University of GenoaPh.D. School in

Science and Technology for Information and KnowledgeCycle XXII

February 2010

Vibration-Based Energy Scavengingfor Power Autonomous Wireless

Sensor Systems

by

Luigi Pinna

A dissertation submitted to the University of Genoafor the degree of Doctor of Philosophy

Ph.D. Course in Nanotechnologies

Coordinator: Ph.D. Chiar. mo Prof. Ermanno Di ZittiAdvisor: Ph.D. Chiar. mo Prof. Maurizio Valle

Co-Advisor: Ph.D. Ravinder S. DahiyaCo-Advisor: Ph.D. Ing. Gian Marco Bo

Settore Scientifico-Disciplinare [SSD]: ING-INF/01 Elettronica

To Family and Friends

Preface

Now, the name of this talk is ”There is Plenty of Room at theBottom” - not just - ”There is Room at the Bottom.” What Ihave demonstrated is that there is room - that you can decreasethe size of things in a practical way. I now want to show that thereis plenty of room. I will not now discuss how we are going to doit, but only what is possible in principle - in other words, whatis possible according to the laws of physics. I am not inventinganti-gravity, which is possible someday only if the laws are notwhat we think. I am telling you what could be done if the lawsare what we think; we are not doing it simply because we haven’tyet gotten around to it.

Richard P. Feynman

This thesis describes the work carried out between January 2007 and Febru-ary 2010, at the Canovatech-DIBE joint Lab, University Campus of Savona,DIBE-University of Genoa, Genoa, Italy. I was the recipient of a doctoralfellowship to work at the DIBE-Canova Tech joint Lab under the supervi-sion of Prof. Maurizio Valle from DIBE, University of Genoa, and Ing. GianMarco Bo from Canova Tech, Srl, Padova, Italy.

This thesis is about energy scavenging or harvesting for power autonomouswireless micro/nano sensor-based systems with focus on vibration to elec-tricity conversion. The work presented in this thesis is primarily focused onthe design and implementation of a power unit for the power supply of avibration-based power autonomous wireless sensor system. The power unitis composed by two basic blocks, which are the vibration-based energy har-vester (scavenger) and an integrated power management circuit, which iscomposed by an AC-DC converter that rectifies the AC voltage generated bythe vibration-based generator and a DC-DC converter or voltage regulator.In particular, this thesis work is related to the design of the integrated power

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management circuit powered by a Piezoelectric Bender Generator (PBG)which converts ambient mechanical vibrations into electricity.

The thesis contains 8 chapters. Chapter 1 introduces the motivationsabout why the need of replacing a battery as power source for the new gen-eration of electronic wireless sensor systems, with MEMS or nano sensorsarrays, integrated on single silicon chip with ultra low power CMOS-basedelectronics. An overview of the general energy harvesting state of art is alsodiscussed in the Chapter 1 in order to introduce the energy harvesting topicand what could be the better renewable ambient energy source from whichharvesting the energy - opportunely conditioned by a transducer and a powermanagement circuit - to be used to power the wireless sensor system in placeof batteries. Then, by presenting the reference system for this work thevarious steps, issues and objectives are also explained in the last section ofChapter 1.

Chapter 2 focuses on vibration-based transducers giving the reader theknow how about a vibration-based generator general model and the stateof the art of the three basic vibration-based generators (i.e. electrostatic,electromagnetic, piezoelectric). The study of the state of the art of vibration-based generators (VBG) must first be addressed in order to identify whatVBG is suitable 1) to be used to convert ambient mechanical vibrations toelectricity and hence powering the embedded units of the reference system;2) to be fabricated with MEMS technologies and integrated with CMOS-based electronics. A comparison among the advantages and disadvantagesof vibration-based generators - discussed in the Chapter 2 - addressed usto explore the possibility of using piezoelectric bender generator (PBG) asharvester (scavenger) to convert mechanical vibrations to electricity.

A feasibility case study - reported and discussed in the Chapter 3 - hasthe goal to explore and study the use of PBG as power source for wirelesssensor systems, in particular for a wireless tire pressure measurement systemembedded on the wheel of a car. The wheel of the car is a very extreme en-vironment where mechanical vibrations and radial accelerations magnitudecan reach values three order of magnitude larger than those ones of com-mon ambient vibrational sources. In regard to the integration of the wirelesssensor system, knowing if a VBG scaled at micro/nano sizes could still beable to power a wireless sensor system and the knowledge of the limits of theVBG is an important aspect that an electronic designer should know. By thisknowledge the electronic designer can design and optimize the electronic cir-cuits in order to adapt them to the energy made available by the micro/nanoharvester. Chapter 3, therefore, attempts to explain these aspects with anumber of examples.

Another important aspect that must be addressed and that is also useful

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for an electronic designer is the availability of having an equivalent model ofthe power source - which in this case is the piezoelectric generator - in SPICE.If the electromechanical model of the scavenger can be in fact implementedin SPICE, then, it is extremely convenient to analyze the complete system(i.e. mechanical and electrical and electronic parts) in SPICE. Therefore,Chapter 4 presents the development of the SPICE model of the piezoelectricbender generator, based on an electromechanical model - suited to be mod-eled in SPICE - from literature which takes into account both geometricaland physical parameters of the generator itself.

