Noise Analysis and Characterization of a Sigma-Delta

352IEEE JOURNAL OF SOLID-STATE CIRCUITS,VOL.41,NO.2,FEBRUARY 2006

Noise Analysis and Characterization of a Sigma-Delta

Capacitive Microaccelerometer

Haluk Külah ,Member,IEEE ,Junseok Chae ,Member,IEEE ,Navid Yazdi,and Khalil Naja?,Fellow,IEEE

Abstract—This paper reports a high-sensitivity low-noise ca-pacitive accelerometer system with one micro-g

Hz resolution.The accelerometer and interface electronics together operate as a second-order electromechanical sigma-delta modulator.A detailed noise analysis of electromechanical sigma-delta capacitive accelerometers with a ?nal goal of achieving

sub-g resolution is also presented.The analysis and test results have shown that ampli?er thermal and sensor charging reference voltage noises are dominant in open-loop mode of operation.For closed-loop mode of operation,mass-residual motion is the dominant noise source at low sampling frequencies.By increasing the sampling frequency,both open-loop and closed-loop overall noise can be reduced signi?cantly.The interface circuit has more than 120dB dynamic range and can resolve better than 10aF.The complete module operates from a single 5-V supply and has a measured sensitivity of 960mV/g with a noise ?oor of

1.08g Hz in open-loop.This system can resolve better than

10

g Hz in closed-loop.Index Terms—Capacitive readout,inertial sensors,microac-celerometers,micro-g,sigma-delta,switched capacitor.

I.I NTRODUCTION

H

IGH-PRECISION accelerometers with micro-g

(g,

g

m/s )resolution have many applications,including

inertial navigation and guidance,microgravity measurements in space,tilt control and platform stabilization,seismometry,and GPS-aided navigators for the consumer market.To

achieve g resolution,a few transduction techniques,device structures,and system approaches have been reported [1]–[5].Recently,capac-itive accelerometers have become very attractive for high-pre-

cision g applications due to their high sensitivity,low temper-ature sensitivity,low power consumption,wide dynamic range of operation,and simple structure.However,no micromachined capacitive accelerometer system has yet been reported in the lit-erature with

sub-

g Hz noise ?oor at atmospheric pressure.The microaccelerometer system consists of two main parts:the sensing structure and the interface electronics.As well as the sensor structure itself,the interface electronics also plays a critical role in the overall system performance.In fact,noise analysis of the accelerometer,electronic circuit,and the overall

Manuscript received July 17,2003;revised September 1,2005.This work was supported by the Defense Advanced Research Projects Agency (DARPA)under Contract F30602-98-2-023and made use of Engineering Research Centers Shared Facilities supported by the National Science Foundation under Award Number EEC-0096866.

H.Külah was with the Center for Wireless Integrated Microsystems (WIMS),University of Michigan,Ann Arbor,MI 48109-2122USA.He is currently with the Department of Electrical and Electronics Engineering,Middle East Tech-nical University,06531Ankara,Turkey (e-mail:kulah@53619d47fe4733687e21aa82.tr).

J.Chae,N.Yazdi,and K.Naja?are with the Center for Wireless Integrated Microsystems (WIMS),University of Michigan,Ann Arbor,MI 48109-2122USA.

Digital Object Identi?er 10.1109/JSSC.2005.863148

system shows that as the device performance improves,the in-terface electronics limit the overall system resolution.

Sigma-delta

(

)modulators are very popular for low-fre-quency analog-to-digital conversion in applications such as speech processing where the oversampling ratio can be con-siderably high and the noise rejection is very ef?cient [6].In micromechanical accelerometers,since the mechanical band-width is usually quite small

(2kHz),sigma-delta conversion can effectively reduce noise and improve overall performance [7]–[14].In most of the reported systems,the sensor’s me-chanical noise is the dominant factor limiting the overall performance.Therefore,the general trend is toward improving the accelerometer itself rather than analyzing the electrical interface electronics and improving the overall system noise performance.

