A Micropower Front-End for CapacitiveMicroaccelerometers

Mika Kamardinen, Mikko Saukoski and Kari HalonenElectronic Circuit Design LaboratoryHelsinki University of Technology

Espoo, Finland

Abstract- This paper presents the measurement results of amicropower differential switched-capacitor front-end designed forcapacitive microaccelerometers. Before considering the measure-ment results, the negative effects of the electrostatic forces areanalysed. The designed front-end is capable of reducing theseeffects. Chopper stabilisation is used to decrease the offset voltage.The front-end was realised with a 0.13pm CMOS process. Thesilicon area of the front-end is 0.325 mm2. The measurementsshow that the functionality of the front-end is in line with thetheory and it achieves a 53.2 dB maximum SNR with 10 kHzsampling frequency. The worst case current consumption from a1.8 V supply is 39 ,uA, when four masses are read.

I. INTRODUCTION

Microaccelerometers are micromachined acceleration sensorswith dimensions ranging from 1 to 100 micrometers. Thedevices can be for example piezoelectrical, piezoresistive orcapacitive. Capacitive accelerometers have advantages suchas zero static biasing current and excellent thermal stability.Further, by using bulk micromachined devices with a largeseismic mass, very high sensitivity can be reached.With a proper configuration, a single capacitive accelerom-

eter can measure accelerations along all three axes simulta-neously [1], [2]. These devices are built such that the seismicmass forms four differential capacitor pairs. By measuring thesecapacitances and taking their proper linear combinations, allthree vector components of linear acceleration (x-, y- and z-directional) can be evaluated. With four masses, these devicesalso offer redundancy so that fault conditions can be detected.The SEM pictures of the sensor element presented in [1] and thebehaviour of the four masses under y-directional accelerationare shown in Fig. 1.An inexpensive yet reliable and highly-sensitive three-axis

accelerometer with low power consumption would have a widerange of applications, from hand-held mobile terminals andtoys to industrial applications and automotive chassis controlsystems. In order to realise this kind of a sensor, the read-out electronics has to be integrated together with the sensorelement, forming a microelectromechanical system (MEMS).The accelerometer should ideally have a fully digital output.

In this paper, the measurement results of a differentialswitched-capacitor (SC) front-end for capacitive accelerometersare presented. The simulation results were discussed previouslyin [3]. The front-end is designed to read a capacitive three-axis accelerometer by time-multiplexing between four channels.The front-end is mainly used to read DC signals but it is

Fig. 1. Left: Three-axis accelerometer presented in [1]; Right: Top view of thestructural wafer of the accelerometer. (Images courtesy of VTI Technologies,Vantaa, Finland); Bottom: The behaviour of the four masses under y-directionalacceleration.

designed for the case where the maximum signal frequencyin each channel is 1 kHz, the sampling frequency for a singlechannel is 10 kHz, and the total sampling frequency is 40 kHz.Chopper stabilisation is used to reduce the offset voltage. Thefront-end was implemented with a 0.13 ,um CMOS process.

In Section II, the negative effects of the electrostatic forcesare analysed and then the designed front-end is introduced.The measurement results are presented in Section III. Finally,conclusions are drawn in Section IV.

II. DESIGNED CIRCUIT

A. Electrostatic Forces

A capacitive accelerometer can be modelled by a threeter-minal component that consists of two capacitors, CDP andCDN, with a common middle electrode. If the capacitors areconsidered to be simple plate capacitors, their capacitancesunder acceleration can be written as

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CDP

CDN

AE,Eo_ =c dd- Ad Cd-dA'

d+Ad d+Ad J

TABLE I

PARAMETERS FOR A TYPICAL MICROMECHANICAL ACCELEROMETER.

Er M K

1 lmg 15N/m(1)

Here, A is the plate area, Er the relative permittivity of theinsulator, Eo the permittivity of vacuum, d the initial distancebetween the capacitor plates, Ad the change in plate distanceinduced by acceleration, and Co the capacitance with Ad = 0.

