High-Performance Closed-Loop Interface Circuit for High-Q Capacitive Microaccelerometers

IEEE SENSORS JOURNAL, VOL. 13, NO. 5, MAY 2013 1425

High-Performance Closed-Loop Interface Circuit forHigh-Q Capacitive MicroaccelerometersZhenhua Ye, Haigang Yang, Member, IEEE, Tao Yin, Guocheng Huang, and Fei Liu

Abstract— High-Q sensory microsystems are desirableespecially in low noise applications. However this makesimplementation of the closed-loop control a great challenge.An in-depth investigation into high-performance closed-loopinterface circuit design for high-Q capacitive microaccelerometersis presented. Focus is placed on an analogue force feedbackscheme with proportional-derivative compensation. Such anapproach is differing from the commonly used electromechanical�� technique, since the latter one often suffers severe problemsin balancing between the loop stability and other essentialcharacteristics in the presence of high-Q sensing element.A comprehensive analysis concerning the system linearity andbandwidth is conducted, aiming for performance optimization.The adverse impact arising from several electronic noise sourcesin the system is studied in order for minimization. Accordingly,a prototype interface circuit is designed and fabricated in acommercial 0.35-μm CMOS process. The chip measures 2.5 ×2.5 mm2 and operates from a single 5 V supply. The quiescentcurrent is about 10mA. The test results show that it offers a fullscale acceleration of ±1.2 g correspondingly with integrated non-linearity (INL) of 6.6%, wide-band noise equivalent accelerationof nearly 1 μg/

√Hz over a signal bandwidth of about 1.2 kHz.

Index Terms— Analogue force feedback, closed-loop, high-Q,microaccelerometer, proportional-derivative.

I. INTRODUCTION

M ICROMACHINED inertial sensors are becomingincreasingly attractive in providing micro-scale, low

power, low cost, and high performance solutions for a broadrange of applications such as aerospace, military, automo-tive, and numerous consumer electronic industries. In onedirection of the related research, capacitive micromachinedaccelerometers gain growing popularity in recent years [1].

Electromechanical closed-loop architecture is imperativefor high performance design, which imposes very stringentrequirements on features like resolution, linearity, signal band-width, power dissipation, linear input range, long-term stability

Manuscript received March 20, 2012; revised October 20, 2012; acceptedDecember 10, 2012. Date of publication December 24, 2012; date of currentversion March 26, 2013. This work was supported by the National NaturalScience Foundation of China through Project 61106025 and the CAS/SAFEAInternational Partnership Program for Creative Research Teams. The associateeditor coordinating the review of this paper and approving it for publicationwas Dr. Patrick Ruther.

The authors are with the Institute of Electronics, Chinese Academy ofSciences, Beijing 100190, China (e-mail: [email protected];[email protected]; [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSEN.2012.2236312

temperature insensitivity, etc. The interface circuit in a closed-loop device reads the sensor signal and uses the feedback tomaintain the proof mass around a null position with reduceddisplacement, in contrast to an open-loop operation. This way,the overall sensor linearity, dynamic range and bandwidthshould be improved. High-Q sensor is beneficial for achievinghigh resolution. And in the application of combining severalsensors into a combo unit, the accelerometer is requiredto work at the low pressure together with gyroscopes andmagnetometers. Thus, the accelerometer should operate ata high-Q condition. Managing such a configuration wouldbe a great step towards implementation of combo sensors.High-Q sensor brings the risk of instability to the closed-loop. Electromechanical �� closed-loop, as a widely usedscheme, has merit of direct digital output, but encounters someproblems such as the difficulties in balancing among the loopstabilization, the noise shaping [2] and the limitation of theinput range [3], in the presence of high-Q sensing element.These shortcomings originate from the fact that digital forcefeedback mechanism is applied in the electromechanical ��loop, which serves as a time-averaging function to the externalstimulus [4]. Hence severe non-linearity is induced into theclosed-loop, making the effective control difficult to achieve.Furthermore, implementation of a high-order electromechani-cal �� loop is very hard and complicated in design [2], [3],[5]–[7].

