WIRELESS DRIVE OF PIEZOELECTRIC COMPONENTS SATYANARAYAN BHUYAN 2011

Transcription

1 WIRELESS DRIVE OF PIEZOELECTRIC COMPONENTS SATYANARAYAN BHUYAN 011 WIRELESS DRIVE OF PIEZOELECTRIC COMPONENTS SATYANARAYAN BHUYAN SCHOOL OF ELECTRICAL & ELECTRONIC ENGINEERING 011

2 SATYANARAYAN BHUYAN WIRELESS DRIVE OF PIEZOELECTRIC COMPONENTS SATYANARAYAN BHUYAN School of Electrical & Electronic Engineering A thesis subitted to the Nanyang Technological University in partial fulfilent of the requireent for the degree of Doctor of Philosophy 011

3 ACKNOWLEDGEMENTS ACKNOWLEDGMENTS It is a great pleasure to express y deep appreciation to y supervisor, Prof. Hu Junhui, who has given e the exciting research opportunity to perfor this Ph.D work. I a deeply indebted to hi for introducing e to the interesting field piezoelectric and ultrasonic devices. Thanks to his insightful guidance, advice, discussions and experience. I a also grateful to Prof. Chang Qing Sun, for his kind help and support. I would like to thank the technical staffs of Sensor and Actuator lab, for their kindly assistance. I would like to thank all the ebers in our research group for their help, knowledge sharing and valuable discussions. I would like to thank Nanyang Technological University, especially School of Electronic and Electrical Engineering, for giving e a chance to pursue Ph.D prograe. I would like to express y boundless gratitude to y faily ebers and all of y friends for their support and encourageents. Special thanks to y Sili, Sibul, Babool and Seshadev. Last but not least, I would like to express y heartiest gratitude to y elder brother Nigaananda Bhuyan for his oral support, love and patience all the way along. i

4 Table of Contents Table of Contents Acknowledgents Table of contents Suary List of Figures List of Tables i ii vii xi xxii CHAPTER 1 INTRODUCTION Motivation 1 1. Research Objectives 1.3 Major Contributions Organization of the Thesis 1 CHAPTER BACKGROUND AND BASIC THEORY 14.1 The Fundaental Mechanis of Piezoelectricity Historical overview The piezoelectric effect Piezoelectric aterials Dynaic behavior of piezoelectric coponents Piezoelectric constitutive relations 0. Piezoelectric Devices and Applications..1 Piezoelectric transducers.. Piezoelectric actuators 4..3 Piezoelectric transforers 4..4 Piezoelectric sensors 6 ii

5 Table of Contents.3 Needs of Wireless drive of Piezoelectric Coponents 6 CHAPTER 3 EQUIVALENT CIRCUIT MODEL OF A WIRELESSLY DRIVEN PIEZOELECTRIC COMPONENT Physical Properties of Piezoelectric Coponents 8 3. Concept of the Thickness Vibration Mode Theoretical Analyses Configuration and operating echanis Derived equivalent circuit odel Ipedance Analyses Measured ipedance characteristics Equivalent circuit paraeters Suary 44 CHAPTER 4 WIRELESS ENERGY TRANSMISSION TO PIEZOELECTRIC COMPONENTS BY PARALLEL PLATE CAPACITOR STRUCTURE Experiental Setup and operating echanis Experiental Conditions Results and Discussion Frequency characteristics of the output power Dependence of the output power on electrical load Effect of vibration odes on the output power Effect of electric field on the output power Effect of electrode pattern on the output power Suary 60 iii

6 Table of Contents CHAPTER 5 WIRELESS DRIVE OF PIEZOELECTRIC COMPONENTS BY FOCUSED ELECTRIC FIELD Wireless Drive of Piezoelectric Coponents by Focused Electric Field Generator Experiental setup and operating echanis Frequency characteristics of the output power Effect of live electrode area on the output power Effect of ground electrode area on the output power Effect of the distance on the output power Effect of electrical load on the output power Analyses of electric field pattern by FEM Effect of the size of piezoelectric plate Energy conversion efficiency characteristics Suary Theoretical Analyses of Nano-vibration Characteristics Of a Piezoelectric Coponent Wirelessly Driven by Focused Electric Field Structure and principle Analyses of electric field by FEM Analyses of vibration displaceent characteristics Results and discussion Suary Wireless Drive of Piezoelectric Coponents by Capacitor- like Structure in Electric Resonance with an Inductor Experiental setup and operating echanis 96 iv

7 Table of Contents 5.3. Frequency characteristics of the output power Electrical load characteristics of the output power Effect of vibration odes on the output power Dependence of the distance on the output power Energy conversion efficiency characteristics Suary 107 CHAPTER 6 CHARACTERISTICS OF PIEZOELECTRIC COMPONENTS WIRELESSLY DRIVEN BY ANTENNA-LIKE ELECTRIC FIELD GENERATORS Characteristics of Piezoelectric Coponents by Dipole Antenna-like Structure Structure and principle Theoretical analyses of electric field by FEM Equivalent circuit odel Results and discussion Enhanceent in driving power of PZT plate Suary Wireless Energy Transission to Piezoelectric Coponents by Flat Spiral Coil Antenna-like Structure in Electric Resonance with a capacitor Structure and principle Experiental results and discussion Suary Coparative Study 141 v

8 Table of Contents CHAPTER 7 MERGING OF MICRODROPLETS BY A WIRELESSLYDRIVEN PIEZOELECTRIC STAGE Experiental Setup and Operating Mechanis Results and Discussion Calculation of electric field Measureent of vibration displaceent Effect of ultrasonic vibration on single droplet Frequency characteristics of contact angle Merging of icrodroplets Suary 160 CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS Conclusions Equivalent circuit odel Parallel plate capacitor structure Focused electric field Antenna-like electric field generators Coparative study Mechanical vibration characteristics Microdroplets erging Recoendations for Further Research 171 AUTHOR S PUBLICATIONS 175 BIBLIOGRAPHY 178 vi

9 SUMMARY SUMMARY Piezoelectric devices are widely used due to their copact size, high power density, low power consuption, high output force, high precision positioning, etc. In ost applications, electric energy is applied to the piezoelectric devices through lead wires soldered on the electrodes of piezoelectric coponents. Fundaental liitations of applying electric energy to the piezoelectric devices via lead wires necessitate the pursuit of wireless drive of piezoelectric coponents. To widen the application range of piezoelectric devices, new techniques of transitting electric energy wirelessly to piezoelectric coponents have been proposed and investigated by the author. In the work reported by the thesis, an A.C. electric field is used to drive piezoelectric coponents wirelessly. The piezoelectric coponents are ade of lead zirconate titanate (PZT) ceraic aterial, and poled along the thickness direction. An equivalent circuit odel is derived by using the fundaental constitutive piezoelectric equations, and then proposed by the author for a piezoelectric coponent operating in the thickness ode wirelessly driven by an A.C. electric field. The equivalent circuit of the wirelessly driven piezoelectric coponent has a current source, resulting fro the external electric field. This is different fro the equivalent circuit of conventional piezoelectric coponent driven by a voltage applied via lead wires. The concept of using a current source in the equivalent circuit ay be applied to the wirelessly driven piezoelectric coponents operating in the other vibration odes. vii

10 SUMMARY Various new techniques including wireless drive of piezoelectric coponents by parallel plate capacitor structure, focused electric field, focused electric field structure in electric resonance with an inductor, dipole antenna-like structure and flat spiral coil antenna-like electric field generator in electric resonance with a capacitor are proposed and investigated by the author. Both theoretically and experientally, it has been found that the real output power achieved wirelessly by the piezoelectric coponent depends on the operating frequency, vibration ode, electrical load, electrode pattern, position and size of the piezoelectric coponent, separation distance of electrodes, area of live and ground electrodes, and the electric field generated by the electric field generators. The theoretical results agree well with the experiental ones. The output power of the piezoelectric coponent reaches the axiu at resonance. If the piezoelectric coponent is detuned fro the resonance, the output power of the piezoelectric coponent drops suddenly. The output power at resonance of the piezoelectric coponent, operating in the thickness vibration ode, is significantly higher than that of the coponent operating in the other odes like width and length extensional vibration odes. The output power at resonance reaches axiu at an optiu load resistance. At the resonant frequency and with an optiu electrical load, the output power of piezoelectric coponent increases with the decrease of the size of piezoelectric coponent, the increase of electrodes area, and the decrease of distance of piezoelectric coponent fro the live and ground electrodes of electric field generators. As a coparison, it has been found that the energy conversion efficiency of the piezoelectric coponent wirelessly driven by focused electric field structure in viii

11 SUMMARY electric resonance with an inductor is significantly higher than that wirelessly driven by the other proposed electric field generators. When the focused electric field generator and inductor are in electric resonance, a axiu output power of W, and an energy conversion efficiency of 1.0% have been achieved wirelessly by a sall piezoelectric coponent with an area of 40 operating in the thickness vibration ode at resonance frequency of 78 khz, optiu electrical load resistance of 1365 Ω, input A.C. source power of 0.1 W (applied to the series of focused electric field generator and inductor), 1 c live and ground electrodes separation, and a live electrode area of 900 c of the focused electric field structure. The technique of wireless drive of piezoelectric coponents by focused electric field structure in electric resonance with an inductor enables a relatively larger output power achieved wirelessly by the piezoelectric coponent than the other structures for a given input A.C. source voltage. Copared to the other proposed techniques, the technique of wireless drive of piezoelectric coponents by an antenna-like structure is robust for the free otion of piezoelectric coponents, and also ay be effective to drive icro piezoelectric coponents in rotary achines. The finite eleent ethod (COMSOL Multiphysics) siulation has been carried out in order to assess the electric field strength on the surface of the piezoelectric coponent wirelessly driven by an A.C. electric field produced fro the electric field generator. It is seen that the value of the electric field on the surface of the wirelessly driven piezoelectric coponent depends on the structure of the electric field generator, size and position of the piezoelectric coponent for a given input A.C. source voltage. ix

12 SUMMARY The echanical vibration characteristics of a piezoelectric coponent operating in the thickness ode wirelessly driven by focused electric field have been investigated theoretically. The effects of electric field, operating frequency, electrical load, position, and size of the piezoelectric coponent on the vibration displaceent are studied. It is seen that the vibration displaceent at resonance increases with the electrical load resistance, the area of the piezoelectric coponent, and decreases with the thickness of the wirelessly driven piezoelectric coponent. Furtherore, a ethod to erge icrodroplets by using a wirelessly driven piezoelectric stage is proposed and investigated, to siplify the device structure for icrodroplets erging and extend the application range of this technology. The icrodroplets to erge are dispensed onto the surface of a piezoelectric stage. The ultrasonic vibration of the piezoelectric stage is transitted into the icrodroplets and induces the erging of icrodroplets. It has been observed that the tie for erging of water icrodroplets depends on the vibration displaceent of the stage, separation distance and volue of icrodroplets. At the resonant frequency of 776 khz, two water icrodroplets each of volue 0.8 µl separated by a distance of 0.6 are erged together 16 seconds after the echanical vibration displaceent of 0.11 µ is excited in the stage with an area of 40. Unlike the conventional ethod of erging, the proposed device offers a few key advantages: there is no need to use icrochannels for the otion of droplets; the icrodroplets can be dispensed on to the actuating surface siultaneously or at different tie; two droplets with the sae size and viscosity can be erged successfully; and the wireless drive provides the potential for iniaturization of the piezoelectric stage. x

13 List of Figures LIST OF FIGURES Fig..1 (a) Pervoskite-type PZT unit cell in the syetric cubic state above T c (before poling); (b) Tetragonally distorted PZT unit cell below T c (after poling). 18 Fig.. Axis designations. Fig..3 Piezoelectric transducers. 3 Fig..4 Piezoelectric actuators. 4 Fig..5 Piezoelectric transforer. 5 Fig..6 Piezoelectric sensor. 5 Fig.3.1 Fig.3. Fig.3.3 Fig.3.4 Fig.4.1 (a) The piezoelectric plate operating in the thickness vibration ode wirelessly driven by an electric field; (b) The thickness vibration of the piezoelectric plate shown by the dotted lines. Basic configuration of a piezoelectric plate operating in the thickness vibration ode wirelessly driven by electric field. Derived equivalent circuit of the piezoelectric plate operating in the thickness vibration ode wirelessly driven by electric field. Measured ipedance characteristics of the piezoelectric plate at the thickness vibration ode. Experiental setup to drive a piezoelectric plate wirelessly by parallel plate capacitor structure. (a) Scheatic diagra; (b) Photograph Fig.4. Configuration of the piezoelectric plate. (a) Scheatic 48 xii

14 List of Figures Fig.4.3 Fig.4.4 Fig.4.5 diagra; (b) Photograph. Frequency characteristics of the output power of the piezoelectric plate operating in the thickness vibration ode at different load resistances. Dependence of the output power on the electrical load at resonance frequency of the piezoelectric plate operating in the thickness ode. Equivalent circuit of the piezoelectric plate wirelessly driven by electric field. is is the current source resulting fro Fig.4.6 Fig.4.7 Fig.4.8 Fig.4.9 electric field E and V is the output voltage across the load resistance R. L, L and resistance. turn ratio. C and R are the inductance, capacitance Cd is the claped capacitance and n is the Effects of vibration odes on the output power of piezoelectric plate. Dependence of the axiu output power of the piezoelectric plate on the input voltage and gap thickness between the two parallel brass plate electrodes. The axiu power is for frequency and electric load. Configuration of the piezoelectric plate having two separated electrodes. Frequency characteristics of the output power of the piezoelectric plates with different electrode length ratios, operating in the thickness ode xiii

15 List of Figures Fig.4.10 Fig.4.1 Fig.5.1 Fig.5. Fig.5.3 Fig.5.4 Fig.5.5 Dependence of the output power at resonance on the electrical loads and electrode length ratios for the wirelessly driven piezoelectric plates operating in the thickness vibration ode. Dependence of the output power and electrical load on the electrode length ratio at resonance frequency of the piezoelectric plate, operating in the thickness vibration ode. (a) Experiental setup to drive a piezoelectric plate wirelessly by focused ac electric field; (b) Configuration of the piezoelectric plate wirelessly driven by electric field. Frequency characteristics of the output power of the wirelessly driven piezoelectric plate operating in the thickness ode. (a) Piezoelectric plate placed equidistantly in-between live and needle ground electrodes at a distance of 4 fro each electrode; (b) placed to the needle ground electrode. Effect of live electrode area on the output power at resonance of the piezoelectric plate operating in the thickness vibration ode. Effect of ground electrode area on the output power at resonance of the piezoelectric plate operating in the thickness vibration ode. Dependence of the axiu output power on the distance between the lower surface of piezoelectric plate and needle ground electrode. The axiu output power is for xiv

16 List of Figures Fig.5.6 Fig.5.7 frequency and electrical load. Dependence of the output power at resonance on the electrical load. Equivalent circuit of the piezoelectric plate wirelessly driven by electric field. is is the current source resulting fro 7 7 Fig.5.8 Fig.5.9 Fig.5.10 electric field E and V is the output voltage across the load resistance R. L, L and resistance. turn ratio. C and R are the inductance, capacitance Cd is the claped capacitance and n is the Geoetry used for -D finite eleent ethod (COMSOL Multiphysics) siulation of electric field pattern around a piezoelectric plate wirelessly driven by focused electric field structure. Siulated -D electric field pattern around the piezoelectric plate wirelessly driven by focused electric field. (a) Dependence of the output power at resonance on the area of PZT plate and electrical load; (b) Effect of calculated average electric field and easured equivalent resistance on the area of PZT plate Fig.5.11 Frequency dependence energy conversion efficiency 79 characteristics at the optiu load of the piezoelectric plate operating in the thickness vibration ode, wirelessly driven by focused electric field. Fig.5.1 (a) Focused electric field structure to drive piezoelectric plate 83 xv

17 List of Figures Fig.5.13 Fig.5.14 Fig.5.15 Fig.5.16 Fig.5.17 Fig.5.18 Fig.5.19 Fig.5.0 wirelessly; (b) Configuration of a wirelessly driven piezoelectric plate operating in the thickness vibration ode. Calculated -D electric field pattern around the piezoelectric plate wirelessly driven by focused electric field structure. Distribution of the electric field on the surface of wirelessly driven piezoelectric plate along the x-direction, x= to x= Equivalent circuit of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. Theoretical frequency characteristics of the vibration displaceent of wirelessly driven piezoelectric plate operating in the thickness ode. Theoretical electric load characteristics of the vibration displaceent at resonance of the piezoelectric plate wirelessly driven by focused E-field. Effect of the area on vibration displaceent at resonance of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. Effect of the calculated average electric field and easured equivalent resistance on the area of the wirelessly driven piezoelectric plate. Effect of the thickness on the vibration displaceent at resonance of the piezoelectric plate operating in the thickness ode wirelessly driven by focused electric field Fig.5.1 (a) Experiental setup to drive piezoelectric coponent 98 xvi

18 List of Figures Fig.5. Fig.5.3 Fig.5.4 Fig.5.5 wirelessly by capacitor-like structure in series with an inductor; (b) Configuration of piezoelectric plate-a; (c) Configuration of piezoelectric plate-b. Frequency characteristics of the output power of the piezoelectric plates A and B at optiu load resistance for: (a) electric field generator with inductor and (b) without an inductor. Dependence of the output power at resonance on the electrical load for piezoelectric plates A and B, operating in the thickness vibration ode. Effect of vibration odes on the output power of wirelessly driven piezoelectric plate B when the electric field generator is in electric resonance with the inductor. Dependence of the axiu output power on the distance between the live and needle ground electrodes. The axiu output power is for resonance frequency and optiu electrical load of the piezoelectric plate placed equidistantly fro the live and needle ground electrodes Fig.5.6 Frequency dependence energy conversion efficiency 106 Fig.5.7 characteristics at the optiu load resistance of piezoelectric plates A and B, operating in the thickness vibration ode, when the electric field generator is in electric resonance with the inductor. Dependence of energy conversion efficiency on the electrical load resistance at resonance of the piezoelectric plate B 107 xvii

19 List of Figures Fig.6.1 Fig.6. Fig.6.3 Fig.6.4 Fig.6.5 Fig.6.6 Fig.6.7 Fig.6.8 Fig.6.9 operating in the thickness vibration ode. Experiental setup to drive piezoelectric plate wirelessly by an electric dipole antenna-like structure. Configuration of piezoelectric plate wirelessly driven by an electric dipole antenna-like electric field generator. Geoetry used for D finite eleent odel of electric field analysis of piezoelectric plate wirelessly driven by dipole antenna-like structure. Siulated D electric field pattern around the piezoelectric plate wirelessly driven by dipole antenna-like structure. Distribution of the electric field on the surface of wirelessly driven piezoelectric plate along the x-direction, x= to x= Equivalent circuit of the piezoelectric plate wirelessly driven by an ac electric field generated fro dipole antenna-like structure. Theoretical and experiental dependence of the output power on the electrical load resistance at resonance frequency of the piezoelectric plate. Theoretical and experiental frequency characteristics of the output power of the wirelessly driven piezoelectric plate. Effect of the electrode area of dipole antenna-like structure on the output power at resonance frequency and optiu load resistance of the piezoelectric plate Fig.6.10 Theoretical and experiental dependence of the output 16 xviii

20 List of Figures Fig.6.11 Fig.6.1 Fig.6.13 Fig.6.14 Fig.6.15 Fig.6.16 power at resonance on the distance of piezoelectric plate fro the electrode plane of dipole antenna-like structure. (a) Curve fitting with the experiental dependence of the output power on the distance of piezoelectric plate fro the electrode plane of the dipole antenna-like structure; (b) Residuals of linear and non-linear curve fit. Experiental setup to increase the driving power of the wirelessly driven piezoelectric plate by cascading an inductor in series with the dipole antenna-like structure. Frequency characteristics of the output power of PZT plate when the dipole antenna-like structure is in electric resonance with an inductor. (a) Experiental setup to drive piezoelectric plate wirelessly by using a flat spiral coil antenna-like electric field generator in electric resonance with a capacitor. (b) Configuration of the wirelessly driven PZT plate. Frequency characteristics of the output power of the piezoelectric plate at the optiu load resistance for spiral coil antenna-like electric field generator in electric resonance with, and without capacitor. Dependence of the output power on the electrical load at the resonance frequency of the piezoelectric plate for a spiral coil antenna-like electric field generator in resonance with, and without capacitor Fig.6.17 Dependence of the output power at resonance frequency on 138 xix

21 List of Figures Fig.6.18 Fig.6.19 Fig.7.1 Fig.7. Fig.7.3 Fig.7.4 Fig.7.5 the distance of piezoelectric plate fro the plane of spiral coil antenna-like electric field generator along the central axis. The proposed E-field generators to drive the piezoelectric coponent wirelessly. The energy conversion efficiency of the piezoelectric plate wirelessly driven by parallel plate capacitor structure, focused electric field generator, capacitor-like structure in electric resonance with an inductor, flat spiral coil antennalike electric field generator in electric resonance with a capacitor, and dipole antenna-like structure in resonance with an inductor. (a) Experiental setup for the erging of droplets by a piezoelectric stage wirelessly driven by focused electric field; (b) Configuration of wirelessly driven piezoelectric stage operating in the thickness vibration ode. Calculated D electric field pattern around the piezoelectric stage wirelessly driven by focused electric field. Distribution of electric field on the surface of wirelessly driven piezoelectric stage along x direction, x=0.145 to x= Experiental setup for easuring the vibration displaceent of piezoelectric stage wirelessly driven by a focused e -field. The pictures of the easured point are taken by the icroscope when the piezoelectric stage is (a) without xx

22 List of Figures Fig.7.6 Fig.7.7 Fig.7.8 Fig.7.9 Fig.7.10 Fig.7.11 Fig.7.1 vibration, and (b) in vibration. (a) Water icrodroplet on top surface of the wirelessly driven piezoelectric plate without vibration; (b) Water icrodroplet flows down due to the vibration of the piezoelectric plate. Illustration of a water droplet on plastic substrate placed inside a focused electric field generator. (a) Without electric field; (b) with electric field. The frequency characteristics of the contact angle of water droplet placed on the surface of piezoelectric stage operating in the thickness ode. The contact angle of liquid droplets on the horizontal surface of the wirelessly driven piezoelectric stage without vibration and in vibration. Merging of two water droplets placed on the surface of a wirelessly driven piezoelectric plate operating in the thickness vibration ode. (a) without vibration; (b) after 10 seconds of sonication ; (c) after 16 seconds of sonication. Dependence of the tie for erging of water icrodroplets on the distance and volue of water droplets. Curve fitting with the experiental dependence of the erging tie on the distance of water icrodroplets xxi