We have previously reported a high-performance silicon mi-croaccelerometer [15]and its open-and closed-loop operation using a switched-capacitor readout circuit [16],[17].The per-formance parameters of the system have shown that although the sensor’s mechanical noise ?oor is less than

1

g Hz,the overall system noise is larger,indicating that the interface elec-tronics is the dominant noise source.In this paper,a detailed

noise analysis of

the

microaccelerometer system is pre-sented and a

1

g Hz accelerometer system is demonstrated.In Section II,a brief overview of the micro-g accelerometer is presented.Then,the front-end circuit operation is described in Section III.The noise analysis of the overall system is presented in Section IV .Finally,measurement results are discussed in Sec-tion V .

II.M ICRO -G A CCELEROMETER

The accelerometer,shown in Fig.1,is all-silicon and fabri-cated on a single silicon wafer using a combined surface and bulk micromachining fabrication process [15].Fig.2shows the cross section of the accelerometer fabricated in this technology.The device consists of a wafer-thick proof mass suspended symmetrically between two stiffened polysilicon electrodes on top and bottom.In the presence of an external acceleration in the z -direction,the silicon frame moves with respect to the proof mass,and the air gaps separating the proof mass from top and bottom electrodes change in opposite directions.Hence,

the difference

between

and provides a capac-itance change that is a measure of the applied acceleration.The device has a large proof mass (milligrams),control-lable/small damping,and narrow air gap that result in large capacitance variation and low mechanical noise ?oor.It also offers a low offset and long term gain stability as it is all-silicon and no wafer bonding is used in its fabrication process.The

0018-9200/$20.00?2006IEEE

K üLAH et al.:NOISE ANALYSIS AND CHARACTERIZATION OF A SIGMA-DELTA CAPACITIVE MICROACCELEROMETER

353

Fig.1.SEM of a device with 2mm 21mm proof

mass.

Fig.2.Cross-sectional diagram of mixed surface and bulk micromachined

all-silicon accelerometer.

measured differential sensitivity of the sensor with a double clamped-clamped bridge suspension is about 4.9pF/g on top of a 38pF rest capacitance for a device with 2

mm 1mm proof mass (2.2mgr)in a full-bridge con ?guration and the resonance frequency is around 1kHz.The sensitivity can be increased by more than an order of magnitude by using a cantilever suspension instead.In order to increase the sensitivity of the microaccelerometer and improve the overall signal-to-noise ratio,a narrow air gap of

1.5m is used.This narrow gap and small resonance frequency result in limited linearity and range in an open-loop mode of operation.However,in this mode the required interface IC is simpler and no stability concerns exist.In order to extend the linearity,range,and bandwidth of the accelerometer,it can be operated in closed-loop.

The interface circuit needs to

resolve 10aF capacitance in spite of the large rest capacitance and parasitics (tens of pFs)associated with hybrid packaging of the sensor-interface IC module to attain

sub-g overall resolution.Also in order to provide closed-loop operation and null the large proof mass motion,the interface chip needs to provide tens

of N elec-trostatic force,which is relatively large for microsensors with limited

(5V)power supply.Furthermore,the IC is required to have very low offset,and good gain and offset stability (0.01%full-scale)to qualify the micro-g accelerometer for inertial navigation

applications.

Fig.3.Block diagram showing the major building blocks of the implemented circuit.

III.I NTERFACE C IRCUIT

The microaccelerometer is interfaced with a capacitive readout circuitry to form a second-order electromechanical sigma-delta modulator.Interface electronics detect the ca-pacitance change and operate the sensor in open-loop or force-rebalance the proof mass in closed-loop.Fig.3shows the block diagram of the interface circuit [18]–[20].The circuit consists of a switched-capacitor charge integrator,digital feed-back (latching comparator and digital compensator),a clock generator,and a start-up circuit.Two ?xed reference capacitors are used to form a balanced full-bridge with the sensor capac-itive half-bridge,and the sensor top and bottom electrodes are used as the input nodes to the chip front-end.