In order to be able to convert the capacitance to voltage, thesensor structure needs to be biased. This biasing is usually donewith either a constant voltage or a constant charge.When a voltage VB is connected over a capacitor with

capacitance C, charge Q = C VB flows into it. The electrostaticforce between the capacitor plates can then be written asF = Q2/ (2Er oA). By substituting (1) into this, we get

AE,EOVB K 12

FCDP,es A2Vd-i(d )

FcDN,eS A V (d+lAd) (2)

To understand the negative effects of the electrostatic forces,let us imagine a situation where the three-axis accelerometeris in negative z-directional acceleration. Now, there are fourforces acting on the read mass: a force induced by the staticacceleration Fa, a spring force Fs and the electrostatic forces,shown in Fig. 2. The acceleration-induced force is the productof the mass M and acceleration a, Fa = M a, correspondinglythe spring force is the product of the spring constant K andAd, Fs = K Ad.

A d1mm2 5/im

-vB = °vBVB =v

4.... VB= 4V

Fig. 3. Solutions of Eq. (3) for three different values of VB.

From Fig. 3 it can be seen that if there is no biasing voltage(VB = 0), the electrostatic forces do not affect the read mass,therefore Ad is linearly proportional to a. When VB is increasedto 1 V, the electrostatic forces cause distortion and the masstouches either one of the metal electrodes if a is more thanabout ±16 mr/s2. This electrostatic effect is known as pull-in[4]. If VB is increased to 4 V not only distortion and pull-in aredetected, but also a strong change of the slope can be seen. Theexplanation for this effect is that the electrostatic forces reduceK by a factor of Kes, which is called the electrostatic springconstant. By using Taylor approximation for Eq. (2), Eq. (3)can be simplified to a first order polynomial. From it, Ad canbe solved to be

Fig. 2. Forces acting on the read mass when the three-axis accelerometer isin negative z-directional acceleration.

At equilibrium position the sum of the four forces has tobe zero. By simplifying this sum, we can write the fifth orderpolynomial

kAd5 -MaAdd4(kd4

- 2Kd2Ad3 + 2Mad2Ad2 +

2EOErAVBd)Ad -Mad4 = 0

for Ad. Solving this equation numerically for a typical mi-cromechanical accelerometer with parameters shown in TableI, for three different values of the biasing voltage VB, the curvespresented in Fig. 3 can be obtained.

MAd = 2eOeV a

K c~VB ad3

From this equation, it can be deduced that Kes is

Ke_ 20ErAVBes-3

(4)

(5)

It can be concluded that to retain the wide acceleration range,the electrostatic forces have to be taken into account in thedesign of the front-end. In the constant charge biasing methodthe electrostatic forces are equal. The implementation of thisbiasing method has challenges, for example how exactly sameamount of charge can be brought into the capacitors CDP andCDN and how these charges can be kept in the capacitorswithout any leakage. These challenges are hard enough fora single mass accelerometer and they become even harderfor the three-axis accelerometer. In the designed circuit, the

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electrostatic forces are balanced by changing the voltage of themiddle electrode.

B. Implemented StructureThe designed front-end shown in Fig. 5 is based on the

single-ended self-balancing bridge (SBB), originally presentedin [5]. This known structure was developed to be differentialand proper for the three-axis accelerometer. Chopper stabilisa-tion was used to reduce offset voltage.The differential difference amplifier (FDDA) [6] in the first

integrator was used to convert the single-ended signal from thesensor into differential form. All the signal paths of the front-end are differential, except the one connected to the middleelectrode of the sensor, improving power supply and substratenoise rejection. Differential signal paths are used, because lotsof digital signal processing circuitry is required to be integratedin the same chip with the three-axis accelerometer front-end.The three-axis accelerometer can be modelled with four

capacitor pairs of Eq. (1). From the clock phases shown inFig. 5, it can be concluded that the read mass is connected to thefront-end while the other masses are connected to the middleelectrode of the sensor DMID. At the beginning of the clockphase 02, the read mass is changed and the output voltage ofthe previous cycle is loaded into the capacitors C4p and C4N.This voltage was stored in the capacitors of the latter integratorC3p, and C3Nn, n being the index of read mass. Thus thevoltage of DMID is same as VOUTP. In the clock phase 31,the read mass is connected to the reference voltages and thenew value is read and stored. This same cycle is repeated afterthe other three masses are read in turn. The maximal samplingrate is 40 kHz and thus each mass is read using 10 kHz clockfrequency. The output voltage is held in 02 and can be sampledby an A/D-converter.