23 List of Tables LIST OF TABLES Table 3.1 Physical properties of representative piezoelectric aterials. 30 Table 3. A coparison of the calculated and easured equivalent circuit paraeters of the driven piezoelectric plate operating in the thickness ode. 43 Table 5.1 Relevant properties of the piezoelectric plate. 89 Table 5. Equivalent circuit paraeters of the piezoelectric plate. 89 Table 5.3 Measured equivalent circuit paraeters of the piezoelectric plates. 99 Table 6.1 Relevant aterial properties of the used PZT plate. 10 Table 6. Equivalent circuit paraeters of the used PZT plate. 11 Table 6.3 Coparison of all the proposed wireless drive techniques. 144 xxii

24 Chapter 1 Introduction CHAPTER 1 INTRODUCTION The extensive research on piezoelectric properties, aterials and devices has revealed interesting and proising devices for novel applications and that can be realized using various technologies [1-9]. The difficulties associated with the drive of piezoelectric coponents by using lead wires have resulted in an initiative to explore wireless drive to widen the application range of piezoelectric devices. 1.1 Motivation Piezoelectric devices generate electric signals in response to echanical vibrations and produce echanical energy in response to electric signals [10]. The piezoelectric devices which include transducers [11-1], actuators and otors [13-17], transforers [18-1], oscillators [-4], filters [5-7], generators [8-9], and sensors [30-3] are extensively used due to their copact size, high power density, low power consuption, high output force, high precision positioning, etc. As a result of their unique advantages, they have been eployed in various areas such as iniature driving echaniss [33-36], precision positioning [37-41], particle anipulations [4-45], counication systes [46-47], switching power supplies [48-49],vibration control [5054], cheical engineering [55-56], bioedical engineering [57-59], and icrofluidics [60-6]. In ost applications, electric energy is applied to the piezoelectric devices via 1

25 Chapter 1 Introduction lead wires soldered on the electrodes of piezoelectric coponents. However, this conventional ethod of applying electric energy to the piezoelectric devices via lead wires has soe ajor disadvantages. At high input voltage, large vibration aplitudes or high teperature, the lead wires ay fall off, causing the breakdown of the piezoelectric devices. The soldering of lead wires thus liits the iniaturization of the devices. As devices becoe increasingly saller, challenges also faced in soldering of lead wires in icro and nano piezoelectric coponents. The soldering ay affect the properties of icro and nano-scale devices. The lead wires also obstruct the applications of piezoelectric devices in rotary echaniss and icro systes. Therefore, there is a need to introduce an alternative approach to apply electric energy to the piezoelectric devices, in response to the above stated challenges. The difficulties associated with the direct drive of piezoelectric coponents by using lead wires have resulted in an initiative to explore wireless ethods to drive piezoelectric coponents. To iniaturize and widen the application range of piezoelectric devices, wireless drive of piezoelectric coponents by an A.C. electric field have been proposed and investigated by the author. The lack of such a wireless drive is seen as a bottle neck for wide spread applications of icro and nano-systes. In this thesis, a fundaental theoretical odel together with experiental investigations have been carried out in order to provide deep physical insights and help develop a better wireless drive of piezoelectric coponents. 1. Research Objectives The need for wireless drive of piezoelectric coponents has otivated the

26 Chapter 1 Introduction following ajor objectives of this research work to: (i) (ii) (iii) Explore new techniques of wirelessly driven piezoelectric coponents. Study the proposed structures and operating echanis. Investigate the characteristics of wirelessly driven piezoelectric coponents. (iv) Outline the effects of paraeters to optiize the wireless energy transission. (v) Develop a fundaental theoretical equivalent circuit odel for a piezoelectric coponent wirelessly driven by an A.C. electric field. (vi) Verify the effectiveness of the proposed odel by coparing the theoretical and experiental characteristics. (vii) Investigate the echanical vibration characteristics of wirelessly driven piezoelectric coponents. (viii) Explore the application of wirelessly driven piezoelectric coponents. 1.3 Major Contributions The ajor contributions achieved in this study are suarized as follows: 1. An A.C. electric field is used to drive wirelessly piezoelectric coponents which are ade of lead zirconate titanate (PZT) ceraic aterial, and poled vertically across its thickness. The thickness vibration direction and applied electric field are both parallel to the poling direction. So far, there has been no equivalent circuit odel for a piezoelectric coponent wirelessly driven by electric field. A theoretical odel is proposed by the author, and suarized into an equivalent circuit to investigate the structure, operating echanis, and perforance of a piezoelectric 3

27 Chapter 1 Introduction coponent operating in the thickness vibration ode wirelessly driven by electric field. Different fro the equivalent circuit of conventional piezoelectric coponents driven by a voltage applied through lead wires, the equivalent circuit of a wirelessly driven piezoelectric coponent has a current source, resulting fro the external electric field. The concept of using a current source in the equivalent circuit ay be applied to the wirelessly driven piezoelectric coponents operating in the other vibration odes.. Various new techniques of transitting electric energy wirelessly to piezoelectric coponents have been proposed and explored by the author. These techniques include the wireless drive of piezoelectric coponents by using a parallel plate capacitor structure, focused electric field generator, focused electric field structure in electric resonance with an inductor, dipole antenna-like structure, and flat spiral coil antenna-like electric field generator in electric resonance with a capacitor. 3. The wireless electric energy transission to piezoelectric coponents by using a parallel plate capacitor structure is explored. In the experiental design, for the generation of an A.C. electric field, an A.C. input voltage with tunable frequency is connected to the two brass plate-shaped live and ground electrodes ounted on a plastic table with a fixed separation which fors a parallel plate capacitor structure. The piezoelectric plate is inserted at the center of the gap between the two brass electrodes of the parallel plate capacitor structure. Fro the experient, it has been seen that the output power achieved by the piezoelectric plate depends on various factors like the operating frequency, electrical load, vibration ode and electrode 4

28 Chapter 1 Introduction pattern of the piezoelectric coponent, and the electric field. At the resonance frequency of 78 khz, a axiu output power of 1.84 W and an energy conversion efficiency of 0.1% have been achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode with a 1 c gap thickness, and an input A.C. source power of 1.5 W across the parallel plate capacitor structure. It is also observed that the output power at resonance of the piezoelectric plate operating in the thickness vibration ode is significantly higher than that of the piezoelectric plate operating in the other vibration odes like width and longitudinal vibrations. 4. A new ethod of wireless drive of piezoelectric coponents by eploying a focused electric field is proposed and investigated. The A.C. electric field is focused, by using a stainless steel needle ground electrode and a brass plate-shaped live electrode to the piezoelectric plate placed in between the. The needle ground electrode enables better transission of electric energy. The effects of electrode areas on the output power of the piezoelectric plate are investigated in order to optiize the wireless electric energy transission to the piezoelectric plate. The output power of the piezoelectric plate depends on the operating frequency, electrical load, diensions of the piezoelectric coponent, electric field, distance, and size of live and ground electrodes of the electric field generator. When the frequency of the A.C. electric field is close to the echanical resonance frequency of the piezoelectric plate operating in the thickness vibration ode, the output power reaches the axiu. At the resonance frequency of 78 khz, a axiu output power of W and an energy 5

29 Chapter 1 Introduction conversion efficiency of 0.51% have been achieved wirelessly by the piezoelectric plate operating in the thickness ode with a needle ground electrode, an optiu electrical load of 1365 Ω, an input A.C. source power of.1 W across live and needle ground electrodes, a 1 c electrodes separation, and a live electrode area of 900 c of the focused electric field structure. Theoretically, the electric field pattern is also studied by finite eleent ethod siulation (COMSOL Multiphysics) to elucidate the focusing of electric field by a needle ground electrode with a brass plate-shaped live electrode to the piezoelectric coponent placed in between the. 5. Nano-vibration characteristics of a piezoelectric coponent operating in the thickness ode, wirelessly driven by a focused electric field have been investigated. A echanical resonance vibration is excited in the piezoelectric plate wirelessly driven by the A.C. electric field. Theoretically, it has been found that the vibration displaceent depends on the electric field, operating frequency, electrical load, and diensions of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. The electric field pattern is theoretically calculated to assess the electric field produced on the surface by the focused electric field structure. It has been observed that the vibration displaceent of the wirelessly driven piezoelectric plate reaches the axiu at resonance frequency, and the axiu vibration displaceent is in the nanoeter range. It is also found that the vibration displaceent at resonance increases with the electrical load resistance, and the plate s lateral size, and decreases with the thickness of the wirelessly driven piezoelectric coponent. 6

30 Chapter 1 Introduction 6. In order to drive high power piezoelectric coponents wirelessly, an iproved ethod of wireless drive of piezoelectric coponents is experientally investigated by using the electric resonance of a focused electric field generator and an inductor in series. With an optiu area of a brass plate-shaped live electrode, a stainless steel needle ground electrode is used to for a focused electric field generator. In the focused electric field generator, the A.C. electric field is focused to the needle ground electrode fro the plate-shaped live electrode through a piezoelectric plate placed in between the. When the focused electric field generator and inductor exhibit a series electric resonance, the wireless electric energy transission to the piezoelectric coponent can be enhanced. This technique enables a relatively large output power achieved by the piezoelectric plate wirelessly. Experientally, it has been found that the real output power of the wirelessly driven piezoelectric plate depends on the operating frequency, electrical load, vibration ode of the piezoelectric coponent, distance between the electrodes, and the electric field focused by the needle ground and live electrodes of the focused electric field generator. When the focused electric field generator and inductor are operating at electric resonance, a axiu output power of W, and an energy conversion efficiency of 1.0% have been achieved by the wirelessly driven piezoelectric plate operating in the thickness vibration ode at a resonance frequency of 78 khz, an optiu electrical load resistance of 1365 Ω, an input A.C. source power of 0.1 W applied to the focused electric field structure cascaded in series with the inductor, a1 c live and ground electrodes separation, and a live electrode area of 900 c 7

31 Chapter 1 Introduction of the focused electric field generator. The output power at resonance of the piezoelectric plate operating in the thickness vibration ode is significantly higher than that obtained when operating in the other odes, e.g. width and length extensional vibration odes. 7. Wireless drives of piezoelectric coponents by focused electric field and the electric field generated fro parallel plate capacitor structure were proposed and investigated by the author. However, the structures of the proposed electric field generators constrain the free otion of the wirelessly driven piezoelectric coponents. To explore the possibility of solving this difficulty and widen the application range of piezoelectric devices, a wireless drive of piezoelectric coponents by using a dipole antenna-like electric field generator is proposed, and its characteristics are investigated. Two equal square size brass plate-shaped live and ground electrodes are used to for an electric dipole antenna-like structure to transit A.C. electric fields wirelessly to the piezoelectric plate. The effects of the electrode areas of this dipole antenna-like structure, electric field, operating frequency, electric load, and position of the plate on the real output power of piezoelectric plate are investigated in order to optiize the wireless electric energy transission. The electric field pattern is calculated by finite eleent ethod to assess the electric field on the surface of piezoelectric plate wirelessly driven by dipole antenna-like structure. A theoretical odel is also developed for the wirelessly driven piezoelectric plate operating in the thickness vibration ode, which can explain the experiental results well. It is observed that at the resonance frequency and with an optiu electrical load, the output power achieved wirelessly by 8

32 Chapter 1 Introduction the piezoelectric coponent increases with the electrodes area, the strength of electric field, and decreases with the distance of the piezoelectric coponent fro the plane of electrodes of dipole antenna-like structure. In order to enhance the driving power, the electric dipole antenna-like structure is used in series with an inductor. When the electric dipole antenna-like structure and inductor are in electric resonance, a axiu output power of 1.9 W and an energy conversion efficiency of 0.01% have been achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode, placed at the centre 4 away fro antenna plane with an optiu electrical load resistance of 350 Ω, a 1 c electrodes separation, a 500 c electrode area of electric dipole antennalike structure, and an input A.C. source power of W applied to the series of dipole antenna-like structure and inductor. 8. An iproved copact electric field generator is also explored to transit relatively large aounts of electric energy wirelessly to piezoelectric coponents by using the electric resonance of a flat spiral coil antenna-like structure and a capacitor in series. When the spiral coil antenna-like electric field generator and capacitor are in electric resonance, the wireless electric energy transission to the piezoelectric coponent placed in a plane perpendicular to the plane of antenna can be enhanced. This technique enables a relatively large output power achieved wirelessly by the piezoelectric coponent. At the resonance frequency of 77 khz and with an optiu electrical load resistance of 350 Ω, a axiu output power of 0.36 W and an energy conversion efficiency of 0.07% have been achieved wirelessly by the piezoelectric plate operating in the thickness 9

33 Chapter 1 Introduction vibration ode, placed 4 away fro antenna plane with an input A.C. source power of 1.94 W applied to the series of flat spiral coil antennalike structure and capacitor, and an inductance of H of the flat spiral coil antenna-like structure. 9. A coparative study of all the proposed and investigated wireless energy transission techniques has been conducted. It has been found that the energy conversion efficiency of the piezoelectric coponent wirelessly driven by the focused electric field structure in electric resonance with an inductor is significantly higher than that wirelessly driven by the other structures such as parallel plate capacitor structure, focused electric field generator, dipole antenna-like structure in resonance with inductor, and flat spiral coil antenna-like electric field generator in resonance with a capacitor. When the focused electric field generator and inductor are in electric resonance, an energy conversion efficiency of 1.0% has been achieved wirelessly by a sall piezoelectric plate with an area of 40 operating in the thickness vibration ode at the resonance frequency of 78 khz, under an optiu electrical load resistance of 1365 Ω, with an input A.C. source power of 0.1 W (applied to the series of focused electric field generator and inductor), a 1 c electrodes separation, and a live electrode area of 900 c of the focused electric field generator. The technique of wireless drive of piezoelectric coponents by focused electric field structure in electric resonance with an inductor enables a relatively large output power achieved wirelessly by the piezoelectric coponent than the other structures for a given input A.C. source voltage. Copared to the other proposed techniques, the technique of wireless drive of 10

34 Chapter 1 Introduction piezoelectric coponents by antenna-like structure is robust for the free otion of piezoelectric coponents, and also ay be effective to drive icro piezoelectric coponents in rotary achines. 10. Furtherore, a ethod to erge icrodroplets by using a wirelessly driven piezoelectric stage is proposed and investigated by the author. The separated icrodroplets (with volues varying fro 0.5 µl to µl) to be erged are dispensed onto the top surface of a piezoelectric stage wirelessly driven by a focused electric field. The ultrasonic vibration of the piezoelectric stage is transitted into the icrodroplets and induces their erging. Experientally, it has been observed that the erging tie of water icrodroplets depends on the vibration displaceent of piezoelectric stage, separation distance, and initial volue of the icrodroplets. The erging tie of two water icrodroplets decreases with the separation distance between the icrodroplets, and increases with their volue. At the resonance frequency of 776 khz, two water icrodroplets, each with a volue of 0.8 µl, separated by a distance of 0.6 are erged together 16 seconds after the echanical vibration displaceent of 0.11 µ is excited in the piezoelectric stage with an area of 40. The proposed device has sipler structure and the potential to be saller than the conventional devices for icrodroplet erging. It is also ore flexible in the size and physical properties of icrodroplets to erge. The novelty of this research work is that we are the first to propose and explore the wireless drive of piezoelectric coponents by using a properly designed electric field. As a first author, a total nuber of fourteen research articles 11

35 Chapter 1 Introduction related to this work have been published and counicated in international journals and conference proceedings. (See author s publications at page. 175). 1.4 Organization of the Thesis This thesis includes eight chapters. In Chapter 1, the otivation, objectives, ain contributions, and organization of the thesis are presented. Chapter introduces the fundaental echanis of piezoelectricity, practical piezoelectric aterials, dynaic behavior, driving techniques and various applications of piezoelectric devices. The desirable characteristics of piezoelectric devices are outlined to justify the direction of the research pursuits of this work. In Chapter 3, a theoretical odel is proposed, and suarized into an equivalent circuit to investigate the structure, operating echanis, and perforance of a piezoelectric coponent wirelessly driven by an A.C. electric field. In Chapter 4, a new technique of transitting electric energy wirelessly to piezoelectric coponents is proposed. The characteristics of wireless energy transission to piezoelectric coponents by parallel plate capacitor structure are investigated experientally. The experiental result shows the feasibility to drive piezoelectric devices wirelessly by using a properly designed electric field. 1

36 Chapter 1 Introduction In Chapter 5, the wireless drive of piezoelectric coponents by focused electric field is proposed and experientally investigated. The electric field pattern is also theoretically analyzed by finite eleent ethod siulations to elucidate the focusing of the electric field by a stainless steel needle ground electrode with a brass plate-shaped live electrode to a piezoelectric coponent placed in between the. The nano-vibration characteristics of a piezoelectric coponent operating in the thickness ode wirelessly driven by focused electric field have been investigated. To explore the possibility of enhancing wireless electric energy transission to the piezoelectric coponents and widen the application range of piezoelectric devices, wireless drive of piezoelectric coponents is experientally investigated by using the electric resonance of a focused electric field generator and an inductor in series. In Chapter 6, the theoretical and experiental characteristics of piezoelectric coponents wirelessly driven by an electric dipole antenna-like structure and a flat spiral coil antenna-like electric field generator have been investigated. The theoretical results are verified with the experiental ones. Also, a coparative study of all the proposed and investigated wireless energy transission techniques has been conducted. Chapter 7 presents a ethod to erge icrodroplets by using a piezoelectric stage which is wirelessly driven by an A.C. electric field. Finally, the conclusions and recoendations for future work are presented in Chapter 8. 13

37 Chapter Background and Basic Theory CHAPTER BACKGROUND AND BASIC THEORY In piezoelectric device research, a eticulous understanding of the piezoelectric effect and of its theory provides deep insight into the aspects of device design, aterials selection, and optiu driving conditions. This chapter introduces the theoretical background of piezoelectric devices, practical aterials, dynaic behavior, driving techniques and typical applications. After a coprehensive review, the fundaental liitations of the conventional ethods of applying electric energy to the piezoelectric coponents through lead wires soldered on the electrodes are outlined. This would subsequently enable us to explore the wireless ethods of electric energy transission to the piezoelectric coponents..1. The fundaental echanis of piezoelectricity This section begins with a brief historical background of piezoelectricity and introduces soe fundaental concepts related to the phenoenon Historical overview The history of piezoelectricity dates back to 1880 when Pierre and Jacques Curie first discovered the piezoelectric effect in various substances including Rochelle salt, touraline, cane sugar and quartz [63-64]. They showed that the crystals generate electrical polarization fro echanical stress. The 14

38 Chapter Background and Basic Theory phenoenon of electric polarization of crystals caused by deforation in certain directions was later given the nae piezoelectricity by Hankel [64]. Converse piezoelectricity was atheatically deduced fro fundaental therodynaic principles by Lippann in 1881, and the existence of the converse effect was iediately confired by the Curies [64]. Since then, piezoelectricity has been known as the interaction between the electrical and echanical fields in solids. Shortly thereafter, Lord Kelvin described piezoelectric behavior using a precise therodynaic theory [65] and later this work is carried out with ore detailed forulation by Woldenar Voigt, which is the basis for the forulation of piezoelectric constitutive equations [66-68]..1.. The piezoelectric effect When a piezoelectric crystal is echanically strained, or when it is defored by the application of an external stress, electric charges appear on certain crystal surfaces. If the direction of the strain reverses, the polarity of the electric charge is also reversed. This is called the direct piezoelectric effect, and the crystals that exhibit it are classed as piezoelectric crystals. Conversely, when a piezoelectric crystal is placed in an electric field, or when charges are applied by external eans to its faces, the crystal exhibits strain, i.e. the diensions of the crystal change. When the direction of the applied electric field is reversed, the direction of the resulting strain is reversed. This is called converse piezoelectric effect [64, 65] Piezoelectric aterials Quartz crystals are the first coercially exploited piezoelectric aterial [8, 66]. But scientists searched for higher-perforance aterials. After the 15

39 Chapter Background and Basic Theory breakthrough invention of the high dielectric constant aterial bariu titanate, scientists focused on piezoceraic aterials directly derived fro it. In the 0 th century, very strong and stable piezoelectric effects were discovered on etal oxide-based piezoelectric ceraics which are physically strong, cheically inert and relatively inexpensive to anufacture. Ceraics anufactured fro forulations of lead zirconate or lead titanate exhibit greater sensitivity and higher operating teperatures, relative to ceraics of other copositions. Lead Zirconate Titanate (PZT) ceraic is the ost widely used piezoelectric ceraic, as it exhibits both the direct and inverse piezoelectric effects. PZT ceraics are available in any variations and are still the ost widely used aterials for actuator or sensor applications [8]. Many scientists have been working independently to iprove the piezoelectric characteristics of ceraics, especially lead zirconate titanate. Production of the aterials with desired characteristics such as good teperature stability, low hysteresis, high electroechanical coupling factor, and high linearity is the ain challenge. PZT ceraics have crystal structures belonging to the perovskite faily. A perovskite structure is any aterial with the sae type of crystal structure as calciu titaniu oxide (CaTiO 3 ), known as the perovskite structure or XII A +VI B 4+ X 3 with the oxygen in the face centers [67]. The general cheical forula for pervoskite copounds is ABX 3, where A and B are two cations of very different sizes, and X is an anion that bonds to both. The cheical forula for PZT is Pb[Zr x Ti 1-x ]O 3, 0<x<1. The pervoskite type lead zirconate titanate crystal structure is shown in Fig..1. PZT crystallites are centrosyetric cubic (isotropic) before poling, as shown in Fig..1 (a) and after poling exhibit tetragonal syetry ( anisotropic structure) below the Curie 16