Vibration-based generators produces AC voltages that need to be con-verted, regulated and stabilized in DC before being used to power electronicsystems. A diode bridge rectifier is the common and simplest approach fol-lowed in literature to realize the AC-DC conversion. However, the integrationof only passive devices as diodes on chip does not take advantage of the flex-ibility of active devices usage along with optimized control circuits whichcould give the possibility to manage in a smart way the power and voltagegenerated by VBGs. Performance, efficiency and low-power consumptioncan be improved, and this is an important aspect above all in the contextof energy scavenging applications, where the available energy may be poor.However, a fully active solution for the bridge rectifier, might need a morecomplicated control circuit to drive the active devices, which can increasethe complexity and power consumption of the system. Therefore, trade-offs among simplicity, efficiency, flexibility and performance are necessaries.Moreover, because of the PBG is able to generate high level output volt-ages, power devices could be more suitable to be used for the bridge rectifier.Therefore, a semi-active approach for the bridge rectifier with power passiveand active devices is presented and developed in the Chapter 5.

A DC-DC switching converter with its high efficiency - around the 90% -is a basic unit of a power management system. It can be used to regulate andadapt the diverse voltage levels needed to power the electronics belonging asystem and also can be used to optimize the power transfer towards the finalload. Moreover, because of they are realized with active devices which needto be controlled suitable control algorithms can be implemented. The majoreffort in the development of the power management circuit is therefore thedesign of the driver circuit, which controls the switches of the converter.In this work, the voltage regulated by a step-down buck converter is usednot only for being compared with a reference voltage in order to performthe regulation, but, also is used to power the control circuits of the powermanagement system - i.e. the rectifier control circuit and the driver circuit.The design issues addressed to make the voltage regulator self-powered arediscussed in the Chapter 5. Moreover, the simulation results of the reciprocal

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interaction between PBG and the scavenging system - SPICE model of thePBG, the semi-active bridge and voltage regulator - is presented, in terms ofstress, strain rate, mechanical and electrical powers.

Chapters 6 and 7 concern the design, development and fabrication of aprototype ASIC and test printed circuit board and the experimental valida-tion test results. The developed ASIC comprises of the semi-active bridgerectifier and the switching part of the buck converter which have been inte-grated on chip. The control circuits and the LC filter of the step-down buckconverter have been inserted in the test PCB. This hybrid solution - ASICand PCB - has been adopted in order to have more flexibility in the designand for the experimental tests, integrating the key components - rectifierand switching part of the DC-DC converter - in the ASIC, while, the othercomponents - control circuits and LC filter - left outside the ASIC.

In order to validate the SPICE equivalent model of the PBG is necessaryto compare it with a realistic PBG. By performing experimental tests with theprototype PBG and hence comparing the measured results with the simulatedones, it would allow understanding what are the limits of the developedSPICE model and hence, through a careful study and understanding of theresults obtained, optimizing the developed SPICE model in order to makeit closer to the realistic counterpart. The concluding chapter of this workpresents then the preliminary experimental tests realized with a fabricatedPBG prototype, either tested alone or connected to the ASIC and test board.

Finally, a critical evaluation of the work, through Chapter 1 to Chapter 7,is done and presented in the conclusions section. Moreover, in the context ofthe future trends, an analytical mathematical analysis of a vibration-basedhybrid generator, realized joining a PBG with an electromagnetic generatoris also presented.

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Acknowledgements

The path to a Ph.D. has been a long and winding one. The route was notalways well illuminated, but there have been many people who lighted upthe way by providing guidance, encouragement and support. It would bebelittling their efforts if I don’t express my gratitude to them.

I wish to start expressing my gratitude with my supervisors, not becauseit is customary, but because they have been showing me the way all along.Prof. Maurizio Valle has been a very patient supervisor of this ever expandingproject, which he strongly supported with inspiring enthusiasm, right frombeginning. His support, critical reviews and appreciation provided importantclues and guidelines.

I would like to thank Ing. Gian Marco Bo for his support, friendly advices,generously sharing his expertise and pervasive knowledge in the field of powermanagement circuits and electronic engineering and I am sure this knowledgewill help me shape my professional career.

A really special thanks goes to Ravinder who has been extremely support-ive, kept always an eye on the progress of my work and always was availablewhenever I needed his advises and help. This last year of my Ph.D. wouldhave never been as it has been without his friendship, help and support.

Besides the support from supervisors, a thesis also needs the helpinghands of fellow researchers and colleagues that make the work more comfort-able.

I would like to thank Alessandro and the Canova Tech company for fund-ing and sponsoring the project related my Ph.D. on the development of apower management system for energy scavenging applications.

My gratitude goes also to all other members of Canova Tech for theirtechnical support, generous hospitality and the pleasant time they gave meduring my stays in Padova.

I would like to thank Fabrizio from Canova Tech who has been generouswith his time in helping me understand circuit design issues and in helpingwith instrumentation.

Among many colleagues I would like to thank Andrea Guerra who has

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been a very great friend and flatmate during the first year of my Ph.D. herein Savona. I would like to thank Sergio from Canova Tech and Leonardo,colleague, friend and flatmate during these three years and Marco Antonio -associated with MUSES lab at University Campus of Savona and also Can-dice, Andrea and Lorenzo - all associated with microelectronics lab at DIBE,University of Genova.

I am ever grateful to my Father, Mario, my Mather, Lucia, my Sister,Rosy and her Husband, Mirko, who have given me their unequivocal supportthroughout, for their constant love and confidence in me, as always, for whichmy mere expression of thanks likewise does not suffice.

I am very grateful for my girlfriend and loved one, Sabina, for her love,support, understanding and patience during the last two years of my Ph.D.

By any chance, if your name is not listed, rest assured that my gratitudeis not less than for those listed above.