The voltage of DMID of the read mass changes until itachieves a value for which the charges in CDp(,) and CDN(n)are equal. To be able to solve this balance voltage, the transferfunction for the front-end has to be derived. The transferfunction can be shown to be

H(z)

It can be seen from (8) that the amplitude of the output voltageis twice as large as in the single-ended case. If the simplificationof Eq. (1) is used, the latter equation of (8) is achieved.This equation shows that the output voltage of the front-endis ratiometric, in other words the output voltage is linearlyproportional to Ad.From Eq. (8), it can be deduced that the balance voltage is

Ad. VREF/d. When a mass is being read, the voltages overthe capacitors CDp(,) and CDN(,) are VREF- VOUTP andVOUTP -(-VREF), respectively. By substituting these biasvoltages into Eq. (2), we have

FCDP FCDNCo VREF22 d (9)

According to Eq. (9), the forces are equal sizes and thus thefront-end reduces the negative effects of the electrostatic forces.The front-end causes offset voltage to the output voltage of

the read mass. In this front-end, the purpose of the chopperstabilisation is to reduce this offset voltage. In chopper stabil-isation, the masses are read first directly and then reversed, asshown in Fig. 4. Hence, the signal VSIG changes its sign, butthe offset voltage of the front-end VOS does not. By dividingthe difference of VOUT,CHOP and VOUT,CHOP by two, thefinal output voltage becomes

VOUTVSIG + VOS - (-VSIG + VOS)

2(10)

It can be seen that the offset voltage Vos is eliminated.

+VREF

CDP

CDN

-VREREF

VREF

VSI OUT,CHOP

CDPv+AGND E g

CDN

VREF

Vos

+ I = vAN

V ANV OUr CHOPVSIG

Fig. 4. Mass is read directly and reversed in chopper stabilisation.VOUT

VREF2 )(CDp(n) -CDN(n)) 1' (6)

a (I1- z-1) + (CDP(n) + CDN(n) ) Z-

where

a = C (2 * Cl + CDp(n) + CDN(n) + CPAD) (7)C2

for each n C {1 ... 4}. In Fig. 5, the upper and lower branchesare identical, and therefore only the first character of thesubindex of the capacitors in Eqs. (6) and (7) is used. CPADis the parasitic capacitance from the sensor middle electrode toground.

At DC, the transfer function simplifies to

H(C)= 2. DP(n) CDN(n)CDp(n) + CDN(n)

Ad2.

d

The capacitor matrices Cip, C1N, C2p and C2N are neededto readjust the -3 dB point of each channel to be one quarter ofthe sampling frequency, in which case the front-end is uncondi-tionally stable [3]. The binary weighted capacitor matrices CDPand CDN constitute an internal sensor model that is used in themeasurements. The capacitance values of the matrices can beadjusted from 0 to 3.875pF with steps of 0.125pF. The clocksignals of the internal sensor model, named 5xx INSEN, areactive only when the internal sensor model is used.

III. MEASUREMENT RESULTS

The front-end was realised with a 0.13,um CMOS process.The microphotograph of the chip is shown in Fig. 6. The siliconarea of the front-end is 0.325 mm2

Both functionality and performance measurements were per-formed for the implemented front-end. The used supply voltage

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0, & CHOP,02 & 2 MID / 02 OUT

Pl & ()Pl CTHOPP2& ()P2 CHOPp3& ()P3 CHO-P

(p4 &()P7HO-P()Pl-MID

2 MID

3 MID

P4 MID

CDP(n)

10CDN(n,

CHOPPERr

02 & 02 MID / 02 OUT() HO-PYl)ICHOP(Pl-CHOP

()P2 CTHOP()P3 CTHOP()P4 CTHOP()Pl CHOP

()2 CHOP

(P3-CHOP( P4 CHOP

Fig. 5. The circuit topc

Fig. 6. Chip microphotograph.

was 1.8 V. The maximum current consumption was measuredto be 39 ,uA. In the measurement set-up, the differential outputvoltage of the front-end was converted to a single-ended volt-age, amplified with an instrumentation amplifier and convertedto the digital form by using 12-bits A/D-converter (AnalogDevices AD8626).