On the contrary, another scheme using analogue force feed-back should better maintain the closed-loop as a linear system[8], [9]. Therefore, the loop stability can be easily enhancedby using a lead compensator in the forward path [2], [3],[6]–[9] or in the feedback path [10]. All these design efforts tryto eliminate the adverse effect of the complex poles resultingfrom the high-Q sensing element, in a way of introducingextra left-plane zeros into the loop transfer function. Never-theless, there are two drawbacks in analogue force feedbackscheme. One is the potential threat of “pull-in” in a shockcondition, which can be solved to a large extent by utilizingmechanical stoppers [5] or by charge control using switched-capacitor feedback circuits [11]. The other is the imperfectlinearity of voltage-to-force transduction due to the non-idealities of the actuation capacitors [12]. Also, this problemcan largely be solved with a new mechanism of analogue forcefeedback [13].

This paper is organized as follows. Section II presentsa brief overview of the micro-accelerometer system design.Section III describes a novel system topology, based on which

1530-437X/$31.00 © 2012 IEEE

1426 IEEE SENSORS JOURNAL, VOL. 13, NO. 5, MAY 2013

proofmass

Fmechanical-spring=k·xFmechanical-damp=B·v

Felectrical-damp=kfbkdkx/v·v

Fext

xv

Felectrical-spring=kfbkpkx/v·x+

neutral positionInterface Circuit

kx/v kdd(·)/dt

kp

kfbForce Feedback

Compensator

PositionSensing

electrical damper

electrical spring

PROOF MASS

Z

XY

SPRING

SPRING

Micromachined Accelerometer

TOP COVER

BOTTOM COVER

Fext: external inertial forceFmechanical-spring/Felectrical-spring: mechanical /electrical spring forceFmechanical-damp/Felectrical-damp: mechanical/electrical damping forcex: proof-mass displacementv: proof-mass transient velocityB: mechanical damping coefficientk: mechanical spring coefficientkx/v: position sensing coefficientkp/kd: proportional/derivative coefficientkfb: electrostatice force feedback coefficient

Fig. 1. Accelerometer and the system design overview.

comprehensive analysis of the essential characteristics is givenin Section IV and V, with the emphasis on the performanceoptimization. The prototype implementation and test resultsare discussed in Section VI. Section VII concludes with somekey results.

II. MICROACCELEROMETER AND SYSTEM DESIGN

Fig. 1 illustrates a high-Q capacitive micromachinedaccelerometer. The core of the accelerometer is a cantileverstructure proof mass. The proof mass and the suspensionsprings form a mass-spring-damper system. In the presence ofan external acceleration ain in the z-direction, the proof massdeviates from the neutral position by a certain displacementx . According to ref. [1], the transfer function from ain to x is:

Hm(s) = x(s)

ain(s)= 1

s2 + Bm s + k

m

= 1

s2 + ωnQ s + ω2

n(1)

The resonant frequency ωn is related to the suspensionspring constant k and the proof mass m. The quality factorQ is a function of the damping coefficient B , the proof massm, and the resonant frequency ωn .

The mechanical noise is primarily due to Brownian motionof the gas molecules surrounding the proof mass and Brownianmotion of the suspension springs. The total noise equivalentacceleration [g/

√Hz, g: gravity] is [1]:

√4kBT B

9.8m= 1

9.8

√4kBT ωn

Qm(2)

where kB is the Boltzmann constant and T is the temperaturein Kelvin. Equation (2) clearly indicates that a higher Qshould improve the mechanical noise floor for a given resonantfrequency, i.e., the ratio of m to k is maintained. For a typicalbulk-micromachined sensor with ωn = 1000 rad/s, m =10 milligram, and Q = 10, the noise level should belower than 0.1μg/

√Hz at room temperature. However from

Equation (1), it is noted that a high-Q transducer may sufferfrom the lack of mechanical damping, hence the proof massmotion would exhibit frequency response peaking at the res-onant frequency and ringing in the step response.

There are five fundamental motivations for the interfacecircuit to be included in an electromechanical closed-loop ofhigh-Q sensor, referring to Fig. 1. First, it precisely convertsthe mechanical motion into an electric signal for furtherprocessing. There exists various position sensing methods,including modulation-demodulation [8], [10], charge sensitiveamplification [3], [5]–[7], [9], [14] and others [15]. The chargesensitive amplifier scheme is used in this work primarily for itslow power dissipation and temperature-insensitivity. Secondly,it provides electrostatic force actuation for closed-loop control.Implementation include analogue [8]–[10], [13] and digital[3], [5]–[7] approaches. In this work, analogue force feedbackis preferred for system robustness. Thirdly, since the loopinstability originates from insufficiency of the mechanicaldamping, “electrical damper” is possible to compensate themechanical part. Further, to considerably decrease the proofmass displacement, which is the dominant cause of the systemnon-linearity, “electrical spring” is also comprised in thecompensator By carefully selecting kp and kd , performanceoptimization with respect to the signal bandwidth, the lin-earity, and the noise level could be achieved, as discussedin Sections III and IV. Last but not least, low noise circuitdesign is demanded to attenuate the electric noise below thenoise floor of the mechanical part. Chop stabilization andcorrelated double sampling (CDS) are two common techniquesto suppress the low-frequency noise [16]. CDS technique isused in this work. For wide-band noise reduction, attentionshould be paid on the critically noisy components of the signalpath, such as the operational amplifiers and switch transistorsat the input stage. Elaborate analysis on this issue is proposedin Section III.