The readout front-end is a fully differential charge integrator with correlated double sampling (CDS)to cancel 1/f noise,am-pli ?er offset and compensate ?nite ampli ?er gain as shown in Fig.4.Fig.5shows the clock diagram for operating this circuit.The operation principle of this circuit has been presented in de-tail in [18].The next section discusses the noise sources of this system.

IV .N OISE A NALYSIS

There are several noise sources affecting the overall system resolution of an accelerometer system.These noise sources can be classi ?ed in two main groups:mechanical and electrical [19],[20],[22],[23].Mechanical noise is due to the Brownian mo-tion of the proof mass and is directly related to the sensing structure design and environment.It has been shown that this noise can be decreased down to

0.1

g Hz [15],[16],[21].These accelerometers achieve high device sensitivity,low me-chanical noise ?oor,and controllable damping by combining surface and bulk micromachining.The central idea behind the process is to use the whole wafer thickness to attain a large proofmass,to utilize a sacri ?cial thin ?lm to form a uniform and conformal gap over a large area,and to create electrodes by depositing polysilicon on the wafer [15],[16],[21].The elec-tronic noise has different components including the front-end

ampli ?er

noise,

noise,noise due to mass residual motion,

354IEEE JOURNAL OF SOLID-STATE CIRCUITS,VOL.41,NO.2,FEBRUARY

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Fig.4.Schematic view of the switched-capacitor front-end

circuit.

Fig.5.Clock diagram for the switched-capacitor front-end circuit.

sensor charge referencing voltage noise and clock jitter noise.Some of these noise sources are dominant in open-loop opera-tion,whereas the others are critical in closed-loop mode of op-eration.The following subsections analyze these noise sources inpidually.

A.Mechanical (Brownian)Noise

Mechanical noise is generated by the proof mass itself.This Brownian noise corresponds to an equivalent acceleration noise of [23],

[24]:

(1)

where

is the Boltzman ’s

constant,is the temperature in Kelvin,

and is the damping coef ?cient in (N m/s),

and

is the proof mass.

As the equation shows,this noise is totally dependent on sensing structure mass and damping coef ?cient.The z axis ac-celerometers in the hybrid system tested in this paper have a

0.7

g Hz noise ?oor at atmospheric pressure.This value can be improved further by operating the accelerometer in a vacuum environment,or by increasing the size of the proof mass.B.Front-End Ampli?er Noise

The front-end ampli ?er noise consists of two parts:thermal and ?icker noise.Since CDS is employed in the switched-capacitor circuit,the ampli ?er ?icker noise is reduced consider-ably,and hence the thermal noise is the dominant source.Fig.6shows the schematic of the ampli ?er used in the front-end of the switched capacitor circuit.This is a fully differential folded-cascode ampli ?er,and in this structure none of the tran-sistors in the common-mode part contributes to the noise of the ampli ?er,since the output is taken differentially [6].Similarly,the transistors in the biasing path do not contribute any noise.

Cascode

devices

,

,,

and do not affect the total noise either,due to the large impedance in the source leg of these devices.The input-referred noise contribution of the remaining transistors can be derived by multiplying the noise power by the square of the ratio of that device ’s transconduc-tance to the input device ’s transconductance.Therefore,the input-referred noise can be expressed as

[6]

(2)

where

,,

and are the transistor transconduc-tances

and

,,

and are the thermal noise voltages generated by the transistors.

The factor of 2in this equation results from the fact that the fully differential circuit consists of two matched halves and the noise of those two halves is uncorrelated.Therefore,the total

K üLAH et al.:NOISE ANALYSIS AND CHARACTERIZATION OF A SIGMA-DELTA CAPACITIVE MICROACCELEROMETER

355

Fig.6.Schematic view of the ampli ?er used in the front-end

circuit.