VOUT

CINX T WI

2 (> P4 ~~~~~~CH,3N3Co02~~ ~~~~~->2 -< CH P

0,,P3 1HCHOPI,

QPHPC3N2-CHOP¢P CO P

P~~~~~~~~HP,SEN-OUT DC

q)2

)logy of the front-end.

A. Functionality Measurements

The goals for the functionality measurements were to confirmboth the general functionality of the front-end and the transferfunction of Eq. (8).The sensor was modelled by using eight 2 pF capacitors.

Because the accuracy of the capacitors is not very good,the capacitors differ from each other. The four masses causedifferent voltages to the output of the front-end and thereforethe read masses can be detected from the output voltage. Whenthese capacitors were read with 40 kHz sampling rate withand without chopper stabilisation, the output voltage of theinstrumentation amplifier was measured to be like in Fig. 7.It can be seen that the four masses are read first directly andthen reversed when chopper stabilisation is used, as discussedearlier.The internal sensor model was used to confirm the transfer

function of Eq. (8). Three different capacitance values for CDPand CDN, 1 pF, 2 pF and 3 pF were used. The referencevoltage VREF was 0.5 V. By growing the difference of thesecapacitor matrices by steps of 0.25 pF, taking several sampleswith sampling rate 10 kHz from the output voltage of the front-end with the A/D-converter, and calculating the average of thesesamples for every capacitance step, the curves for the outputvoltage of the front-end as a function of the capacitance changeof each matrix AC shown in Fig. 8 can be obtained. When thechopper stabilisation is used, the same kind of transfer functionmeasurements can be done, but the values of the output voltagehave to be converted by using Eq. (10). The curves for the

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0.5X NormalChopper

0.4-

0.3-

10.2-

< 0

;-,-O.1i \-

1 -0.2

-0.3

-0.4

."'. ~~

0.8 DP -DN-1 pF0DP 0DN 2p

0.6 - |O CDP=CDN=3 pF

0.4

- 0.2 -

-0.5-0.1 -0.05

-0.8

t [ms]0.05 0.1 0.15

Fig. 7. The measured operation of the front-end when four masses are readwith and without the chopper stabilisation.

0DP 0DN 1PFDP DN PDP DN P

CDP,CDNpF

2 pF3 pF

CDP,CDNpF

2 pF3 pF

-1II-1 -0.5 0 0.5 1AC [pF]

Fig. 9. Transfer function measurements with the chopper stabilisation.

TABLE II

TRANSFER FUNCTION MEASUREMENTS

No chopper stabilisation

Measured0.978430.488800.33379

Measured0.955050.481700.33004

Slope [V/pF]Calculated Rel. error

T 1 T0.021571/2 0.02240

_7 1/3 0.00137Chopper stabilisationSlope [V/pF]Calculated Rel. error

1 0.044951/2 0.03660

1/3 0.00988

Offsetvoltage [V]

-0.0142-0.0156-0.0142

Offsetvoltage [V]

0.00410.00230.0017

-0.5 0 0.5AC [pF]

Fig. 8. Transfer function measurements without the chopper stabilisation.

chopper stabilisation presented in Fig. 9 can be achieved.By using Matlab, a linear function can be fitted to the points

of the curves of Fig. 8. From this function both the slope andoffset voltage can be directly determined. In Table II the resultsof the measurements and calculations are collected.From Table II, it can be seen that there is a relative error

between the measured and calculated slopes. This may beexplained by the mismatch of the capacitors of the matricesCDP and CDN. If Figs. 8 and 9 are viewed near the origin,where the smallest and hence the most mismatch sensitivecapacitors of 0.125pF are changed, it can be seen that thecurves make bend which supports the mismatch theory of theslope error. It is noteworthy to see that the offset voltage isreduced when the chopper stabilisation is used.

B. Performance Measurements

The noise level was measured for both the internal and ex-

ternal 2 pF sensor model. The used sampling rate was 10 kHzand the noise was calculated for signal bands of 1 Hz -1 kHzand 1 Hz -5 kHz from the spectrum. The SNR was calculated

for a maximum signal voltage of 500 mV. The results of thenoise measurements are shown in Table III.