III. NOVEL SYSTEM TOPOLOGY

Fig. 2 shows a novel system topology. The accelerometer ismodeled as a pair of intra-die variable sensing capacitors Cs1and Cs2, plus a pair of intra-die fixed parasitic capacitors Cp1and Cp2. Cs1 and Cs2 vary differentially with respect to theexternal acceleration, generating a capacitance difference. Theinterface circuit consists of a charge sensitive amplifier (CSA)to sense the capacitance difference, a proportional-derivativecompensator (PD) for system stabilization, a multiplicator(MX) for input range expansion, and the feedback controller(FB) for electrostatic actuation.

The operation of the interface circuit involves four phases,namely, discharge (�gnd,�1,�2,�3,�4), autozero (�2p,�3p), sense (�1!, �2!, �3!, �4dd), and force feedback(�4ddd, �fb). In the discharge phase, the potentials of TOP,CENTRE, and BOTTOM electrodes are reset to ensure correctbiasing, while the capacitors are discharged to erase the mem-ory from the previous cycle. During the autozero phase, theoffset and low frequency noise of the amplifiers are sampled sothey can be cancelled out to a large extent in the subsequentsense phase. In the sense phase, the potential polarities of

YE et al.: HIGH PERFORMANCE CLOSED-LOOP INTERFACE CIRCUIT 1427

fb

4

gnd

2

1ctr

0 1 2 3 4 5 6 7 30 31

4dd4ddd

3

2p

3p

Ts

1!

2!

3p!

3!

Tfb

ctr

CI2p

2

CSA

2!

OTA1+

_

Cu3p

3

PD

3!

OTA2+

_Cp

Cd 3p!3!

3!3

Ct3p

3

MX

3!

OVA1+

_Cmx

4ddd

FB

4

OVA2+

_ CF4dd

1 1!

11!

Vn

gnd

Vp

Vn Vp

Trimming Capacitor

Array

TOP

BOTTOM

CENTRE

off-chip low-pass filter

fb

...

...

outputMicromachined Accelerometer

Cs1 Cp1

Cs2 Cp2

Fig. 2. Simplified schematic diagram of a typical system topology and thetiming diagrams for the operation clock signals.

TOP and BOTTOM electrode reverse, causing a small amountof differential charge which is a measure of the capacitancedifference between Cs1 and Cs2 flow into the integratingcapacitor CI of CSA. The readout signal of CSA is furtherprocessed by PD and MX to generate a proper force feedbackcontrol signal Vfb. In the force feedback phase, the potentialof CENTRE electrode is driven to Vfb while the potentialpolarities of TOP and BOTTOM electrode reverse again.Consequently, two electrostatic forces in opposite directionsare superimposed on the proof mass. Assuming the parallelplate approximation is applied to the intra-die capacitors, wehave:

Cs1 = εA1

d1 − x, Cs2 = εA2

d2 + x(3)

where ε is the dielectric, A1(A2) is the plate capacitor area ofCs1(Cs2), and d1(d2) is the neutral air gap of Cs1(Cs2), x isthe proof mass displacement. Then the net electrostatic forceon the proof mass is given as [20]:

Ffb(Vfb) = Tfb

Ts

[εA2(Vp − V f b)

2

2(d2 + x)2 − εA1(V f b − Vn)2

2(d1 − x)2

](4)

where T f b is the force feedback portion in each cycle Ts .Quiescent current consumed in the CSA and FB blocks

constitute two major power dissipation sources in this work.This is mainly due to the requirements of fast charging to thevery large sensing capacitance (about 400pF) of the microac-celerometer. Meanwhile, the demand for low-noise front-endalso imposes a trade-off between low power dissipation andlow noise level with regard to design of the CSA.

m 2 2n nQ

1H (s) =s + (ω )s + ω/

senp nC/V

-sH (s) = (1+ )2 I

TV VC

e−

2 22 p fb nbf1bf

22 1

2fbs

( ) ( ) ][2( ) 2( )

=a A V VT A V VmT d x d x

ε ε− −−

+ −

1p dPDH (z) = (1 z )k k −− − −

mxMXH (z) = k−LPF1H (s) =

1+ s/ uf

1 2

1 2C = A A

d x d xε ε

−− +

Δ

Fig. 3. Behavioral macro-model of the entire system. fu approximatelyequals the unity-gain bandwidth of the amplifier used in FB.

