196 • 2012 IEEE International Solid-State Circuits Conference

ISSCC 2012 / SESSION 11 / SENSORS & MEMS / 11.1

11.1 A ΔΣ Interface for MEMS Accelerometers Using Electrostatic Spring-Constant Modulation for Cancellation of Bondwire Capacitance Drift

Pedram Lajevardi1, Vladimir Petkov2, Boris Murmann1

1Stanford University, Stanford, CA2Robert Bosch, Palo Alto, CA

Precision accelerometers are used in a variety of automotive applications, navi-gation systems, and low-level vibration-monitoring systems. Currently, thesesensors are factory-calibrated to null their input offset. However, the residualoffset drifts mainly due to thermal and mechanical stress and humidity. As aresult, the offset accuracy of high-end MEMS accelerometers is specified on theorder of ±100mg [1]. With continuously increasing precision requirements, it isdesirable to develop new techniques that address post-calibration drift. In thispaper, we describe an accelerometer interface that continuously measures andcancels offset drift due to change in parasitic capacitance of the bondwires in asystem-in-package-type MEMS accelerometer [2]. The proposed techniquereduces the bondwire offset of the measured prototypes by 41dB down to6.24mg.

The accelerometer used in this work employs a capacitive MEMS sensor ele-ment and a CMOS chip connected with bondwires (Fig. 11.1.1). Input accelera-tion (ain) causes displacement of a proof-mass (m), which is read out by meas-uring the difference between the sense capacitors, CSP-CSM. The electronic inter-face is based on a force-feedback ΔΣ loop that incorporates the sensor elementas part of the loop filter [3,4]. The sensor is rebalanced near its neutral positionthrough a highly oversampled 1b electrostatic feedback signal (Sout), whichaccurately represents the desired output after decimation filtering. The sensor istime-multiplexed over three phases. The first two are used for signal sensing(C/V conversion) and force-feedback. The third phase is not used in convention-al interfaces and is added to enable offset measurements using the shadedblocks in Fig. 11.1.1, described below. The time multiplexing occurs at a speedthat is far beyond the MEMS bandwidth, i.e. the sensor element low-pass filtersand superimposes the stimuli applied during different phases.

The main sources of offset in this accelerometer stem from mismatches in thereadout electronics, the MEMS element, and the parasitic capacitance betweenthe bondwires, Coff=CBP-CBM. In practice, the electronic offset is mitigated usingcorrelated double-sampling. The MEMS offset is calibrated during productiontest, and is known to drift mainly due to mechanical stress. However, there arevarious stress-mitigating techniques to diminish this drift. On the other hand,the bondwire parasitics can drift appreciably due to deformations from thermaland mechanical stress and absorption of moisture by the package, whichchanges the permittivity of the dielectric between the bondwires. For instance, adisplacement of the wires by only 1μm causes an input offset of 14mg in thisaccelerometer.

At first glance (considering Fig. 11.1.1) it seems impossible to isolate the bond-wire parasitics from the sense capacitances during normal operation of thedevice (with unknown ain present). However, using parametric modulation it ispossible to up-convert the bondwire offset to an out-of-band frequency where itcan be measured and nulled. As shown in Fig. 11.1.2, we model the systemusing three main blocks: H1 (sensor element), H2 (electronic loop-filter) and FB(force feedback). Due to the large loop gain (at low frequencies of interest), thetransfer function from Fin to Sout is ~1/FB. However, the transfer function fromCoff to Sout is ~1/(FB⋅H1), i.e. dependent on the sensor element parameters andspecifically the spring-constant k. In our system, we electrostatically superim-pose a time-varying spring-constant component kmod that induces a spectralreplica of Coff at the modulation frequency. This modulation is based on the so-called “spring-softening effect” and requires applying a force that is proportion-al to the displacement of the proof-mass. Detailed analysis shows that applyinga common-mode voltage to the differential sensor electrodes accomplishes this.In this prototype, we apply a 244Hz square wave (generated by the MOD blockof Fig. 11.1.1) with amplitude VMOD during Φ3. The loop output is then contin-uously background-correlated against this modulation in the LMS block, whichinjects a corrective offset (via the offset DAC (ODAC) into the loop filter) to sup-press Coff.

Figure 11.1.3 shows details of the C/V circuit and loop-filter realization and sys-tem timing. The loop filter contains an integrator to ensure that the in-band noiseis not limited by quantization noise [5]. The compensator ensures loop stability.All of the OTAs use a folded-cascode architecture. The system’s 4μs (250kHz)clock cycle is partitioned into six phases. During reset1, the sensor voltage isreset and the noise and offset of the OTAs are sampled on the CH capacitors.During the readout phase, the proof-mass displacement is measured, and thesignal propagates through the electronic loop-filter. At the end of this phase, thesignals have settled and the quantizer makes a decision. During the force-feed-back phase, a differential voltage is applied to the sensor capacitors to push theproof-mass back towards the center of the gap. During reset2, the sensor ele-ment is reset again to ensure that no residual signal-dependent force carries intothe next phase. During the k-mod phase, VMOD is applied as described above.

