IMTC 2003 Instrumentation and Measurement Technology Conference Vail, CO, USA, 20-22 May 2003 Mechanical Spectrum Analyzer in Silicon using Micromachined Accelerometers with Time-Varying Electrostatic Feedback L.A. Rocha, E. Cretu *, G. de Graaf and R.F. Wolffenbuttel Delft University of Technology, Faculty ITS, Dept. for Micro-electronics, Mekelweg 4, 2628 CD Delft, The Netherlands Phone +31 15 278 6518, Fax. +31 15 278 5755, E-mail: L.Rocha@its.tudelft.nl * also at Melexis, Belgium Abstract Capacitive accelerometers with electrostatic force feedback are widely employed, because of performance and robustness. The force feedback acts as a means for electronic modulation of the spring constant of the suspension. Commonly, the electrostatic feedback is employed for null-based acceleration measurement. A suitable electrostatic time-varying actuation could instead be used to make the accelerometer selectively sensitive to a coherent mechanical frequency component. By sweeping the frequency of the drive voltage over a selected range, the mechanical spectrum is analyzed in the mechanical domain. The resulting spectrum analyzer features many advantages compared to conventional techniques for condition monitoring of mechanical machines. An inverted pendulum type of accelerometer structure has been fabricated in silicon using micromachining techniques and operated using electrostatic momentum feedback. I. INTRODUCTION Many applications require processing of the spectral content of the input mechanical signal. For instance, vibration monitoring for early failure detection generally uses algorithms operating in the frequency domain, rather than the time domain [1]. From a sensing perspective, two main approaches are used: 1. Vibration analysis in the electrical domain, which is conventionally implemented in a straightforward way by having an accelerometer to measure a time series and a DSP (Digital Signal Processor) to perform a FFT (Fast Fourier Transform) [2]. However, the DSP die size and power dissipation makes such a solution difficult in a microinstrument. 2. An array of tuned resonators measures the mechanical vibration. Each resonator is tuned on a specific frequency, so several spectral lines are obtained in parallel [3]. The flexibility of the scheme is reduced compared with the first approach, but allows an improvement of the signal-to-noise ratio for the chosen resonant frequencies. In this paper an alternative approach is pursued, in which a micromachined accelerometer structure is operated using electrostatic feedback with an AC drive component introduced in the loop [4]. This is basically an extension of the electrostatic force feedback in servo-operated accelerometers with a DC voltage used for setting the loop gain [5]. The AC voltage enables the realization of a mechanical spectrum analyzer with frequency selectivity in the mechanical domain. A wideband accelerometer can be made selectively sensitive to a narrow mechanical frequency component that is coherent with the electrically driving forces. By sweeping the electrical frequency over a selected range, the mechanical frequency components are obtained sequentially with a resolution determined by the details of the feedback loop. II. DEVICE DESCRIPTION The accelerometer operation provides the mechanical frequency components sequentially, rather than a time series of the acceleration. Electrostatic force feedback is provided in such a way that only a spectral component coherent to the frequency of the AC component in the electrostatic driving voltage observes a positive feedback. By scanning the AC voltage in time through the desired part of the frequency spectrum, the vibration spectrum can be directly obtained. The principle is general, and could be applied to any type of accelerometer, provided that the structure allows for electrostatic driving. In the present work, a clamped inverted balance accelerometer structure is used. The conceptual device is the conventional single-sided clamped inverted pendulum in the gravitational field, as shown in Fig. 1. The weight of the seismic mass, m, is assumed to be concentrated at the top. The clamped beam has only elastic properties, and for the time being is considered massless. In the absence of any horizontal acceleration component, the vertical position is an equilibrium one. Any horizontal inertial force causes a displacement from the vertical position, φ, until the reaction developed at the clamping point equilibrates the external action. 0-7803-7705-2/03/$17.00 '2003 IEEE 1197
Fig. 1. Operating principle of the inverted pendulum in the gravitational field. The same principle remains valid if the vertical gravitational field is replaced with an electrostatic one. The added value is in the electronic control of this field, and thus the potential of dynamic tuning of the feedback effect. In the micro device under investigation, the DC gravitational field is replaced by an AC electrostatic field superimposed on a DC field. The frequency of the AC drive voltage determines the mechanical frequency for which this positive feedback actually takes place. The spectrum is measured by sweeping the frequency of an AC drive voltage through the part of the mechanical spectrum of interest and measuring the displacement in a servo configuration. The differential AC voltage is superimposed on a DC common mode level that ensures linear displacement and provides a means for controlling the loop gain in the positive feedback loop. The actual structure fabricated in silicon using micromachining techniques is planar, rather than vertical, and is shown in Fig. 2. The anchor point is shown in the upper-left corner and interdigitated finger electrodes are available for electrostatic actuation and capacitive detection of displacement. Stoppers are included on either side of the freestanding tip to limit the lateral displacement range. Prototypes have been realized in the Bosch epipoly process [6,7]. Basically an 11 µm thick polysilicon layer is patterned and released in a surface-micromachining-alike process. 1198 Fig. 2. Photograph showing a detailed view of the tip of the fabricated microstructure. The claimed advantages, as compared to the microsystem based on a conventional accelerometer plus data-acquisition components in combination with a FFT algorithm implemented in a DSP or micro-controller, are: (1) reduced system complexity and (2) reduced power dissipation and a given response time. III. DEVICE PERFORMANCE The DC component in the electrostatic field that provides force feedback is conventionally used for the electronic introduction of a negative compliance in capacitive servo accelerometers. The overall effect is a reduced stiffness of the physically available suspension. The stiffness of the suspension in the non-powered condition can be large, greatly adding to device reliability. The tuning of the spring constant also allows electronic tuning of the sensitivity or the resonant frequency of the structure. The simplified block diagram of the system with the generic transfer function is shown in Fig.
