFig. 4, where a peak is visible cor-responding to the natural frequency of the beam at 67.1 kHz.The value is in good agreement with the prediction obtainedby Eq. (1), though slightly lower. This can be ascribed tothe microbeam boundary conditions that are more compliantthan in the ideal clamped-clamped case, and to the effect oft

F ircuita

To predict the effect on the microbeam frequencyf1 of theccelerationa applied normally to the cantilever surface,

ollowing method was followed. By finite-element simuions the effect ofa on the axial forceF was determined firs

value ofF of 490× 10−6 N for a = 100 g was found. Thesultant forceF was then inserted into Eq.(1) to calculatehe frequency shift for unit acceleration, i.e. the acceleraensitivity of the microbeam resonant frequency. A sensty of 35 Hz/g was obtained. The same result was confiry deriving the frequency shift as a function of the appcceleration entirely by finite-element simulations, withsing Eq.(1).

The accelerometer bandwidth is limited to below theatural frequency of the cantilever, which was calculatee around 5 kHz. Therefore, a conservative estimation occelerometer bandwidth is the 0–3 kHz range.

No stops were inserted into the microstructure to preailure due to mechanical overloading, since the adopte

ensions already provide a conservatively high range waximum admissible acceleration in excess of 104 g.

. Sensor driving and active cross-talk compensation

To provide excitation to the resistive heater and detecscillation induced into the microbeam by the electrothectuation, the circuit shown inFig. 3was adopted.

The sinusoidal excitation signalvi (t) = ViM sin(ωt) is su-erimposed on a DC biasVbiasand then applied to the heaesistorRh. The heating powerp(t) depends on the square

he temperature rise caused by the driven heater.

ig. 4. Sensor frequency response with the excitation–detection cround the microbeam resonant frequency.

V. Ferrari et al. / Sensors and Actuators A 123–124 (2005) 258–266 261

Fig. 5. Model of the electrical cross-talk between heater and piezoresistor.

The resonant–antiresonant behaviour observable inFig. 4with a reduced phase shift around the peak is attributed to thestray cross-talk between the heater and the piezoresistor or,more generally, between the sensor input and output.

In resonant sensors, cross-talk phenomena between in-put and output ports are important[21,22], and they be-come increasingly influential when the mechanical reso-nance has a low quality factor. This can have the detri-mental effect of preventing the accurate detection and track-ing of the resonant frequency, and also limits the operatingrange.

A major cause of cross-talk is the input-output stray elec-trical coupling. In a rather general way, the electrical cross-talk, considered as a linear phenomenon, can be representedby a lumped model that includes the coupling impedancesZik, as shown inFig. 5.

In the present case, by examining the physical layout ofthe sensor and the routing of the electrical connections to thebonding pads, it can be assumed that theZik are infinite at DCand, at parity of frequency,Z13∼= Z24, Z23∼= Z14, |Z13| < |Z23|and|Z24| < |Z14|.

By considering the connection of the sensor terminals 3and 4 to the amplifier circuit terminals A and B, two differentvariants are possible. They are shown in the AC circuit ofFig. 6, whereZA andZB represent the equivalent impedancesseen at nodes A and B. From the analysis of the circuits ofF that

F nd thec

Fig. 7. MeasuredVo/Vi frequency response in the two connection variantsshown in Fig. 6: (a) case a; (b) case b.

the electrical interference on the output due to the excitationinput is smaller in case (a) than in case (b) at anyω.

The frequency response betweenvi andvo was measuredin the cases (a) and (b) ofFig. 6. The results are shown inFig. 7(a) and (b), respectively. The expectations are confirmed, witha cross-talk significantly higher in case (b) than in case (a).Incidentally, the natural frequency of the cantilever at around5 kHz can be observed.

An input-output cross-talk due to thermal coupling is alsopresent. From Eq.(2), two different thermal coupling pathscan be predicted.