40 Chapter Background and Basic Theory teperature (T c ), as shown in Fig..1(b). The PZT-based copounds are coposed of the cheical eleents lead and zirconiu and the cheical copound titanate which are cobined under extreely high teperatures. To prepare a piezoelectric ceraic, fine powders of the coponent etal oxides are ixed in specific proportions, then heated to for a unifor powder. The powder is ixed with an organic binder and is fored into structural eleents having the desired shape (discs, rods, plates, etc.). The eleents are fired according to a specific tie and teperature progra, during which the powder particles sinter and the aterial attains a dense crystalline structure. The eleents are cooled, then shaped or tried to specifications, and electrodes are applied to the appropriate surfaces. Above a critical teperature, the Curie point, each perovskite crystal in the fired ceraic eleent exhibits a siple cubic syetry with no dipole oent (Fig..1a). At teperatures below the Curie point, however, each crystal has tetragonal or rhobohedral syetry and a dipole oent (Fig..1b). The crystal structure of the coercially available Fuji C-03 PZT is tetragonal pervoskite structure. The piezoceraic eleents are anufactured by dry and press foring syste. The fabrication of C-03 PZT involves the following ethods: (a) raw aterial blending (b) ixing, (c) Teporary firing, (d) grinding, (e) granulating, (f) foring, (g) ain firing, (h) processing, (i) silver coating, (j) silver firing, (k) polarization, (l) inspection, packaging and shipent. 17

41 Chapter Background and Basic Theory Fig..1: (a) Pervoskite-type PZT unit cell in the syetric cubic state above T c (before poling); (b) Tetragonally distorted PZT unit cell below T c (after poling) Dynaic behavior of piezoelectric coponents The dynaic perforance relates to the behavior of a aterial when subjected to alternating electric fields and stresses. The perforance of each piezoelectric aterial is liited by soe paraeters like input frequency, electric field, echanical stress and operating teperature. Operating a aterial outside of these liitations ay cause partial or total depolarization of the aterial, and a diinishing or loss of piezoelectric properties. Influence of input frequency- A piezoelectric ceraic eleent exposed to an alternating electric field changes diensions cyclically, at the frequency of the field. The frequency at which the eleent vibrates ost readily in response to the electrical input, and ost efficiently converts the electrical energy input into echanical energy, is the resonance frequency which is deterined by the coposition of the ceraic aterial and by the shape and volue of the eleent [1-3]. As the frequency of cycling is increased, the eleent's oscillation first approaches a frequency at which the ipedance is iniu. This is the 18

42 Chapter Background and Basic Theory resonance frequency. As the frequency is further increased, ipedance increases to a axiu, which also is the anti-resonance frequency. The values of the iniu and axiu ipedance frequencies can be used to calculate the electroechanical coupling factor (k), an indicator of the effectiveness with which a piezoelectric aterial converts electrical energy into echanical energy or echanical energy into electrical energy [1]. The electroechanical coupling factor depends on the ode of vibration and the shape of the ceraic eleent. Dielectric losses and echanical losses also affect the efficiency of energy conversion. Electrical liitations- A piezoelectric ceraic can be depolarized by a strong electric field with polarity opposite to the original poling voltage. The liit on the field strength is dependent on the type of aterial, the exposure tie, and the operating teperature. An alternating current will have a depolarizing effect during each half cycle in which polarity is opposite that of the field [1, 3]. Mechanical stress- High echanical stress can depolarize a piezoelectric ceraic. The liit on the applied stress is dependent on the type of ceraic aterial, and duration of the applied stress [1, 8]. Operating teperature- As the operating teperature increases, the piezoelectric perforance of a aterial decreases, until coplete and peranent depolarization occurs at the aterial's Curie teperature [1, 8]. The Curie point is the absolute axiu exposure teperature for any piezoelectric ceraic. Also, sudden teperature fluctuations can generate relatively high voltages, capable of depolarizing the ceraic eleent. The aterial's teperature liitation decreases with greater continuous operation or 19

43 Chapter Background and Basic Theory exposure. At elevated teperatures, the ageing process accelerates, piezoelectric perforance decreases and the axiu safe stress level is reduced. Mishandling the eleent by exceeding its electrical, echanical, or theral liitations can accelerate the stability of piezoelectric eleent [1, 3, 5] Piezoelectric constitutive relations The constitutive relations of piezoelectric crystals are originated fro the appropriate therodynaic functions [68-70]. The relevant therodynaic functions depend on the choice of an independent variable set. For electrical variables, either polarization P or electric displaceent (flux density) D can be selected as the extensive variable, although the intensive variable is always electric field E. The echanical variables are generally strain S, and stress T. A coon for of the constitutive equations derived fro the therodynaic functions based on the following convention is [68-70]: T E ij i D cijkl Skl hkij Dk (.1) S hkij Skl ik Dk (.) Where T ij = Eleents of the echanical stress tensor S kl = Eleents of the echanical strain tensor c ijkl = Eleents of the stiffness tensor h kij = Eleents of the piezoelectric constant tensor β S ik = Eleents of the dielectric ipereability tensor D k = Eleents of the dielectric displaceent vector E i =Eleents of the electric field vector 0

44 Chapter Background and Basic Theory At this point it is appropriate to adopt a convention to denote the aterial s axial directions and polarization. The direction in which tension or copression develops polarization parallel to the strain is called piezoelectric axis. In quartz, this axis is known as the X-axis, and in poled ceraic aterials such as PZT, the piezoelectric axis is referred to as the Z-axis. The new convention is shown in Fig.. [70-71]. The direction of polarization is conventionally taken as the third axis, with axes 1 and perpendiculars to this. The ters 4, 5, and 6 refer to shear strains associated with the 1,, and 3 directions. The application of an electric field along the axis 3 can result in piezoelectric coupling along any of the six directions shown in Fig... For a tetragonal structure, the crystal will only defor along the three principal directions, whereas rhobohedral and orthorhobic structures can also exhibit shear coupling. Such coupling is usually designated with two subscript nubers. For exaple, the coupling coefficient d 31 shows that an electric field oriented along axis 3 results in a strain along axis 1 [70-71]. This idea is used throughout the constitutive equations for both the elastic and perittivity constants. The atrix equations (.1) and (.) are often further siplified to scalar equations to represent the ost coonly considered actuation scenarios such as the 31-ode and 33- ode, which gives [1, 68 and 69]: and D T1 c11s1 h31d3 (.3) S E3 h31s1 33D3 (.4) D T3 c33s3 h33d3 (.5) S E3 h33s3 33D3 (.6) 1

45 Chapter Background and Basic Theory Fig..: Axis designation These constitutive equations are now well-suited for odeling the behavior of piezoelectric coponents in ost practical piezoelectric device applications... Piezoelectric Devices and Applications The actions, designs, driving techniques and applications of the piezoelectric devices will be discussed in the following sections. The desirable characteristics of the piezoelectric devices are outlined to justify the direction of the research pursuits of this work. Additionally, the historical ilestones in the developent of piezoelectric devices are discussed to recognize iportant researcher s contribution to this field...1. Piezoelectric Transducers Piezoelectric transducers containing a piezoelectric eleent convert electrical pulses to echanical vibration, often sound or ultrasound, and then convert the returned echanical energy into electrical energy [1]. Piezoelectric transducers are shown in Fig..3 [7]. Piezoelectric transducers that generate audible

46 Chapter Background and Basic Theory sounds afford significant advantages, relative to alternative electroagnetic devices. They are copact, siple, highly reliable, and inial energy can produce a high level of sound. These characteristics are ideally atched to the needs of wireless-powered equipent. Microanipulation can also be achieved with a piezoelectric actuator [73]. Piezoelectric icrocantilever transducers based on PZT thin fil have received considerable interest because of their wide potential applications in nanotechnology, biosensors and icroelectroechanical systes [74]. Piezoelectric transducers are used for applications in bioengineering to disrupt cells, to affect the rate of bio-reactions and yields of etabolites, and for bio-separation [75]. Various solutions also have been developed in structural health onitoring systes eploying piezoelectric transducers to alleviate soe probles [76]. Ultrasonic transducers are used for ultrasonic iaging systes, ultrasonic treatent and treatent of wound [77]. Fig..3: Piezoelectric transducers 3

47 Chapter Background and Basic Theory Fig..4: Piezoelectric actuators.... Piezoelectric Actuators Piezoelectric actuators are devices that convert electrical signal into a echanical otion. The piezoelectric actuators are foring a new field between electronic and structural ceraics [1]. Actuation aking use of piezoelectric eleents becae widespread starting fro the 1990s, and this is an iportant step forward for icrosystes since it is very easy to integrate, it is relatively powerful and easy to use. Piezoelectric icroactuators offer several advantages such as low power requireent (low voltage and current), ease of control, scaling to saller diensions, speed, icrofabrication copatibility and siplicity of fabrication and packaging. Considerable research has been conducted on piezoelectric icroactuators for nano positioning [78], icro anipulations [79-80], and iniature driving echaniss [81-8]. Exaples of piezoelectric actuators are shown in Fig..4 [7]...3. Piezoelectric Transforers When input and output terinals are fabricated on a piezo-device and input/output voltage is changed through the vibration energy transfer, the device 4

48 Chapter Background and Basic Theory is called a piezoelectric transforer [5]. Recent lap-top coputers with a liquid crystal display require a very thin, no electroagnetic-noise transforer to start the glow of fluorescent back-lap. This application recently accelerated the developent of piezoelectric transforers. These devices can be used in D.C.- A.C. inverters to drive cold cathode fluorescent laps, A.C./D.C. adaptors for low voltage applications such as the power supply for coputers, D.C./D.C. adaptors and chargers. Since the original piezoelectric transforer was proposed by C. A. Rosen [83], there have been a variety of such transforers investigated. The Rosen transforer is shown in Fig..5. Fig..5: Piezoelectric transforer, Source: C. A. Rosen Fig..6: Piezoelectric sensor. 5

49 Chapter Background and Basic Theory..4. Piezoelectric Sensors A sensor converts a physical paraeter, such as acceleration or pressure, into an electrical signal [5]. In soe sensors the physical paraeters acts directly on the piezoelectric eleent; in other devices an acoustical signal establishes vibrations in the eleent and the vibrations are, in turn, converted into an electric signal. Often, the syste provides a visual, audible, or physical response to the input fro the sensor. Piezoelectric sensors are used for quality assurance, process control, and for research and developent in any different industries. Detection of pressure variations in the for of sound is the ost coon sensor application, e.g. piezoelectric icrophones [46]. Piezoelectric icrobalances are used as very sensitive cheical and biological sensors [84]. A piezoelectric sensor is shown in Fig..6 [7]..3. Needs of Wireless Drive of Piezoelectric Coponents There has been rearkably rising interest in the applications of piezoelectric devices due to their copact size, high power density, low power consuption, high output force, high precision positioning etc. In ost of the applications of piezoelectric devices discussed above, electric energy is applied to the devices through lead wires soldered on the electrodes of piezoelectric coponents. But this conventional ethod of applying electric energy to the piezoelectric devices through lead wires has soe ajor disadvantages. The lead wires soldered on the electrodes of piezoelectric coponents ay fall off at large vibration, high input voltage or high teperature, and this causes the breakdown of piezoelectric devices. The soldering of lead wires also poses probles for the iniaturization of the piezoelectric devices, as it affects on the 6

50 Chapter Background and Basic Theory properties of icro and nano piezoelectric devices. The lead wires also obstruct the applications of piezoelectric devices in rotary echaniss. The fundaental liitation of applying electric energy to the piezoelectric devices necessitates the pursuit of this research work. Therefore, there is a need to introduce a wireless approach to apply electric energy to the piezoelectric coponents. To explore the possibilities of solving the difficulties in the conventional way of applying electric energy via lead wires which is the bottleneck for further widespread applications of icrosystes and widen the application range of piezoelectric devices, wireless energy transission to piezoelectric coponents has been investigated. The potential reward for exploring wireless drive of piezoelectric coponents is significant, but it is a foridable challenge. In this research work, new techniques of transitting electric energy wirelessly to piezoelectric coponents have been proposed and investigated. The technique of wireless drive of piezoelectric coponents has the potential for iniaturization of the piezoelectric devices. This technique ay be effective to drive icro piezoelectric coponents wirelessly in rotary achines, while at the sae tie it ay also enable a higher operating teperature. 7

51 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent CHAPTER 3 EQUIVALENT CIRCUIT MODEL OF A WIRELESSLY DRIVEN PIEZOELECTRIC COMPONENT A theoretical odel is essential to investigate the structure, operating echanis and perforance of a piezoelectric coponent wirelessly driven by electric field. Moreover, a good theoretical odel can provide deep physical insight to develop a better ethod of wireless drive of piezoelectric coponents by electric field. In the first section of this Chapter, the ost iportant physical properties of the piezoelectric coponents are indexed. The concept of the thickness vibration ode of the piezoelectric has been discussed. The theoretical analyses of a piezoelectric coponent operating in the thickness vibration ode wirelessly driven by electric field will be presented in the second section of this chapter. The basic configuration and operating principle of the wirelessly driven piezoelectric coponent is also illustrated. So far, no equivalent circuit odel of a piezoelectric coponent wirelessly driven by electric field has been reported. An equivalent circuit odel is derived here by using the fundaental constitutive piezoelectric equations, and then proposed by the author for a piezoelectric coponent operating in the thickness ode wirelessly driven by an A.C. electric field. The equivalent circuit of the wirelessly driven piezoelectric coponent has a current source, resulting fro the external 8

52 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent electric field. This is different fro the equivalent circuit of a conventional piezoelectric coponent driven by a voltage applied via lead wires. The concept of using a current source in the equivalent circuit ay be applied to the wirelessly driven piezoelectric coponents operating in the other vibration odes. Furtherore, the ipedance characteristics of the piezoelectric coponent operating in the thickness vibration ode are depicted in the last section of this chapter. The calculated and easured equivalent circuit paraeters of the wirelessly driven piezoelectric plate are also copared. The calculated equivalent circuit paraeters well agree with the easured ones Physical Properties of Piezoelectric Coponents This section suarizes the physical properties of the piezoelectric aterials [103]. Table 3.1 shows the aterial paraeters of soe iportant applied piezoelectric aterials. It is seen that the single crystal lithiu niobate (LiNbO 3 ) has a high echanical quality factor and low piezoelectric loss, but its piezoelectric constants are low. The typical perovskite bariu titanate (BaTiO 3 ) has relatively high piezoelectric constants, but its Q is low. Copared with the single crystal and perovskite piezoelectric aterials, the lead zirconate titante (PZT) also has the high piezoelectric constants and high echanical quality factor. The PZT also has a larger electroechanical coupling factor ( k 33 ) than that of the single crystal lithiu niobate (LiNbO 3 ) and perovskite bariu titanate (BaTiO 3 ). Thus, C-03 PZT (supplied by Fuji Ceraics Corporation, Japan) is chosen as the original aterial for the experients and analyses. 9

53 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent Property Units BaTiO 3 PZT LiNbO 3 k Coupling factors k k t N * khz Frequency constants N * khz N * khz t d 10-1 C/N Piezoelectric charge constants d 10-1 C/N T Relative dielectric constants T Dissipation factor Mechanical tan % Q quality factor Density 10 3 kg/ Curie teperature T C c Table 3.1: Physical properties of representative piezoelectric aterials. 30

54 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent 3.. Concept of the Thickness Vibration Mode of Wirelessly Driven Piezoelectric Plate Fig.3.1 (a) illustrates the thickness vibration ode of a piezoelectric plate wirelessly driven by an electric field. The piezoelectric plate is ade of the Fuji C-03 PZT ceraic aterial, and is poled vertically across its thickness. (a) (b) Fig.3.1 (a): The piezoelectric plate operating in the thickness vibration ode wirelessly driven by an electric field; (b) The thickness vibration of the piezoelectric plate shown by the dotted lines. 31

55 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent When an A.C. electric field penetrates the piezoelectric plate, a echanical vibration is excited in the piezoelectric plate by the converse piezoelectric effect. The excitation of the piezoelectric plate takes place along its thickness direction at a resonance frequency of the thickness ode which is related with the thickness ode frequency constant and the thickness (t) of the piezoelectric plate. The thickness vibration direction and applied electric fields are both parallel to the poling direction. In the thickness vibration, the vibration is unifor on the surface of the piezoelectric plate which is shown by the dotted lines in Fig.3.1 (b). The electroechanical coupling factor (k ) of the thickness vibration ode is higher than that of the other vibration odes of the piezoelectric plate. The electroechanical coupling can be stronger as the applied electric field and echanical vibrations of the piezoelectric plate are in the sae direction. So, the output power and efficiency of the piezoelectric plate operating in the thickness vibration ode wirelessly driven by the A.C. electric field is significantly higher than that of the other vibration odes like width and length extensional vibration odes. 3

56 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent 3.3. Theoretical Analyses of a Piezoelectric Coponent Operating in the Thickness Mode Wirelessly Driven by Electric Field Configuration and operating echanis Fig.3. illustrates the basic configuration of a piezoelectric plate operating in the thickness vibration ode wirelessly driven by an electric field. The piezoelectric plate is ade of the ceraic aterial Fuji C-03 PZT, and is poled vertically across its thickness. The top and botto surfaces of the piezoelectric plate are fully covered by silver etal electrodes. The thickness vibration direction and applied electric field are both parallel to the poling direction. A load resistor R L is connected across the two electrodes of the piezoelectric plate for easuring the real power which the piezoelectric plate delivers. Fig.3.: Basic configuration of a piezoelectric plate operating in the thickness vibration ode wirelessly driven by electric field. 33

57 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent When an A.C. electric field penetrates the piezoelectric plate, a echanical vibration can be stiulated in the piezoelectric plate by the converse piezoelectric effect. When the frequency of the applied electric field is close to the echanical resonance frequency of the piezoelectric plate, a echanical resonance can be excited in the plate. This echanical resonance can generate a relatively large voltage across the output electrodes due to the piezoelectric effect Derived equivalent circuit odel To explore the underlying physical phenoena, operating echanis, resonant echanical vibration and output power characteristics, an equivalent circuit odel has been developed for the piezoelectric plate operating in the thickness ode wirelessly driven by electric field. The one-diensional thickness vibration along the z -direction of a piezoelectric plate with length l and constant cross sectional area A satisfies the following dynaical equation [1]: ut ut D c33 (3.1) t z where, u, and c D 33 represent density, displaceent and elastic stiffness constant of the piezoelectric plate respectively. The general solution of the equation (3.1) for thickness vibration ode is u t jt jt A z Bcos ze ue sin (3.) where A and B are two constants, is the angular resonance frequency, and is the wave nuber in the z -direction, 34

58 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent D c 33 (3.3) and the displaceent of the piezoelectric plate is u Asin z Bcos z. (3.4) When the piezoelectric plate works at its resonance frequency, the following displaceent of the piezoelectric plate ay be obtained by substituting (3.4) into the basic electroechanical equations of the ceraic plate. u u 1 u1 u u sin z cos z (3.5) t t sin cos where u 1 and u are the displaceent of the two surfaces at z t t and z, respectively, and t is the thickness of the piezoelectric plate. As the displaceent at z t and z t has the sae aplitude but opposite direction, we have u u1 u0. (3.6) Then, the displaceent of the piezoelectric plate can be expressed as u0 sin z u (3.7) t sin The one diensional constitutive equations of a piezoelectric plate operating in the thickness vibration ode are as follows [1], T D 3 c33s3 h33d3 (3.8a) E S 3 h33s3 33D3 (3.8b) where T 3 is the stress, S 3 is the strain, E3 is the electric field vector, D3 is the 35

59 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent S electric displaceent vector, h 33 is the piezoelectric coefficient, and is the piezoelectric peritivity constant. Fro equation (3.8b), the electric displaceent is D E h. (3.9) S S S The echanical and electrical conditions are given by S S 0, (3.10) 1 D 3 0. (3.11) z Also u S3 (3.1) z Fro (3.9), (3.-11) and (3.1), we get 33 E z 3 Thus h 33 z u (3.13) u E3 h33 a, (3.14) z where a is an integral constant. There is a voltage V across the piezoelectric plate because of the external electric field on surface of the wirelessly driven piezoelectric plate operating in the thickness ode, and is given by t V E dz. (3.15) 3 t Fro (3.6), (3.14) and (3.15), the integral constant a is V h a 33 ( u 0), (3.16) t t 36

60 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent Fro (3.14) and (3.16) E u V h33 h33 ( 0) (3.17) z t t 3 u Thus, fro (3.9) and (3.17) D V h33 ( 0). (3.18) S S t t 3 u The current flowing through the piezoelectric plate is i l j w ( y) dy. (3.19) l where (y) is the surface charge density and w is the width of the piezoelectric plate. According to Gauss s law, the charge on the surface electrode of the piezoelectric plate is y) D E( ). (3.0) ( 3 0 y where 0 is the perittivity of the free space. Fro equations (3.18) to (3.0), the current flowing through the piezoelectric plate can be obtained as ~ i j VC nu EA. (3.1) d 0 0 where the claped capacitance is defined as C d A S t, (3.a) 33 the turn ratio Ah33 n, (3.b) S t 33 and the average electric field on the surface of the wirelessly driven piezoelectric plate is l ~ 1 E E( y) dy. (3.c) l l Fro equation (3.1), the equivalent circuit of the wirelessly driven 37

61 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent piezoelectric plate operating in the thickness vibration ode shown in Fig.3.3 is derived. i A I B 1:n R C L R L V A C d i s B v Fig.3.3: Derived equivalent circuit of the piezoelectric plate operating in the thickness vibration ode wirelessly driven by electric field. The ipedance of the loop on the right hand side of the equivalent circuit is given by nv 1 Ah 33 Z j. (3.3) j u S 0 33t j D A C33 Fro (3.3), the inductance of the loop is given by Ah33 S 33 L, (3.4) t and the capacitance of the loop at resonance is S 33t 33 C. (3.5) Ah The resistance R of the circuit can be calculated using the coplex fors of S the piezoelectric coefficient ( h 33 ), iperitivity constant ( ), and stiffness constant ( calculated fro D c 33 ) in equation (3.3). However, in practice the resistance is 38 33

62 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent R L Q. (3.6) where Q is the echanical quality factor of the piezoelectric plate. The otional current shown in Fig.3.3 is I n. (3.7) where is the vibration velocity of the wirelessly driven piezoelectric plate operating in the thickness ode. The source current resulting fro external electric field shown in Fig.3.3 is ~ i S j 0 EA. (3.8) Fro Fig.3.3 and eqn. (3.1), it is seen that there is a current source in the equivalent circuit of a wirelessly driven piezoelectric plate operating in the thickness ode. This is different fro the equivalent circuit of conventional piezoelectric coponent which is driven by an input voltage applied via lead wires. The concept of using a current source in the equivalent circuit ay also be applied to the wirelessly driven piezoelectric coponents operating in the other vibration odes. After establishing the equivalent circuit odel, the characteristics of the piezoelectric coponent wirelessly driven by electric field can be explored. When the piezoelectric plate operates near its echanical resonance frequency, the real power delivered to the electrical load resistor connected across the output electrodes of the wirelessly driven piezoelectric plate can be 39

