Discussion

As shown in Fig. 19 and Fig. 20, the transmitted power does not increase along with the number of IDT electrodes; neither the voltage output of the IDT sensor increase along with the number of IDT electrodes. Besides, Fig. 21 also didn’t show the higher reflectivity with larger fingers of reflector. These simulation results somehow contradict with our intuition of IDT functionality. These simulation results will be investigated in future.

The deviation of our prediction and experimental data, as shown in Fig. 22 and Fig. 23, may come from the way we combined the COM theory and crossed-field model to model the whole system. For example, the input to crossed-field model should be both of particle force and velocity. However, in this simulation, we used Coriolis force as the force input while the velocity is obtained by assuming the maximum power transmission. This could be erroneous and should be investigated later on.

Furthermore, we have assumed that the metallic dot arrays have no effect on the transmitted power generated by the IDT resonator, but to generate Coriolis force the sensing IDT. The assumption is obviously impractical since the metallic dots have mass loading on the surface wave motion. Besides, the edges of metallic dots could cause diffraction and interfered with the wave propagation along Y-direction. All these effect will need further investigation.

Chapter 4

Conclusion and Future Work

4.1 Conclusion

In this work, the design of a gyroscope, consisted of surface acoustic wave (SAW) resonator and sensor, is presented. The SAW resonator is designed and optimized using COM theory, while the design of SAW sensor is based on the crossed-field model. The output of the COM theory is the square root of power of transmitted wave in SAW resonator, while the input to the SAW sensor needs to be the force for crossed-field modeling. We have successfully used the “electromechanical interaction” method to obtain a relation between surface potential and particle displacement, so as to obtain the particle velocity for the calculation of Coriolis force.

The simulation results shows that the optimal performance can be achieved by 11 electrodes of the IDT, 47 electrodes of the reflector in the SAW resonator at both ends; 89 electrodes of the IDT in the SAW sensor. This design is different from what shown in the report [9, 10]. The deviation could be due to the way we combined COM theory and crossed-field model, and the mass loading from metallic dots.

4.2 Future Works

The more complete simulations and experiments must be done in the future. Some future works are listed below.

1. Better understand the methods utilized for the SAW devices analysis.

2. Analyze the behavior of the metallic dot array in the cavity between IDTs in two ends.

3. Implement the SAW gyroscope when the analyses work is completed.

Other than that, the effects of metallic dot array contain mass loading, reflection, and electrical interaction. Further investigation will be needed to take all these effect into consideration. One possible approach to model the mass loading effect from metallic dots could be treating them as a reflector in a SAW device since they are located in a way similar

to parallel strips in view of the one-dimension propagation waves. If so, they can be simulated by various methods such as piezoelectric permittivity method, impulse response model, COM theory, and etc.

Reference

[1] N. Yazdi, F. Ayazi, K. Najafi, “Micromachined Inertial Sensors,” Proceedings of the IEEE, Vol.86, No.8, pp.1640-1659, Aug. 1998.

[2] S. Park, “Adaptive Control Strategies for MEMS Gyroscopes," University of California, Berkeley, Department of Mechanical Engineering, Ph.D. Thesis, 2000.

[3] D. S. Ballantine, Acoustic wave sensors: theory, design, and physico-chemical applications, Academic Press, Boston, 1996.

[4] D. S. Ballantine et al. “Acoustic wave sensors /theory, design, and physico-chemical application,” Academic Press, Boston, 1996.

[5] 吕志清, 胡爱民, “MEMS-IDT声表面波陀螺,” Micronanoelectronic Technology, Vol.40, No.4, 2003.

[6] FuQian Yang, “Electromechanical Interaction of Linear Piezoelectric Materials with a Surface Electrode,” Journal of Materials Science, Vol.39, No.8, pp.2811-2820, 2004.

[7] B. Y. Lao, “Gyroscopic effect in surface acoustic waves,” IEEE Transactions on Sonic and Ultrasonic, Vol.28, No.5, pp.687-691, 1980.

[8] M. Kurosawa, Y. Fukuda, M. Takasaki, T. Higuchi, “A surface-acoustic wave gyro sensor,” Sensors and Actuators A-Physical, Vol.66, No.1-3, pp.33-39, Apr. 1998.

[9] V. K. Varadan, W. D. Suh, P. B. Xavier, K. A. Jose, V. V. Varadan, “Design and development of a MEMS-IDT gyroscope,” Smart Materials & structures, Vol.9 No.6, pp.898–905, Dec. 2000.