Again, thank you all!

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Contents

Preface i

Acknowledgements v

1 Introduction 11.1 Motivation: wireless micro/nano sensor-based electronic system 11.2 Wireless power autonomous micro/nano sensor-based system . 5

1.2.1 Renewable ambient energy sources . . . . . . . . . . . 61.2.2 Vibrational sources: a powerful option to batteries . . . 7

1.3 Thesis objectives: proposed harvesting system architecture . . 9

2 Vibration-based energy harvesting 162.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 General model of a vibration-based generator . . . . . . . . . 162.3 State-of-the-art of vibration-based generators . . . . . . . . . . 21

2.3.1 Electrostatic generators . . . . . . . . . . . . . . . . . 222.3.2 Electromagnetic generators . . . . . . . . . . . . . . . . 242.3.3 Piezoelectric bender generators . . . . . . . . . . . . . 27

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Case Study: Piezoelectric Bender Generator for WirelessTire Pressure Measurement Systems 363.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Wireless smart sensors energy/power requirements estimation 373.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 403.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4 SPICE model of Piezoelectric Bender Generator 474.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

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4.2.1 Analytical model . . . . . . . . . . . . . . . . . . . . . 484.2.2 Mechanical side and electrical block equations . . . . . 504.2.3 Piezoelectric coupling equations . . . . . . . . . . . . . 514.2.4 PBG model transfer function with resistive load . . . . 51

4.3 SPICE implementation . . . . . . . . . . . . . . . . . . . . . . 524.4 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 544.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5 Design and analysis of a Vibration-Based Energy ScavengingSystem 585.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.2 Vibration-Based Energy Scavenging Circuit . . . . . . . . . . 59

5.2.1 Semi-Active Bridge Rectifier . . . . . . . . . . . . . . . 595.2.2 Voltage regulator . . . . . . . . . . . . . . . . . . . . . 615.2.3 Transient and steady-state . . . . . . . . . . . . . . . . 65

5.3 SPICE simulation results . . . . . . . . . . . . . . . . . . . . . 705.3.1 Semi-Active Bridge rectifier simulation results . . . . . 715.3.2 Voltage regulator simulation results . . . . . . . . . . . 72

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6 Test chip design 816.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.2 ESD protections . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.2.1 LV input pad protection . . . . . . . . . . . . . . . . . 836.2.2 HV IO protections to protect the HV switches . . . . . 87

6.3 Layout of the test chip . . . . . . . . . . . . . . . . . . . . . . 89

7 Test board design and experimental validation 917.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

7.1.1 Test board voltage level shifter . . . . . . . . . . . . . 937.1.2 Test board driver . . . . . . . . . . . . . . . . . . . . . 94

7.2 Test board experimental validation results . . . . . . . . . . . 957.2.1 Efficiency of the test board voltage regulator . . . . . . 96

7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

8 Conclusions and future trends 1038.1 Preliminary experimental results . . . . . . . . . . . . . . . . . 1088.2 A proposal for a hybrid vibration-based generator . . . . . . . 1148.3 Electromechanical analytical model of a vibration-based piezo-

electric and electromagnetic generator . . . . . . . . . . . . . . 114

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8.3.1 PBEMG model with resistive load: coil connected inparallel with the PBG output . . . . . . . . . . . . . . 118

8.4 Combining piezoelectric and electromagnetic SPICE models . 1218.4.1 SPICE modeling of the mechanical and electrical sides 122

A Publications 124

B SPICE Netlist of the Piezoelectric Bender Generator 126

C AMIS I3T50u devices overview 127C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127C.2 n-type VDMOS transistor: VFNDM50 . . . . . . . . . . . . . 128C.3 p-type VDMOS transistor: LFPDM50 . . . . . . . . . . . . . 129C.4 High Voltage diode: FID50U . . . . . . . . . . . . . . . . . . . 129

D Semi-Active Bridge rectifier dimensioning 131

Bibliography 135

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List of Figures

1.1 block diagram of a battery-supplied wireless sensor system. . . 21.2 (a) Top view and cross-sectional diagrams of nanosensors ar-

ray with silicon CMOS circuitry [Xu et al., 2004]. (b) Micro-graphs of the test chip with an array of nanowires and red-outcircuit and the UWB transmitter chip [Narayanan, 2004]. . . . 4

1.3 Comparison of powers generated from vibrations, solar, andvarious battery chemistries with respect to the life time of thepower source expressed in years [Roundy et al., 2004]. . . . . . 9

1.4 Block diagram of a wireless power autonomous sensor system. 101.5 Block diagram of the wireless power autonomous sensor sys-

tem with semi-active bridge and DC-DC switching voltage reg-ulator blocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.6 Block diagram of the power management blocks realized asASIC and PCB. . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1 General model of the linear mass-spring-damper system rep-resenting the resonant inertial generator (a). Free-body dia-grams at an arbitrary instant including effects of the absolutemotion of the frame, y(t) (b). . . . . . . . . . . . . . . . . . . 18

2.2 Electrostatic generators structures: in-plane overlap converter(left), in-plane gap closing converter (center), out-of-plane gapclosing converter (right) . . . . . . . . . . . . . . . . . . . . . 23

2.3 Electromagnetic generators: (a) MEMS-based by Beeby et al.,Wang et al., respectively; (b) Millimeter scale by Torah et al.,by Glynne et al., respectively . . . . . . . . . . . . . . . . . . 24

