Electrostatic Kinetic Energy Harvesting

Harvesting kinetic energy is a good opportunity to power wireless sensor in a vibratory environment. Besides classical methods based on electromagnetic and piezoelectric mechanisms, electrostatic transduction has a great perspective in particular when dealing with small devices based on MEMS technology. This book describes in detail the principle of such capacitive Kinetic Energy Harvesters based on a spring-mass system. Specific points related to the design and operation of kinetic energy harvesters (KEHs) with a capacitive interface are presented in detail: advanced studies on their nonlinear features, typical conditioning circuits and practical MEMS fabrication.

Philippe Basset, Associate professor at Université Paris-Est, ESYCOM, ESIEE Paris, France

Dimitri Galayko, associate professor at Sorbonne Universités, UPMC Univ., Paris, France

Elena Blokhina, research manager at School of Electrical, Electronic and Communications Engineering, University College Dublin, Ireland

Preface ix

Introduction: Background and Area of Application xi

Chapter 1. Introduction to Electrostatic Kinetic Energy Harvesting 1

Chapter 2. Capacitive Transducers 7

2.1. Presentation of capacitive transducers 7

2.2. Electrical operation of a variable capacitor 11

2.3. Energy and force in capacitive transducers 12

2.3.1. Energy of a capacitor 12

2.3.2. Force of the capacitor 14

2.3.3. Capacitive transducers biased by an electret layer 17

2.4. Energy conversion with a capacitive transducer 20

2.5. Optimization of the operation of a capacitive transducer 21

2.6. Electromechanical coupling 23

2.7. Conclusions 24

2.8. Appendix: proof of formula [2.32] for the energy converted in a cycle 24

Chapter 3. Mechanical Aspects of Kinetic Energy Harvesters: Linear Resonators 27

3.1. Overview of mechanical forces and the resonator model 27

3.1.1. Linear resonator as the main model of the mechanical part 27

3.1.2. The nature and effect of the transducer force 30

3.1.3. Remarks on mechanical forces 33

3.2. Interaction of the harvester with the environment 36

3.2.1. Power balance of KEHs 36

3.2.2. Efficiency of KEHs 40

3.3. Natural dynamics of the linear resonator 42

3.3.1. Behavior of the resonator with no input 42

3.3.2. Energy relation for the resonator with no input 44

3.3.3. Forced oscillator and linear resonance 45

3.3.4. Periodic external vibrations 49

3.3.5. Energy relation for a forced resonator 50

3.4. The mechanical impedance 52

3.5. Concluding remarks 54

Chapter 4. Mechanical Aspects of Kinetic Energy Harvesters: Nonlinear Resonators 55

4.1. Nonlinear resonators with mechanically induced nonlinearities 55

4.1.1. Equation of the nonlinear resonator 55

4.1.2. Free oscillations of nonlinear resonator: qualitative description using potential wells 60

4.1.3. Free oscillations of nonlinear resonator: semi-analytical approach 62

4.1.4. Forced nonlinear resonator and nonlinear resonance 63

4.2. Review of other nonlinearities affecting the dynamics of the resonator: impact, velocity and frequency amplification and electrical softening 68

4.3. Concluding remarks: effectiveness of linear and nonlinear resonators 71

Chapter 5. Fundamental Effects of Nonlinearity 75

5.1. Fundamental nonlinear effects: anisochronous and anharmonic oscillations 75

5.2. Semi-analytical techniques for nonlinear resonators 79

5.2.1. Normalized form of nonlinear resonators 79

5.2.2. Anharmonic oscillations demonstrated by straightforward expansion 81

5.2.3. Anisochronous oscillations demonstrated by the LPM 84

5.2.4. Multiple scales method 88

5.2.5. Nonlinearity of a general form 91

5.3. Concluding remarks 95

Chapter 6. Nonlinear Resonance and its Application to Electrostatic Kinetic Energy Harvesters 97