As the first thermal coupling path, the static power[V 2

bias+ (V 2iM/2)]/Rh, depending on both DC bias and AC

amplitude, produces a static temperature distribution alongthe microbeam, with an average temperature increase�Twith respect to the temperature of the thermal sink repre-sented by the beam clamps at the seismic mass and substrate.

The temperature increment�T causes a static variation inthe resistanceRp of the piezoresistor due to both its temper-ature coefficient and the static stress in the microbeam. Botheffects do not reflect onvo thanks to the AC output coupling.

As an additional effect, the temperature increment�T in-duces a compressive axial forceFT on the microbeam thatcan be estimated as:

F

ig. 6 and the previous considerations, it is expected

ig. 6. Possible connections between the sensor outputs 3 and 4 aircuit inputs A and B.

T = AEαth�T (3)

262 V. Ferrari et al. / Sensors and Actuators A 123–124 (2005) 258–266

Fig. 8. Block diagram of the microbeam including the cross-talk paths and the excitation–detection circuit.

whereA = wh is the beam cross section,E is the Young’smodulus, andαth = 2.5 ppm/K is the thermal expansion co-efficient of silicon. The increment�T as a function of thestatic power can be calculated given the dimensions of thebeam and the heater[9], resulting in�T ∼= 1 K at 2 mW.The value ofFT for �T = 1 K calculated from Eq.(3) resultsaround 150× 10−6 N, which, according to the coefficient of4.9× 10−6 N/g derived in Section2, corresponds to an equiv-alent acceleration of about 30 g.

This effect, though apparently high enough to obscure thesensor response to acceleration, only produces an initial offsetin the sensor resonant frequency, which is negative in signbelow the buckling limit[8] and results in an inessential zeroerror. Provided that the static power [V 2

bias+ (V 2iM/2)]/Rh

remains constant, such an offset essentially does not varywith the ambient temperature, being the offset related to theovertemperature�T of the heated microbeam.

Only in the case that the static power varies due to eitherViM, Vbias, or both, an effect is produced on the resonantfrequency that can be erroneously interpreted as an externalacceleration. In this sense, this effect can be considered as akind of an indirect cross-talk. For example, a 1% change inthe static power around the value of 2 mW causes a changein �T of 0.01 K, resulting in an equivalent acceleration of0.3 g. Such a figure can be considered acceptably small withrespect to the sensor range.

werc

produce temperature distributions harmonic atω and 2ω inthe heater area. In principle, such dynamic components couldbe parasitically reflected at the output via the piezoresistorresponse. However, thermal waves at frequencies in the orderof the resonant frequency are significantly attenuated whilepropagating along the microbeam, producing a temperaturegradient that vanishes at the piezoresistor end. In fact, thepenetration depth of a heat wave in silicon is about 20�m at70 kHz, and the distance between heater and piezoresistoris 500�m. Therefore, the dynamic thermal cross-talk isexpected to be negligible.

Fig. 8 shows a block diagram that schematically sum-marizes the different cross-talk contributions discussed. Theblocks 1, 2, and 3, respectively represent the electrical cross-talk, the thermal coupling to the piezoresistor with vanishingsmall AC component and DC component filtered at the out-put, and the thermal effect on the microbeam expected as ashift in the resonant frequency. From the above considerationsit is foreseen that block 1 is influential, block 2 is negligible,and block 3 causes no effect on the resonant frequency of themicrobeam as long as the static power to the heater is keptconstant.

To actively compensate for the cross-talk, the circuitshown inFig. 9was developed. It includes an additional paththat can be adjusted in magnitude and phase to counteractthe effect of block 1 by injecting the compensating currentii hisw ding

connec

As the second thermal coupling path, the dynamic poomponents [−V 2

iM/2 cos(2ωt) + 2VbiasViM sin(ωt)]/Rh

Fig. 9. Block diagram of the sensor

Cnto the virtual ground of the active-bridge amplifier. In tay, the compensation circuit does not produce any loa

ted to the excitation–compensation circuit.