2.4 Illustration of the two modes of piezoelectric conversion frominput mechanical stress (denoted as σ1). In the figure thestrain is denoted as S1. . . . . . . . . . . . . . . . . . . . . . . 27

2.5 Vibration-based piezoelectric generators: (a) Micromachinedcantilever by Marzencki et al., Choi et al. and Fang et al.,respectively; (b) Millimeter scale by Roundy et al. and Lelandet al., respectively. . . . . . . . . . . . . . . . . . . . . . . . . 29

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2.6 Piezoelectric nanogenerator based on Zinc Oxide nanowire ar-rays by Wang, Z. L. et al.. . . . . . . . . . . . . . . . . . . . . 30

3.1 (a) Centripetal force progress during the roto-translationalmotion of an automobile tire, and its action onto PiezoelectricBender Generator. (b) Schematic of the energy harvesting cir-cuit. (c) Set up of the experiment with the test board mountedon the outer rim of the wheel of an automobile. . . . . . . . . 40

3.2 Measured Voltage and computed energy curves for differentcar speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3 Measured Voltage and computed energy curves for differentPBG thicknesses. . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.4 Measured Voltage and computed energy curves for differentdistances of PBG from the wheel center. . . . . . . . . . . . . 42

3.5 Power flow from PBG to sensor and radio block in case ofnot considering and considering the minimum supply voltagerequired by the sensor and radio block to operate. . . . . . . 44

4.1 (a) Piezoelectric bender generator with a proof mass placed onthe free end of the bender. (b) Piezoelectric bender generatorwired for series and parallel operation mode. . . . . . . . . . . 49

4.2 (Bimorph electromechanical circuit model. . . . . . . . . . . . 494.3 SPICE schematic subcircuit of the Piezoelectric Bender Gen-

erator model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.4 Comparison among the MATLAB and SPICE (a) and the

Roundy simulated and experimental measured (b) powers andvoltages versus load resistance in case of bimorph wired for theparallel operation mode. . . . . . . . . . . . . . . . . . . . . . 55

4.5 SPICE and MATLAB powers (a) and voltages (b) versus loadresistance in case of bimorph wired for the series operationmode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.1 Block diagram of vibration based energy scavenging systemwith PBG (excited by a vibration source), the voltage regula-tor system and control circuit (supplied by the output of theDC-DC voltage regulator). . . . . . . . . . . . . . . . . . . . . 59

5.2 Schematic of the semi-active bridge rectifier with the ZCCcontrol circuit inside the dashed rectangle. . . . . . . . . . . . 60

5.3 Schematic of the voltage regulator circuit with the semi-activebridge rectifier and the SPICE model of the PBG. . . . . . . . 62

5.4 Internal schematic view of the monostable circuit. . . . . . . . 63

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5.5 Internal schematic view of the flip flop D master slave. . . . . 635.6 Internal schematic view of the SPICE model of a one-pole

comparator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.7 Voltage regulator control circuit cycle timing diagram in case

of Iout,PBG < (IV dd,Driver + ILoad). . . . . . . . . . . . . . . . . 675.8 Voltage regulator control circuit cycle timing diagram in case

of Iout,PBG ≥ (IV dd,Driver + ILoad). . . . . . . . . . . . . . . . . 705.9 (a) Simulated rectifier average input power (left) and load

power (right) of the semi-active and diode bridge rectifiersvs. load resistance. (b) Simulated rms load voltage (left) andefficiency (right) of the semi-active bridge and diode bridgerectifiers vs. load resistance. . . . . . . . . . . . . . . . . . . . 72

5.10 Simulated mechanical input power for the 3.3 V, 1.8 V and1.4 V regulated voltages versus load resistance (a). Simulatedmechanical input power, PBG output power and load Powerat various load resistances in case of the 3.3 V regulation (b). . 73

5.11 Efficiency (a) and simulated PBG output current curves (b)for the 3.3 V, 1.8 V and 1.4 V regulated voltages versus theload resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.12 Simulated strain rate curves for the 3.3 V, 1.8 V and 1.4 Vregulated voltages versus the load resistance (a). SimulatedPBG output voltage curves for 3.3 V, 1.8 V, 1.4 V versus loadresistance (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.13 Simulated stress curves for the 3.3 V, 1.8 V and 1.4 V regulatedvoltages versus the load resistance (a). Comparison among thethree different regulated voltage curves versus load resistance(b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.14 Simulated load power for 3.3 V, 1.8 V, 1.4 V versus load re-sistance (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.1 SPICE schematic of the test chip core. . . . . . . . . . . . . . 826.2 Test chip connection diagram and top view of the Dual-In Line

Package pin out of the test chip. . . . . . . . . . . . . . . . . 826.3 Test Chip core SPICE symbol with ESD protections blocks

diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846.4 LV input protection scheme based on local ESD clamp protec-

tions and the path follow by the ESD event from the input padto VSS or VDD, and viceversa. In the figure are also shownthe AMIS I3T50u standard cells for the ESD1, ESD2, ESD3and ESD4 blocks. . . . . . . . . . . . . . . . . . . . . . . . . . 85

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6.5 Test chip core with 40V HV IO ESD protection strategy bothfor the LFPDM50 in HS configuration (right) and for theVFNDM50 in LS configuration (left) schematic diagrams. . . . 88

6.6 Layout of the test chip with ESD protections (a). SEM pictureof the test chip (b). . . . . . . . . . . . . . . . . . . . . . . . 90