[10] K. A. Jose, W. D. Suh, P. B. Xavier, V. K. Varadan, V. V. Varadan, “Surface acoustic wave MEMS gyroscope,” Wave Motion, Vol.36, No.4, pp.367-381, Oct.

2002.

[11] V. K. Varadan, K. A. Jose, P. Xavier, D. Suh, V. V. Varadan, “Conformal MEMS-IDT gyroscopes and their performance comparison with fiber optic gyroscope,” in: V.K. Varadan (Ed.), Proceedings of the SPIE Symposium on Smart Electronics and MEMS, Vol.3990, pp. 335–344, 2000.

[12] R. C. Woods, H. Kalami, B. Johnson, “Evaluation of a Novel Surface Acoustic Wave Gyroscope,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol.49, No.1, pp.136-141, Jan. 2002.

[13] C. K. Campbell, Surface Acoustic Wave Devices for Mobile and Wireless Communications, Academic Press, New York, 1998.

[14] J. R. Pierce, “Coupling-of-modes of propagation,” Journal of Applied Physics, Vol.25, No.2, pp.179-183, Feb. 1954.

[15] P. S. Coss, R. V. Schmidt, “Coupled surface acoustic wave resonator,” Bell System Technical, Journal, Vol.56 No.8, pp.1447-1481, Oct. 1977.

[16] H. Haus, P. V. Wright, “The Analysis of Grating Structures by Coupling-of-Modes Theory,” Proceedings of the IEEE Ultrasonics Symposium, Vol.1 pp. 277-281, Nov.

1980.

[17] D. Royer, E. Dieulesaint, Elastic waves in Solids Ⅱ: Generation, Acousto-optic Interaction, Applications, Springer-Verlag, Berlin, 2000.

[18] W. R. Smith, H. M. Gerard, J. H. Collins, T. W. Reeder, H. J. Shaw, “Analysis of Interdigital Surface Wave Transducers by Use of an Equivalent Circuit Model,”

IEEE Transactions on Microwave Theory and Techniques, Vol.17, No.11, pp.856-864, Nov. 1969.

[19] W. R. Smith, Jr., “Studies of Microwave Acoustic Transducers and Dispersive Delay Lines,” Stanford University, Department of Applied Physics, Ph.D. Thesis, pp.1-147, 1969.

[20] W. P. Mason, “Electromechanical Transducers and Wave Filters,” van Nostrand-Reinhold, 2nd Edition, Princeton, New Jersey, pp.201-209, pp.399-409, 1948.

[21] W. R. Smith, H.M. Gerard, J. H. Collins, T. W. Reeder, H. J. Shaw, “Design of surface wave delay lines with interdigital transducers,” IEEE Transactions on Microwave Theory and Techniques, Vol.17, No.11, pp.865-873, Nov. 1969.

[22] W. R. Smith, “Experimental Distinction Between Crossed-Field and In-Line Three-Port Circuit Models for Interdigital Transducers,” IEEE Transactions on Microwave Theory and Techniques, Vol.22, pp.960-964.

[23] W. R. Smith, H.M. Gerard, W. R. Jones, “Analysis and Design of Dispersive Interdigital Surface-Wave Transducers,” IEEE Transactions on Microwave Theory and Techniques, Vol.20, No.7, pp.458-471, 1972.

[24] V. Parton, B. Kudryavtsev, N. Senik, J. Tani, “Rayleigh Waves Excitation Using a Pair of Oppositely Charged Electrodes,” International Journal of Applied Electromagnetics in Materials, Vol.5, No.4, pp.291-310, 1994.

[25] 周卓明，壓電力學，全華，台北，2003。

[26] S.V. Biryukov, G. Martin, V. G. Polevoi, M. Weihnacht, “Derivation of COM Equations Using the Surface Impedance Method,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol.42, No.4, pp.602 – 611, 1995.

[27] K. Nakamura, “A Simple Equivalent Circuit for Interdigital Transducers Based on the Coupled-Mode Approach,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol.40, No.6, pp.763 -767, 1993.

[28] Dong-Pei Chen, A. H. Herman, “Analysis of Metal-Strip SAW Gratings and Transducers,” IEEE Transactions on Sonic and Ultrasonic, Vol.SU-32, No.3, pp.395-408, 1985.

[29] W. Soluch, “Admittance Matrix of a Surface Acoustic Wave Interdigital Transducer,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol.40, No.6, pp.828-831, 1993.

[30] D. Royer, E. Dieulesaint, Elastic Waves in Solids Ⅰ: Free and Guided Propagation, Springer-Verlag, Berlin, 2000.