Fig.7.Simpli ?ed schematic view of the readout circuit for the equivalent thermal noise calculation.

noise power will be twice the noise power of one of the half-cir-cuits.Also,by setting the current ratios on the branches prop-erly,the transconductances

of

and can be set such that the ?rst term in (3)dominates.In this case,only the two input transistors will be the main sources of noise and the input equiv-alent noise can be represented

by

(3)

Fig.7shows the simpli ?ed diagram for the switched capac-itor implementation of this ampli ?er for noise calculation.The ampli ?er thermal noise is sampled and folded and also ?ltered by the ampli ?er in this loop.The equivalent noise at the output of this circuit is

[23]

(4)

where

is the sensing

capacitance,is the parasitic capac-itance at the

front-end,

is the integration

capacitance,is the sampling frequency,

and is the ampli ?er unity gain fre-quency given

by

(5)

where

is the output capacitance.By replacing (3)and (5)in (4),the equivalent noise can be obtained as

[23]

(6)

It should be noted here that the equivalent noise due to ampli-?er thermal noise is independent of transistor parameters.It is mainly dependent on the capacitance values and the sampling frequency.By increasing the sampling frequency and the inte-gration capacitance,it is possible to reduce this noise.

C.

Noise

Another major noise source for the interface electronics is

the

noise generated by thermal noise sampling of the switches.Integration capacitance plays a dominant role in this noise and the output equivalent noise can be expressed

as

-(7)

As indicated in the equation,this noise component is also in-versely proportional to sampling frequency and integration ca-pacitance,which means that it can be decreased by increasing these two factors.

Sensors used in our accelerometer systems have large base capacitances (tens of pFs)as explained in the previous section.Therefore,the capacitances employed in the switched-capacitor

circuit are also large resulting in

low

noise compared to other accelerometer systems.

D.Sensor Charging Reference Voltage (SCRV)Noise Sensor readout is performed by charging the sense capaci-tance with a ?xed reference voltage in each cycle and detecting this charge by the interface electronics.Therefore,any noise on this reference voltage directly contributes to the overall noise performance,which is known as sensor charging reference

356IEEE JOURNAL OF SOLID-STATE CIRCUITS,VOL.41,NO.2,FEBRUARY 2006

TABLE I

E LECTRICAL N OISE C OMPONENTS AND T HEIR V ALUES FOR D IFFERENT

S AMPLING F REQUENCIES AND I NTEGRATION C

APACITANCES

C +C =100pF,C =10pF,V is the charging reference voltage noise assumed to be white with a spectral density of 10nV =p Hz,C =10

pF.

Fig.8.Simpli ?ed schematic for SCRV noise calculation.

voltage 53619d47fe4733687e21aa82rge low-frequency components of this noise can easily dominate the system noise performance,while wide-band noise is folded to the baseband due to sampling on sense capacitors.Fig.8shows the simpli ?ed circuit schematic for calculation of this noise.Note that in this case,the ?nite “on ”resistance of the switches and the sense capacitor form an RC ?lter and limit the noise bandwidth.The total noise can be integrated and the noise density in band can be calculated by

piding the total noise

by

.The output equivalent noise can be represented by the

equation

(8)

where is the switch resistance,

and is the reference

voltage noise.E.Quantization Noise

Quantization noise is present in closed-loop operation [22].The effective quantization noise for the

second-order mod-ulator with an oversampling ratio

of

can be expressed

as (9)

where

is the rms value of the unshaped quantization noise.For a single-bit modulator with comparator

levels

and ,the rms noise value

is .For a micromechanical accelerometer operating as a

second-order

modulator,

is the full-scale electrostatic feedback acceleration,which is

1.35g (for 5-V power supply)in this

case.

is the over-sampling ratio de ?ned as the ratio of the bandwidth over the sampling frequency.For low quantization noise,it is required to

have a low bandwidth compared to the sampling frequency,and

this is

why

modulators are so popular for low-frequency bandwidth applications.Since the resonant frequency of the accelerometer is less than 1kHz,the 1-MHz sampling clock provides a high oversampling ratio,which results in negligible quantization noise.Quantization noise is less than

