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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…mehr
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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.
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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Wiley
- Seitenzahl: 244
- Erscheinungstermin: 12. Februar 2016
- Englisch
- Abmessung: 240mm x 161mm x 18mm
- Gewicht: 536g
- ISBN-13: 9781848217164
- ISBN-10: 1848217161
- Artikelnr.: 41561496
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
- Verlag: Wiley
- Seitenzahl: 244
- Erscheinungstermin: 12. Februar 2016
- Englisch
- Abmessung: 240mm x 161mm x 18mm
- Gewicht: 536g
- ISBN-13: 9781848217164
- ISBN-10: 1848217161
- Artikelnr.: 41561496
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
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
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
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
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