V. Ferrari et al. / Sensors and Actuators A 123–124 (2005) 258–266 263

Fig. 10. Microbeam frequency response with the cross-talk compensationinserted.

on the active-bridge amplifier, therefore it does not modifythe pre-existent cross-talk level but simply cancels its effectat the amplifier output.

The components ofiC in phase and quadrature withviare derived by scalingvi by two independent signed gainsand applying the resulting voltages across the compensating

Ft

resistorRC and capacitorCC, respectively. The capacitorC1only provides DC decoupling, and it is suitably high in valueto be negligible at the frequencies of interest.

Fig. 10shows the results obtained with the compensationcircuit. The peak corresponding to the fundamental resonantfrequency of the beam can be observed, with a significantimprovement over the plot ofFig. 4. A quality factorQ ofabout 170 results. Such a value is rather low, consistentlywith the operation of the resonator at atmospheric pressure.

Fig. 11(a) and (b) show the frequency response in polarrepresentation around the resonant frequency, for both theuncompensated and compensated cases. It can be observedas the compensation appropriately recenters the circle fromthe offset position due to the cross-talk.

The indirect thermal effect, represented in block 3 ofFig. 8, was tested on a sensor of the same batch activelycompensated by the previously described circuit. Themeasurement results are shown inFig. 12(a) and (b), whichrespectively refer to variations ofVbias and of ViM. Thepredictions are confirmed, with a decrease in the resonantfrequency at higher power levels, and a gain enhancementproportional toVbias in agreement with Eq.(2).

The effect caused on the microbeam resonant frequencyby variations in the ambient temperature, considered to actuniformly on the whole sensor chip, is responsible for thetemperature coefficient of the sensor output frequency. Ifs tcheso the

ig. 11. Polar plot of the microbeam frequency response: (a) without cross-alk compensation, (b) with cross-talk compensation.

Fo

tress effects induced by thermal expansion mismaf different materials and packaging are excluded,

ig. 12. Indirect thermal effect of the static power on the resonant frequencyf the microbeam: variations ofVbias (a); variations ofViM (b).

264 V. Ferrari et al. / Sensors and Actuators A 123–124 (2005) 258–266

Fig. 13. Phase-locked loop oscillator circuit.

temperature coefficient of the frequency (∂f/∂T)/f is de-termined by the thermal expansion coefficientαth and thetemperature coefficient of the Young’s modulus ((∂E/∂T)/E)of silicon [5].

Starting from Eq.(1), under the simplifying assumptionthat the term due to the axial forceF is small enough to beneglected, withαth = 2.5 ppm/K and (∂E/∂T)/E = 75 ppm/K,the frequency temperature coefficient (∂f/∂T)/f results in theorder of 30 ppm/K. At 70 kHz this reflects into an estimatedthermal sensitivity of 2.1 Hz/K, corresponding to an acceler-ation temperature sensitivity of 0.06 g/K.

4. Electronic oscillator and closed-loop results

The sensor and the excitation–compensation circuit ofFig. 9were connected in a purposely designed phase-lockedloop (PLL) oscillator, as depicted inFig. 13.

The PLL is formed by a voltage controlled oscillator(VCO) with sinusoidal output (MAX038), a phase detectormade by a±1 synchronously-switched gain stage, and a loopfilter with a pole in the origin and a suitably tailored frequencyresponse to ensure loop bandwidth and stability. The PLL os-cillator outputs a sinusoidal signal with a frequency equal tothe beam resonant frequency by keeping locked to the con-d ◦

Fig. 14. Oscillator output frequency vs. sensor static inclination (cantileverthickness not to scale in the insert drawings for better clarity).

The sensor connected to the oscillator was mounted on arotating fixture and subject to variable inclinations between−90◦ and 90◦, i.e. static accelerations between−g and g.

Fig. 14shows the measured oscillator frequencyfo versusthe inclination angleϑ, where it can be observed an excel-lent agreement with the theoretically predicted sensitivity of35 Hz/g and the expected behaviour proportional to sinϑ.