63 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent ~ L d L d L d L L L R R C C L C R C L R C R n R C L R R EA P (3.9) The above eqn. (3.9) shows that the output power of the piezoelectric coponent is a function of the operating frequency, electric load, size, and aterial properties of the piezoelectric plate, and electric field. The optiu load resistance can be explained by the equivalent circuit of piezoelectric plate operating in the thickness ode, shown in Fig.3.3. A axiu power can be delivered to the electric load resistor, when 0 L L dr dp (3.30) Fro (3.9) and (3.30), we get the following relation of the optiu load resistance for which the piezoelectric coponent delivers axiu power to the electrical load resistance R L connected across the two electrodes of the piezoelectric plate L d d d d d d C L C L R R C L C C C n C C L C n L C R C n (3.31) The analytical solution of the optiu load resistance for the wirelessly driven piezoelectric plate is given by d d d d d d L C L C C C n C C L C n L C R C n C L C L R R (3.3) Using the above solution and equivalent circuit paraeters, the optiu load

64 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent 41 resistance can be found for the wirelessly driven piezoelectric plate operating in the thickness vibration ode. The vibration characteristics of a piezoelectric coponent operating in the thickness ode wirelessly driven by electric field can be analyzed by using the derived equivalent circuit as depicted in Fig.3.3. The vibration displaceent at the electrode surface of the wirelessly driven piezoelectric plate operating in the thickness ode can be obtained fro the equivalent circuit as ~ 0.5 L d L d L d L L R R C C L C R C L R C R n R R EAn u (3.33) The vibration velocity of the wirelessly driven piezoelectric plate operating in the thickness vibration ode can be 0 1 ~ 0.5 L d L d L d L L R R C C L C R C L R C R n R R EAn. (3.34) The above equations (3.33) and (3.34) show that both the vibration displaceent and vibration velocity of the piezoelectric plate wirelessly driven by electric field are function of the operating frequency, electric load, diensions, and aterial properties of the piezoelectric plate, and electric field Ipedance Analyses Measured ipedance characteristics The ipedance characteristic at the thickness vibration ode of the driven

65 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent piezoelectric plate with the diensions of c 3 is shown in Fig.3.4. An ipedance analyzer (HP 4194A) was used for the easureent. The ipedance was easured without electric field fro the port AA of the equivalent circuit of the piezoelectric plate as shown in Fig.3.3. Fro the frequency constants of the piezoelectric aterial and ipedance characteristic, it is found that the resonance frequency of the driven piezoelectric plate in the thickness vibration ode is 77 khz Equivalent circuit paraeters of the piezoelectric plate The calculated and easured equivalent circuit paraeters of the wirelessly driven piezoelectric plate operating in the thickness vibration ode are shown in Table 3.. The equivalent circuit paraeters of the piezoelectric plate are calculated by using equations (3.a), (3.4), (3.5), (3.6) and the piezoelectric aterials constants in Table 3.1. L, C and R are the equivalent inductance, capacitance and resistance of the piezoelectric plate looking fro port BB as shown in Fig.3.3. The equivalent circuit paraeters are easured by an ipedance analyzer (HP4194A) fro the port AA. It is seen that the calculated equivalent circuit paraeters agree well with the easured ones. The sall differences ay result fro the error in the aterial constants used for the theoretical calculation, and the error in our easureent. 4

66 Ipedance () Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent Thickness vibration ode PZT area= Fig.3.4: Measured ipedance characteristics of the piezoelectric plate at the thickness vibration ode. Driving frequency (khz) Paraeters Calculated Measured L (H).8.39 R (Ω) 47 4 C (pf) C d (nf) Table 3.: A coparison of the calculated and easured equivalent circuit paraeters of the driven piezoelectric plate operating in the thickness ode. 43

67 Chapter 3 Equivalent Circuit Model of a Wirelessly Driven PZT Coponent 3.5. Suary In suary, a theoretical odel for a wirelessly driven piezoelectric coponent operating in the thickness ode is proposed and expressed by an equivalent circuit. In contrast with the equivalent circuit of conventional piezoelectric coponents driven by a voltage applied via lead wires, the equivalent circuit of a wirelessly driven piezoelectric coponent has a current source resulting fro the external electric field. The concept of using a current source in the equivalent circuit ay be applied to the wirelessly driven piezoelectric coponents operating in the other vibration odes. The ipedance characteristics of the piezoelectric coponent operating in the thickness vibration ode are investigated. The calculated and easured equivalent circuit paraeters of the wirelessly driven piezoelectric plate are also copared. The calculated equivalent circuit paraeters agree well with the easured ones. 44

68 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure CHAPTER 4 WIRELESS ENERGY TRANSMISSION TO PIEZOELECTRIC COMPONENTS BY PARALLEL PLATE CAPACITOR STRUCTURE A new technique of transitting electric energy wirelessly to piezoelectric coponents has been proposed, and explored in this work. An A.C. electric field is used to drive a piezoelectric plate wirelessly, which is ade of lead zirconate titanate (PZT) ceraic aterial. The piezoelectric plate is poled vertically across its thickness direction. When an electric field generated by an A.C. source penetrates the piezoelectric plate, an attenuated voltage is obtained across the output electrodes of the piezoelectric plate. When the frequency of the electric field is close to the echanical resonance frequency of the piezoelectric plate the power received by the electrical load connected to the output electrodes of the piezoelectric plate reaches axiu. In the experiental design, for the generation of an A.C. electric field, an A.C. voltage source is connected to the two brass plate-shaped live and ground electrodes ounted on a plastic table with a tunable separation which fors a parallel plate capacitor structure. The piezoelectric plate is inserted at the center of the gap between; equidistant fro; and parallel with the two brass electrodes of the parallel plate capacitor structure. The experient has shown that the output 45

69 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure power achieved by the piezoelectric plate depends on various factors like the operating frequency, electrical load, vibration ode and electrode pattern of the piezoelectric coponent, and the electric field. At the resonance frequency 78 khz, a axiu output power of 1.84 W and an energy conversion efficiency of 0.1% have been achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode with 1 c gap thickness and an input power of 1.5 W across the parallel plate capacitor structure. Fro the experient, it was also observed that the output power at resonance of the piezoelectric plate operating in the thickness vibration ode is significantly higher than that of the piezoelectric plate operating in the other vibration odes like width and longitudinal vibration odes Experiental Setup, Phenoenon and Operating Mechanis To transit electric energy to piezoelectric coponents, a parallel plate capacitor structure is used as shown in Fig.4.1 (a). The photograph of the experiental set up for the easureent is shown in figure 4-1(b). The brass plate shaped live and ground electrodes with diensions of c 3, ounted on a fixed plastic table with a tunable separation are used to for a parallel plate capacitor structure. An A.C. voltage source (a function generator Tektronix AFG 30 and an aplifier HAS 4014) with tunable frequency is connected to the two brass electrodes of the parallel plate capacitor structure. The piezoelectric plate is inserted into the gap between the two brass electrodes, parallel to and equidistant fro the, and the plate is aligned along the central 46

70 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure axis of the gap. There is no direct connection between the piezoelectric plate and the two brass electrodes. To easure the output power, two lead wires are soldered onto the output electrodes and a load resistor is connected across the output electrodes of the piezoelectric plate. (a) (b) Fig.4.1: Experiental setup to drive a piezoelectric plate wirelessly by parallel plate capacitor structure. (a) Scheatic diagra; (b) Photograph. 47

71 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure Fig.4. (a) shows the configuration of the piezoelectric plate used in the experient. The photograph of the piezoelectric plate is shown in Fig.4. (b). The piezoelectric plate is ade of PZT (supplied by Fuji Ceraics, Japan) with a size of c 3, poled along the thickness direction. The top and botto surfaces of the piezoelectric plate are fully covered by silver electrodes. (a) (b) Fig.4.: Configuration of the piezoelectric plate. (a) Scheatic diagra; (b) Photograph of PZT C

72 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure When the electric field generated by the A.C. voltage penetrates the piezoelectric plate, a voltage was observed across the output electrodes. It was found that the output power reached the axiu at resonance frequency of the piezoelectric plate. When the frequency of the electric field in the gap between two brass electrodes is close to the echanical resonance frequency of the piezoelectric plate, a echanical resonance can be excited due to the converse piezoelectric effect. This echanical resonance can generate a voltage across the output electrodes due to the piezoelectric effect. 4.. Experiental Conditions The experients are perfored under the following conditions. All the experiental piezoelectric plates are ade of the sae ceraic aterial PZT with a size of c 3, and are poled vertically across the thickness direction. The relevant properties of the PZT ceraic are shown in Table 3.1. In each case the piezoelectric plate is aligned along the central axis of the gap between the two brass electrodes. There is no direct connection between the piezoelectric plate and the two brass electrodes. The ediu is air for the wireless electric field transission to piezoelectric plates. Unless otherwise specified, the input A.C. voltage is 150 V rs across the live and ground electrodes of parallel plate capacitor structure, and 1 c gap thickness between the two brass plate-shaped live and ground electrodes. Fro the frequency constants of the piezoelectric aterial shown in Table 3.1 (supplied by Fuji Techno Syste, Japan), and also fro the easured ipedance characteristics depicted in Fig.3.3, it is known that the easured resonance frequency of the piezoelectric plate operating in the thickness ode is 77 khz. 49

73 Output power (W) Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure 4.3. Results and Discussion Frequency characteristics of the output power of wirelessly driven piezoelectric plate The frequency characteristics of the output power of piezoelectric plate operating in the thickness vibration ode are shown in Fig.4.3. It is observed that at the resonance frequency of 77 khz, a axiu output power is achieved by the piezoelectric plate Thickness ode R L =350 R L =1365 R L = Operating frequency (khz) Fig.4.3: Frequency characteristics of the output power of the piezoelectric plate operating in the thickness vibration ode at different load resistances. 50

74 Output power at resonance (W) Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure When the frequency of the electric field in the gap is close to the echanical resonance frequency of the piezoelectric plate, a relatively large vibration can be excited in the piezoelectric plate by the converse piezoelectric effect. This echanical resonance generates a relatively large voltage across the output electrodes of the piezoelectric plate by the piezoelectric effect. Due to the capacitance of the piezoelectric plates, there is also output power but that power does not reach the axiu at resonance. Hence the peaks of the output power are only due to the piezoelectric resonance Dependence of the output power on electrical load of PZT plate Fig.4.4 shows the dependence of output power at resonance on the electrical load for the wirelessly driven piezoelectric plate, operating in the thickness vibration ode Thickness ode V in =70 V rs V in =150 V rs f r = 77 khz Electrical load resistance (k) Fig.4.4: Dependence of the output power on the electrical load at resonant frequency of the piezoelectric plate operating in the thickness ode. 51

75 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure i 1:n R C L R L V C d i s Fig.4.5: Equivalent circuit of the piezoelectric plate wirelessly driven by electric field. i s is the current source resulting fro electric field E and V is the output voltage across the load resistance R. L, inductance, capacitance and resistance. n is the turn ratio. L C and R are the Cd is the claped capacitance and It can be seen that the output power at resonance reaches the axiu at an optiu load resistance. The output power at resonance frequency of 77 khz reaches the axiu at an optiu load resistance of 350 Ω, and the axiu output power is 0.46 W where V in =150 Vrs. The optiu load resistance can be explained by the equivalent circuit of wirelessly driven piezoelectric plate operating in the thickness ode, as shown in Fig.4.5. The real power ( P L ) delivered to the electrical load resistor at resonance calculated fro the equivalent circuit is P L R n R L EA C 0 d RL R Cd RL RLL C 1 L C L 1 C C d RLR. (4.1) A axiu power can be delivered to the electric load resistor, when dp dr L L 0. (4.) Fro eqns. (4.1) and (4.), we get the following analytical solution of the 5

76 Maxiu output power (W) Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure optiu load resistance for which a axiu power is delivered to the electrical load. R L n 4 C d R 4 R C d L L 1 C d n C L L C C C d n C C d d C L C (4.3) Using the above solution and the equivalent circuit paraeters in Table 3., it is found that the calculated optiu load resistance is 358 Ω, which well agrees with the easured value 350 Ω of the wirelessly driven piezoelectric plate operating in the thickness vibration ode Effects of the vibration odes on the output power of the PZT plate The effects of the vibration odes on the output power of the wirelessly driven piezoelectric plate have also been investigated here Thickness vibration ode R L = Width vibration ode R L = Length vibration ode R L = Operating frequency (khz) Fig.4.6: Effects of the vibration odes on the output power of the piezoelectric plate. 53

77 Maxiu output power (W) Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure Fig.4.6 shows the effects of vibration odes on the output power, at the optiu loads and resonance frequencies of the piezoelectric plate, wirelessly driven by the A.C. electric field generated fro the parallel plate capacitor structure. It is seen that the output power of the piezoelectric plate operating in the thickness vibration ode is significantly higher than that obtained in the length and width extensional vibration odes. Thus, the vibration ode has an effect on the output power of the piezoelectric plate wirelessly driven by a parallel plate capacitor structure Effect of electric field on the output power of the piezoelectric plate The effect of the electric field on the output power achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode is investigated here Thickness ode V in = 70 V rs V in = 100 V rs V in = 150 V rs R L = 350 f r = 77 khz Gap thickness between two brass electrodes (c) Fig.4.7: Dependence of the axiu output power of the piezoelectric plate on the input voltage and gap thickness between the two parallel brass plate electrodes. The axiu power is for frequency and electric load. 54

78 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure The dependence of the axiu output power of the piezoelectric plate on the input voltage and gap thickness between the two brass plate-shaped live and ground electrodes of the parallel plate capacitor structure is shown in Fig.4.7. The axiu output power is for resonance frequency and optiu electric load resistance of the wirelessly driven piezoelectric plate operating in the thickness ode. It is seen that the axiu output power of the piezoelectric plate achieved wirelessly is inversely proportional with the gap thickness and directly proportional with the input voltage between the live and ground electrodes of the parallel plate capacitor structure. When the input voltage (V in ) increases and gap thickness (d) between the brass plate shaped live and ground electrodes decreases, the average electric field V in d of the parallel plate capacitor structure increases. Hence, the axiu output power of the piezoelectric plate achieved wirelessly increases. Therefore, the axiu output power of the piezoelectric plate can be increased wirelessly by increasing the input voltage (V in ) and by decreasing the gap thickness (d) between the two brass plate-shaped live and ground electrodes of the parallel plate capacitor structure. It is seen that an output power of 0.46 W has been achieved with an optiu load resistance 350 Ω, resonance frequency of 77 khz, input voltage of 150 V rs and gap thickness of 1 c across the live and ground electrodes of parallel plate capacitor structure Effect of electrode pattern on the output power of the PZT plate To study the effect of the electrode pattern on the output power of the piezoelectric plate wirelessly driven by an A.C. electric field, the electrodes on the top and botto surface of the piezoelectric plate are electrically separated 55

79 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure into two sections, P and Q. The electrodes of sections P and Q are isolated by a narrow insulating gap along the width direction of the PZT plate, and the lengths of two electrodes are changeable in this experient. Fig.4.8 shows the configuration of the wirelessly driven piezoelectric plate operating in the thickness ode, which has two electrically separated sections P and Q. A resistance load is connected across the two electrodes of section P of the piezoelectric plate for easuring the real power which section P delivers. The frequency characteristics of the output power at the optiu loads of the piezoelectric plates operating in the thickness vibration ode with different electrode length ratios are depicted in Fig.4.9. It is seen that the output power is axiu at the resonance frequencies of the piezoelectric plates having different electrode length ratios of Q to P, whose values depend on the Q to P electrode length ratio of the piezoelectric plate. When the frequency of the transitted electric field generated by the parallel plate capacitor structure is close to the echanical resonance frequencies of the piezoelectric plates with different electrode length ratios, a axiu echanical vibration can be stiulated in the piezoelectric plates by the converse piezoelectric effect. This axiu echanical vibration generates a axiu voltage across the piezoelectric plates by the piezoelectric effect. Fig.4.8 Configuration of the piezoelectric plate having two separated electrodes. 56

80 Output power at resonance (W) Output power (W) Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure Thickness ode Q:P = 5:1; R L = 1365 Q:P = 3:1; R L = 1000 Q:P = 1:3; R L = 555 Q:P = 1:5; R L = 555 Q:P = 0:1; R L = Fig.4.9: Frequency characteristics of the output power of the piezoelectric plates with different electrode length ratios, operating in the thickness ode Operating frequency (khz) Thickness ode Q:P = 5:1; f r = 78 khz Q:P = 3:1; f r = 780 khz Q:P = 1:3; f r = 777 khz Q:P = 1:5; f r = 773 khz Q:P = 0:1; f r = 77 khz Electrical load (k) Fig.4.10: Dependence of the output power at resonance on the electrical loads and electrode length ratios for the wirelessly driven piezoelectric plates operating in the thickness vibration ode. 57

81 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure Fig.4.10 shows the dependence of the output power at resonance on the electrical loads and electrode length ratios of the wirelessly driven piezoelectric plates, operating in the thickness ode. It can be seen that the output power at resonance reaches the axiu at an optiu load resistance whose value resistance depends on the electrode length ratio of Q to P. For the piezoelectric plate whose electrode length ratio of Q to P is 5:1, the output power at resonance frequency 78 khz reaches the axiu at an optiu load resistance of 1365 Ω, and the axiu output power is 1.84 W. The equivalent circuit of the wirelessly driven piezoelectric plate shown in Fig.4.5 can be used to explain these results. When the electrical load resistance R L is not uch larger than ( C ), the output voltage V increases with R L for a given 1 d A.C. electric field. When R L is uch larger than ( C ), the load branch can 1 d be regarded as an open circuit. In such a case, V is constant and the output power V R L decreases as the electrical load resistance R L increases. The dependence of axiu output power at resonance and the optiu electrical load on the electrode length ratio of the wirelessly driven piezoelectric plates operating in the thickness vibration ode is depicted in Fig It is seen that both the axiu output power at resonance and the optiu electrical load resistance increase as the electrode length ratio of Q to P increases. A high output power of 1.84 W has been achieved for a large electrode length ratio of 5:1. When the electrode length ratio of Q to P increases, the claped capacitance (C d ) of section P decreases. Then, ( C ) increases 1 d with the decrease of C d for a given frequency. This increases the output voltage V. When the change of R L is not very large, the output power increases as the 58

82 Maxiu output power (W) Optiu electrical load () Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure output voltage V increases. Hence the axiu output power at resonance of the wirelessly driven piezoelectric plate with large electrode length ratio is significantly higher than that obtained in other conditions (outside resonance). Furtherore, it has been experientally found that the energy conversion efficiency (the ratio of real power delivered to the electrical load resistor connected across the piezoelectric plate to the real power applied to the parallel plate capacitor structure) depends on the operating frequency, electric load and electric field. An energy conversion efficiency of 0.1% has been achieved by the wirelessly driven piezoelectric plate (electrode length ratio of Q to P is 5:1) operating in the thickness vibration ode at resonance frequency 78 khz, optiu electrical load resistance of 1365 Ω, real input A.C. source power of 1.5 W across the live and ground electrodes of parallel plate capacitor structure, and a 1 c gap thickness between two brass electrodes of the parallel plate capacitor structure Output power Electrical load Electrode length ratio Q to P of the PZT plate Fig.4.11: Dependence of the output power and electrical load on the electrode length ratio at resonance frequency of the piezoelectric plate. 59

83 Chapter 4 Wireless Energy Transission by Parallel Plate Capacitor Structure 4.4. Suary In suary, a ethod of wireless electric energy transission to piezoelectric coponents is proposed here and the output power characteristics of the piezoelectric coponents are investigated experientally. The output power of the piezoelectric plate depends on the operating frequency, electrical load, vibration ode and electrode pattern of the piezoelectric coponent, and the electric field generated by parallel plate capacitor structure. The output power attains the axiu at resonance frequency and an optiu load resistance of the piezoelectric plate. The piezoelectric plate with properly divided electrode has a large output power than the one with whole electrode. The output power at resonance of the piezoelectric plate operating in the thickness vibration ode is significantly higher than that of the plate operating in the other odes, like width and longitudinal vibrations. At the resonance frequency 78 khz, a axiu output power of 1.84 W and an energy conversion efficiency of 0.1% have been achieved wirelessly by the piezoelectric plate operating in the thickness ode, with an optiu load 1365 Ω, 1 c gap thickness of the two brass electrodes, and input A.C. source power of 1.5 W across the live and ground electrodes of the parallel plate capacitor structure. 60

84 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field CHAPTER 5 WIRELESS DRIVE OF PIEZOELECTRIC COMPONENTS BY FOCUSED ELECTRIC FIELD To explore the possibility of enhancing wireless electric energy transission to the piezoelectric coponents and widen the application range of piezoelectric devices, the wireless drive of piezoelectric coponents by focused electric field has been investigated. In the first section of this chapter, a new ethod of wireless drive of piezoelectric coponents by focused electric field is proposed and explored. A botto stainless- steel needle ground electrode is used to focus the A.C. electric field fro a top square brass plate live electrode through a piezoelectric plate placed in between the. The needle ground electrode enables better transission of electric energy. The effects of electrode areas on the output power of the piezoelectric plate are investigated in order to optiize the wireless electric energy transission to the piezoelectric plate. The output power of the piezoelectric plate depends on the operating frequency, electrical load, diensions of the piezoelectric coponent, electric field, distance, and size of the live and ground electrodes of the electric field generator. When the frequency of the A.C. electric field is close to echanical resonance frequency of the piezoelectric plate operating in the thickness vibration ode, the output power reaches the axiu. At the resonant frequency 78 khz, a axiu 61