7.1 Schematic of the circuit comprising of the Power Amplifierand transformer to step up the AC voltage magnitude of theFunction Generator till 36 Vpeak (a). Voltage level shiftercircuit (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.2 Schematic internal view of the driver circuit. . . . . . . . . . . 947.3 Test board schematic circuit set for the start up verification. . 967.4 Test board schematic circuit set for the control switches rec-

tifier verification. . . . . . . . . . . . . . . . . . . . . . . . . . 967.5 (left) Rectified voltage measured at the output VO1 (top wave

form) and single voltage wave form measured at the input AC1(bottom wave form). (right) Rectified voltage measured at theoutput VO1 (top wave form) and pulse wave form applied atthe gate G1 of the chip (bottom wave form). . . . . . . . . . . 97

7.6 Measured load voltage (a) and output power (b) with respectto the resistive load and for different input voltage values ininput to the test chip. . . . . . . . . . . . . . . . . . . . . . . 98

7.7 Set up to estimate the effective input power. . . . . . . . . . . 997.8 Measured input power (a) and efficiency (b) with respect to

the resistive load and for different input voltage values in inputto the test chip. . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.9 Test board circuit and set up of the experimental tests. . . . . 101

8.1 The fabricated prototypes - PBG1 and PBG2 - made of PSI-5A4E with a steel proof mass attached to the free end, andclamped to a steel support. . . . . . . . . . . . . . . . . . . . . 110

8.2 The prototype generator (PBG1) mounted on the vibrometer(Tira TV50018) used to perform the experimental tests. . . . . 110

8.3 Schematic diagram of the test set up for the open circuitvoltage (left) and resistive load voltage measurements (right)across the output of the PBG prototype. . . . . . . . . . . . . 111

8.4 Measured open circuit voltages (peak values) at various fre-quencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.5 Measured open circuit voltages (peak values) and powers vs.load resistance at 32 Hz (resonance frequency of the PBG) . . 112

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8.6 Measured PBG output voltage and rectified voltage with re-spect to time (a). Voltage regulator measured open circuitvoltage and for a 10 kΩ resistive load (b). . . . . . . . . . . . 113

8.7 Model of a linear vibration-based electromagnetic generator. . 1168.8 Equivalent electromechanical Piezoelectric Bender ElectroMag-

netic Generator model. . . . . . . . . . . . . . . . . . . . . . . 1198.9 Equivalent electromechanical Piezoelectric Bender ElectroMag-

netic Generator model, in case of parallel connection of the coiloutput with the PBG output. . . . . . . . . . . . . . . . . . . 119

8.10 Equivalent SPICE model circuit of the Piezoelectric BenderElectroMagnetic Generator. . . . . . . . . . . . . . . . . . . . 122

C.1 Symbol and cross-section of the VFNDM50 and LFPDM50VDMOS transistors and cross-section of the FID50U diode,respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

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List of Tables

1.1 Comparison of various power sources for power au-tonomous sensor systems. . . . . . . . . . . . . . . . . . . 8

2.1 Summary of vibration-based electrostatic genera-tors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 Summary of vibration-based electromagnetic gen-erators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3 Summary of vibration-based piezoelectric bendergenerators . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1 ATA6285/6 parameters. . . . . . . . . . . . . . . . . . . . 383.2 Summary of the energy/power consumption estima-

tions to perform a sensor sampling and transmis-sion for power autonomous wireless sensors. . . . . 39

6.1 Summary of the ESD protection cells specifications. 846.2 NPOR electrical parameters. . . . . . . . . . . . . . . . 866.3 HIPOR electrical parameters. . . . . . . . . . . . . . . 89

C.1 Summary of the AMIS I3T50-U devices used. . . . . . 128C.2 VFNDM50 device parameters. . . . . . . . . . . . . . . . 128C.3 LFPDM50 device parameters. . . . . . . . . . . . . . . . 129C.4 FID50U device characteristics. . . . . . . . . . . . . . . 130

D.1 Results of the parametric analysis in case of Typ-ical (Typ), Worst Case Speed (WCS), Worst CasePower (WCP), conditions operation. . . . . . . . . . . 132

D.2 Results of the parametric analysis in case of Typi-cal (Typ), Minimum (Min) and Maximum (Max) con-ditions operation obtained by varying the multi-plier of the diode. . . . . . . . . . . . . . . . . . . . . . . 133

xv

Chapter 1

Introduction

1.1 Motivation: wireless micro/nano sensor-

based electronic system

The demand for completely self-powered integrated electronic systems for anumber of applications, such as implantable devices [Platt et al., 2005], real-time monitoring of the health of infrastructures, environmental monitoring,medical/health care systems, has resulted in an increased research activityfor energy harvesting devices and systems, micro and nano electromechani-cal systems (MEMS/NEMS), nanosensors, ultra low power electronics. Suchsystems comprising of on-chip sensors or actuators, power management elec-tronics, elaboration unit or also DSPs, and suitable RF circuitry, require theirown power supply which in most cases is the conventional electrochemicalbattery, as shown in Fig. 1.1. In the recent years the research community hasfocused its effort on 1) increasing the energy/power efficiency of electronicsystems, or stated in other terms, in the effort of reducing as much as pos-sible the current and power consumption of each embedded basic electroniccomponent of a wireless sensor system, in the optic to enhance the lifetime ofthe system; 2) scaling as much as possible the dimensions of sensors and elec-tronic units to make the wireless system, ubiquitous, pervasive, non-invasive;3) integrating all the units composing the system on single silicon chip.