0.02g in 1-Hz bandwidth for 1-MHz sampling clock

and g.F .Mass Residual Motion

This noise source is only effective in closed-loop mode of operation like the quantization noise.It is the result of digital feedback in force-rebalancing [22].Electrostatic feedback is ap-plied by means of a pulsewidth modulated (PWM)digital pulse train.This pulse train results in a periodic motion of the proof mass around the equilibrium condition,even under zero external acceleration.This movement of the proof mass cannot be sepa-rated from an external acceleration and appears as noise in the input.This movement can be represented by the equation

[22]

(10)

where is the maximum acceleration

and is the sam-pling frequency.

For g

and

MHz,is equal to

5.410m.For a z axis accelerometer with 2

mm 1mm area and

1.5m gap,this movement creates an equiva-lent acceleration of

0.05

g Hz.Notice that this noise source is inversely proportional

to ,whereas the other sources are inversely proportional

to .Therefore,for low sampling fre-quencies,this noise source can rise considerably and become dominant,resulting in tens

of g overall resolution.

Table I presents the inpidual noise components,their expressions and values for different parameters.As the table shows,most of the electrical noise sources mainly depend on sampling frequency and the value of integration capacitance.Fig.9shows the dependence of total electronics noise on integration capacitance and sampling frequency.As seen from the ?gure,it is possible to minimize the total noise consider-ably by increasing the sampling frequency and the integration capacitance.However,the sampling frequency cannot be in-creased arbitrarily due to circuit limitations,such as ampli ?er

K üLAH et al.:NOISE ANALYSIS AND CHARACTERIZATION OF A SIGMA-DELTA CAPACITIVE MICROACCELEROMETER

357Fig.9.Total system noise for different sampling frequencies and integration

capacitances.

slew rate and unity gain bandwidth.Increasing the integration

capacitance decreases the sensitivity of the front-end charge

integrator,and hence decreases the signal-to-noise ratio even

though it improves the absolute voltage noise.Therefore,the

integration capacitance and the sampling frequency should be

optimized to achieve desired resolution and open-loop dynamic

range.

According to simulations,it is possible to improve the

overall system resolution down to hundreds of nano-g level

while achieving a high dynamic range by operating the circuit

at 1-MHz sampling clock with a 15-pF integration capacitance.

However,operating the system under this condition requires

a high-performance front-end circuit capable of driving high

capacitive loads with a high slew rate and low noise.In this

design,a high-slew-rate front-end ampli ?er with 85-dB DC

gain and 12.3-MHz unity gain bandwidth was implemented.

Moreover,the input-referred noise of each inpidual circuit

block has been minimized to achieve a low overall system noise

performance.The next section summarizes the implementation

of this new circuit and presents the test results.

V .I MPLEMENTATION AND T EST R ESULTS

According to the noise analysis summarized in the previous

section,the interface electronics was designed for high-fre-

quency operation.The noise analysis shows that increasing

the sampling frequency from 200kHz to 1MHz improves the

noise performance signi ?cantly,but a further increase does

not provide such a drastic improvement.Therefore,the chip is

designed to operate at sampling frequencies higher than 1MHz.

The inpidual blocks of the circuit,such as the operational

ampli ?er and bias generator,were improved to achieve lower

noise ?oor.

The interface chip was designed in

0.5-m three-metal two-

poly n-well CMOS process.Fig.10shows the fabricated circuit.