85 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field output power of W and an energy conversion efficiency of 0.51% have been achieved wirelessly by the piezoelectric plate operating in the thickness ode with a needle ground electrode, optiu electrical load of 1365 Ω, input average power of.1 W fro A.C. source across the live and needle ground electrodes, 1 c electrodes separation, and a live electrode area of 900 c of the focused electric field structure. Theoretically, the electric field pattern is also studied by finite eleent ethod siulation (COMSOL Multiphysics) to elucidate the focusing of electric field by a needle ground electrode with a brass plate live electrode to the piezoelectric coponent placed in between the. Nano-vibration characteristics of a piezoelectric coponent operating in the thickness ode wirelessly driven by focused electric field have been investigated in this work, reported in the thesis in section 5. of this chapter. A echanical resonance vibration is excited in the piezoelectric plate wirelessly driven by an A.C. electric field. Theoretically, it has been found that the vibration displaceent depends on the electric field, operating frequency, electrical load, and diensions of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. The electric field pattern is theoretically calculated to assess it on the surface of the piezoelectric plate wirelessly driven by the focused A.C. electric field produced with the needle structure. It has been observed that the vibration displaceent of the wirelessly driven piezoelectric plate reaches the axiu at resonance frequency, and its agnitude is in the nanoeter range. It is also found that the vibration displaceent in resonance increases with the electrical load resistance, the area of piezoelectric coponent, but is inversely proportional with the thickness of 6

86 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field the piezoelectric plate operating in the thickness vibration ode wirelessly driven by the focused electric field. In section three, an iproved ethod of wireless drive of piezoelectric coponents is experientally investigated by using the electric resonance of a focused electric field generator and an inductor in series, in order to drive high power piezoelectric coponents wirelessly. When the focused electric field generator and the inductor are in series electric resonance, the wireless electric energy transission to the piezoelectric coponent can be enhanced and a relatively large output power can be achieved by the piezoelectric plate wirelessly. Experientally, it has been found that the real output power of the wirelessly driven piezoelectric plate depends on the operating frequency, electrical load, vibration ode of the piezoelectric coponent, distance between the electrodes, and the electric field focused by the needle ground and live electrodes of the focused electric field generator. When the focused electric field generator and inductor are in electric resonance, a axiu output power of W and an energy conversion efficiency of 1.0% have been achieved by the wirelessly driven piezoelectric plate operating in the thickness vibration ode at the resonance frequency of 78 khz, optiu electrical load resistance of 1365 Ω, input source power of 0.1 W (applied to the series of focused electric field structure and inductor), 1 c live and ground electrodes separation, and a live electrode area of 900 c of the focused electric field generator. The output power at resonance of the piezoelectric plate, operating in the thickness vibration ode, is significantly higher than that of the piezoelectric plate operating in the other odes like width and length extensional vibration odes. 63

87 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field 5.1. Wireless Drive of Piezoelectric Coponents by Focused Electric Field Generator Wireless electric energy transission to a piezoelectric plate using a focused A.C. electric field is explored in this work. The A.C. electric field is focused by using a botto stainless-steel needle ground electrode and a top brass square plate live electrode connected to the piezoelectric plate placed in between the. The needle ground electrode enables better transission of the electric energy. The effects of the botto electrode surface area on the output power achieved by the piezoelectric plate are investigated in order to optiize the wireless electric energy transission to the piezoelectric plate Experiental Setup, Operating Conditions and Mechanis To transit a relatively large electric energy to the piezoelectric plate, a focused A.C. electric field generator is used, as shown in Fig.5.1 (a). With a square brass plate live electrode, a stainless steel needle ground electrode is used to focus the A.C. electric field to enhance the electric energy transission to the piezoelectric plate. The needle ground electrode is placed below perpendicular to the live electrode which is suspended above the piezoelectric plate. The piezoelectric plate is placed in between the live and needle ground electrodes. Fig.5.1 (b) shows the configuration of piezoelectric coponent used in the experients. The piezoelectric coponent is ade of PZT ceraic aterial, and poled vertically across its thickness. The top and botto surfaces of the PZT plate are fully covered by silver electrodes. In order to easure the output power, a load R L is connected across the output electrodes of the PZT plate. 64

88 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field (a) (b) Fig.5.1: (a) Experiental setup to drive a piezoelectric plate wirelessly by focused ac electric field; (b) Configuration of the piezoelectric plate wirelessly driven by electric field. The experients are perfored under the following conditions. The piezoelectric plate operates in the thickness vibration ode; the square size 65

89 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field brass plate-shaped live electrode area (A) is 900 c ; the ground electrode is a etal needle whose tip is assued to have zero area; the ediu between the live and ground electrodes is air. Unless otherwise specified, the input A.C. voltage applied to the focused electric field structure is 150 Vrs; the diension of the piezoelectric plate is c 3 ; the piezoelectric plate is placed equidistantly in between the live and needle ground electrodes; the distance (d) between the live and ground electrodes is 1 c. When an A.C. electric field penetrates the piezoelectric plate, a echanical vibration can be excited in the piezoelectric plate by the converse piezoelectric effect. When the frequency of electric field is close to echanical resonance frequency of the piezoelectric plate, a echanical resonance can be excited in the plate. This echanical resonance can generate a relatively large voltage across the output electrodes due to the piezoelectric effect Frequency characteristics of the output power of piezoelectric plate Fig. 5. (a) shows the frequency characteristics of the output power of the wirelessly driven piezoelectric plate operating in the thickness vibration ode placed at the iddle in between the live and needle ground electrodes of focused electric field structure at a distance of 4 fro each electrode. Fig.5. (b) shows the frequency characteristics of the output power of the driven piezoelectric plate, just to the needle ground electrode fro the lower surface of piezoelectric plate. It is observed that at the resonance frequency 77 khz of the wirelessly driven piezoelectric plate operating in the thickness ode, a axiu output power is achieved. 66

90 Output power (W) Output power (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field V in = 70 V rs V in = 150 V rs R L = 350 Area A= 900 c (a) Driving frequency (khz) V in = 70 V rs V in = 150 V rs R L = 350 Area A= 900 c (b) Driving frequency (khz) Fig.5.: Frequency characteristics of the output power of the wirelessly driven piezoelectric plate operating in the thickness ode. (a) Piezoelectric plate placed equidistantly in between live and needle ground electrodes at a distance of 4 fro each electrode; (b) placed to the needle ground electrode. 67

91 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field When the A.C. electric field produced fro focused electric field structure penetrates the piezoelectric plate, a echanical vibration can be excited in the piezoelectric plate by the converse piezoelectric effect. When the frequency of the transitted electric field is close to echanical resonance frequency of the piezoelectric plate, a echanical resonance can be excited in the plate. This echanical resonance generates a voltage across the output electrodes of piezoelectric plate by the piezoelectric effect. Hence the peaks of the output power are only due to the piezoelectric resonance. If the piezoelectric plate is detuned fro the resonance, the output power of the wirelessly driven piezoelectric plate drops suddenly. It is also found that the axiu output power achieved wirelessly by the piezoelectric plate placed at the iddle at a distance of 4 fro each electrode and to the needle ground electrode is.8 W and 3.46 W, respectively. This is because larger electric field is focused fro the live electrode to the piezoelectric plate placed very near to the needle ground electrode, and enhances the output power of piezoelectric plate Effect of live electrode area on the output power of PZT plate The effect of the live electrode surface area on the output power at resonance of the driven piezoelectric plate operating in the thickness ode is shown in Fig.5.3. It is seen that the output power of the wirelessly driven piezoelectric plate increases with the increase of live electrode area (A), when the electrode area is less than 900 c. At larger live electrode area, the output power becoes ore saturated. For larger live electrode area, the electric field near the edge of the live electrode cannot be focused to the needle ground electrode, and the output power becoes saturated. 68

92 Output power at resonance (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field V in = 70 V rs V in = 150 V rs R L = 350 f r = 77 khz Area of live electrode, A (c ) Fig.5.3: Effect of live electrode area on the output power at resonance of the piezoelectric plate operating in the thickness vibration ode Effect of the ground electrode surface area on the output power of piezoelectric plate The effect of ground electrode surface area on the output power at resonance of the wirelessly driven piezoelectric plate operating in the thickness vibration ode is depicted in Fig.5.4. It is observed that the output power of the wirelessly driven piezoelectric plate decreases with the increase of ground electrode area (B). Thus, the needle ground electrode is responsible for focusing the A.C. electric field, and enhancing the electric energy transission wirelessly to the piezoelectric plate operating in the thickness vibration ode placed in between the live and ground electrodes of the focused electric field structure. 69

93 Output power at resonance (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field V in = 70 V rs V in = 150 V rs R L = 350 f r = 77 khz Area A= 900 c Area of ground electrode, B (c ) Fig.5.4: Effect of ground electrode surface area on the output power at resonance of the piezoelectric plate operating in the thickness ode Effect of the distance between the lower surface of the piezoelectric plate and needle ground electrode on the axiu output power Fig.5.5 shows the dependence of axiu output power on the distance between the lower surface of wirelessly driven piezoelectric plate and needle ground electrode of focused electric field structure. The axiu output power occurs at the resonance frequency and optiu load of the piezoelectric plate, operating in the thickness ode. It is seen that the axiu output power achieved wirelessly by the PZT plate increases with the decrease in the distance between the lower surface of the piezoelectric plate and needle ground for a given input ac voltage. This is because the electric field at the piezoelectric plate increases as the piezoelectric plate is oved towards the needle ground electrode, for a given input A.C. source voltage. 70

94 Maxiu output power (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field V in = 150 V rs V in = 70 V rs R L = 350 f r = 77 khz Area A= 900 c Distance between PZT plate and needle ground (c) Fig.5.5: Dependence of the axiu output power on the distance between the lower surface of piezoelectric plate and needle ground electrode. The axiu output power is for frequency and electrical load Effect of the electrical load on the output power of PZT plate The dependence of the output power at resonance on the electrical load for the wirelessly driven piezoelectric plate operating in the thickness vibration ode was experientally investigated and the result are shown in Fig.5.6. It is found that the output power at the resonance reaches axiu at an optiu load resistance. The output power at resonance frequency of 77 khz of the wirelessly driven piezoelectric plate operating in the thickness vibration ode, reaches the axiu at an optiu load of 350 Ω for a needle ground electrode and live electrode area of 900 c. 71

95 Output power at resonance (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field V in = 70 V rs V in = 150 V rs f r = 77 khz Area A= 900 c Electrical load (k) Fig.5.6: Dependence of the output power at resonance on the electrical load for a wirelessly driven piezoelectric plate operated with a focused electric field. i 1:n R C L R L V C d i s Fig.5.7: Equivalent circuit of the piezoelectric plate wirelessly driven by electric field. i s is the current source resulting fro electric field E and V is the output voltage across the load resistance R. L, C and inductance, capacitance and resistance. n is the turn ratio. L R are the Cd is the claped capacitance and 7

96 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field The equivalent circuit of the wirelessly driven piezoelectric plate operating in the thickness vibration ode which is shown in Fig.5.7 can be used to explain this result. When the load resistance R L is not uch larger than ( C ), the 1 d output voltage V increases with the load resistance R L for a given input source current i S, resulting fro the external electric field. When R L is uch larger than ( C ), the load branch can be regarded as open circuit. In this latter 1 d case, V is constant and the output power ( V R L ) decreases as the electrical load R L increases. Hence, there will be an optiu load for which a axiu power can be delivered to the electrical load connected across the output electrodes of the piezoelectric plate wirelessly driven by the focused e- field. When the piezoelectric operates near its resonance, the real power ( P L ) delivered to the electrical load resistor calculated fro the equivalent circuit is P L R n R L C EA d 0 R L R C d RL RLL C 1 L C L 1 C C d RLR. (5.1) A axiu power can be delivered to the electric load, when dp dr L L 0. (5.) Fro equations (5.1) and (5.), we get the following solution of the optiu load resistance for which a axiu power is delivered to the electrical load resistance connected across the output electrodes of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. 73

97 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field R L n 4 C d R 4 R C d L L 1 C d n C L L C C C d n C C d d C L C (5.3) Fro the above solution and the calculated equivalent circuit paraeters listed in Table 3., it is found that the calculated optiu load resistance is 358 Ω, which agrees well with the easured value of 350 Ω of the wirelessly driven piezoelectric plate operating in the thickness vibration ode Analyses of the focused e- field pattern by finite eleent ethod In order to study the electric field pattern around the piezoelectric plate wirelessly driven by focused electric field structure, finite eleent ethod siulation (COMSOL Multiphysics) has been carried out. Here the finite eleent analyses are perfored using the -D in-plane electrostatics application ode of COMSOL Multiphysics. The following steps are taken into consideration to obtain the distribution of the electric field on the surface of the piezoelectric plate wirelessly driven by the focused electric field structure. The first step is to define the overall odel and draw its geoetry. The finite eleent odel presented in this work is based on the geoetry as shown in Fig.5.8. The -D finite eleent odel geoetry consists of an air box ( ) that contains the piezoelectric plate ( ) wirelessly driven by the focused electric field structure fored by a brass plate live electrode ( ) and a stainless steel needle ground electrode whose tip is assued to have zero area. The piezoelectric plate is placed at the iddle of live and needle ground electrodes separated by 1 c. 74

98 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field After defining the odel geoetry, the next task is to define the aterial properties of the calculation doains and the boundaries. The boundaries of the live electrode are defined with an electric potential of 150 Vrs and the needle electrode boundary is defined as ground. The finite eleent calculations are solved using non-unifor esh sizes. The results presented in this work are found to be independent of the esh refineent when the esh consists of at least eleents. After solving the proble, COMSOL Multiphysics shifts to its post processing ode and plots siulated -D electric field pattern around the piezoelectric plate wirelessly driven by the focused electric field structure, as shown in Fig.5.9. It has been observed that the A.C. electric field is focused, by using a needle ground electrode and a plate-shaped live electrode between which the piezoelectric plate is located. The needle ground electrode enables better transission of electric energy wirelessly. Fig.5.8: Geoetry used for -D finite eleent ethod (COMSOL Multiphysics) siulation of electric field pattern around a piezoelectric plate wirelessly driven by focused electric field structure. 75

99 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Fig.5.9: Siulated -D electric field pattern around the piezoelectric plate wirelessly driven by the focused electric field Dependence of the output power on the size of piezoelectric plate The size effect in wireless drive of piezoelectric coponents by focused electric field has also been investigated here in order to drive a high power piezoelectric coponent wirelessly. Fig.5.10 (a) shows the dependence of the easured output power at resonance on the electrical load and area of the wirelessly driven piezoelectric plates, operating in the thickness vibration ode. The effect is studied for the wirelessly driven piezoelectric plates of constant thickness. It can be seen fro Fig.5.10 (a) that the output power at resonance reaches the axiu at an optiu load resistance, and the optiu load resistance depends on the size of the piezoelectric plate. It is also observed that the easured output power at resonance becoes large when the size of piezoelectric plate is reduced. 76

100 Average electric field (x 10 5 V/) Equivalent resistance R (k) Output power at resonance (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Area= 40 ; f r = 78 khz Area= 80 ; f r = 776 khz Area= 160 ; f r = 774 khz Area= 40 ; f r = 77 khz V in = 150 V rs Electrical load (k) (a) Calculated E-field Measured R Area of the piezoelectric plate (c ) (b) Fig.5.10: (a) Dependence of the output power at resonance on the area of PZT plate and electrical load; (b) Effect of calculated average electric field and easured equivalent resistance on the area of PZT plate. 77

101 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field A axiu output power of W has been achieved wirelessly by a sall piezoelectric plate with an area of 40 operating in the thickness vibration ode at the resonant frequency of 78 khz, optiu load of 1365 Ω, input voltage of 150 Vrs across the live and needle ground electrodes, 1 c electrodes separation, and a live electrode area of 900 c of focused electric field structure. The change of output power at resonance with the area of piezoelectric plate is caused by the change of calculated average electric field on the easured area of the piezoelectric plate, and the change of easured equivalent resistance of the piezoelectric plate as shown in Fig.5.10 (b) Energy conversion efficiency characteristics Fig.5.11 shows the frequency dependence energy conversion efficiency characteristics at the optiu electrical load resistance of a sall piezoelectric plate with an area of 40, operating in the thickness vibration ode. The energy conversion efficiency is the ratio of the real power delivered to the electrical load resistor connected across the output electrodes of the piezoelectric plate and the real power applied to the live and needle ground electrodes of focused electric field structure. Experientally, it is found that the energy conversion efficiency depends on the operating frequency, electrical load, electrode size, and distance between the electrodes. An energy conversion efficiency of 0.51% has been achieved wirelessly by a sall piezoelectric plate with an area of 40 operating in the thickness ode at resonance frequency of 78 khz, optiu electrical load resistance of 1365 Ω, real input power of.1 W across the live and needle ground electrodes, 1 c electrodes separation, and a live electrode area of 900 c of the focused e-field structure. 78

102 Energy conversion efficiency (%) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Area of PZT plate = 40 R L = 1365 V in = 150 V rs Driving frequency (khz) Fig.5.11: Frequency dependence energy conversion efficiency characteristics at the optiu load of the piezoelectric plate operating in the thickness vibration ode, wirelessly driven by focused electric field Suary In suary, a ethod of wireless drive of piezoelectric plate by focused electric energy transission is proposed and explored in this work reported by the thesis. A needle ground electrode is used to focus the A.C. electric field and enhances the wireless energy transission. The output power achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode depends on the operating frequency, electrical load resistance, distance between the piezoelectric plate and needle ground electrode, size of the piezoelectric coponent, electric field, and areas of the live and ground electrodes of the 79

103 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field focused electric field structure. The electric field pattern is also theoretically studied by finite eleent ethod siulation (COMSOL Multiphysics) to illustrate the electric field focusing by using a needle ground electrode with a brass plate-shaped live electrode to the piezoelectric coponent placed in between the. When frequency of the A.C. electric field is close to the echanical resonance frequency of the piezoelectric plate operating in the thickness vibration ode the output power reaches the axiu. The output power and energy conversion efficiency of the wirelessly driven piezoelectric plate with saller size are significantly higher than that of the driven piezoelectric plate with larger size. A axiu output power of W and an energy conversion efficiency of 0.51% have been achieved wirelessly by a sall piezoelectric plate with an area of 40 operating in the thickness vibration ode at the resonance frequency of 78 khz, optiu electrical load resistance of 1365 Ω, real input A.C. source power of.1 W across the live and needle ground electrodes, 1 c electrodes separation, and a live electrode area of 900 c of the focused electric field generator. 80

104 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field 5.. Theoretical Analyses of Nano-vibration Characteristics of a Piezoelectric Coponent Wirelessly Driven by Focused Electric Field To widen the application range of piezoelectric devices, several types of wireless drives of piezoelectric coponents have been investigated by the author using a properly designed electric field. It has been observed that the energy in an A.C. electric field can be transitted to a piezoelectric plate. However, the echanical vibration characteristic of the driven piezoelectric coponent has not been studied yet. Therefore, the vibration displaceent characteristic of the wirelessly driven piezoelectric coponent needs to be investigated further. The vibration characteristics of a piezoelectric plate operating in the thickness vibration ode wirelessly driven by focused electric field have been investigated here. A echanical resonance vibration is excited in the piezoelectric plate wirelessly driven by the A.C. electric field produced fro focused electric field structure. The effects of the electric field, operating frequency, electrical load, and diensions of the piezoelectric coponent on the vibration displaceent of the wirelessly driven piezoelectric plate operating in the thickness vibration ode are studied theoretically. The electric field pattern is theoretically calculated to assess the electric field on the surface of the piezoelectric plate. It was noticed that the vibration displaceent reaches the axiu at resonance frequency, and the axiu vibration displaceent of the driven piezoelectric plate is in the nanoeter range. It has also been observed that the vibration displaceent at resonance increases with the 81

105 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field electrical load resistance, the area of piezoelectric plate, and is inversely proportional to the thickness of piezoelectric plate Structure and principle To investigate the echanical vibration characteristics of a wirelessly driven piezoelectric coponent operating in the thickness ode, a focused electric field structure was used as shown in Fig.5.1 (a). With a square size brass plateshaped live electrode, a stainless steel needle ground electrode is used to focus the ac electric field, and enhance the electric energy transission to the piezoelectric plate wirelessly. The needle ground electrode is placed below perpendicular to the live electrode which is suspended above the piezoelectric plate. The piezoelectric plate is placed equidistantly in between the live and needle ground electrodes of the focused electric field structure at a distance of 4 fro each electrode. The optiu live electrode area is c. Fig.5.1 (b) shows the configuration of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. The piezoelectric plate is ade of PZT (supplied by Fuji Ceraic Corporation, Japan) with the diensions of c 3. It is poled vertically across the thickness direction. The PZT plate is fully covered by silver electrode on its top and botto surfaces. The vibration direction and applied electric field are both parallel to the poling direction. A load resistor R L is connected across the two electrodes of the piezoelectric plate to study the effect of the electrical load on the vibration displaceent. When an A.C. electric field penetrates the piezoelectric plate, a echanical vibration can be stiulated in the plate by the converse piezoelectric effect. 8

106 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field When the frequency of the A.C. electric field generated by the focused electric field structure is close to echanical resonance frequency of the piezoelectric plate, a echanical resonance vibration can be excited in the plate. (a) (b) Fig.5.1: (a) Focused electric field structure to drive piezoelectric plate wirelessly; (b) Configuration of a wirelessly driven piezoelectric plate operating in the thickness vibration ode. 83

107 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field The theoretical calculations are perfored under the following conditions. The wirelessly driven piezoelectric plate operates in the thickness vibration ode; the live electrode area is 900 c ; the ground electrode is a etal needle whose tip is assued to be have zero area; the A.C. input source voltage across the focused electric field structure is 150 Vrs; the live and needle ground electrodes separation is 1 c. Unless otherwise specified, the piezoelectric plate is placed equidistantly in between the live and needle ground electrodes Theoretical analyses of electric field by finite eleent ethod The finite eleent ethod (COMSOL Multiphysics) siulation has been carried out for the wirelessly driven piezoelectric plate in order to assess the electric field on the surface of the piezoelectric plate. Fig.5.13: Calculated -D electric field pattern around the piezoelectric plate wirelessly driven by focused electric field structure. 84

108 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Fig.5.13 shows the calculated -D electric field pattern around the piezoelectric plate wirelessly driven by focused electric field structure. The distribution of electric field on the surface of the piezoelectric plate along the x-direction is shown in Fig It is seen that the electric field on the surface of the piezoelectric plate wirelessly driven by focused electric field structure is nonunifor. For a piezoelectric plate with the diensions of c 3, optiu live electrode area of 900 c, 1 c live and needle ground electrodes separation, and an input source voltage of 150 Vrs across the live and needle ground electrodes of focused electric field structure, the average value of the electric field on the surface of the piezoelectric plate is V/, which is used in our calculation. Fig.5.14: Distribution of the electric field on the surface of wirelessly driven piezoelectric plate along the x-direction, x= to x=