The sensor was then tested under AC acceleration. To thispurpose, the circuit ofFig. 13 was modified as shown inFig. 15. A time-variable accelerationa(t) produces a corre-spondent variation in the microbeam resonant frequency, i.e.

dulato

ition where the phase betweenvi andvo is equal to 90.

Fig. 15. Block diagram of thef-to-V demo

r circuit for AC acceleration measurements.

V. Ferrari et al. / Sensors and Actuators A 123–124 (2005) 258–266 265

Fig. 16. Comparison between reference accelerometer output and sensorvoltage outputvo: applied peak acceleration of 1 g (a), applied peak accel-eration of 2 g (b).

a frequency modulation of the carrierfo tracked by the PLLoscillator. The demodulation is obtained by taking the VCOinput voltage suitably amplified out of the loop, so that theresultant output voltagevo(t) is directly proportional tofo(t)and, in turn, to the accelerationa(t).

A sinusoidal accelerationa(t) was applied to the sensorby mounting it on a calibration exciter (Bruel & Kjær, 4290)having a built-in reference accelerometer with a sensitivityof 1 V/g.Fig. 16shows the results obtained at g and 2 g peakamplitudes at 300 Hz. A good reproduction of the sinusoidalacceleration is obtained, with the phase inversion being dueto the negative sign of the VCO sensitivity.

5. Conclusions

A silicon bulk-micromachined resonant accelerometerwith thermal excitation and piezoresistive detection was re-alized, analyzed with respect to the input-output cross-talk,and tested. The sensor structure is a seismic mass supporteby two parallel flexure hinges, with a resonating microbeamlocated between the hinges subject to axial stress under anapplied acceleration.

The accelerometer has a sensitivity of 35 Hz/g at a fre-quency of about 70 kHz, corresponding to the first bendingm es unsa

The electrical component of the cross-talk was found tobe dominant and, as expected, it could be reduced by adopt-ing a proper readout scheme of the piezoresistor. The thermalcomponent of the cross-talk produces a dynamic effect, whichis negligible because the thermal wave at the frequencies inquestion essentially does not propagate from the heater tothe piezoresistor, and a static effect that can be eliminated byAC coupling. The static temperature increment in the heatedmicrobeam, set by the driving level of the heater resistor, in-fluences the resonant frequency by adding a negative offset.This can be considered as a kind of an indirect cross-talkeffect, and the control of the heater excitation level is there-fore necessary to minimize frequency fluctuations that couldbe erroneously interpreted as an acceleration signal. A 1%variation in the static power level of 2 mW causes a changein the microbeam average temperature that translates into anequivalent acceleration of 0.3 g.

A circuit for the active compensation of the cross-talk wasproposed and successfully verified. The circuit employs anadjustable cancellation of the cross-talk, without introducingany modifications on the pre-existent cross-talk level due tothe cancellation circuit itself.

A dedicated phase-locked loop (PLL) oscillator was de-veloped to sustain and track the resonant frequency of thecompensated sensor. The accelerometer coupled to the cross-talk compensation circuit and the PLL oscillator was testedu alityf osedc xcel-l n thep

A

thes hankV ensorm ofS sorb d ont

R

tuators

ant1994,

ional’87),

roc.

ctu-

ode of the resonant microbeam. The resonator operatealed at ambient pressure, causing a quality factorQ as lows 170 that makes it vulnerable to cross-talk effects.

d

-

nder DC and AC accelerations. Despite the poor quactor of the sensor, the followed approach and the propircuits have provided experimental results that are in eent agreement with the theoretical predictions based ourely-mechanical analysis of the sensor.

cknowledgments

The contribution of Giorgio Fagnani in the design ofensor layout is greatly acknowledged. The authors tegar Dalsrud and SensoNor for assistance during sanufacturing, Micropto, Milan, and Massimo MaglioccoTMicroelectronics, Cornaredo, Milan, for support in senonding and packaging. The project was partially funde

he COFIN 2002 programme by the Italian MIUR.