6.1. Forced nonlinear resonator and nonlinear resonance 97

6.1.1. Analysis of forced oscillations using the multiple scales method 97

6.1.2. Forced oscillations with a general form of nonlinear force 102

6.2. Electromechanical analysis of an electrostatic kinetic energy harvester 105

6.2.1. Statement of the problem 105

6.2.2. Mathematical model of the constant charge circuit 106

6.2.3. Steady-state nonlinear oscillations 109

6.2.4. Dynamical effects and bifurcation behavior 113

6.2.5. Other conditioning circuits 115

6.3. Concluding remarks 119

Chapter 7. MEMS Device Engineering for e-KEH 121

7.1. Silicon-based MEMS fabrication technologies 121

7.1.1. Examples of bulk processes 122

7.1.2. Thin-film technology with sacrificial layer 123

7.2. Typical designs for the electrostatic transducer 124

7.2.1. Capacitive transducers with gap-closing electrode variation 125

7.2.2. Strategies on the stopper’s location in gap-closing e-KEH 128

7.2.3. Capacitive transducers with overlapping electrode motion 130

7.3. e-KEHs with an electret layer 133

Chapter 8. Basic Conditioning Circuits for Capacitive Kinetic Energy Harvesters 135

8.1. Introduction 135

8.2. Overview of conditioning circuit for capacitive kinetic energy harvesting 136

8.3. Continuous conditioning circuit: generalities 138

8.3.1. Qualitative discussion on operation of the circuit 139

8.3.2. Analytical model in the electrical domain 140

8.4. Practical study of continuous conditioning circuits 141

8.4.1. Gap-closing transducer 141

8.4.2. Area overlap transducer 145

8.4.3. Simple conditioning circuit with diode rectifiers 148

8.5. Shortcomings of the elementary conditioning circuits: auto-increasing of the biasing 149

8.5.1. Appendix: listing of the Eldo netlist used to obtain the presented plots 152

Chapter 9. Circuits Implementing Triangular QV Cycles 155

9.1. Energy transfer in capacitive circuits 155

9.1.1. Energy exchange between two fixed capacitors 155

9.1.2. Case of a voltage source charging a capacitor 156

9.1.3. Inductive DC-DC converters 157

9.1.4. Use of a variable capacitor 161

9.2. Conditioning circuits implementing triangular QV cycles 163

9.2.1. Constant-voltage conditioning circuit 163

9.2.2. Constant-charge conditioning circuits 165

9.2.3. Analysis of the circuit implementing a constant-charge QV cycle 166

9.2.4. Practical implementation 169

9.3. Circuits implementing triangular QV cycles: conclusion 171

Chapter 10. Circuits Implementing Rectangular QV Cycles, Part I 173

10.1. Study of the rectangular QV cycle 173

10.2. Practical implementation of the charge pump 178

10.2.1. Evolution of the harvested energy 180

10.3. Shortcomings of the single charge pump and required improvements 182

10.3.1. Need for a flyback 182

10.3.2. Auto-increasing of the internal energy 183

10.4. Architectures of the charge pump with flyback 184

10.4.1. Resistive flyback 184

10.4.2. Inductive flyback 185

10.5. Conditioning circuits based on the Bennet’s doubler 188

10.5.1. Introduction of the principle . 188

10.5.2. Analysis of the Bennet’s doubler conditioning circuit 191

10.5.3. Simulation of a Bennet’s doubler 199

Chapter 11. Circuits Implementing Rectangular QV Cycles, Part II 203

11.1. Analysis of the half-wave rectifier with a transducer biased by an electret 203

11.2. Analysis of the full-wave diode rectifier with transducer biased by an electret 205

11.3. Dynamic behavior and electromechanical coupling of rectangular QV cycle conditioning circuits 210

11.4. Practical use of conditioning circuits with rectangular QV cycle 215

11.5. Conclusion on conditioning circuits for e-KEHs 216

Bibliography 217

Index 225

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