IV. LINEARITY AND SIGNAL BANDWIDTH

A. Behavioral Macro-Model

Fig. 3 shows the behavioral macro-model of the describedsystem. The micromachined accelerometer serves as a second-order loop filter. The operation of CSA is referred to Fig. 2.By applying the charge conservation law, the discrete-timeequivalent transfer function of CSA is obtained:

HCSA(z) = 2Vm

CI

(1 + z− Tsen

Ts

)(5)

where Vm = (Vp − Vn)/2, CI is the integration capacitance,Tsen is the time taken by the sense phase during each cycle Ts .Equation (5) indicates that CSA yields a transfer function witha high-frequency pole resulting from an appreciable sensingtime Tsen. Therefore the high-frequency characteristic of CSAshould be closely examined for loop stabilization.

The macro-model of FB consists of three parts. A seriesof rectangular voltage pulses is reshaped by a zero-order-hold(ZOH) together with an ideal switch. Accordingly, the forcefeedback operation is carried out by the v/acc module as shownin Fig. 3 where the transfer function of the module is alsodenoted. For convenience of simulating actual settling time ofthe voltage propagation, a low-pass filter (LPF) is added.

B. Linearity

The total non-linearity of a closed-loop system is affectedby those of the forward signal path and the feedback block.Generally, the latter one should dominate since the forwardsignal path non-linearity is significantly depressed by the loopgain. Detailed analysis on the feedback non-linearity is givenas follows. The structure of the accelerometer is practicallyasymmetric (A1 �= A2, d1 �= d2) due to the non-idealitiesof micromachined fabrication process. Thus, Equation (4) isrearranged as:

Ffb

(Vfb

Vm

)≈ 2εA2V 2

m

d22

[(λ

4

)+

(1 + λ

2

+2εA2V 2m

d22

1

ω2nd2 Aloop

) (Vfb

Vm

)+ λ

4

(Vfb

Vm

)2


2 2n nQ

1s + (ω )s + ω/

p nc/v

I

V Vk

C−

=020

/c = 2x

εAkd

0 p nfb2

0s

( )F =

A V VTT md

ε −

11+ s/ uf

Fig. 4. Continuous-time linear model of the entire system. The phase lagof the rectangular voltage pulses reshaping block is relatively small and canthen be ignored for simplification.

+(

2εA2V 2m

d22

1

ω2nd2 Aloop

)(Vfb

Vm

)3]

(6)

where A2 is the plate capacitor area of Cs2 as the reference, d2is the neutral air gap of Cs2 as the reference, λ = |A1 − A2|/A2 + |d1 − d2|/d2 as the total mismatch coefficient of theaccelerometer, Aloop is the dc loop gain.

Equation (6) indicates that mechanical asymmetries willintroduce offset, feedback factor error, and second-order har-monic distortion (HD2) into the feedback transfer function,while finite dc loop gain only results in feedback factor errorand third-order harmonic distortion (HD3).

C. Signal Bandwidth

Considering that the sampling frequency fs is always muchhigher than the signal bandwidth, the mixed-signal macro-model of Fig. 3 can be converted to a continuous-timeequivalent as shown in Fig. 4. The proof mass displacementx is loop controlled so that it is normally small and itsinfluence on the x/c and v/acc block of Fig. 3 can besafely ignored. Meanwhile, the micro-fabrication related non-idealities discussed in the previous subsection are neglectedfor simplification. Accordingly, the system transfer functionbetween the acceleration input and the feedback voltage outputis approximately given as:

Hsys(s)≈k0

(k p+ kd

fss)

(1+ s

fu

) [s2+

(ωnQ + k0 F

fskd

)s+(

ω2n +k0 Fk p

)](7)

where k0 = kx/c · kc/v · kmx, and fs = 1/Ts is the samplingfrequency.