In these last years the research activity has addressed at the developmentof power management techniques both hardware and software, in order toreduce the power consumption of the electronic units of a wireless sensorsystem, and hence, increasing the life time of the wireless sensor battery.The hardware approach has addressed at lowering as much as possible theenergy consumption of electronic devices, by developing techniques like Dy-namic Voltage Scaling (DVS) [Pering et al., 1998], optimized wake-up pro-

1

Figure 1.1: block diagram of a battery-supplied wireless sensor system.

cedures [Ostmark et al., 2006], and so forth. Data converters, whose FOM(Figure Of Merit) of recent ADCs is better than 50fJ/conversion; micro-controllers, microprocessors or DSPs, which are reaching the 10µW/MMAC(Watts per millions of multiply-accumulate operations per second) accord-ing to Gene’s law1; transceiver or RF units, which are reaching the level of3nJ per received-transmitted bit. This trend and effort has the aim to buildup an energy/power autonomous system [Belleville et al., 2009]. The soft-ware approach has addressed at developing optimized algorithms to makerunning on the CPU unit of a wireless sensor system, allowing managing ina smart way the low useful power made available by batteries and, at thesame time, increasing the lifetime of batteries and of wireless sensor system[Barboni and Valle, 2008].

Even if, both hardware and software approaches are important for limit-ing the power consumed by electronic systems, however, they do not solve theproblem of the battery which always needs to be replaced. Task this, whichcan become very tedious, expensive and risky especially in cases like im-plantable devices. Besides, in case of ecologically-sensitive places, like lakes,rivers [Harnett, 2008], forests, the use of wireless sensor systems, poweredby batteries, could be impractical not only for the issue due to the batteryreplacement for hundreds or thousands of wireless sensor systems spread ev-erywhere to realize a network in the environment to be monitored, but also

1Gen’s Law states that power dissipation will be reduced at roughly the same rate thatperformance increases. Performance is suppose to double every 18 months, so accordingto Gene’s Law, power dissipation will decrease by half every 18 months. Of course, thispresents a problem because now leakage power is approaching the same level as activepower dissipation.

2

because they could be physically embedded in the environment itself. Fur-ther, batteries contain toxic chemicals and need to be quickly retrieved, afterthe batteries discharge.

At nano and micro scale sizes, powering nano and microelectromechanicalsystems (MEMS) by means of batteries could become unpractical. Moreover,because of the size of the battery, compromising also the big effort of scalingthe electronic devices. In fact, the size of a battery is the most limiting factorfor reducing the wireless sensor system sizes. As example, the Crossbow micamote is powered by two AA size batteries that occupy 90% of the entire devicevolume. Even if the battery technology is improved in the last years, batteriesare the largest and most expensive component of a wireless sensor system, andfurthermore, the most limiting factor for the life time of the wireless sensoritself because of the limited lifespan of the battery. Therefore, wireless sensorsystems need other powering techniques and renewable energy/power sourcesfrom ambient for replacing batteries and hence really making ubiquitous andself-sustaining the wireless sensor systems.

MEMS-based devices (sensors and actuators) have been integrated withsuccess in a lot of different electronic applications, to build up integratedmicrosystems. One of the key advantages of MEMS-based devices is thatthey can be integrated with state-of-the-art silicon microelectronics on a verylarge scale (e.g. micromachined accelerometers for automobile crash tests anddetection [Ferraresi and Pozzi, 2009], microsystems integrating chemical/gassensors on a single chip with CMOS-based readout electronic to build upelectronic noses [Yang et al., 2010], and so forth). MEMS systems can thensense a wide variety of different phenomena at low cost and efficiently, andthey can be integrated and used with success in Wireless Sensor Networksand practically in a wide range of industrial sectors: automotive, telecom-munications, aerospace, data storage and biotechnology.

Nanotechnology is a field of research, which is rapidly growing and evolv-ing and it is offering to researchers a way for manipulating and controllingthe matter at an extremely small scale size, even to the level of moleculesand atoms. Nanoscale engineering (by the use of top-down2 and bottom-up3 approaches) can offer both control and manipulative ability over indi-

2The top-down approach often uses the traditional workshop or microfabrication meth-ods where externally-controlled tools are used to cut, mill, and shape materials into thedesired shape and order. Micropatterning techniques, such as photolithography and inkjetprinting belong to this category.

3The bottom-up approach uses the chemical properties of single molecules to causesingle-molecule components to self-organize or self-assemble into some useful conformation,or rely on positional assembly. These approach utilizes the concepts of molecular self-assembly and/or molecular recognition.

3

(a)

(b)

Figure 1.2: (a) Top view and cross-sectional diagrams of nanosensors arraywith silicon CMOS circuitry [Xu et al., 2004]. (b) Micrographs of the testchip with an array of nanowires and red-out circuit and the UWB transmitterchip [Narayanan, 2004].

vidual atoms and molecules, determining physical, chemical and even bio-logical material properties. The sensitivity that nano scale sensors can ob-tain can therefore be much greater than the sensitivity of microsensors andother MEMS-based sensors. In addition, due to the incredibly tiny dimen-sions of nanosensors, a large number of low-power-consuming nanosensorswith diverse functionalized properties can be array-connected and integratedon a single silicon chip along with CMOS-based electronics, as shown inFig. 1.2 [Xu et al., 2004]. Already developed nanosensor devices includingNEMS-based cantilever sensors [Li et al., 2007], which are sensitive to ultra-small masses and forces, nanowires [Fan et al., 2008] and carbon nanotubes[Li et al., 2004] used as chemical, pressure, humidity, accelerometers, biosen-

4

sors [Jang, 2009] all deployed in array configurations, can allow a sensorsystem having high surface to volume ratio, which can improve detectionsensitivity and response time due to more reaction area per volume and re-duced diffusion time. Examples, of integration of nanosensors array withCMOS-based electronics using the technique called dielectrophoretic (DEP)assembly and the design of a low-power transmitter for wireless communi-cations can be found in [Narayanan, 2004], as shown in Fig. 1.2. Otherinteresting work can be found in [Fan et al., 2008], where Scientists at theU.S. Department of Energy’s Lawrence Berkeley National Laboratory andthe University of California at Berkeley have created the world’s first all-integrated sensor circuit based on nanowire arrays, combining light sensorsand electronics made of different crystalline materials.