A custom interface IC was designed to evaluate the efficacy of the proposedtechnique in a system-in-package setting that closely resembles the practicalapplication. This interface is fabricated in a 0.18μm 3V CMOS technology, and ispackaged and tested with a MEMS sensor element. The CMOS chip contains allof the above-described precision circuitry, while the shaded blocks of Fig. 11.1.1are emulated off-chip. Figure 11.1.4 shows the measured output spectrum of atypical device at rest. The tones from the spring-constant modulation are visiblein the out-of-band frequency range from 240Hz to 10kHz. The observed ampli-tudes correspond to 700mg of offset, while the full-scale (FS) range is 9.14g. Asshown, the tones are suppressed by 41dB once the offset-cancellation loop isenabled and the ODAC code has converged. This corresponds to a residual off-set of 6.24mg. The sensitivity to DC input acceleration is 0.1094 FS/g both whenthe loop is on and off, indicating that the loop does not affect the input signal.Figure 11.1.5 shows a similar result in presence of an input acceleration of 1gat 100Hz, which is generated on a shaker table. In order to minimize the effectof out-of-band input accelerations (e.g. harmonics of the shaker signal) on theLMS loop, a spread-spectrum modulation signal can be used instead of thesquare wave tone used in this measurement. In the experiment shown in Fig.11.1.6, we purposely deflected the bondwires to introduce a very large offset.Without the offset cancellation loop, the DC output changes by 38.4×10-3 FS,indicating an offset of 351mg. With the loop turned on, the DC output changesby 76.6×10-6 FS, which corresponds to 0.7mg residual offset.

The overall performance of this interface compares well with state-of-the-artaccelerometers, such as [6]. The active circuit area is 1.35mm2, which is 32%less than [6]. The CMOS readout dissipates 3.1mW (64% less than [6]). Themeasured noise-floor is 220μg/√Hz and is dominated by the MEMS’ Browniannoise ([6] achieves lower Brownian noise due to lower resonant frequency andhigher Q in the MEMS structure at the expense of less robustness to shock). Thebandwidth of the interface is 1kHz. However, since part of the spectrum is usedfor modulation, we specify the usable bandwidth as 200Hz (the bandwidth in [6]is 400Hz). The full-scale range of 9.14g is 6.5× larger than that of [6].

Acknowledgements:The authors thank the Robert Bosch RTC for project funding. We also thankChristoph Lang and Kofi Makinwa for helpful discussions.

References:[1] “SCA830-D05 Single Axis Accelerometer with Digital SPI Interface,” VTITechnologies, Finland, 2006.[2] J. Marek, “MEMS for Automotive and Consumer Electronics,” ISSCC Dig.Tech. Papers, pp. 9-17, 2010.[3] T. Smith, O. Nys, M. Chevroulet, Y. DeCoulon, and M. Degrauwe, “A 15 bElectromechanical Sigma-Delta Converter for Acceleration Measurements,”ISSCC Dig. Tech. Papers, pp. 160-161, 1994.[4] M. Lemkin and B.E. Boser, “A Three-Axis Micromachined Accelerometer witha CMOS Position-Sense Interface and Digital Offset-Trim Electronics,” IEEE J.Solid-State Circuits, vol. 34, pp. 456-468, Apr. 1999.[5] V. P. Petkov and B.E. Boser, “A Fourth-Order ΣΔ Interface for MicromachinedInertial Sensors,” IEEE J. of Solid-State Circuits, vol. 40, pp. 1602- 1609, Aug.2005.[6] M. Yucetas, J. Salomaa, A. Kalanti, L. Aaltonen, and K. Halonen, “A Closed-Loop SC Interface for a ±1.4g Accelerometer with 0.33% Nonlinearity and2μg/vHz Input Noise Density,” ISSCC Dig. Tech. Papers, pp. 320-321, 2010.

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Figure 11.1.1: System block diagram. Figure 11.1.2: System model.

Figure 11.1.3: C/V converter, electronic loop filter and overall system timing.

Figure 11.1.5: Measured output spectrum and loop convergence with a 1g signal at 100Hz.

Figure 11.1.6: Measured output for different offsets with and without cancellation loop.

Figure 11.1.4: Measured output spectrum and loop convergence.

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Figure 11.1.7: Die micrograph.