All critical inpidual blocks of the interface chip were tested

extensively and the functionality was veri ?ed.It was observed

through the noise measurements that the CDS technique elim-

inates the 1/f noise signi ?cantly,as expected theoretically.The

circuit dissipates less than 7.2mW from a single 5-V supply and

operates from a 1-MHz clock.It has an adjustable sensitivity

between 0.2and 1.2V/pF using a laser trimmable

capacitance Fig.10.Die micrograph of the noise improved readout circuit.TABLE II P ERFORMANCE P ARAMETERS OF THE N OISE -E NHANCED I NTERFACE C

HIP array.Table II summarizes the performance parameters of the interface chip.The CMOS interface chip is combined with a z -axis ac-celerometer to verify the performance improvement in the system.Fig.11shows the z -axis hybrid system with the sensor and the circuit assembled onto a PC board and mounted inside a standard DIP package.Since the sensor ’s mechanical noise is very low,there is no need to use vacuum packaging.

358IEEE JOURNAL OF SOLID-STATE CIRCUITS,VOL.41,NO.2,FEBRUARY

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Fig.11.Hybrid packaged accelerometer and the interface chip in a standard 24-pin IC DIP

package.

Fig.12.Open-loop test results for the hybrid system with a z -axis device.Overall sensitivity is 960mV/g.

A.Open-Loop Tests

Open-loop tests were performed on a piding head,in a 1-g gravitational ?eld,by changing the acceleration on the sensor from 1g

to 1g.While changing the applied acceleration,the differential analog output voltage of the interface electronics was measured.Fig.12shows a measured open-loop sensitivity of 960mV/g.

The output noise of the hybrid module is measured at a 1-MHz sampling frequency by using an HP 3561dynamic signal analyzer with a

50-k reference resistor as shown in Fig.13.This ?gure indicates that the resistor has 32

nV Hz noise density which matches well with the estimated thermal noise of the resistor (note that the measurement bandwidth is 11.72Hz),thus verifying the calibration of the measurement setup.From the measured output,the hybrid module can re-solve

1.08

g Hz.It is believed that the periodic peaks in this measurement are due to environmental factors and are not due to the accelerometer system.

Fig.14shows the dependence of the open-loop noise ?oor on sampling frequency.As shown in the ?gure,although there is a little difference between the two curves for all frequencies,the theoretical and measured curves have the same trend and the noise ?oor decreases with increasing sampling frequency as

expected.

Fig.13.Noise spectrum of the hybrid system with a z -axis device,showing 1.08 g =p Hz noise ?

oor.

Fig.14.Measured noise levels at different frequencies.

B.Closed-Loop Tests

The closed-loop test setup uses a shaker table,a data acquisi-tion board,and LABVIEW and MATLAB programs for signal processing.Since the interface electronics uses a high over-sampling sigma-delta modulation technique,the PWM output bit stream has to be processed to obtain a useful signal.This is realized by transferring the digital output to a computer by means of a data acquisition board,and processing the signal (decimating and digital ?ltering).A

sinc ?lter,FIR ?lter,dec-imator,and digital-to-analog converter have been implemented in MATLAB for this purpose.

The entire system has been operated in closed-loop and the functionality of the system has been veri ?ed through extensive tests.Fig.15shows the decimated PWM digital outputs for (a)a pure 1-g DC input,and (b)a 0.25-g sinusoidal input acceleration on top of a 1-g DC signal.As the ?gure shows,the applied input acceleration is recovered successfully.Note that in Fig.15(a),the only applied acceleration is the 1-g gravitational ?eld.The output voltage is constant,except for variations due to noise generated in the system and/or picked up from the environment.Fig.16shows the Fourier transform of the processed PWM output for 1-g DC bias for sampling frequencies of 100kHz and 400kHz.As the ?gure shows,by increasing the sampling fre-quency four times,the noise ?oor decreases by approximately 16times.This means that the noise is inversely proportional to

K üLAH et al.:NOISE ANALYSIS AND CHARACTERIZATION OF A SIGMA-DELTA CAPACITIVE MICROACCELEROMETER

359

Fig.15.Closed-loop measurement results for the hybrid sensor system:(a)for 1-g DC input acceleration,and (b)for 0.25-g sinusoidal input acceleration on top of 1-g DC

input.