Next future step will be the integration of biosensors [Jang, 2009] andnano-scale devices (e.g. nanosensors) [Xu et al., 2004] into low-cost, ultra-low power wireless sensor systems. Besides, nanosensors, ultra low-powerelectronics (i.e. front-end electronic, ADC, DSP, and RF unites, power man-agement circuitry), and ambient energy scavengers can be integrated on atiny single silicon-based chip to build up the next generation of ubiquitouspower autonomous wireless sensor systems.

1.2 Wireless power autonomous micro/nano

sensor-based system

A big effort in the research activity has therefore been done for reducing size,improving sensors sensitivity with micro and nano sensor devices, improv-ing efficiency and reducing the power consumption of all electronic blockscomposing a wireless sensor system. However, the vast reduction of size andpower consumption of CMOS-based circuitry has led to a large research ef-fort based in the context of the vision of ubiquitous networks of wirelesssensor systems, and also highlight the issue of finding suitable power supplysources in place of batteries. Moreover the new grand challenge faced bycircuits and systems communities is to design green electronic devices andsystems that consume less energy, thus lead to the reduction of global CO2

emission (e.g. 2010 International Conference on Green Circuits and Sys-tems). Therefore, one of the major challenge for the developing of a powerautonomous wireless sensor system is to realize a power unit composed by1) a suitable device as alternative to batteries that can be miniaturized us-ing microfabrication technologies; it should be silicon-compatible in orderto be integrated with CMOS-based electronics; and above all it should be

5

able to harvest the whole energy needed for the power supply of the wire-less sensor system from a renewable power source present in the ambientwhere the system itself operates - this eliminate the need to have a localenergy reservoir which contains a limited energy and the entire lifetime ofthe wireless sensor system; 2) designing and developing a low power/currentconsuming and integrated power management circuit, which is efficient andoptimized to manage the environmental energy in order to make the sys-tem - already communication-autonomous thanks to the wireless technology- self-sustaining and ambient-aware.

1.2.1 Renewable ambient energy sources

Renewable power sources like light, thermal, radio frequency, sonic wavesand kinetic energy present within the sensor environment can be used togenerate electrical energy for the power supply of low power and ultra-lowpower electronic devices. Many transducers exist to harvest the ambientenergy and converting it into electrical one and among them the most knownare the solar cells.

Solar cells can offer energy densities of about 100 mW/cm2, when they areenlightened by direct sunlight and of about 100 µW/cm2, when enlightenedby artificial light [Paradiso and Starner, 2005]. However, due to the not sohigh efficiency conversion of solar cells (i.e. about 10-24%), in case of outdoorenvironment, only 15 mW/cm2 of power density can be truly harvested, andin case of indoor environment the harvested power density decreases at only10 µW/cm2. Besides, solar cells are limited in dim ambient light conditionsand obviously unsuitable in embedded applications where no light may bepresent.

Thermo Lifer Energy, Corp., developed and designed some little andcompact Low Power Thermoelectric Generators (LPTG), which allow (usingsome thermopile couples which exploit the Seebeck effect) converting gradienttemperature to electrical energy. When both heat couple plates are thermallyconnected with a heat source and a heat sink, heat flows through thermopilesand is converted directly into electricity. With gradient temperatures of only5 C, these LPTGs can supply powers of 30 µW, and up to 135 µW if thegradient temperature goes up to 10 C.

Other energy harvesting approach, involves broadcasting RF energy topower remote devices (e.g. electronic ID tags, smart cards). This solutionanyway is limited by the distance between the device to be powered andthe RF energy source. Using the simple expression of the power receivedby an anisotropic antenna, which neglects reflections and interferences, here

6

reported

Pr =P0λ

2

4πR2(1.1)

where P0 is the transmitted power, λ is the wavelength of the signal, R isthe distance between transmitter and receiver, the power received by theelectronic device to be powered [Smith, 1998], if it is assumed a distance be-tween transmitter and receiver of 5 meters, a transmitted power of 1 W atthe frequency of 2.5 GHz, is about 50 µW. In an indoor environment, how-ever, a more likely figure is 1/R4, rather than 1/R2. Passive radio-frequencyidentification (RFID) systems derive their energy inductively, capacitively,or radiatively from the tag reader. RFID tags generally consume between 1and 100 µW, but the RF energy source should be very close to the tag inorder to succeed to power it.

In [Dietterich, 2009] an ultra-low power temperature sensor node has beendeveloped to harvest radio frequency energy broadcasted by a base station(standard electric-powered) placed on the center of a wireless sensor networkradio frequency-covered area of 30 m of diameter. The developed sensor nodeprototype includes a temperature sensor, an RF energy harvesting circuit, abinary frequency shift keying (BFSK) receiver and transmitter, which sharethe same antenna. The ultra-low power temperature sensor node succeededto measure a range of temperatures from -10 to 40 C, with an accuracy of±0.5 C, consuming only 1 nJ per measurement.