Fig. 3. Gain control by DC voltage modulation in the electrostatic feedback structure The DC is also used in the inverted pendulum for control of the loop gain. The structure shown in Fig. 2 has been operated in this mode and measurement results clearly indicate that an increase on DC correspond to an increase on sensitivity. These observations are in agreement with the reduced stiffness of the suspension with voltage. A more advanced use of the structural coupling between the mechanical and electrostatic fields results in the case of a time-varying actuation voltage. The qualitative idea is to create a frequency-selective feedback loop. An AC actuation voltage is used for instance to actually enable operation as mechanical spectrum analyzer. The basic system concept is shown schematically in Fig. 4, in the case of cuasistatic operating mode (actuation frequencies lower than the mechanical resonance frequency). This is basically an extension of the chopper combined with coherent detector that is often used in instrumentation and measurement. The chopper is basically composed of two accelerometers with AC drive voltage in quadrature. The main difference, as compared to the conventional coherent detector preceded by a chopper (AM-modulator), is that here the modulation parameter (actuation voltage) is present, not in the forward, but in feedback path. Moreover, this parameter is squared. As a consequence, DC-level and higher harmonics are present in the expression of the gain function. To eliminate them, a twin-accelerometer structure is used. The two identical accelerometers are actuated in quadrature; the squaring law will transform the initial phase shifts, and thus the differential output will eliminate all the even harmonics of the transfer function, including the DC component. The distortions, compared to a classic harmonic modulation, will be significantly lower than in the case of a single channel scheme. Fig. 4. Block diagram of the system used for AC electrostatic feedback for mechanical spectral analysis. 1199
The differential output will contain a signal ~ aext ( t ) cos ( 2ω1t ), where aext is the input acceleration, while ω1 is the frequency of the electrostatic driving force. An averaging filter will generate therefore the cosine spectral component of frequency 2ω1 present in the signal. A similar quadrature actuation, but with a phase difference of π / 4, will generate an output ~ aext ( t ) sin ( 2ω1t ). In such a case, the output of the averaging filter will correspond to the sine spectral component of frequency 2ω1 present in the input acceleration signal aext(t). A simulation result is presented in Fig. 5, where the input acceleration signal contains three spectral components and an additive noise. A tuning of the harmonic actuation voltage on the frequency ω1/2 extracted the real and imaginary part of spectral component A ( jω1 ) from the mechanical vibration spectrum. Fig. 5. Extraction of the spectral line A ( jω1 ) from the acceleration signal Fig. 6. Five spectral components acceleration: a) FFT, and b) electromechanical spectrum scan. IV. EXPERIMENTAL RESULTS For experimental validation, a vibration table has been used to generate an input acceleration waveform, containing three frequency components. The output of the accelerometer, in the absence of electrostatic actuation, was acquired with 50 khz sampling rate, for 2 sec, and the spectrum computed in matlab. The real-time spectrum extraction scheme was then applied, keeping the same integration time of 2 sec. The comparative results are presented in Fig. 6. On Another test case, the spectrum of a signal with two closely spaced components was retrieved. An input signal, consisting of two components, of 160Hz and 170Hz respectively and a 28dB difference in peaks, was applied to the input. An Acquisition and integration time, of 4 sec, was used. The comparative results are shown in Fig. 7, and again prove the soundness of the concept. 1200 V. CONCLUSIONS The method presented here basically involves electronically controlled spectral filtering in the mechanical domain. The critical part is compromise between achievable sensitivity and the distortion level, given by the judicious choice of the spring modulation factor β. The capacitive transducer in combination with low-power readout circuits has the potential for lower power consumption compared to a digital system running a Fast Fourier Transform (FFT) algorithm. The method presented here is very suitable for low-power, low-cost applications. This advantage becomes even more apparent in applications where, based on prior knowledge on failure mechanisms involved, one can decide to only monitor some known spectral components. This is often the case in condition monitoring systems.
REFERENCES [1] G.T.A. Kovacs, Micromachined Transducers Sourcebook, Boston, McGraw-Hill,1998. [2] R.A. Collacott, Vibration Monitoring and Diagnosis, London, Gowdin, 1979. [3] M.H-Bao, Micro Mechanical Transducers. Pressure sensors, accelerometers and gyroscopes, Elsevier, 2000. [4] E. Cretu, M. Bartek, R.F. Wolffenbuttel, Spectral analysis through electro-mechanical coupling, Sensors and Actuators, Vol. A85 (2000), No 1-3, pp. 23-32 [5] R.P. van Kampen, R.F. Wolffenbuttel, Modeling the mechanical behavior of bulk-micromachined silicon accelerometers, Sensors and Actuators A: Physical 64 (2), 1998, pp. 137-150. [6] http://www.vdivdeit.de/mst/imsto/ Europractice/ Bosch/default.html [7] M. Offenberg, F. Lärmer, B. Elsner, H. Münzel and W. Riethmüller, Novel process for an integrated accelerometer, Proc. Transducers95, 1995, vol.1, pp. 589-593. Fig. 7. Distinction between two closely separated frequencies (160Hz and 170Hz) with 28dB peak difference: a) FFT, and b) scanned spectrum. ACKNOWLEDGMENT This work is supported by the Netherlands Technology Foundation (STW) under grant DEL55.3733. 1201