[31] Y. C. Fung, Foundations of Solid Mechanics, Prentice-Hall, 1965.

[32] J. W. Gardner, V. K. Varadan, O. O. Awadelkarim, Mircosensors MEMS and Smart Devices, John Wiley & Sons, 2001.

[33] W. Matthijs den Otter, “Approximate Expressions for the Capacitance and Electrostatic Potential of Interdigital Electrodes,” Sensors and Actuators A, Vol.96, No.2-3, pp.140-144, 2002.

LIST OF FIGURES

a = Ω× 2 v

Ω

Fig. 1 The Coriolis effect [1].

Fig.2a Displacement of particles on the surface of half space due to the Rayleigh wave [31].

Fig. 2b Interdigital transducer, formed by patterning electrodes on the surface of a piezoelectric crystal, for exciting surface acoustic wave: (a) SAW electrical potential, (b) plan view, (c) side view [4].

Fig. 3 Configuration of the IDTs, the reflectors and the perturbation electrodes.

Fig. 4 (a) Basic elements of gyroscope: IDT, acoustic spacing and reflector. (b) Schematic representation of a SAW devices using transmission matrix [9].

Sensor IDT Generator IDT

Perturbation Masses Reflector

Fig. 5 The SAW reference planes at the ith element of a SAW reflection grating of length L [13].

Fig. 6 Schematic representation of electrical and acoustic ports [13].

Λ4 reflection grating of length

L

Fig. 7 Schematic matrix representation of a two-port SAW resonator [9].

Fig. 8 An instantaneous E-field direction in the crossed-field model [32].

L =Half-wavelength

− + −

E

E

Fig. 9 (a) Representation of the SAW IDT as a three network, Port 1 and 2 are

normally assigned to the “ acoustic” ports, while Port 3 is the electrical port. (b) In the crossed-field model, acoustic signals at Port 1 and 2 are converted to equivalent electrical transmission-line parameters [13].

( )

Fig. 10 Crossed-field model of equivalent circuit representation [13].

3

1 1

Fig. 11 (a) The ABCD matrix representation of a transmission-line section of length d, with characteristic impedance Z and propagation constant k. (b) The matrix ₀ evaluation of cascaded two-port networks [13].

Fig. 12 Transducer composed N number of fingers, acoustically in cascade and ^t electrically in parallel [18].

V

1

V

2

V

3

I

1

I

₂

I

3

Fig. 13 Block diagram of receiving transducer configurations. Transducer with acoustic generator at port 1.

1 2

Nt

x3

x1

0

V e⁻i t^ω

− V e₀ ^{−i tω}

−a

−b a b

s

0

V e⁻i t^ω 0

V e⁻i t^ω

−

Fig. 14 Layout of the system for the excitation of surface Rayleigh waves in a piezoelectric medium.

Z

Y

X

Fig. 15 Coriolis forces acting on particles [8].

Fig. 16 Working principle of the MEMS SAW gyroscope [10].

Fig. 17 Design of SAW gyroscope.

IDT

Reflector

Metallic dots Resonator

Sensor

Fig. 18 The design of interdigital transducer.

Fig. 19 Result of the numbers of RIDT electrodes vs. transmitted power.

Reference plane Λ 2

Λ

W

Fig. 20 SIDT output voltage vs. number of electrodes of SIDT.

Fig. 21 The transmitted power with different fingers of reflector of SAW resonator on two ends.

Fig. 22 The sensing resolution of the proposed SAW gyroscopes with 90 fingers of sensor IDT and calculated data by Varadan et al. [10]

Fig. 23 The sensing resolution of the proposed SAW gyroscopes with 89 fingers of sensor IDT and calculated data by Varadan et al. [10]

Appendix

Material constants for LiNbO

₃

z Density: 4700 kg 3 5.78 5.02 17.0 -1.01 -1.47 -1.02

z Stiffence z Piezoelectric Strain

15 22

Piezoelectric Strain Constants

(

¹⁰⁻¹² coulomb newton

)

d_iJ =d_Ji d15 d₂₂ d₃₁ d₃₃

68 21 -1 6

z Piezoelectric Stress

Piezoelectric Stress Constants

(

^{coulomb m2}

)

eiJ =eJi

e15 e₂₂ e₃₁ e₃₃ 3.7 2.5 0.2 1.3

z Relative Permittivity

11

Relative Permittivity Constants for Piezoelectric Materials

11 0

在文檔中 表面聲波陀螺儀的設計 (頁 33-0)