Characterization of MEMS Vibration Sensor using Heterodyne based Phase Sensitive Detection

Transcription

1 Characterization of MEMS Vibration Sensor using Heterodyne based Phase Sensitive Detection Mukul Pancholi Dept. of Electrical Engg. IIT Bombay Mumbai, India Teza Bhamidi Dept. of Electrical Engg. IIT Bombay Mumbai, India Abstract Vibration monitoring is critical in many applications involving machinery, to keep track of machine health and abnormal use. Accurate and precise measurement of vibration is hence crucial. In this project we have tried to characterize an indigenous low cost vibration sensor exhibiting drift. Various circuits were explored and a Phase Sensitive Detection based circuit using heterodyning was designed and implemented and shown to be significantly more precise than traditional circuits. Using this highly precise circuit, sensor was characterized and shown to measure sinusoidal vibrations fairly accurately but exhibits significant drift and hysteresis. Index Terms Instrumentation Amplifier, Vibration Sensor, Phase Sensitive Detection. I. INTRODUCTION One can observe that any machine usually goes bad when they start vibrating out of the ordinary. Same is the scenario with many other household or industrial machines, and hence vibration monitoring has become a key aspect of performance measurement of machines in the long run. The objective of this project report is to study a novel, low price vibration sensor and characterize the sensor along with designing the circuit required to use it for the application described above. The vibration sensor used was made by the MEMS department at IIT Bombay. On visual examination we can see that a conductive material a foam coated with carbon particle) is sandwiched between the contact points, which upon deformation varies the resistance offered by the sensor and hence the cost effectiveness of the sensor comes into play. This sensor is highly susceptible to even very small intensity vibrations coming form 50Hz feedback of the circuit and can also be used in applications where vibration change leading to even µv of change in the sensing voltage. The undeformed resistance of the sensor was measured to be in the range of )Ω. This paper is divided into six sections: Section I gives brief introduction about the sensor under test and the circuit used during experimentation, Section II describes the in-depth analysis of the explored circuits during the characterization of the sensor, Section III discusses the circuit that has been selected for further analysis on the the basis circuit performances, Section IV is based on the frequency domain analysis of the circuit and Section V-VI talks about the results and conclusion followed by the acknowledgement and individual contributions respectively. II. CIRCUITS EXPLORED Since the staticundeformed) resistance of the vibration sensor of interest was of the order of a kilo ohms, we chose a comparable of about 1kΩ. The exact value upon measurement using a digital LCR meter was found to be: = Ω. This was be our reference resistor throughout the project. We have explored some simple circuits to measure a fixed resistor against the reference of an accurately known resistor ). The fixed resistor emulating R sens in static scenario was measuring using the LCR meter to be: R sens =.1504kΩ. This was taken as the true value for comparison with mean and standard deviation of measurement processes. A. Circuit 1: Inverting Amplifier A simple inverting amplifier based circuit was tried out, as shown in Fig.1. Here, R sens is the sensor, and is a V in t) R sens Fig. 1: Inverting Amplifier based vibration sensing V out t) reference resistor which is known to a high degree of accuracy. Then, R sens may be measured using this setup, as: R sens = V in = 1) meas G meas V out where G meas is measured gain of the amplifier, obtained by dividing the measured output voltage by the measured input voltage to the circuit. The circuit was evaluated for two cases:

2 S.No. Circuit Excitation Mean Std. Dev. 1 Inverting Amplifier DC.101kΩ 9.9Ω Inverting Amplifier AC.114kΩ 48.36Ω 3 Wheatstone Bridge DC.060kΩ 48.36Ω 4 PSD Heterodyne) AC.10kΩ 3.9Ω TABLE I: Measurement Statistics of various circuits in different excitation modes, measuring the same test resistor 1) DC excitation: DC voltage of varying amplitude is applied at V in t). Measurement Statistics are listed in Table I. ) AC excitation: AC voltage of varying amplitude is applied at V in t). Measurement Statistics are listed in Table I. B. Wheatstone Bridge We also tried out a Wheastone Bridge based network, as shown in the Fig.. R sens t) LPF Fig. 3: Phase sensitive detection based circuit for vibration sensing where G mix is mixer gain. Also, output of the filter maybe V fil t) = A.G mix.g fil senst) 4) R sens R 1k where G fil is the filter gain. Hence from the filtered output, one can measure R sens t), as: ) Vfil t) R sens t) = A 1.G mix.g fil 5) V dc R.k V R pot Fig. : Wheatstone Bridge based vibration sensing Sensing voltage of the wheatstone bridge was amplified using an instrumentation amplifierinamp) of gain A 39.5, which was measured using a Digital Multimeter. R pot was used to balance the right side of the bridge. DC excitation voltage was varied and resistance calculated as: ) A a R sens = R.k ) A a where a = V out /V dc is the sensed gain at the output of the INAMP. 1) Phase Sensitive Detection: Phase sensitive measurement is reported to have very good accuracy as compared to the other methods. A third circuit based on the principle of Phase Sensitive Detection was conceived, as given by Fig.3: Assuming that a sinusoidal excitation is applied across the positive terminal of the opamp with an angular frequency ω c and amplitude A, the mixer output can be V mix t) = A.G mix senst) [1 cos ω c t] 3) Sinusoidal input of frequency KHz was applied to the circuit. Parts that were used to build the above circuit were:tl071 OPAMPs and MPY634 multiplier from Texas Instruments. A 4th order butterworth realization of the lowpass filter was used, implemented using the TL071 OPAMPs and discrete components. However, due to unpredictable performance of the multiplier MPY634, in the homodyne configuration both inputs to multiplier have same frequencies), we could not proceed further using this circuit. Further modifications were needed to be made, and final circuit designed and used for measurement is described in the following section. III. FINAL CIRCUIT USED The final circuit used Fig.4) was in essence a modification to the phase sensitive detection citcuit of the previous section. Here we have used a heterodyning instead of homodyning in the previous circuit. Now circuit takes two sinusoidal inputs: V 1 t) = Asinπf 1 t) and V t) = Bsinπf t) at two different frequencies f 1 and f. Hence, now, the mixer output can be V mix t) = AB.G mix senst) [cos πf 1 f )t cos πf 1 f )t] 6) where G mix is mixer gain. Also, output of the filter maybe

3 R sens t) 3 LPF V 1 t) = Asinπf 1 t) 1 4 V t) = Bsinπf t) Fig. 4: Final Circuit Used: Block Diagram V fil t) = AB.G mix.g fil senst) cos πf 1 f )t 7) where G fil is the filter gain. Hence for a constant stress on sensor, from the peak to peak value of filtered output, one can measure R sens t), as: ) V fil,pp R sens = 1 AB.G mix.g fil Output of the LPF is fed to a Digital Storage osccilloscope which acquires data samples over a duration of time, and sends data over LAN to a computer operating LabView. LabView records several such frames of data of V fil,pp ), from which R sens is calculated. A. Low Pass filter For better out of band rejection, a 4 th order -stage Butterworth low pass filter has been designed. This filter is intended to reject the f 1 f sinusoidal component as given in eq.6). However, the selection of frequencies f 1 and f ) is based on the feasibility of the available of components available to design filter. Also, sensor can respond to the bandwidth of 1kHz, the designed filter has a 3-dB cutoff at f 1 f 1kHz overdesigned). Based on the above constraints we have chosen the frequencies f 1 = 6kHz and f = 4kHz. LPF was designed and its measured response is shown in Fig.5. IV. CIRCUIT OPERATION IN FREQUENCY DOMAIN As explained in previous section that the circuit in Fig.4) is an amplitude modulator followed by heterodyne reception, this in principle can be explained as: The input signal V 1 t) is a 6kHz, V p p signal whose frequency domain spectra is shown in fig.6a) However we can see that the resistance R sense t) is also being stressed using a single-tone sinusoidal vibration signal at a frequency of 00Hz which lead to spectra shown in fig.6b) At node- we will observe an amplitude modulated signal as in fig.6c), with the vibrations to the sensor being the modulating signal. 8) Fig. 5: LPF response Mixer will further modulate the signal obtained at node- with the signal V t) which is a 9V pp oscillating with the frequency of 4kHz giving fig.6d) output at node-3 Finally low pass filter designed for a 3-dB cut off of 3kHz, will filter out the other components and based on the intensity of vibrations applied we will get positive frequency spectrum as shown in fig.6e) at node-4. During experiment sensor is subjected to vibrations of various intensity, this will lead to different side lobes magnitudes. V. EXPERIMENTS PERFORMED, RESULTS AND CONCLUSIONS We have performed some experiments to characterize performance of the designed circuit and the vibration sensor. Firstly, to characterize the circuit, we have measured the.k resistor using circuits described in Section II. The mean and standard deviation of these measurements are also summarized in Table I, and visually represented in Fig.8. It can be clearly seen that the PSD heterodyne) method offers the best precision least standard deviation), and at the same time not sacrificing too much accuracy deviation of measurement mean from true value) and hence has been selected for further measurements. A scatter plot of measurements done for this standard.k resistor using circuit in Section III is shown in Fig.7, this plot shows the confidence in repeatably of the circuit under following variations:

4 a) Frequency Spectra of V 1t) b) Frequency Spectra of applied vibrations Fig. 7: Scatter plot of measurements of.k resistor using designed circuit c) Modulated signal spectra at node- d) Modulated signal spectra at node-3 e) Output demodulated signal spectra Fig. 6: Frequency Response of the circuit All the data points are taken over various time instants, Some of these data points also taken over temperature variations Supply variation from ±15V to ±11V are also included Secondly, we have measured the resistance of the sensor when i) not subject to vibrations static), these measurements also take into account all which has been done for standard.k resistor and ii) subject to single tone 00 Hz) vibrations of varying amplitude dynamic). As before, scatter plots of these measurements are produced in Fig.9 and Fig.10. In Fig.9, measurements were put against DMM measurements, and high compliance is observed. Hysteresis was observed in the sensor in dynamic case and same is evident in Fig.9. In conclusion, the PSD heterodyne) method offers the most precise solution to measure a resistance when compared with Wheatstone bridge and Inverting amplifier based methods. The design of the circuit eliminated most sources of error and noise, and can be used successfully to characterize a resistance based sensor such as the one used in this project. Also, fig.9) encapsulates the drift over time and environment changes observed in the sensor data no dominance of circuit drift can be seen from fig.7)). The sensor also shows the hysteresis behaviour when subjected to different intensities of vibration fig10)). VI. INDIVIDUAL CONTRIBUTIONS AND ACKNOWLEDGEMENTS Following are the individual contributions of Mukul Pancholi: Circuit implementation on Breadboard Data analysis LabView data acquisition Report and presentation Following are the individual contributions of Teza Bhamidi: Circuit design Test methodology Data analysis Report and presentation The authors would like to sincerely thank Mr. Maheshwar Mangat of WEL lab, IIT Bombay for creating the LabView data acquisition apparatus. The sensor was provided to us by Mr. Amit Tiwari, PhD of MEMS dept., and Mrs. Madhumita Date, WEL lab incharge for her support. Finally, the authors would like to thank Prof. Siddharth Tallur for his patience and guidance. REFERENCES [1] EE617:Sensors in Intrumentation class notes [] Simon Haykin Communication Systems 5th ed.). Wiley Publishing. [3]

5 Fig. 8: Comparison of various circuits in terms of their precision and accuracies Fig. 9: Scatter plot of measurements of sensor using designed circuit, static case Fig. 10: Scatter plot of measurements of sensor using designed circuit, dynamic case