The dynamic characteristic of the system is dependent onthe pole-zero location of the close-loop transfer function. Thesignal bandwidth is maximized when the system is criticallydamped:

kd = fsωn

k0 F(2

√1 + k0 Fk p

ω2n

− 1

Q) ≈ 2 fs

√k p

k0 F(8)

and the maximum 3-dB signal bandwidth is given:

fc,max =√√

2 − 1

√1 − k0 Fk p

ω2n

ωn

2π≈ 0.64

√1 + Aloop

ωn

2π(9)

Fig. 5. Schematic view of the amplifier used in CSA.

Equation (9) indicates that the signal bandwidth can beexpanded simply by increasing the dc loop gain Aloop, which isusually done by increasing kp . However, according to Equation(8), this also requires a larger derivative coefficient kd toensure loop stability, thus raising the derivation effect noisesignificantly, as referred in the following section.

V. NOISE ANALYSIS

The overall system resolution is affected by both themechanical and electronic noise level. It has been reportedthat the mechanical noise level can be reduced down tosub-μg/

√Hz [6]. Therefore, great effort should be made to

suppress the electronic noise down to ultra-low level. Thereare several dominant electronic noise sources in such anaccelerometer system as shown in Fig. 2, including the opera-tional amplifier noise, kT/C noise, noise due to the derivationeffect, noise due to proof mass residual motion, and chargingreference voltage noise. Individual analysis on these noisesources are given in the following subsections.

A. Operational Amplifier Noise

The operational amplifier noise consists of the thermal andflicker noise. Since CDS technique is applied in CSA, theeffect arising from the flicker noise sources is depressed con-siderably. Fig. 5 shows the schematic view of the single endedcurrent-mirror operational transimpedance amplifier (OTA)used in CSA. The input-referred thermal noise is dominatedby transistors PM3∼PM6, NM1∼NM4:

e2t,n ≈ 16kBT

3gmPM3

(1 + κgmNM1κgmNM3 + gmPM5

gmPM3

)(10)

where gmPM3, gmNM1, gmNM3, and gmPM5 are the transistortransconductances, and κ = ((W/LNM1,2)/(W/LNM3,4))

2.Fig. 6 shows the simplified diagram for operational amplifier

noise calculation. The thermal noise sources of the operationalamplifier are sampled and folded into the baseband frequencyrange [17]. The acceleration equivalent amplifier thermal noise


Fig. 6. Simplified diagram for operational amplifier noise calculation.

Fig. 7. Simplified diagram for derivation effect analysis.

is given after dividing the output noise by the transfer functionbetween acceleration input and CSA output:

√a2

t,n ≈ Ctot

CI

√2BWu

fse2

t,n ×(

CI

2Vm

ω2nd0

Cs1 + Cs2

)(11)

where Csenser = Cs1 + Cs2 + Cp1 + Cp2, Ctot = Csensor +Cpar+CI , Cpar is the parasitic capacitance at the negative inputnode of amplifier, d0 is the normal neutral air gap of sensingcapacitor, and BWu is the amplifier unity gain frequency givenby

BWu = 1

2π

gm P M3

CI + Cp + Cd(12)

where Cp and Cd are the proportional and derivative capaci-tance of PD block.

By substituting (10) and (12) into (11), we have:

√a2

t,n ≈√

16kBT (1 + χ)

3π fsCout

Ctot

Cs1 + Cs2

ω2nd0

2Vm(13)

where χ = κgmN M1+gmN M3+gm P M5gm P M3

, Cout = CI + Cp + Cd .It is clear that the noise can be reduced by increasing the

sampling frequency and the total capacitance at the outputnode. However, this will incur higher power consumption.Trade-off between these two issues is needed in design.

B. Derivation Effect

The derivation effect is caused by the noise-shaping effectof the proportional-derivative part in PD block, as shown inFig. 7. Prior to being sampled and folded into the baseband,the amplifier thermal noise is filtered by the high-pass RC

Fig. 8. Simplified schematic diagram for CRV noise calculation.

network. Consequently, the output noise is no more with auniform spectral density:

e2o,n( f ) = (1 + k p)

2e2t,n +

(kd

fs2π f

)2

e2t,n (14)

Hence the acceleration equivalent noise is roughly given as:

√a2

t,n =√

2

fs

∫ BWn

0e2

o,n( f ) · d f ×(

1

k p

CI

2Vm

ω2nd0

Cs1 + Cs2

)(15)

By replacing (14) in (15), we have:

√a2

t,n ≈ 2πkd

k p

√2

3

(BWn

fs

)3

e2t,n ×

(CI

2Vm

ω2nd0

Cs1 + Cs2

)(16)

Note that the first item of (14) is ignored, since we have(BWn/ fs)

3 >> BWn/ fs . Equation (16) indicates that thederivation effect noise is proportional to kd .