,and hence the mass residual motion is dominant.It has been observed that this noise source is not dominant for higher sam-pling frequencies.Moreover,as the span of the measurement increased beyond 15Hz,the undesired peaks become insigni ?-cant and the noise level stays constant at higher frequencies.These results indicate that at sampling frequencies lower than 400kHz,the mass residual motion is the dominant noise source in closed-loop mode of operation.As the sampling frequency is increased more than 400kHz,this noise source becomes in-signi ?cant compared to others and the overall noise is improved by the square root of the sampling frequency.The system can re-solve better than

10g in closed-loop mode for a sampling fre-quency of 400kHz.Table III summarizes the measured system parameters.

VI.C ONCLUSION

A second-order electromechanical sigma-delta microac-celerometer system has been analyzed in terms of noise

to

Fig.16.Measured noise spectrum for closed-loop operation under 1-g DC bias.

TABLE III

P ERFORMANCE P ARAMETERS OF THE H YBRID S

YSTEM

identify the limiting factors and an improved system has been implemented.Brownian noise,front-end ampli ?er thermal

noise,

noise,mass residual motion,sensor charge refer-encing voltage (SCRV)noise,and quantization noise are the main noise components affecting the sigma-delta modulator performance.The noise analysis and the test results have shown that in open-loop operation,the front-end ampli ?er thermal noise and SCRV noise are dominant.In closed-loop mode of operation,the mass residual motion becomes critical especially at low sampling frequencies,whereas the ampli ?er and SCRV noises become dominant at sampling frequencies higher than 400kHz.Sensors have

0.7

g Hz Brownian noise and ap-proximately 1-kHz bandwidth.The system provides 960mV/g sensitivity with

1.08

g Hz noise ?oor in open-loop.The closed loop operation of the system provides a resolution better than

10

g Hz.Since the open-loop noise at the 1-MHz sampling frequency is

1.08

g Hz,the expected noise ?oor

360IEEE JOURNAL OF SOLID-STATE CIRCUITS,VOL.41,NO.2,FEBRUARY 2006

in the closed-loop mode of operation is around

1.5

g Hz.The discrepancy in the measured and theoretical values has not been explicitly determined,but could be due to test setup and environmental factors.

A CKNOWLEDGMENT

The authors thank Dr.A.Salian for his contributions to this work,and R.Gordenker and B.Casey for device bonding and testing.

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1993.

Haluk K ülah (S ’97–M ’03)received the B.Sc.and M.Sc.degrees in electrical engineering with high honors from Middle East Technical University (METU),Ankara,Turkey,in 1996and 1998,respec-tively,and the Ph.D.degree in electrical engineering from the University of Michigan,Ann Arbor,in 2003.

From 2003to 2004,he was employed as a Research Fellow at the Department of Electrical Engineering and Computer Science,University of Michigan.In August 2004,he joined the Electrical

and Electronics Engineering Department of METU as an Assistant Professor.His research interests include micromachined sensors,mixed-signal interface electronics design for MEMS sensors,and MEMS-based energy scavenging.Dr.Kulah was the winner of several prizes in the Design Automation Confer-ence (DAC)2000,2002,and 2002Student Design Contests,which is sponsored by a number of companies including CADENCE,Mentor Graphics,TI,IBM,Intel,and Compaq.His M.Sc.thesis received the 1999Thesis of the Year Award given by the Prof.M.N.Parlar Education and Research Foundation of

METU.

Junseok Chae (S ’02–M ’03)received the B.S.degree in metallurgical engineering from Korea University,Seoul,Korea,in 1998,and the M.S.and Ph.D.de-grees in electrical engineering and computer science from the University of Michigan,Ann Arbor,in 2000and 2003,respectively.

Since 2003,he has been a Postdoctoral Research Fellow.He gave an invited talk at Microsoft Inc.re-garding “MEMS technology for consumer electronic applications.”He holds two U.S.patents.His areas of interests are MEMS sensors,mixed-signal inter-face electronics,MEMS packaging,and ultra-fast pulse (femtosecond)laser for micro/nanostructures.