109 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Theoretical analyses of vibration displaceent characteristics The one-diensional thickness vibration of a piezoelectric plate with length l and constant cross sectional area A is analyzed here to study the vibration displaceent characteristics of the wirelessly driven piezoelectric coponent operating in the thickness ode. The thickness vibration in the z -direction satisfies the following dynaical equation (Ikeda, 1984): ut ut D c33 (5.4) t z where, u, and c D 33 represent density, displaceent and elastic stiffness constant, respectively. The general solution of the equation (5.4) for thickness vibration ode is u t jt jt A z Bcos ze ue sin (5.5) where A and B are two constants, is the angular resonance frequency, and is the wave nuber in the z -direction, D c 33 (5.6) and the displaceent of the piezoelectric plate is u Asin z Bcos z. (5.7) When the piezoelectric plate works at its resonance frequency, the following displaceent of the piezoelectric plate ay be obtained by substituting (5.7) into the basic electroechanical equations of the ceraic plate. u u 1 u1 u u sin z cos z (5.8) t t sin cos where u 1 and u are the displaceent of the two surfaces at z t t and z, 86

110 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field respectively, and t is the thickness of the piezoelectric plate. As the displaceent at z t and z t has the sae aplitude but opposite direction, we have u u1 u0. (5.9) Then, the displaceent of the piezoelectric plate can be expressed as u0 sin z u (5.10) t sin The vibration displaceent of the piezoelectric plate operating in the thickness vibration ode can be obtained fro the derived equivalent circuit of the wirelessly driven piezoelectric plate as shown in Fig.5.15, in which L, C and R are the inductance, capacitance, and resistance, respectively. n is the turn ratio and C d is the claped capacitance of the wirelessly driven piezoelectric plate. They are given by Ah33 S 33 L, (5.11a) t S 33t 33 C, (5.11b) Ah R L Q (5.11c) C d A S t, (5.11d) 33 Ah33 n. (5.11e) S t 33 where Q is the echanical quality factor. h 33 and S 33 are the piezoelectric 87

111 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field coefficient and iperitivity constant, respectively. The calculated vibration displaceent of the wirelessly driven piezoelectric plate operating in the thickness vibration ode is u 0 R n R L C d ~ 0.5 EAn R 0 C d RL RLL C L L 1 C C d RLR.(5.1) where 0 is the perittivity of the free space. The average electric field on the surface of the wirelessly driven piezoelectric plate is given by l ~ 1 E E( y) dy. (5.13) l l where E(y) is the external non-unifor electric field on surface of piezoelectric plate. The current source resulting fro the external electric field shown in Fig.5.15 is ~ i S j 0 EA. (5.14) The otional current also shown in Fig.5.15 is I n. (5.15) where is the vibration velocity of the wirelessly driven piezoelectric plate. i A I B 1:n R C L R L V A C d i s B v Fig.5.15: Equivalent circuit of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. 88

112 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field The relevant aterial properties of the piezoelectric plate (PZT C-03, coercially available fro Fuji Techno syste, Japan) used in the calculations are listed in Table 5.1. The equivalent circuit paraeters inductance L ), resistance ( R ) and capacitance ( C ) of the piezoelectric plate looking ( fro port BBare listed in Table 5.. Their experiental values are easured by an ipedance analyzer (HP4194A) fro port AA without external electric field. Properties Electroechanical coupling factor Frequency constant (*khz) Relative dielectric constant Piezoelectric coefficient (10-1 C/N) Value k N T d Density (10 3 kg/ 3 ) 7.7 Diensions ( 3 ) t wl 8 30 Table 5.1: Relevant aterial properties of the piezoelectric plate. Paraeters Measured Calculated L (H).39.8 C (pf) R (Ω) 4 47 C d (nf) Table 5.: Equivalent circuit paraeters of the piezoelectric plate. 89

113 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Results and Discussion Fig.5.16 shows the calculated frequency characteristics of vibration displaceent of the wirelessly driven piezoelectric plate operating in the thickness vibration ode when the electrical load resistances are R L = (open circuit), R L =0 (short circuit), and R L = 350 Ω (output power is axiu across the piezoelectric plate). It is found that a relatively large vibration displaceent of 8.40 n has been achieved when the load branch is open circuited. The reason for this phenoenon can be explained by the equivalent circuit of the wirelessly driven piezoelectric plate operating in the thickness ode, as depicted in Fig Fig.5.16: Theoretical frequency characteristics of the vibration displaceent of wirelessly driven piezoelectric plate operating in the thickness ode. 90

114 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field When the load branch is open circuited, the current i through the load resistance R L is zero, resulting a large otional current I n. However, when the load branch is short circuited, all i S passes through the load branch, and thus the otional current I is zero. Hence the vibration displaceent is relatively large when the load branch is open circuited, and the vibration displaceent is zero when the load branch is short circuited. The theoretical electrical load characteristic of the vibration displaceent at resonance of the piezoelectric plate, operating in the thickness vibration ode wirelessly driven by focused electric field is shown in Fig Fig.5.17: Theoretical electric load characteristics of the vibration displaceent at the resonance of the piezoelectric plate wirelessly driven by focused electric field. 91

115 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field It is observed that the vibration displaceent at resonance increases with the electrical load resistance, and reaches a stable value when R L is very large. For a given operating frequency when the electrical load resistance R L increases, the current i through the load resistance R L decreases, and thus the otional current I increases. Hence the vibration displaceent at resonance increases with the electrical load resistance R L. Fig.5.18 shows the effect of the area of the piezoelectric plate on the vibration displaceent at resonance with the constant thickness and electric load resistance of the piezoelectric plate operating in thickness ode wirelessly driven by the focused electric field structure. The effect is studied for a piezoelectric plate thick and with an electrical load resistance R L =. Fig.5.18: Effect of the area on vibration displaceent at resonance of the wirelessly driven piezoelectric plate operating in the thickness ode. 9

116 Average electric field (x 10 5 V/) Equivalent resistance R (k) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Calculated E-field Measured R Area of the piezoelectric plate (c ) Fig.5.19: Effect of the calculated average electric field and easured equivalent resistance on the area of the wirelessly driven piezoelectric plate. It is found that the vibration displaceent at resonance increases with the area of the piezoelectric plate. The theoretical calculation is based on the calculated average electric field and easured equivalent resistance R of the piezoelectric plate as depicted in Fig The change of vibration displaceent at resonance with the area of the wirelessly driven piezoelectric plate is caused by the change of calculated average electric field on the easured area of the piezoelectric plate, and the change of easured equivalent resistance R of the piezoelectric plate. The effect of the thickness on the vibration displaceent at resonance has been 93

117 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field investigated theoretically for a wirelessly driven piezoelectric plate, operating in the thickness vibration ode with constant length, width and electrical load resistance. The effect is studied for a piezoelectric plate of length 30, width 8, and the electrical load resistance R L is. The effect of thickness on the vibration displaceent at resonance is depicted in Fig.5.0, for a wirelessly driven piezoelectric plate of constant area operating in the thickness vibration ode. Theoretically, it is found that the vibration displaceent at resonance decreases with the thickness of piezoelectric plate. This is because the electric field strength at the piezoelectric plate decreases with the thickness of the piezoelectric plate operated in the thickness vibration ode wirelessly driven by focused electric field structure. Fig.5.0: Effect of the thickness on the vibration displaceent at resonance of the piezoelectric plate operating in the thickness ode wirelessly driven by focused electric field. 94

118 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Suary The vibration displaceent characteristics of a piezoelectric plate operating in the thickness vibration ode wirelessly driven by an A.C. electric field produced fro a focused electric field structure have been investigated here theoretically. The electric field pattern is theoretically calculated by finite eleent ethod (COMSOL Multiphysics) to assess the electric field on the surface of the wirelessly driven piezoelectric plate, placed at the iddle inbetween the live and needle ground electrodes of the focused electric field structure. It has been observed that when the electric field produced fro focused electric field structure penetrates the piezoelectric plate, a echanical resonance vibration is excited in the piezoelectric plate. Theoretically, it has been found that the vibration displaceent depends on the electric field, operating frequency, electrical load, and diensions of the driven piezoelectric plate. The vibration displaceent reached a axiu at the resonance frequency, and the axiu vibration displaceent is in the nanoeter range. Theoretically, it is found that at the resonance frequency of khz and electrical load resistance R L =, a axiu vibration displaceent of 8.40 n has been achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode with an input voltage of 150 Vrs across the live and needle ground electrodes, 1 c electrodes separation, and a live electrode area of 900 c of the focused electric field structure. It has been seen that the vibration displaceent at resonance increases with the electrical load resistance, the area of the piezoelectric coponent, and is inversely proportional to the thickness of piezoelectric plate operating in the thickness vibration ode, wirelessly driven by the focused electric field structure. 95

119 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field 5.3. Wireless Drive of Piezoelectric Coponents by Focused Electric Field Structure in Electric Resonance with an Inductor In the earlier proposed wireless energy transission techniques, the output power of wirelessly driven piezoelectric coponent is not high enough. In order to drive a high-power piezoelectric device wirelessly by an electric field and widen the application range of piezoelectric devices, the wireless drive of piezoelectric coponents needs to be investigated further. The wireless drive of piezoelectric coponents is experientally investigated by using the electric resonance of a focused electric field generator and an inductor in series. In this design, an A.C. electric field is focused to a piezoelectric plate placed in between a plate-shaped live and needle ground electrodes which for a focused electric field generator in series with an inductor. The transission of electric energy is enhanced when the focused electric field generator and inductor are in electric resonance. The technique enables a relatively large output power achieved by the piezoelectric plate. The effects of operating frequency, electric load, vibration ode, position and diensions of the piezoelectric plate, on the real output power of the wirelessly driven piezoelectric plate are investigated in order to optiize the wireless electric energy transission to piezoelectric coponents Experiental Setup, conditions and operating echanis To transit a relatively large electric energy to piezoelectric coponents, a 96

120 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field focused electric field generator in series with an inductor is used as shown in Fig.5.1 (a). With an optiu square brass plate-shaped live electrode, a stainless steel needle ground electrode is used to for the focused electric field generator. In the electric field generator, the A.C. electric field is focused to a needle ground electrode fro a plate-shaped live electrode through a piezoelectric plate placed in between the. When the electric field generator and inductor are in electric resonance, the transitted power is increased because of the large voltage across the focused electric field structure. Two piezoelectric plates of different diensions are used in this experient. The upper and lower surfaces of the piezoelectric plates are covered with silver etal electrodes. Both piezoelectric plates are ade of PZT (Fuju C03), and poled vertically across the thickness direction. Piezoelectric charge constant d 33, echanical Q, dissipation factor tanδ, and relative dielectric constant ε T 33 /ε 0 are /V, 000, 0.3 and 1450, respectively. Fig.5.1 (b) shows the configuration of plate A (having the diensions of ) and Fig.5.1 (c) shows the configuration of plate B (size of ), used in these experients. A resistance load is connected across the two electrodes for easuring the real power which the piezoelectric plate delivers. The experients are perfored under the following conditions. The live electrode area is c ; the ground electrode is a etal needle whose tip is assued to have zero area; the inductances (L) have equal values of 1.48 H with piezoelectric plates A and B, respectively, and thus, the electric field generator and inductor are in resonance. Unless otherwise specified, the piezoelectric plate is placed equidistantly at distance of 4 in-between the live and needle ground electrodes positioned perpendicular to each other. The 97

121 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field A.C. input voltage applied to the series of electric field generator and inductor is 150 Vrs, the distance between the live and needle ground electrode is 1 c, and the piezoelectric plates operate in the thickness vibration ode. Table 5.3 shows the easured resonance frequencies, and equivalent circuit paraeters of piezoelectric plates A and B by an ipedance analyzer (HP4194A). (a) (b) (c) Fig.5.1 (a) Experiental setup to drive piezoelectric coponent wirelessly by focused electric field generator in series with an inductor; (b) Configuration of piezoelectric plate-a; (c) Configuration of PZT plate-b. 98

122 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Piezoelectric Resonance Equivalent Equivalent Equivalent Claped plates frequency Resistance Inductance Capacitance Capacitance f r (khz) R (kω) L (H) C (pf) C d (nf) Plate A Plate B Table 5.3: Measured equivalent circuit paraeters of the PZT plates. When the focused electric field electric field generator and inductor are in electric resonance, the current flowing through the electric field generator is very large. Thus, at resonance, a relatively large A.C. electric field can be focused to a needle ground electrode fro the plate-shaped live electrode through a piezoelectric plate placed in between the. When an A.C. electric field penetrates the piezoelectric plate, a echanical vibration can be stiulated in the piezoelectric plate by the converse piezoelectric effect. When the frequency of the A.C. electric field is close to the echanical resonance frequency of the piezoelectric plate, a echanical resonance can be excited in the plate. This echanical resonance can generate a relatively large voltage across the output electrodes due to the piezoelectric effect Frequency characteristics of the output power of piezoelectric plates Fig.5. (a) and 5. (b) show the frequency characteristics of the output power of both piezoelectric plates A and B operating in the thickness vibration ode, placed inside the focused electric field generator. Fig.5. (a) represents the result when the electric field generator is electrically resonant with the inductor. 99

123 Output power (W) Output power (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Fig.5. (b) represents the result without the inductor Thickness ode Plate-A R L = 350 ; L = 1.48 H Plate-B R L = 1365 ; L = 1.44 H (a) Driving frequency (khz) Thickness ode Plate-A R L = 350 Plate-B R L = 1365 (b) Driving frequency (khz) Fig.5.: Frequency characteristics of the output power of the piezoelectric plates A and B at optiu load resistance for: (a) electric field generator with inductor and (b) electric field generator without an inductor. 100

124 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field It is observed that at the resonance frequencies of 77 khz and 78 khz of plates A and B respectively, a axiu output power is achieved. When the frequency of the A.C. electric field is close to the echanical resonance frequency of the plate, a relatively large vibration can be excited in the plate by the converse piezoelectric effect. This echanical resonance generates a relatively large voltage at the output electrodes by the piezoelectric effect. It is also seen that when the electric field generator and inductor are in electrical resonance, the output power of the piezoelectric plate is significantly higher than that of the electric field generator without an inductor. When the electric field generator is in series electric resonance with an inductor, the voltage across the focused electric field structure is five ties greater than the A.C. source voltage. Thus at resonance, a relatively large aount of A.C. electric field can be focused to the needle ground electrode and hence a relatively large electric energy can be transitted to the piezoelectric plate placed in between the live and needle ground electrodes. Therefore, for a given input A.C. voltage, the output power is larger for an electric field generator which is in electric resonance with an inductor Electrical load characteristics of the output power of PZT plates The dependence of the output power at resonance on the electrical load for the piezoelectric plates, operating in the thickness vibration ode is shown in Fig.5.3. It is seen that the output power at resonance reaches the axiu at an optiu load resistance. For plate- B, the output power reaches the axiu at an optiu load resistance of 1365 Ω, and the axiu output power is W. The equivalent circuit of the piezoelectric plate is shown 101

125 Output power at resonance (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field in Fig.5.15, which can be used to explain the optiu load. When the load resistance R L is not uch larger than ( C ), the output voltage V increases 1 d with R L for a given i S. When R L is uch larger than ( C ), the load branch 1 d can be regarded as open circuit. Consequently, V is constant and the output power ( V RL ) decreases as the electrical load R L increases. Fro the equivalent circuit of the wirelessly driven piezoelectric plate, the following solution of the optiu load resistance for which a axiu power is delivered to the electrical load resistance can be obtained. R L n 4 C d R 4 R C d L L 1 C d n C L L C C C d n C C d d C L C (5.16) Fro the above solution and the equivalent circuit paraeters listed in Table 5.3, we found an optiu load resistance of 1358 Ω which agrees well with the easured value of 1365 Ω Thickness ode Plate-B; f r = 78 khz With L = 1.44 H Without L Plate-A; f r = 77 khz With L = 1.48 H Without L Electrical load resistance (k) Fig.5.3: Dependence of the output power at resonance on the electric load. 10

126 Output power (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Effect of vibration odes on the output power of piezoelectric plate The effect of vibration odes on the output power at the optiu load resistance and resonance frequency of the wirelessly driven piezoelectric plate was investigated experientally and the results are shown in Fig.5.4. The output power is easured for the wirelessly driven piezoelectric plate-b when the electric field generator is in electric resonance with an inductor. It is seen that the output power of the wirelessly driven piezoelectric plate operating in the thickness vibration ode is significantly higher than that of the plate operating in the width and length extensional vibration odes. Thus, the vibration ode has an effect on the output power of the piezoelectric plate wirelessly driven by the focused e- field structure in resonance with an inductor. 40 Thickness vibration ode Width extensional vibration ode 1. R L = R L = Length extensional vibration ode R L = Driving frequency (khz) Fig.5.4: Effect of vibration odes on the output power of wirelessly driven piezoelectric plate B when the electric field generator is in electric resonance with the inductor. 103

127 Maxiu output power (W) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Dependence of the distance on the output power at resonance between the live and needle ground electrodes The dependence of the output power at resonance on the distance between the live and needle ground electrodes of the focused electric field generator is shown in Fig.5.5. The output power is easured for piezoelectric plates A and B operating in the thickness vibration ode, when the electric field generator and inductor are in electric resonance. The piezoelectric plate is placed equidistantly in between the live and needle ground electrodes of the focused electric field structure at a distance of 4 fro each electrode. It is seen that the axiu output power increases with the decrease in the distance between the live and needle ground for a given input A.C. voltage Thickness vibration ode Plate A L = 1.48 H R L = 350 ; f r = 77 khz Plate B L = 1.44 H R L = 1365 ; f r = 78 khz Distance between live and needle ground electrodes (c) Fig.5.5: Dependence of the axiu output power on the distance between the live and needle ground electrodes. The axiu output power is for resonant frequency and optiu load of the piezoelectric plate placed equidistantly fro the live and needle ground electrodes. 104

128 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field When the distance between the live and needle ground electrodes of the focused electric field generator is larger than 100 c, the output power of piezoelectric plate is less than 0.004% of that when the distance is 1 c. This is because the electric field at the piezoelectric plate increases as the distance between the live and needle ground electrodes decreases. Hence the output power is inversely proportional to the distance between the live and needle ground for a given input ac voltage for the wirelessly driven piezoelectric plates placed at the iddle of electrodes Energy conversion efficiency characteristics Fig.5.6 shows the frequency dependence energy conversion efficiency (the ratio of the real power delivered to the electrical load resistor connected across the output electrodes of the piezoelectric plate and the real power applied to the series of focused electric field structure and inductor) characteristics at the optiu electrical load resistances of piezoelectric plates A and B, operating in the thickness vibration ode. It is seen that when the electric field generator and inductor are in electric resonance, an energy conversion efficiency of 1.0% has been achieved for the wirelessly driven piezoelectric plate B at the resonance frequency of 78 khz and electrical load resistance of 1365 Ω, which is higher than that of the energy conversion efficiency of 0.7% achieved wirelessly by the piezoelectric plate A at the resonance frequency of 77 khz and electrical load resistance of 350 Ω for a real input power of 0.1 W applied to the series of focused electric field structure and inductor, 1 c live and ground electrodes separation, and a live electrode area of 900 c of the capacitor like electric field generator. 105

129 Energy conversion efficiency (%) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field Thickness ode Plate A ; L = 1.48 H R L = 350 Plate B ; L = 1.44 H R L = Fig.5.6: Frequency dependence energy conversion efficiency characteristics at the optiu load of PZT plates A and B, operating in the thickness vibration ode, when the electric field generator is in electric resonance with the inductor. Driving frequency (khz) The dependence of energy conversion efficiency on the electrical load resistance at resonance frequency of the plate B operating in the thickness vibration ode is depicted in Fig.5.7. This result is obtained when the electric field generator and inductor are in electric resonance for piezoelectric plate B operating in the thickness vibration ode. It is seen that the energy conversion efficiency depends on the electrical load and a axiu efficiency of 1.1% is achieved for piezoelectric plate B at the resonance frequency of 78 khz, electric load resistance of 1450 Ω, real input power of 0.1 W applied to the series of focused electric field structure and inductor, 1 c live and ground 106

130 Energy conversion efficiency (%) Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field electrodes separation, and a live electrode area of 900 c of the capacitor like electric field generator Thickness ode Plate B ; L = 1.44 H f r = 78 khz Electrical load resistance () Fig.5.7: Dependence of energy conversion efficiency on the electrical load resistance at resonance of the piezoelectric plate B operating in the thickness vibration ode Suary In suary, an iproved ethod of wireless drive of piezoelectric coponents is explored by using the electric resonance of a focused electric field generator and an inductor in series. In the focused electric field generator, the A.C. electric field is focused to a needle ground electrode fro the plate-shaped live electrode through a piezoelectric plate placed equidistantly fro the live and 107

131 Chapter 5 Wireless Drive of Piezoelectric Coponents by Focused E-Field needle ground electrodes. When the focused electric field generator and inductor are in electric resonance, the wireless electric energy transission is enhanced. The technique enables a relatively large output power delivered to the piezoelectric plate wirelessly. The output power attains the axiu at resonance frequency of piezoelectric plate, and the plate with sall area has a larger output power than the one with large area. The output power at resonance of the piezoelectric plate, operating in the thickness vibration ode, is significantly higher than that of the plate operating in the other odes like width and length extensional vibration odes. Experientally, it has been found that the real output power of piezoelectric plate depends on the operating frequency, electrical load, vibration ode, diensions of the piezoelectric coponent, distance between the electrodes, and the electric field. When the focused electric field generator and inductor are in electric resonance, a axiu output power of W and energy conversion efficiency of 1.0% have been achieved by the wirelessly driven piezoelectric plate operating in the thickness vibration ode at the resonance frequency of 78 khz, optiu electrical load resistance of 1365 Ω, real input power of 0.1 W (applied to the series of focused electric field structure and inductor), 1 c live and ground electrodes separation, and a live electrode area of 900 c of the focused electric field generator. Methods of increasing the transission power and efficiency will be investigated further both theoretically and experientally. 108