TABLE III

PERFORMANCE OF THE FRONT-END

Sensor model SNR [dB] 1 Hz -1 kHz SNR [dB] 1 Hz -5 kHzInternal 53.2 52.3External 46.9 46.5

The noise for the internal sensor model is over 5 dB betterthan for the external one. When the external sensor model isused, there is a lot of capacitance between the sensor middleelectrode and ground inflicted by the metal lines and solderlumps on a printed circuit board. Therefore the size of CPADis increased remarkably. The dominating noise sources of thefront-end are the amplifiers. If CPAD is increased, the totalnoise of the amplifiers is also increased.The transfer function of Eq. (6) is calculated for the reference

voltage VREF. Normally, DC reference sources are used but ifthe difference between the capacitors CDP and CDN is keptconstant and sinusoidal reference voltages are used, the outputvoltage is sinusoidal, as shown in Fig. 10. A typical outputspectrum for the sinusoidal reference voltages is presented in

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0.8

0.6

0.4

- 0.2

0> -0.2

-0.4

-0.6

-0.8

265

+ VREF,j

CDP

CDN

VREF

I\/ V REF

V OUT CCDP

VAGND A

C DN X

11- v

Vou0

Fig. 10. DC and sinusoidal reference voltage sources.

0

-20

40

- -60C.

_ -80

-100

-120

-140

-160(0

mI

ACKNOWLEDGMENT

The authors wish to thank Nokia Research Center, VTITechnologies and The Finnish Funding Agency for Technology

VAGND and Innovation (TEKES) for financial support. Design toolswere provided by Mentor Graphics.

REFERENCES

[1] T. Lehtonen and J. Thurau, "Monolithic accelerometer for 3D measure-ments", in "Advanced Microsystems for Automotive Applications 2004",J. Valldorf, W. Gessner (eds), pp. 11-22, Springer 2004.

[2] T. Mineta, S. Kobayashi, Y Watanabe, S. Kanauchi, I. Nakagawa, E. Sug-anurna and M. Esashi, "Three-axis capacitive accelerometer with uniformaxial sensitivities", Proc. Solid-State Sensors and Actuators Conferenceand Eurosensors, 1995, vol. 2, pp. 554-557.

[3] M. Kamarainen, M. Saukoski and K. Halonen, "A micropower differen-tial charge-balancing switched-capacitor front-end for capacitive microac-celerometers", Proc. Eur. Conf. on Circuit Theory and Design, 2005, vol.3, pp. 421-424.

[4] S. D. Senturia "Microsystem design", Kluwer Academic Publisher, 2001.[5] H. Leuthold and F. Rudolf, "An ASIC for high-resolution capacitive

microaccelerometers", Sens. Actuators A, vol. 21, pp. 278-281, February1990.

[6] H. Alzaher and M. Ismail, "A CMOS fully balanced differential differenceamplifier and its applications", IEEE Trans. Circ. Syst. II, vol. 48, pp.614-620, June 2001.

500 1000 1500 2000 2500 3000 3500 4000 4500 5000f [Hz]

Fig. 11. Typical output for 1 kHz sinusoidal reference voltages.

Fig. 11. Here, the differential signal amplitude at the front-end output should be 500 mV, but the effect of the -3 dBcorner frequency attenuates the 1 kHz signal. It can be seenthat the magnitude of second harmonic is about -50 dBc. Themeasurement results are collected in Table IV.

IV. CONCLUSION

A new differential switched-capacitor front-end for capaci-tive microaccelerometers was presented. The negative effects ofthe electrostatic forces were analysed. The implemented front-end is capable of reducing these effects. Chopper stabilisationwas used to decrease the offset voltage. The general function-ality and the transfer function of the front-end were verifiedby the measurements. The front-end achieves a maximummeasured SNR of 53.2 dB. The worst case current consumptionof the front-end was measured to be 39 ,uA from 1.8 V supply.

TABLE IVA SUMMARY OF THE MEASUREMENT RESULTS

Technology 0.13,m CMOSFront-end area 0.325mm2

Operating voltage 1.8 VCurrent consumption < 39,A

Bandwidth 1 kHzMax. SNR 53.2dBMax. THD 50 dB

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