Dr.Chae received the ?rst place prize and the best paper award in the Design Automation Conference (DAC)student design contest in 2001with the paper entitled “Two-dimensional position detection system with MEMS accelerom-eter for mouse application.”

KüLAH et al.:NOISE ANALYSIS AND CHARACTERIZATION OF A SIGMA-DELTA CAPACITIVE MICROACCELEROMETER

361

Navid Yazdi received the B.S.degree from the Uni-

versity of Tehran,Tehran,Iran,in1988,the M.S.de-

gree from the University of Windsor,Windsor,ON,

Canada,in1993,and the Ph.D.degree from the Uni-

versity of Michigan,Ann Arbor,in1999,all in elec-

trical engineering.

From November1998to May2002,he was an As-

sistant Professor at Arizona State University.In July

2000,he took an academic leave and joined Corning

IntelliSense Corporation,where he was Director of

Electronics until November2003.He has been a vis-iting Research Scientist at the University of Michigan since December2003. Since April2004,he also has been co-founder and President of Evigia Sys-tems,Inc.,an Ann Arbor-based startup commercializing wireless MEMS-based sensor systems.His research interests and activities include low-power wireless sensors,design and fabrication of microsensors and microactuators,MEMS fab-rication technologies and wafer-level packaging,interface ICs for MEMS,and micro-optical

systems.

Khalil Naja?(S’84–M’86–SM’97–F’00)received

the B.S.,M.S.,and the Ph.D.degrees,all in electrical

engineering,from the Department of Electrical

Engineering and Computer Science,University of

Michigan,Ann Arbor,in1980,1981,and1986,

respectively.

From1986to1988,he was employed as a Re-

search Fellow,from1988to1990as an Assistant Re-

search Scientist,from1990to1993as an Assistant

Professor,from1993to1998as an Associate Pro-

fessor,and since September1998,he has been Pro-fessor and Director of the Solid-State Electronics Laboratory,Department of Electrical Engineering and Computer Science,University of Michigan.His re-search interests include micromachining technologies,micromachined sensors, actuators,MEMS,analog integrated circuits,implantable biomedical microsys-tems,micropackaging,and low-power wireless sensing/actuating systems. Dr.Naja?was awarded a National Science Foundation Young Investigator Award from1992to1997,and was the recipient of the Beatrice Winner Award for Editorial Excellence at the1986International Solid-State Circuits Confer-ence,the Paul Rappaport Award for coauthoring the best paper published in the IEEE T RANSACTIONS ON E LECTRON D EVICES,and the Best Paper Award at ISSCC1999.In2003,he received the EECS Outstanding Achievement Award. He received the Faculty Recognition Award in2001,and the University of Michigan’s Henry Russel Award for outstanding achievement and scholarship in1994,and was selected Professor of the Year in1993.In1998,he was named the Arthur F.Thurnau Professor for outstanding contributions to teaching and research,and received the College of Engineering’s Research Excellence Award.He has been active in the?eld of solid-state sensors and actuators for more than twenty years,and has been involved in several conferences and work-shops dealing with solid-state sensors and actuators,including the International Conference on Solid-State Sensors and Actuators,the Hilton-Head Solid-State Sensors and Actuators Workshop,and the IEEE/ASME Micro-Electromechan-ical Systems(MEMS)Conference.He is the Editor for Solid-State Sensors for IEEE T RANSACTIONS ON E LECTRON D EVICES,an Associate Editor for the Journal of Micromechanics and Microengineering,Institute of Physics Publishing,and an editor for the Journal of Sensors and Materials.He also served as the Associate Editor for IEEE J OURNAL OF S OLID-S TATE C IRCUITS from2000to2004,and the Associate Editor for IEEE T RANSACTIONS ON B IOMEDICAL E NGINEERING from1999to2000.

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