C. kT/C Noise

In switch-capacitor circuit, the sampled and folded switchon-resistance thermal noise (generally referred to as kT/Cnoise) is also significant. For the topology shown in Fig. 6,the acceleration equivalent kT/C noise of CSA is given [18]:

√a2

KTC,n ≈√

2

fs

kB T

Ctot

Ctot

Cs1 + Cs2

ω2nd0

2Vm(17)

Note that kT/C noise is inversely proportional not to theintegration capacitance but to the total capacitance at thenegative input node of amplifier. Besides, it should be reducedby increasing the sampling frequency.

D. Charging Reference Voltage (CRV) Noise

The two charging reference voltage sources Vp and Vn

shown in Fig. 2 are also significant noise sources since theyare at the front-end of the system. Fig. 8 shows the simplifiedcircuit schematic for calculation of this noise. Note that thenoise bandwidth is limited by the RC filter formed by thesensing capacitor and the on-resistance of the switches. Thenoise density is calculated after dividing the total integratednoise power by fs /2 [19]:

√a2

CRV,n ≈

√√√√ 2V 2CRV,n

fs RswitchCsensor

ω2nd0

2Vm(18)

where Rswitch is the switch on-resistance, and VCRV,n is thecharging reference voltage noise.


TABLE I

NOISE COMPONENT AND THEIR EXPRESSIONS AND TYPICAL VALUES

Noise Sources Expressions Typical Values

Operational amplifier noise ∗1√

16kB T (1+χ)3π fs Cout

CtotCs1+Cs2

ω2n d0

2Vm0.55μg/

√Hz

Derivation effect ∗2 2πkdkp

√23 ( BWn

fs)3e2

t,n(CI

2Vm

ω2nd0

Cs1+Cs2) 0.4μg/

√Hz

kT/C noise√

2fs

kB TCtot

CtotCs1+Cs2

ω2nd0

2Vm0.17μg/

√Hz

Charging reference voltage noise ∗3

√2V 2

C RV ,nfs RswitchCsensor

ω2nd0

2Vm0.11μg/

√Hz

Mass residual motion ∗4 amaxω2n

(2π fs )2

√fc 0.3μg/

√Hz

∗1: kB = 1.38 × 10−23J/K, T = 300K, Csensor = 400pF, Cs1 + Cs2 = 120pF, CI = 25pF, Cpar = 10pF,Cout = 40pF, fs = 125k Hz, χ = 0.2, Vm = 2.5V, ωn = 2π × 400 rad, d0 = 3μm∗2:kd /kp=0.5, BWn =2.5MHz, fs =125kHz, et,n= 2nV/

√Hz

∗3: VC RV,n =2nV/√

Hz, Rswitch =200ohm∗4: amax=1.2g, fc=1.2kHz

E. Mass Residual Motion (MRM)

The mass residual motion noise is the result of discrete-timeelectrostatic actuation, which is applied by means of feedinga series of electronic pulses on the proof mass. This pulsetrain results in a periodic motion of the proof mass aroundthe neutral position even under zero acceleration input. Thismovement submerges weak acceleration input and appears asnoise. This noisy movement can be represented as: [20]√

�x2n = amax

(2π fs)2 (19)

where amax is the maximum acceleration input. And theacceleration equivalent noise is given:√

a2MRM,n = amaxω

2n

(2π fs)2√

fc(20)

where fc is the signal bandwidth. From Equation (20), itcan been seen that this noise is inversely proportional to f 2

s ,whereas other noise sources are inversely proportional to

√fs .

Therefore, this noise source should be significantly depressedby increasing the sampling frequency.

Table I lists the expressions and typical values of theindividual noise components.