132 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna CHAPTER 6 CHARACTERISTICS OF PIEZOELECTRIC COMPONENTS WIRELESSLY DRIVEN BY ANTENNA-LIKE ELECTRIC FIELD GENERATORS Earlier, new techniques of wireless energy transission to piezoelectric coponents by focused electric field and the electric field generated fro parallel plate capacitor structure were proposed and investigated by the author. It has been observed that the energy in an A.C. electric field can be transitted to a piezoelectric coponent, placed in between the live and ground electrodes of the electric field generator structures. But the structures of the proposed electric field generators constrain the free otion of the wirelessly driven piezoelectric coponents. To solve the above stated proble, new techniques of wireless drives of piezoelectric coponents by antenna-like structures are proposed. In first section of this chapter, wireless drive of piezoelectric coponents by dipole antenna-like electric field generator structure has been proposed, and its characteristics are investigated. Two equal size square brass plate-shaped live and ground electrodes are used to for an electric dipole antenna-like structure 109

133 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna to transit the A.C. electric field wirelessly to the piezoelectric plate. The effects of electrode areas of dipole antenna-like structure, electric field, operating frequency, electric load, and position of the piezoelectric plate on the real output power of the piezoelectric plate are investigated in order to optiize the wireless electric energy transission to the piezoelectric plates. The electric field pattern is calculated by finite eleent ethod to assess the electric field on the surface of the piezoelectric plate wirelessly driven by dipole antenna-like structure. A theoretical odel is also developed for the wirelessly driven piezoelectric plate operating in the thickness vibration ode, which can explain the experiental results well. It has been observed that at resonance frequency and optiu electrical load, the output power achieved wirelessly by the piezoelectric coponent increases with the electrodes area, the electric field, and decreases with the distance of piezoelectric coponent fro the plane of the electrodes of the dipole antenna-like structure. In order to enhance the driving power, the electric dipole antenna-like structure is used in series with an inductor. When the electric dipole antenna-like structure and inductor are in electric resonance, a axiu output power of 1.9 W and energy conversion efficiency of 0.01% have been achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode, placed at the centre 4 away fro antenna plane with an optiu electrical load resistance of 350 Ω, 1 c electrodes separation, 500 c electrode area of electric dipole antenna-like structure, and input source power of W applied to the series of dipole antenna-like structure and inductor. In the second section of this chapter, an iproved copact electric field generator is explored to transit relatively large electric energy wirelessly to a 110

134 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna piezoelectric coponent by using the electric resonance of a flat spiral coil antenna-like structure and a capacitor in series. In the flat spiral coil antennalike electric field generator, the A.C. electric field is transitted wirelessly to the piezoelectric plate placed perpendicular to the plane of antenna. When the spiral coil antenna-like electric field generator and capacitor are in electric resonance, the wireless electric energy transission to the piezoelectric coponent can be enhanced. This technique enables a relatively large output power achieved wirelessly by the piezoelectric coponent. At resonance frequency of 77 khz and optiu electrical load resistance of 350 Ω, a axiu output power of 0.36 W and energy conversion efficiency of 0.07% have been achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode, placed 4 away fro antenna plane with an input ac source power of 1.94 W applied to the series of flat spiral coil antenna-like structure and capacitor, and an inductance of H of the flat spiral coil antenna-like electric field generator Characteristics of Piezoelectric Coponents Wirelessly Driven by an Electric Dipole Antenna-like Structure Wireless electric energy transission to a piezoelectric coponent operating in the thickness vibration ode, by using an electric dipole antenna-like structure is investigated here both theoretically and experientally. The electric field pattern around the wirelessly driven piezoelectric plate is analyzed by finite eleent ethod (COMSOL Multiphysics). The effects of the electrode areas of the dipole antenna-like structure, as well as of the electric field, operating 111

135 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna frequency, electric load, and position of the piezoelectric plate on the real output power of the wirelessly driven piezoelectric plate are investigated in order to optiize the wireless electric energy transission to the piezoelectric plate by using dipole antenna-like structure Structure and principle To transit electric energy to a piezoelectric plate wirelessly, an electric dipole antenna-like electric field generator is used as shown in Fig.6.1. The square size brass plate-shaped live and ground electrodes are used to for a dipole antennalike structure to transit ac electric field to the piezoelectric plate. An A.C. input source voltage is connected to the live and ground electrodes of the electric dipole antenna-like structure. The piezoelectric plate is placed in a plane perpendicular to the electrodes and equidistant fro the live and ground electrodes of the dipole antenna-like structure. Fig.6.1: Experiental setup to drive piezoelectric plate wirelessly by an electric dipole antenna-like structure. 11

136 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna Fig.6. illustrates the configuration of piezoelectric plate operating in the thickness ode wirelessly driven by an electric dipole antenna-like structure. The piezoelectric plate is ade of PZT aterial, and poled vertically across the thickness direction. The vibration direction and electric field generated by the electric dipole antenna-like structure, both are parallel to the poling direction of the PZT plate. A load resistor R L is connected across the output electrodes of piezoelectric plate for easuring the real output power which the piezoelectric plate delivers. When an A.C. electric field generated by the electric dipole antenna-like structure penetrates the piezoelectric plate placed at the center away fro antenna plane, a echanical vibration can be stiulated in the piezoelectric plate by the converse piezoelectric effect. When the operating frequency of the A.C. electric field is close to the echanical resonance frequency of the piezoelectric plate, a echanical resonance can be excited in the piezoelectric plate. This echanical resonance can generate a voltage across the output electrodes due to the piezoelectric effect. Fig.6.: Configuration of the piezoelectric plate wirelessly driven by an electric dipole antenna-like electric field generator. 113

137 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna The theoretical and experiental studies are perfored under the following conditions. The wirelessly driven piezoelectric plate operates in the thickness vibration ode; the square size brass plate-shaped live and ground electrodes of the dipole antenna-like structure have the sae area 500 c ; the distance between the live and ground electrodes of the antenna-like structure is 1 c; the input A.C. source voltage is 150 Vrs. Unless otherwise specified, the diensions of the piezoelectric plate is c 3, the piezoelectric plate is placed at the center, 4 away fro the antenna plane, and the area of each electrode of the dipole antenna-like electric field generator is 500 c Theoretical analyses of electric field by FEM In order to assess the electric field on the surface of the piezoelectric plate wirelessly driven by dipole antenna-like structure, finite eleent ethod (COMSOL Multiphysics) D in-plane electrostatic siulations have been carried out. The following steps were taken into consideration to obtain the distribution of electric field on the surface of the piezoelectric plate wirelessly driven by the dipole antenna-like structure. The first step is to define the overall odel and draw its geoetry. The finite eleent odel presented in this work is based on the geoetry shown in Fig.6.3. The D finite eleent odel geoetry consists of an air box ( ) that contains the piezoelectric plate ( ) wirelessly driven by dipole antenna-like structure fored by brass plate-shaped live and ground electrodes of the sae area ( ). The piezoelectric plate is placed at the center away fro the electrode plane of dipole antennalike structure. After defining the odel geoetry, the next task is to define the 114

138 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna aterial properties of the calculation doains and the boundaries. The boundaries of the live electrode are defined with an electric potential of 150 Vrs and the other electrode boundary is defined as ground. The finite eleent calculations are solved using non-unifor esh sizes. The results presented in this work are found to be independent of the esh refineent when the esh consists of at least eleents. After solving the proble, COMSOL Multiphysics shifts to its post processing ode and shows the plot of the strealine electric field. Fig.6.4 shows the calculated D electric field pattern around the wirelessly driven piezoelectric plate by an electric dipole antennalike structure. Fig.6.3: Geoetry used for D finite eleent odel of electric field analysis of the piezoelectric plate wirelessly driven by the dipole antenna-like structure. 115

139 Electric field (V/) Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna Fig.6.4: Siulated D electric field pattern around the piezoelectric plate wirelessly driven by dipole antenna-like structure. 6x10 3 4x10 3 x x() Fig.6.5: Distribution of the electric field on the surface of wirelessly driven piezoelectric plate along the x-direction, x= to x=

140 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna The electric field distribution on the surface of the piezoelectric plate along the x-direction is shown in Fig.6.5. It is seen that the electric field on the surface of the wirelessly driven piezoelectric plate is non-unifor. For a 500 c electrode area of the dipole antenna-like structure and input source voltage of 150 Vrs, the average value of the electric field on the surface of the piezoelectric plate is V/, which is used in our calculation Equivalent circuit odel To understand the operating echanis and investigate the characteristics, an equivalent circuit odel is developed for the piezoelectric plate operating in the thickness vibration ode, wirelessly driven by an A.C. electric field generated fro the electric dipole antenna-like structure. Fro the basic piezoelectric constitutive equations (Ikeda, 1984), the electric displaceent of the piezoelectric plate operating in the thickness vibration ode is V h33 D ( u0 ). (6.1) S S t t where h33and S 33 are the piezoelectric coefficient and iperitivity constant, respectively, t is the thickness and u0 is the displaceent at the electrode surface of the piezoelectric plate. A voltage V appears across the piezoelectric plate because of the external electric field. FEM analysis results show that the electric field on the surface of the piezoelectric plate is non-unifor, as depicted in Fig.6.5. Hence, the current flowing through the piezoelectric plate 117

141 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna can be obtained as: i w w j l ( x) dx (6.) where (x) is surface charge density, l is length and w is the width of the driven piezoelectric plate. According to Gauss s law, the charge on the surface electrode of the piezoelectric plate is ( x) D 0E( x) (6.3) where 0 is the perittivity of free space and E (x) is the external non-unifor electric field on the surface of driven piezoelectric plate. Fro Eqs. (6.1) to (6.3), the current flowing to the piezoelectric plate with an electrode area A can be obtained as: ~ i j VCd nu E ) (6.4) ( 0 0 A where w ~ 1 E E( x) dx ; (6.4a) w w claped capacitance C d A S t ; (6.4b) 33 Ah33 turn ratio n. (6.4c) S t 33 The derived equivalent circuit of the piezoelectric plate operating in the thickness vibration ode wirelessly driven by an A.C. electric field generated fro dipole antenna-like structure is shown in Fig.6.6. The inductance, capacitance and resistance of the loop on the right hand side of the equivalent circuit are given by: 118

142 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna Ah L t, (6.5) 33 S 33 t C, (6.6) Ah S R L Q (6.7) where Q is the echanical quality factor of the piezoelectric plate. i A B 1:n R C L R L V A C d i s B Fig.6.6: Equivalent circuit of the piezoelectric plate wirelessly driven by an A.C. electric field generated fro dipole antenna-like structure. When the piezoelectric plate operates near its resonance, the real power delivered to the electrical load resistor can be obtained fro the equivalent circuit P L R n R L ~ ( EA) C 0 d RL R Cd RL RLL C 1 L C L 1 C C d RLR. (6.8) Eq. (6.8) shows that the output power of the piezoelectric plate is a function of the electric field, operating frequency, electric load, size, and aterial properties of the piezoelectric plate. The aterial properties of the piezoelectric plate used in our calculation and experients are listed in Table 6.1. The circuit 119

143 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna paraeters of the piezoelectric plate are calculated by Eqs. (6.4b), (6.5), (6.6), (6.7), and the aterial constants listed in Table 6.1. Properties Electroechanical coupling factor Frequency constants (*khz) k 33 k t N 33 N t Value Relative dielectric constants Piezoelectric coefficients (10-1 C/N) 33 T d Density (10 3 kg/ 3 ) 7.7 Diensions ( 3 ) t wl 8 30 Table 6.1 Relevant aterial properties of the used PZT plate. The calculated and easured equivalent circuit paraeters are shown in Table 6.. L, C and R are the equivalent inductance, capacitance and resistance of the piezoelectric plate looking fro port BB as shown in Fig.6.6. The equivalent circuit paraeters of the piezoelectric plate were easured by an ipedance analyzer (HP4194A) fro port AA. 10

144 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna Paraeters Measured Calculated L (H).39.8 C (pf) R (Ω) 4 47 C d (nf) Table 6.: Equivalent circuit paraeters of the used PZT plate Results and discussion Electrical load characteristics of the driven piezoelectric plate Fig.6.7 shows the theoretical and experiental dependence of the output power on the electrical load at the resonance frequency of the piezoelectric plate. It can be seen that, after a short and rapid increase to the peak power, the output power rapidly decreases with the load resistance. It is seen that the theoretical result agrees well with the experiental one, and the output power at resonance reaches the axiu at an optiu load resistance of 350 Ω. Additionally, the resonance frequency decreases slightly as the load resistance increases, but reains around 77 khz. 11

145 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna Fig.6.7: Theoretical and experiental dependence of the output power on the load resistance at the resonance frequency of the piezoelectric plate. The optiu load resistance can be explained by the equivalent circuit of piezoelectric plate operating in the thickness ode, as shown in Fig.6.6. A axiu power can be delivered to the electric load resistor, when dp dr L L 0. (6.9) Using eqs. (6-8) and (6-9), we get the following solution of the optiu load resistance for which a axiu power is delivered to the load resistor connected across the output electrodes of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. 1

146 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna 13 d d d d d d L C L C C C n C C L C n L C R C n C L C L R R (6.10) Using the above solution and the equivalent circuit paraeters in Table 6., we found an optiu load resistance of 358 Ω for the wirelessly driven piezoelectric plate operating in the thickness ode, which agrees well with the easured value of 350 Ω Frequency characteristics of the output power of PZT plate The theoretical and experiental frequency characteristics of the output power of the driven piezoelectric plate operating in the thickness ode are depicted in Fig.6.8. Fig.6.8: Theoretical and experiental frequency characteristics of the output power of the wirelessly driven piezoelectric plate.

147 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna It can be seen that the theoretical results agree quite well with the experiental results, and the output power of the piezoelectric plate reaches the axiu at its resonance frequency. When the frequency of the transitted electric field generated by the dipole antenna-like structure is equal to the echanical resonance frequency of the piezoelectric plate, a axiu echanical vibration can be stiulated in the piezoelectric plate by the converse piezoelectric effect. This axiu echanical vibration generates a axiu voltage across the piezoelectric plate by the piezoelectric effect. Hence the output power peaks only due to the piezoelectric resonance. The error in the calculated axiu output power and the frequency at which the axiu output power occurs ay be due to the errors of the aterial constants used in the theoretical calculation Effect of electrode area of dipole antenna-like structure The effect of the electrode area of the dipole antenna-like electric field generator on the output power at the optiu load and resonance frequency of the driven piezoelectric plate has been investigated, and is shown in Fig.6.9. It can be seen that the theoretical result agrees well with the experiental one. It was observed that the output power at resonance frequency and optiu load resistance of the piezoelectric plate increases with the increase of electrode area of the dipole antenna-like structure for a given input source voltage. Finite eleent ethod siulations showed that the electric field at the piezoelectric plate, and hence, the output power at the resonance frequency, increase with the electrode area of the dipole antenna-like structure for a given input voltage, as depicted in Fig

148 Output power at resonance (W) Average electric field (V/) Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna 60 6x x Electrode area of dipole antenna (c ) Fig.6.9: Effect of the electrode area of the dipole antenna-like structure on the output power at resonance frequency and optiu load resistance of the piezoelectric plate. Theoretical Experiental R L =350 V in =150 V rs Calculated average E-field x Dependence of the output power on the distance of piezoelectric plate fro electrode plane of the dipole antenna-like structure The theoretical and experiental dependence of the output power at resonance on the distance of the piezoelectric plate fro the electrode plane of the dipole antenna-like structure is shown in Fig It is found that the output power at resonance decreases with the increase of the distance of the piezoelectric plate fro the electrode plane of the dipole antenna-like structure for a given input A.C. voltage of 150 V rs across the electrodes. When the distance between the piezoelectric plate and the electrode plane of the dipole antenna like structure is larger than 60 c, the output power of piezoelectric plate is less than 0.006% of 15

149 Output power at resonance (µw) Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna that when the distance is 4. This is because the electric field at the piezoelectric plate decreases as the plate is oved away fro the electrode plane of the dipole antenna-like structure. Both the nonlinear and linear curve fitting approach has been carried out to investigate the characteristics of the easured output power at resonance and distance of the piezoelectric plate fro the electrode plane of dipole antenna-like structure, as depicted in Fig. 6.11(a). The output power is considered as quadratic polynoial that describes the nonlinear output power-distance characteristics of the piezoelectric plate Theoretical Experiental R L =350 V in =150 V rs Distance of PZT plate fro antenna plane () Fig.6.10: Theoretical and experiental dependence of the output power at resonance on the distance of piezoelectric plate fro the electrode plane of the dipole antenna-like structure. 16

150 Residuals Output power at resonance ( W ) Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna y = *x + 54 y = 0.01*x - 1.1*x + 56 Experiental Data Linear Quadratic Distance of PZT plate fro antenna plane () (a) 1 Linear: nor of residuals =.0746 Quadratic: nor of residuals = linear quadratic Distance of PZT plate fro antenna plane () (b) Fig.6-11: (a) Curve fitting with the experiental dependence of the output power on the distance of piezoelectric plate fro the electrode plane of the dipole antenna-like structure; (b) Residuals of linear and non-linear curve fit. 17

151 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna It is seen fro Fig.6-11(b) that the residual of the nonlinear curve fitting is 0.55% and linear curve fitting is.07%. It is found that the quadratic curve fit ore accurately with experiental results and the output power- distance characteristic is nonlinear. But for saller distance of the piezoelectric plate fro the antenna plane, the output power-distance characteristic is alost linear. Also, the residual of the linear curve fitting is only %, which is norally acceptable. Thus it can be assued that the experiental results agree with the theoretical ones. The sall discrepancy between the non-linear dependence of the easured data and the linear dependence of theoretical results ay be due to the easureent error and power loss across the load resistor connected to the output electrodes of the piezoelectric plate Enhanceent in the driving power of piezoelectric plate In order to increase the driving power, the electric dipole antenna-like structure in series with an inductor is used as shown in Fig.6.1. When the electric dipole antenna-like structure and inductor are in electric resonance, the voltage across the dipole antenna-like structure is nearly five ties greater than the A.C. source voltage. For an input source voltage of 150 Vrs, the voltage across the live and ground electrodes of dipole antenna-like structure is around 70 Vrs. Thus, at series resonance of the electric dipole antenna-like structure with an inductor, a relatively large electric energy can be transitted to the piezoelectric plate. When large electric field is transitted, the voltage across the piezoelectric plate becoes large. If the frequency of the electric field is close to echanical resonance frequency of the piezoelectric plate, a echanical resonance can be excited due to the converse piezoelectric effect. This 18

152 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna echanical resonance can generate a large voltage across the output electrodes due to direct piezoelectric effect. With the increase of the voltage, the current across the piezoelectric plate at resonance increases. Hence larger output power resulted with an increased voltage applied across the piezoelectric plate only due to piezoelectric resonance. Fig.6.13 shows the frequency characteristics of the output power of the piezoelectric plate when the electric dipole antenna-like structure is electrically resonant with an inductor of 1.1 H, and without inductor. It is observed that at resonance frequency 77 khz, optiu load resistance 350 Ω of the piezoelectric plate, and an input A.C. source power of W, a axiu output power of 1.9 W has been achieved for the electric resonance of dipole antenna-like structure and inductor in series. Also, the output power for the dipole antenna-like structure which is in electric resonance with an inductor is larger than that of without inductor Live electrode Piezoelectric Plate Electric Load R L Ground electrode Fig.6.1: Experiental setup to increase the driving power of the wirelessly driven piezoelectric plate by cascading an inductor in series with the dipole antenna-like structure. 19

153 Output power (W) Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna Thickness ode With L= 1.1 H Without L R L = 350 V in = 150 V rs Operating frequency (khz) Fig.6.13: Frequency characteristics of the output power of PZT plate when the dipole antenna-like structure is in electric resonance with an inductor. Furtherore, experientally it has been found that the energy conversion efficiency (the ratio of real power delivered to electrical load resistor connected to the PZT plate and real power applied to the series of dipole antenna-like structure and inductor) depends on the operating frequency, electric load, electrode area, and distance of the piezoelectric plate fro the electrode plane of dipole antenna-like structure. A axiu energy conversion efficiency of 0.01% has been achieved wirelessly by the piezoelectric plate operating at resonance in the thickness vibration ode, placed 4 away fro the electrode plane of the dipole antenna-like structure with an optiu electrical load resistance of 350 Ω, 1 c antenna electrodes separation, 500 c electrode area of electric dipole antenna-like structure, and an input A.C. source power of W applied to the dipole antenna-like structure connected in series with an inductor (L=1.1 H). 130

154 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna Suary Wireless drive of piezoelectric coponents by a dipole antenna-like structure is proposed here, and its characteristics are investigated both theoretically and experientally. The real output power of the piezoelectric plate depends on the operating frequency, electrical load, electrode area of the antenna, and position of the piezoelectric plate. The electric field pattern is studied by finite eleent ethod to assess the electric field on the surface of the piezoelectric plate. A theoretical odel is also developed to investigate the characteristics of wirelessly driven piezoelectric plate operating in the thickness ode. The theoretical results agree well with the experiental results. At resonance frequency and optiu electrical load, the output power achieved wirelessly by the piezoelectric coponent increases with the electrode area of dipole antenna, and decreases with the distance of piezoelectric coponent fro the antenna plane. In order to enhance the driving power, the electric dipole antenna-like structure was used in series with an inductor. When the electric dipole antennalike structure and the inductor are in electric resonance, a axiu output power of 1.9 W and energy conversion efficiency of 0.01% have been achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode, placed at the centre 4 away fro antenna plane with an optiu electrical load resistance of 350 Ω, at a resonance frequency of 77 khz, 1 c electrodes separation, 500 c electrode area of electric dipole antenna-like structure, and input A.C. source power of W applied to the series of dipole antenna-like structure and inductor. This technique provides a ethod of driving wirelessly icro piezoelectric devices in rotary achine such as piezoelectric icroactuators and icrootors. 131

155 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna 6.. Wireless Energy Transission to Piezoelectric Coponents by Flat Spiral Coil Antenna-like Structure in Electric Resonance with a Capacitor An iproved copact electric field generator is proposed to transit relatively large electric energy wirelessly to piezoelectric coponents by using the electric resonance of a flat spiral coil antenna-like structure and a capacitor in series. In the flat spiral coil antenna-like electric field generator, the A.C. electric field is transitted wirelessly to the piezoelectric plate placed in a plane perpendicular to the plane of antenna. When the spiral coil antenna-like electric field generator and capacitor are in electric resonance, the wireless electric energy transission to the piezoelectric coponent can be enhanced. This technique enables a relatively large output power achieved wirelessly by the piezoelectric coponent Structure and principle To transit a relatively large electric energy to a piezoelectric plate wirelessly, a flat spiral coil antenna-like electric field generator in series with a capacitor is used as shown in Fig.6.14 (a). An A.C. input source with tunable frequency is connected to the series of flat spiral coil antenna-like electric field generator and capacitor. In the flat spiral coil antenna-like electric field generator, the coil windings are wound to for a circle of radius 5 c. The piezoelectric plate is placed perpendicular to the plane of spiral coil antenna-like electric field generator, at a distance away fro the centre of the spiral coil. When the spiral coil antenna-like electric field generator and capacitor are in electric resonance, 13