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Biographies

Vittorio Ferrari was born in Milan, Italy, in 1962. In 1988 he obtainedthe Laurea degree in Physics cum laude at the University of Milan. In1993 he received the Research Doctorate degree in Electronic Instrumen-tation at the University of Brescia. He is currently an Associate Professorof Electrical and Electronic Measurements at the Faculty of Engineeringof the University of Brescia. His research activity is in the field of elec-tronic measuring instrumentation and deals with the design of sensors andthe related signal conditioning electronics. Particular topics of interest areacoustic-wave piezoelectric sensors, microresonant sensors and MEMS,oscillators for resonant sensors and frequency-output interface circuits.He is involved in national and international research programmes, and inp

A thel ering,U tober2 s andA een aP cia,B izationo artic-u EMSs

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185–189.17] C. Burrer, J. Esteve, High-precision BESOI-based resonan

celerometer, Sens. Actuators A 50 (1995) 7–12.18] P. Ohlckers, R. Holm, H. Jakobsen, T. Kvisteroy, G. Kittilsland

Larsen, M. Nese, S.M. Nilsen, A. Ferber, An integrated resoaccelerometer microsystem for automotive applications, Sens.ators A 66 (1998) 99–104.

19] C. Burrer, J. Esteve, E. Lora-Tamayo, Resonant silicon acceleeters in bulk micromachining technology – An approach, J. Mielectromech. Syst. 5 (2) (1996) 122–130.

20] D.W. Satchell, J.C. Greenwood, A thermally-excited siliconcelerometer, Sens. Actuators A 17 (1989) 241–245.

21] C.J. van Mullem, H.A.C. Tilmans, A.J. Mouthaan, J.H.J. FluitmElectrical cross talk in two ports resonators, Sens. Actuators(1992) 168–173.

22] K. Funk, T. Fabula, G. Flik, F. Larmer, Piezoelectrically driven renant force sensor: fabrication and crosstalk, J. Micromech. Micro5 (1995) 143–146.

23] P. Bruschi, A. Nannini, F. Pieri, Electrical measurements of the qity factor of microresonators and its dependence on the preSens. Actuators A 114 (2004) 21–29.

24] L. He, Y.P. Xu, Circuit technique to enhance bias stability oficon resonant accelerometer hybrid-packaged under moderatuum, Proc. of the Eurosensors XVIII Conference, Roma, Italy, 1September, 2004.

25] M.B. Othman, A. Brunnschweiler, Electrothermally excited silibeam mechanical resonators, Electron. Lett. 23 (14) (1987) 728

26] C. Burrer, J. Esteve, Thermally driven micromechanical bridgeonators, Sens. Actuators A 41–42 (1994) 680–684.

rojects in cooperation with industries.

lessio Ghisla was born in Brescia, Italy in 1972. In 2001, he receivedaurea degree in electronic engineering from the Faculty of Engineniversity of Brescia, Brescia, Italy. From September 2001 to Oc002 he has been collaborating with the Department of Electronicutomation, University of Brescia. Since November 2002 he has bhD student in “Electronic Instrumentation” at the University of Bresrescia. His main research interests are the design and characterf sensors and of electronic circuit interfaces for sensors, with plar regard to capacitive sensors for position measurement and Mensors.

aniele Marioli was born in Brescia, Italy, in 1946. He obtainedlectrical Engineering degree in 1969. From 1984 to 1989 he wassociate Professor in Applied Electronics and since 1989 he hasFull Professor of Electric and Electronic Measurements at the

ersity of Brescia. His main field of activity is the design anderimentation of analog electronic circuits for the processing of

rical signals from transducers, with particular regard to S/Nptimization.

ndrea Taroni was born in 1942. He received the degree in Physicalnce from the University of Bologna, Italy, in 1966. He was an Assorofessor at the University of Modena from 1971 to 1986. Sincee has been Full Professor of Electrical Measurements at the Univf Brescia. He has done extensive research in the field of sensohysical quantities and electronic instrumentation, both developing

nal devices and practical applications. He is author of more thancientific papers.