VI. IMPLEMENTATION AND TEST RESULTS

According to the design principles and characteristics analy-sis discussed in the previous sections, a prototype inter-face circuit was designed and fabricated in a commercial0.35-μm CMOS process. The interface circuit operates froma single 5 V supply, while the charging reference voltages Vp

and Vn are set to be 5 V and 0 V respectively. An off-chip2-MHz clock source is required to generate a series of on-chip125-kHz operation clock signals. The noise-critical compo-nents of the circuit, such as the operational amplifiers andthe switches on the signal path, were improved to achievelow noise floor. The parameters k p and kd of PD block aredesigned to be adjustable for system performance optimiza-tion. Trimming capacitors array is designed to compensate forthe mechanical offset.

Fig. 9. Micro-photograph of the interface circuit chip.

The micro-photograph of the interface circuit chip is shownin Fig. 9. The active circuit area measures 2.5 × 2.5 mm2.The interface chip is combined with a high-Q capacitivebulk micromachined accelerometer SF1500 with the vacuumpackage from Colibrys Inc [21]. Fig. 10 shows the hybridsystem with the accelerometer and the interface assembledonto a printed circuit board (PCB). A laboratory vibrationgeneration system is used for dynamic characterization. Fig. 11shows the low-pass filtered system response to 1-g 100 Hzsinusoidal input acceleration on top of 0-g bias. The measuredtransfer function of the system is shown in Fig. 12. The 3-dBsignal bandwidth is observed to be about 1200 Hz.

Fig. 13 shows the measured results of system noise levelwith different kd . For better isolating ambient vibration noise,the experiment is carried out in the underground, and the mea-sured accelerometer and interface circuit are further suspendedby a mass-spring system. However, some line-frequency har-monics still exist in the noise spectrum due to the environmen-tal trembling and the power supply interference. As predicted


Fig. 10. Vacumm packaged accelerometer and the interface chip bonded ona printed circuit board.

Fig. 11. Measured results of the system reponse to 100 Hz 1-g sinusoidalinput acceleration on top of a 0-g bias.

in equation (16), the value of kd has a direct influence on thewide-band noise level. With optimized parameters kp and kd ,the noise floor of the entire system is about 1μg/

√Hz. Figs. 14

and 15 illustrate the theoretic and Matlab Simulink simulationresults of the influences of the mechanical asymmetries andlow dc loop gain on system linearity. The Simulink simulationsare based on the macro-model shown in Fig. 3. The theoreticalvalues are obtained using equation (6). Fig. 15 also showshow the experimental values of the total INL changes withrespect to the dc loop gain. It can be seen that high systemlinearity requires not only sufficient dc loop gain, but alsominimum mechanical asymmetry. The dc transfer functionof the prototype from acceleration input to output voltage istested with high precision rotation stage.

Fig. 16 shows the testing results. The maximum residualerror after linear fitting is 13.2 mg or 6.6%. The sensitivityof the entire system is −1.793V/g. Constrained by the powersupply voltage, the full-scale of the system is limited to about±1.2g. A summary of the essential properties for the entiresystem is given in Table II. In comparison, the commercial

Fig. 12. Measured transfer function of the system.

Fig. 13. Measured results of system noise level for different kd .

Fig. 14. Normalized HD2 versus mechanical asymmetries.

micro-accelerometer device SF1500 has some specificationsquoted from the datasheet [21] such as a bandwidth of1500 Hz, sensitivity of 1.2V/g, linear range of ± 3g and noiselevel of 0.5μg/

√Hz. The device is in a piggyback mount of

the micro-sensor over a printed circuit. Dual power supplies of±6V are required and the quiescent current is 11.6 mA. Thus,the prototype interface circuit of this work provides some


Fig. 15. Normalized HD3 due to finite dc loop gain and the experimentresults of the total INL (HD2+HD3) versus dc loop gain.

Fig. 16. Dc transfer function from acceleration input to output voltage (top),and the residual error after linear fitting (bottom).

comparable bandwidth and noise characteristics yet with muchlower power dissipation. Though the single 5V supply in thiswork apparently limits the input scale range, it is better placedto facilitate compatible integration of digital signal processingcircuits where dual power supplies are normally not allowed.

Compared with electromechanical �� schemes [3], [5]–[7],this approach exhibits much better system stability, lowerimplementation complexity and comparable noise perfor-mance. Compared with continuous-time schemes [8], thisapproach has remarkable advantages in terms of lower tem-perature sensitivity and power dissipation. Referring to ourtechnique, the lack of digital output should be overcomeby adding an extra back-end digitization circuit, while rela-tively low linearity characteristic may be circumvented withincluding new mechanism of analogue force feedback [13]or extra boost circuits. High performance characteristics suchas low noise floor, large bandwidth and wide dynamic rangemake the circuit suitable for strong motion applications suchas earthquake and seismology measurements, homeland andborder security, structure monitoring, etc.