156 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna the wireless electric energy transission to the piezoelectric coponent is enhanced because of the large current across the antenna. (a) (b) Fig.6.14: (a) Experiental setup to drive piezoelectric plate wirelessly by using a flat spiral coil antenna-like electric field generator in electric resonance with a capacitor. (b) Configuration of the wirelessly driven PZT plate. 133

157 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna Fig.6.14 (b) illustrates the configuration of the wirelessly driven piezoelectric plate operating in the thickness vibration ode. The piezoelectric plate is ade of PZT ceraic aterial (supplied by Fuji Ceraic Corporation, Japan). It is poled vertically across the thickness direction. The Piezoelectric charge constant d 33, echanical Q, dissipation factor tanδ, and relative dielectric constant ε 33 T /ε 0 are /V, 000, 0.3 and 1450, respectively. The vibration direction and applied electric field both are parallel to the poling direction. A load resistor R L is connected across the two electrodes for easuring the real power which the piezoelectric plate delivers. When the flat spiral coil antenna-like electric field generator and capacitor are in electric resonance, the current flowing through the electric field generator is very large. Thus at resonance, a relatively large A.C. electric field can be transitted to the piezoelectric plate placed in a plane perpendicular to the plane of antenna. When an A.C. electric field penetrates the piezoelectric plate, a echanical vibration can be stiulated in the piezoelectric plate by the converse piezoelectric effect. When the frequency of the A.C. electric field is close to the echanical resonance frequency of the piezoelectric plate, a echanical resonance can be excited in the plate. This echanical resonance can generate a relatively large voltage across the output electrodes due to the piezoelectric effect. The experients were perfored under the following conditions. The diension of piezoelectric plate used in the experient is c 3, and it operated in the thickness vibration ode. In the flat spiral coil antenna- 134

158 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna like electric field generator, the coil windings are wound to for a circle of radius 5 c, and the easured inductance of the spiral coil is H. Thus, the spiral coil antenna-like electric field generator is in electric resonance with a capacitor of 1.09 nf for the wirelessly driven piezoelectric plate operating in the thickness vibration ode. Unless otherwise specified, the piezoelectric plate is placed at the centre 4 away fro the plane of spiral coil antenna-like electric field generator and input ac source voltage is 10 Vrs Experiental results and discussion Fig.6.15 shows the frequency characteristics of the output power of piezoelectric plate operating in the thickness vibration ode, placed in a plane perpendicular to the spiral coil antenna-like electric field generator. It represents the result when the electric field generator is electrically resonant with, and without the capacitor. It is observed that at the resonance frequency of 77 khz, the output power of the piezoelectric plate attains the axiu. If the piezoelectric plate is detuned fro the resonance, the output power of the plate drops suddenly. When the frequency of the A.C. electric field is close to echanical resonance frequency of the plate, a relatively large vibration can be excited in the plate by the converse piezoelectric effect. This echanical resonance generates a relatively large voltage at the output electrodes by the piezoelectric effect. It is also seen that when the electric field generator and capacitor are in electrical resonance, the output power of the piezoelectric plate is significantly higher than that of the electric field generator without a capacitor in series. When the electric field generator is in series electric resonance with a capacitor, the current across the spiral coil antenna-like 135

159 Output power (W) Output power (W) Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna structure is eight ties greater than that without a capacitor in series. Thus at resonance, a relatively large aount of A.C. electric field can be transitted to the piezoelectric plate placed away fro the centre of spiral coil electric field generator. Therefore, for a given input A.C. voltage, the output power is larger for an electric field generator which is in electric resonance with a capacitor Thickness ode With C= 1.09 nf Without Capacitor R L = Operating frequency (khz) Fig.6.15: Frequency characteristics of the output power of the piezoelectric plate at the optiu load resistance for spiral coil antenna-like electric field generator in electric resonance with, and without capacitor. The dependence of the output power at resonance on the electrical load for the wirelessly driven piezoelectric plate, operating in the thickness vibration ode is shown in Fig It can be seen that the output power at resonance reaches the axiu at an optiu load resistance. The output power at resonance frequency of 77 khz reaches the axiu at an optiu load resistance of 350 Ω, and the axiu output power is 0.36 W. The optiu load 136

160 Output power (W) Output power (W) Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna resistance can be explained by the equivalent circuit of piezoelectric plate operating in the thickness ode, as shown in Fig.6.6. It was found that the calculated optiu load resistance is 358 Ω for the wirelessly driven piezoelectric plate operating in the thickness ode, which agrees well with the easured value of 350 Ω Thickness ode With C = 1.09 nf Without Capacitor f r = 77 khz Electrical load resistance (k) 0.00 Fig.6.16: Dependence of the output power on the electrical load at the resonance frequency of the piezoelectric plate for a spiral coil antenna-like electric field generator in resonance with, and without capacitor. The experiental dependence of the output power at resonance on the distance of the piezoelectric plate fro the plane along the central axis of spiral coil antenna-like structure is shown in Fig The output power is easured for the piezoelectric plate operating in the thickness vibration ode, when the spiral coil antenna-like electric field generator and capacitor are in series electric resonance. It is found that the output power at resonance frequency and optiu load resistance of the piezoelectric plate decreases with the distance of 137

161 Output power at resonance (W) Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna the piezoelectric plate fro the plane along the central axis of spiral coil antenna-like electric field generator for a given input A.C. power. When the distance between the piezoelectric plate and spiral coil antenna is larger than 0 c, the output power of the piezoelectric plate is less than 0.09% of that when the distance is 4. This is because the electric field at the piezoelectric plate decreases as the plate is oved away fro the plane of antenna Thickness ode V in = 10 V rs V in = 5 V rs f r = 77 khz R L = 350 C= 1.09 nf Distance of PZT plate fro antenna plane (c) Fig.6.17: Dependence of the output power at the resonance frequency on the distance of the piezoelectric plate fro the plane of spiral coil antennalike electric field generator along the central axis. Furtherore, it has been experientally found that the energy conversion efficiency (the ratio of real power delivered to electrical load resistor, and the real power applied to the series of spiral coil antenna-like electric field generator and capacitor) depends on the operating frequency, electric load, and 138

162 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna distance of the piezoelectric plate fro the plane of spiral coil antenna-like electric field generator. A axiu energy conversion efficiency of 0.07% has been achieved by the piezoelectric plate operating in the thickness vibration ode at the resonance frequency of 77 khz, optiu electrical load resistance of 350 Ω, 4 distance of piezoelectric fro the antenna plane along the central axis of spiral coil, an input ac source power of 1.94 W, and an inductance of H of the flat spiral coil antenna-like generator Suary An iproved copact electric field generator is explored to transit wirelessly relatively large electric energy to a piezoelectric coponent by using the electric resonance of a flat spiral coil antenna-like structure in series with a capacitor. In the flat spiral coil antenna-like electric field generator, the A.C. electric field is transitted wirelessly to the piezoelectric plate placed in a plane perpendicular to the plane of antenna along the central axis of spiral coil. When the spiral coil antenna-like electric field generator and capacitor are in electric resonance, the wireless electric energy transission to the piezoelectric coponent is enhanced. This technique enables a relatively large output power achieved wirelessly by the piezoelectric coponent. At resonance frequency of 77 khz and optiu electrical load resistance of 350 Ω, a axiu output power of 0.36 W and an energy conversion efficiency of 0.07% have been achieved wirelessly by the piezoelectric plate operating in the thickness vibration ode, placed 4 away fro antenna plane, with an input A.C. source power of 1.94 W applied to the series of flat spiral coil antenna-like structure and capacitor, and an inductance of H of the flat spiral coil 139

163 Chapter 6 Wireless Drive of Piezoelectric Coponents by Dipole Antenna antenna-like electric field generator. At the resonance frequency and optiu electrical load, the output power achieved wirelessly by the piezoelectric coponent decrease with the distance of the piezoelectric coponent fro the plane of spiral coil antenna-like electric field generator. This technique provides a copact and flexible ethod of driving wirelessly icro piezoelectric devices in rotary achine and in huan body. 140

164 Coparative Study of All Proposed Wireless Techniques 6.3. Coparative Study of All Proposed Wireless Techniques (a) Parallel plate capacitor structure (b) Focused E-field generator Live electrode Ground electrode Piezoelectric Plate (c) Focused electric field structure in resonance with an inductor (d) Dipole antenna-like structure in resonance with an inductor (e) Flat spiral coil antenna-like structure in resonance with a capacitor Fig.6.18: Proposed E-field generators to drive piezoelectric coponent wirelessly. 141

165 Coparative Study of All Proposed Wireless Techniques A coparative study of all the proposed and investigated wireless energy transission techniques has been conducted. The investigated techniques include wireless drive of piezoelectric coponents by parallel plate capacitor structure, focused electric field generator, focused electric field structure in electric resonance with an inductor, dipole antenna-like structure in resonance with inductor, and a flat spiral coil antenna-like electric field generator in resonance with a capacitor, as shown in Fig For coparison, the experients of all the proposed wireless drive techniques are perfored under the following conditions. The piezoelectric coponent is ade of the Fuji C-03 PZT ceraic aterial, and is poled vertically across its thickness. The thickness vibration direction and applied electric field are both parallel to the poling direction. The diension of the PZT plate is ; the piezoelectric plate operates in the thickness vibration ode; the resonant frequency is 78 khz; the optiu load resistance is 1365 Ω; the distance of the piezoelectric plate fro both the live and ground electrode is 4 ; the input A.C. source voltage is 150 Vrs. The proposed wireless drive techniques are copared and suarized in Table 6.3. The energy conversion efficiency of the piezoelectric plate wirelessly driven by parallel plate capacitor structure, focused electric field generator, focused electric field structure in electric resonance with an inductor, dipole antennalike structure in electric resonance with an inductor, and flat spiral coil antennalike electric field generator in electric resonance with a capacitor is shown in Fig It has been found that the energy conversion efficiency of the 14

166 Coparative Study of All Proposed Wireless Techniques piezoelectric coponent wirelessly driven by focused electric field structure in electric resonance with an inductor is significantly higher than that of any other ethods. Fig.6.19: The energy conversion efficiency of the various wireless drive ethods. 143

167 Coparative Study of All Proposed Wireless Techniques Wireless drive Input A.C. Output Efficiency Rearks techniques source power of (%) power PZT (Advantages/unique (W) plate features) (W) Parallel plate Feasible to drive low capacitor structure power actuators. piezoelectric Focused electric field structure Effective to drive relatively large power icro and nano piezoelectric devices. Focused electric field structure in Higher output power and efficiency than the other resonance an inductor with proposed wireless drive techniques. Dipole antennalike structure in Enable free otion of PZT coponent and effective to resonance an inductor Spiral antenna with coil in drive icro actuators in rotary achine This solution is ore copact, light weight, and resonant with a capacitor robust for free otion of the PZT coponents. Table 6.3: Coparison of all the proposed wireless drive techniques. 144

168 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage CHAPTER 7 MERGING OF MICRO- DROPLETS BY A WIRELESSLY DRIVEN PIEZOELECTRIC STAGE Microdroplet erging has potential applications in icroreactors [85-89], nanoparticle synthesis [90-91], cell encapsulation [9-93], and protein crystallization [94]. Conventionally, two icrodroplets are erged by the difference in speed of icrodroplets oving along the channels in a icrofluidic device. They utilize droplet size and viscosity difference [95], pillar structure [96], fusion chaber [97], and surface properties [98] to induce the difference in speed of icrodroplets. Microdroplets are also erged in an electric field by utilizing charges of opposite sign on two different icrodroplets, thus overcoing the stabilized forces caused by surface tension and lubrication [99-10]. So far, there has been no report on icrodroplets erging by ultrasonic actuation. To siplify the device structure for icrodroplets erging and widen the application range of this technology, a ethod to erge icrodroplets by using a piezoelectric stage which is wirelessly driven by an A.C. electric field is proposed and investigated by the author. The icrodroplets to erge are dispensed onto the surface of a piezoelectric stage. The piezoelectric stage is wirelessly driven by a focused electric field. The ultrasonic vibration of the piezoelectric stage is transitted into the icrodroplets and induces the 145

169 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage erging of icrodroplets. The vibration displaceent of the stage is deterined by the strength of the applied electric field and its operating frequency. The electric field pattern was theoretically calculated by finite eleent ethod (COMSOL Multiphysics) to assess the electric field on the surface of the wirelessly driven piezoelectric stage. Experientally, it has been observed that the tie for erging of water icrodroplets depends on the vibration displaceent of piezoelectric stage, separation distance, and volue of icrodroplets. The tie for erging two water icrodroplets is proportional to the separation distance between two icrodroplets, and the increase in volue of icrodroplets. It was also noticed that the erging speed of larger volue of icrodroplets is significantly higher than that of saller volue icrodroplets. At the resonance frequency of 776 khz, two water icrodroplets each of volue 0.8 µl separated by a distance of 0.6 were erged together 16 seconds after the echanical vibration displaceent of 0.11 µ was excited in the piezoelectric stage with an area of 40. In contrast with the conventional ethod of erging, the proposed device has the following unique features. The proposed device does not need to use icrochannels for the otion of the droplets. Furtherore, the icrodroplets can be dispensed onto the actuating surface siultaneously or at different oents. Two droplets with the sae size and viscosity can be erged successfully The wireless drive provides the potential for iniaturization of the piezoelectric stage. 146

170 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage 7.1. Experiental Setup and Operating Mechanis Fig.7.1 (a) shows the experiental setup for the erging of icrodroplets by a piezoelectric stage wirelessly driven by focused electric field. With a square size brass stage-shaped live electrode, a stainless steel needle ground electrode is used to focus the A.C. electric field to enhance the electric energy transission to the piezoelectric stage. The needle ground electrode is placed below, and perpendicular to the live electrode which is suspended above the piezoelectric stage. The piezoelectric stage is placed equidistantly in between the live and needle ground electrodes of the focused electric field structure. The optiu live electrode area is c. Fig.7.1 (b) shows the configuration of the wirelessly driven piezoelectric stage operating in the thickness ode. The piezoelectric stage is ade of PZT ceraic aterial (Fuji C-03) and is poled vertically across the thickness direction. The Piezoelectric charge constant d 33, echanical Q, dissipation factor tanδ, and relative dielectric constant ε T 33 /ε 0 are /V, 000, 0.3 and 1450, respectively. The plate has silver electrodes on its top and botto surfaces. The diension of the piezoelectric plate used in the experients is The vibration direction and applied electric field both are parallel to the poling direction. Droplets of volue varying fro 0.5 µl to µl are dispensed on to the top surface of the wirelessly driven piezoelectric plate by using a icropipette (Brand CAPP, C1 991). When an A.C. electric field produced fro the focused electric field generator penetrates the piezoelectric plate, a echanical vibration can be stiulated in 147

171 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage the plate by the converse piezoelectric effect. When the frequency of the A.C. electric field is close to the echanical resonance frequency of the piezoelectric plate, a strong enough echanical resonance vibration can be excited in the plate. This echanical vibration of the piezoelectric plate transitted to the icrodroplets placed on its surface, reduces the interolecular forces of attraction or Van der Waal s force between the icrodroplets. The icrodroplets can ove closer to each other due to the vibration of the piezoelectric plate and ultiately erge after soe tie. Distance =4 c (a) (b) Fig.7.1: (a) Experiental setup for the erging of droplets by a piezoelectric stage wirelessly driven by focused electric field; (b) Configuration of wirelessly driven piezoelectric stage operating in the thickness vibration ode. 148

172 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage 7.. Results and Discussion The theoretical and experiental studies are perfored under the following conditions. The piezoelectric plate operates in the thickness vibration ode; its diensions were ; the live electrode area is 900 c ; the ground electrode is a etal needle whose tip is assued to be have zero area; voltage across the live and ground electrodes of focused electric field structure is 6000 Vrs; live and needle ground electrodes separation distance of 4 c Theoretical calculation of electric field by finite eleent ethod The finite eleent ethod (COMSOL Multiphysics) siulation has been carried out in order to assess the electric field on the surface of the piezoelectric plate without droplets on its top surface. Fig.7.: Calculated -D electric field pattern around the piezoelectric plate wirelessly driven by focused electric field structure. 149

173 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage Fig.7.3: Distribution of the electric field on the surface of wirelessly driven piezoelectric plate along the x-direction, x=0.145 to x= Fig.7. shows the calculated -D electric field pattern around the piezoelectric plate wirelessly driven by a focused electric field. The electric field distribution on the surface of the piezoelectric plate along the x-direction is shown in Fig.7.3. It is found that the calculated average value of the electric field on the surface of the piezoelectric stage is V/ Measureent of vibration displaceent The vibration displaceent of the wirelessly driven piezoelectric stage was easured with a icroscope (BX51, Olypus, Japan), as shown in Fig.7.4. In the easureent, a arked point on the edge of piezoelectric stage is chosen to 150

174 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage be the easured point, and its picture is taken by the icroscope without vibration of the piezoelectric stage as shown in Fig. 7.5 (a). When the A.C. electric field penetrates the piezoelectric stage, a echanical vibration is stiulated in the stage by the converse piezoelectric effect. Consequently, the width of the arked point increases. The iage of the easured point is also viewed by the icroscope when the piezoelectric stage is in vibration, as depicted in Fig.7.5 (b).the exposure tie of BX51 has an order of s or larger; while the tie period of the ultrasonic vibration is in icrosecond order ( 78 khz). Therefore, during the exposure tie, there are several thousands of vibration periods. This gives us a quite clear iage of the easured point. The iage of the easured point in vibration is larger than that of without vibration. Taking difference in the width of easured point between the two iages, the peak to peak vibration displaceent can be experientally easured. Based on this principle, a root ean square vibration displaceent of the piezoelectric stage of 0.11 µ was easured. f = r Fig.7.4: Experiental setup for easuring the vibration displaceent of the piezoelectric stage wirelessly driven by a focused electric field. 151

175 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage (a) (b) Fig.7.5: The pictures of the easured point are taken by the icroscope when the piezoelectric stage is (a) without vibration, and (b) in vibration The effect of ultrasonic vibrations on a single icrodroplet The effect of ultrasonic vibrations on a single icrodroplet placed on the top surface of wirelessly driven piezoelectric plate operating in the thickness vibration ode is shown in Fig.7.6. Fig.7.6 (a) shows the water icrodroplet without vibration, and Fig.7.6 (b) shows the water icrodroplet flows down due to vibration of the piezoelectric plate. 15

176 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage (a) (b) Fig.7.6: (a) Water icrodroplet on the top surface of the wirelessly driven piezoelectric plate without vibration; (b) Water icrodroplet flows down due to the vibration of the piezoelectric plate. The volue of the water droplet is µl, and the calculated value of the electric field on the surface of piezoelectric plate is V/. It is observed that at resonant frequency of 776 khz, the water droplet flows down fro top surface of the piezoelectric stage as the vibration of the stage attains the axiu. The water droplet starts to flow down after 4 seconds of excitation of PZT plate. 153

177 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage (a) (b) Fig.7.7: Illustration of a water icrodroplet on plastic substrate placed inside a focused electric field generator. (a) Without electric field, and (b) with E-field. If the wirelessly driven piezoelectric stage operating in the thickness vibration ode is detuned fro resonance, there is no flow down of the water droplet. In order to illustrate the influence of electric field on the water droplet, the sae experient was carried out on the surface of a plastic stage, which has no vibration. Fig.7.7 illustrates the water icrodroplet on a plastic substrate (a) without electric field, and (b) with electric field. It is observed that there is no change in shape of water droplet after 4 seconds, and also even after 15 inutes of experientation. Fro this experient, it is confired that the water droplets cannot erge without the ultrasonic vibration Frequency characteristics of the contact angle of icrodroplets The frequency characteristics of the contact angle of water icrodroplet placed on the surface of the wirelessly driven piezoelectric stage operating in the thickness vibration ode is shown in Fig.7.8. It is seen that the contact angle θ 154

178 Contact angle in vibration (degree) Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage ade by the tangent line to the water droplet at the edge and the surface horizontal line of the piezoelectric stage decreases sharply at resonance frequency of 776 khz, fro to This is because at resonance the vibration of the piezoelectric stage is axiu. When the vibration of the piezoelectric stage goes higher, the interolecular force of attraction between the water olecules is reduced, and the water droplet tends to flatten. Thus, the contact angle easured is iniu at the axiu vibration. The contact angle of the icrodroplets of water, sunflower oil, and olive oil at resonance has also been investigated, and the results are shown in Fig.7.9. At resonance, it is seen that the contact angle of water droplet reduces ore than that of other liquids like sunflower oil and olive oil. This is because the viscosity of the oils (~ 80 Pa.S at roo teperature) is uch larger than that of the water droplet (0.894 Pa.S at roo teperature), and the ultrasonic vibration in the water droplet is uch larger than that in the oils Volue of droplet = l E-field = V/ Driving frequency (khz) Fig.7.8: The frequency characteristics of the contact angle of water droplet placed on the surface of piezoelectric stage operating in the thickness ode. 155

179 Contact angle of droplets (degree) Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage without vibration in vibration volue = l Water Sunflower oil Olive oil Fig.7.9: The contact angle of liquid icrodroplets on the horizontal surface of the wirelessly driven piezoelectric stage without vibration and in vibration Merging of icrodroplets The above experiental results show the feasibility of icrodroplets erging on the surface of a piezoelectric stage wirelessly driven by electric field. Figure 7-10 shows the erging of two water icrodroplets placed with a fixed separation distance on the surface of a wirelessly driven piezoelectric stage operating in the thickness ode. Experientally it has been observed that the erging speed of the icrodroplets depends on the vibration displaceent at resonance of the piezoelectric plate, and the droplets initial separation distance and volue. The dependence of the easured tie for erging of water icrodroplets on the separation distance and volue of the water droplets is shown in Fig

180 Chapter 7 Merging of icrodroplets by a wirelessly driven piezoelectric stage (a) (b) (c) Fig.7.10: Merging of two water icrodroplets placed with a fixed separation distance on the surface of a wirelessly driven piezoelectric plate operating in the thickness vibration ode. (a) without vibration; (b) after 10 seconds of sonication ; (c) after 16 seconds of sonication. 157