TABLE II

PERFORMANCE PARAMETERS OF THE ENTIRE SYSTEM

MEMS Accelerometer

Sensitivity [pF/g] 20 (differential)Quality factor (Q) >30Total intra-die capacitance [pF] >400

Interface Circuit

Fabrication process 0.35 m commercial CMOSPower supply [V] 5Quiescent current [mA] 10Chip area [mm2] 2.5×2.5

Entire System

Sensitivity [V/g] −1.793Signal bandwidth [Hz] 1200Noise floor [μ g/

√Hz] 1

Maximum non-linearity 6.6%Linear input range [g] ±1.2

VII. CONCLUSION

In presence of high-Q sensing element, analog forcefeedback scheme together with proportional-derivative com-pensator may be a better choice for electromechanicalclosed-loop implementation, rather than the commonly usedelectromechanical ��. In-depth investigation of high-performance closed-loop interface circuit design for high-Qcapacitive microaccelerometers is given, together with com-prehensive analysis on the essential characteristics of the entiresystem. Accordingly, a prototype interface circuit is designedand fabricated in a commercial 0.35-μm CMOS process. Thesimulation and experiment results proved that the systemlinearity is to a large extent determined by the force feedbackblock. Critical factors include not only the value of dc loopgain, but also the degree of mechanical asymmetry. The systemwideband noise floor is affected by the mechanical noise, theoperation amplifier noise, the kT/C noise, the derivation effect,the proof mass residual motion, and the charging referencevoltage noise, while the low-frequency electronic noise canbe greatly depressed by CDS technique. By improving thenoise-critical components of the circuit, such as the operationalamplifiers and the switches on the signal path, low widebandnoise floor is achievable.

ACKNOWLEDGMENT

The authors would like to thank D. Chen and D. Jin, ChineseAcademy of Sciences Institute of Electronics, Beijing, China,and S. Li, W. Zhang, and W. Su, Peking University, Beijing,for their help on testing.

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Zhenhua Ye received the B.S. degree from TsinghuaUniversity, Beijing, China, and the Ph.D. degree inmicroelectronics engineering from the Institute ofElectronics, Chinese Academy of Sciences, Beijing,in 2007 and 2012, respectively.

His current research interests include analog cir-cuits design and high-performance sensor interfacesdesign. He is currently with Huawei TechnologiesCo. Ltd.

Haigang Yang (M’–) received the Ph.D. degreefrom University of Cambridge, Cambridge, U.K., in1991.

He is currently with Institute of Electronics,Chinese Academy of Sciences, Beijing, China, asa Professor and the Director of the System-on-Programmable Chip Research Department. He waswith Wolfson Microelectronics, LSI Logic Europe,Hitachi Microsystems Europe, and Altera Europe.His current research interests include analog andmixed signal integrated circuit design, and very large

scale integration design.

Tao Yin received the B.S. and M.S. degrees fromXidian University, Xi’an, China, in 2002 and 2005,respectively, and the Ph.D. degree in microelec-tronics engineering from the Institute of Electron-ics, Chinese Academy of Sciences (CAS), Beijing,China, in 2008.

He is currently with the Institute of Electronics,CAS, as an Associate Professor. His current researchinterests include analog and mixed signal integratedcircuits design and high-performance sensor inter-faces design.

Guocheng Huang received the B.S. degree in elec-tronics science and technology from the BeijingUniversity of Chemical Technology, Beijing, China,in 2011. He is currently pursuing the Ph.D. degreein microelectronics engineering with the Institute ofElectronics, Chinese Academy of Sciences, Beijing.

His current research interests include analog cir-cuits design and micromachined inertial sensor inter-faces design.

Fei Liu received the B.S. degree from NankaiUniversity, Tianjin, China, and the Ph.D. degree inelectronics from Peking University, Beijing, China,in 1995 and 2003, respectively.

He joined Cadence Design Systems Inc., as anApplication Engineer in 2003. Since 2008, he hasbeen with the Institute of Electronics, Chinese Acad-emy of Sciences, Beijing, China, where he is anAssociate Professor. His current research interestsinclude analog, mixed-signal and RF IC. His currentresearch interests include low-power analog IC for

biomedical applications and high-speed analog circuits.

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High-Performance Closed-Loop Interface Circuit for High-Q Capacitive Microaccelerometers