Other studies have been made [Paradiso and Starner, 2004], to under-stand how much energy is possible to extract from human body (e.g. bygradient temperatures, breathing, blood flow, etc.) and from human activ-ities (e.g. walking, keyboard typing, etc.), thus, using this energy to powerportable and wearable electronic devices [Paradiso and Starner, 2005]. Themost energy rich and most easily exploitable human activity energy source,according to what stated in [Paradiso and Starner, 2004], occurs at the footduring the heel strike. Some back-to-back unimorphs piezoelectric shoe in-serts embedded in an insole have been able to generate an average power ofabout 8.4 mW while a person was walking [Shenck and Paradiso, 2001].

1.2.2 Vibrational sources: a powerful option to batter-ies

Among various sources the ambient vibrational one is the most promisingsource from which harvesting or scavenging energy to be converted to electric-ity, and powering low power electronic devices, such as, small electronic com-ponents, wireless sensors, wireless implantable biosensors. Table 1.1 shows a

7

Table 1.1: Comparison of various power sources for power au-tonomous sensor systems.

SourceSource Physical Harvested Power

Characteristic Efficiency (Range)

Solar

Office 0.1 mW/cm2 10-24% 10 µW/cm2

Outdoor 100 mW/cm2 15 mW/cm2

Vibrations

max power is

source and

device

dependent

1-10 m/s2 0.65 µW/cm2

10-500 Hz 375 µW/cm2

8.1 mW/cm2

Thermal Energy

Human 20 mW/cm2 0.1% 25 µW/cm2

Industry 100 mW/cm2 3% 1-10 mW/cm2

RF (EM Energy)

GSM 900MHz 0.3-0.03 µW/cm2 50% 0.1 µW/cm2

1800 Hz 0.1-0.01 µW/cm2

comparison among the various power sources described in the previous sec-tion with the vibrational one. The amount of energy that can be obtaineddepends basically on the quantity and form of vibrational energy presentin the environment, the efficiency, size and kind of the transducer and alsoon the power management electronics. Furthermore, as it can be noted inFig. 1.3 where is shown a comparison among vibration, solar and differenttechnology battery powers with respect to the life time of the power source[Roundy et al., 2004], if the projected lifetime is more than a few years, andsufficient light energy is not available in the environment in which the deviceshould operate, mechanical vibration conversion is the most practical alter-native to batteries and light. The use of vibrational energy available in theambient (such as household goods like microwave oven, refrigerators, washingmachines, industrial plant equipments, automobiles, buildings, bridges, andso forth) where the electronic device operates, would allow the replacementor at least the minimization of the requirement of external power sources orbatteries.

Environmental energy harvesting (scavenging) techniques, therefore, mightalleviate, if not solve altogether, the problem of battery-supplied electronicsystems, by developing meso-scale (order of several centimeters), micro ornano-scale (order of micrometers and nanometers) energy harvesting (scav-

8

Figure 1.3: Comparison of powers generated from vibrations, solar, andvarious battery chemistries with respect to the life time of the power sourceexpressed in years [Roundy et al., 2004].

enging) devices that can ”scavenge” the normally wasted energy from envi-ronment and convert it into usable form, or gathering it into storage devices,like capacitors or batteries, and hence, powering the electronics embeddedon wireless sensor systems. Vibrational sources are the most suitable candi-date as possible power source for the wireless power-autonomous micro/nanosensor-based system, and therefore in this thesis work they have been usedas the renewable ambient energy source.

1.3 Thesis objectives: proposed harvesting

system architecture

The block diagram shown in Fig. 1.4, of a possible newly architecture forwireless power-autonomous micro/nano sensor-based system will be the ref-erence of this thesis work. The system comprises of an array of micro/nanosensors; a suitable interface to allow connecting the sensors array to the signalconditioning circuitry (which performs amplification of the low level sensorsignals from sensors, adjust the output signal swing, sampling, convertingthe signal from analog to digital format); an ultra low power elaborationunit; an ultra low power RF module comprising of a transceiver; a harvester(scavenger) connected to an optimized power management circuit to realizethe small, smart, efficient and low power/current consuming power unit.

The work presented in this thesis is primarily focused on the design andimplementation of the power unit for the power supply of the wireless sen-sor system shown in Fig. 1.4. The power unit is composed by two basicblocks, which are the vibration-based energy harvester (scavenger) and an

9

Figure 1.4: Block diagram of a wireless power autonomous sensor system.

integrated power management circuit, which is composed by an AC-DC con-verter which rectifies the alternative signal delivered by the vibration-basedgenerator; a DC-DC converter or voltage regulator which adapts the level ofvoltage to the storage element characteristics (e.g. battery) in the case ofenergy harvesting systems, or (and) it adapts the voltage to the requirementsof the electronics units embedded in the wireless sensor system, in the caseof energy scavenging (harvesting) applications which require (not require)a continuous operation. In fact, energy harvesting techniques aim to col-lect ambient energy to help power systems, possibly storing energy when itis not required (e.g. buffer batteries, capacitors, springs, supercapacitors)[Ottman et al., 2002]. Energy scavenging techniques aim, on the contrary,to scavenge the energy from the ambient to power electronics systems forcontinuous operation [Metzger et al., 2007]. Therefore, different power man-agement circuit approaches are used for energy harvesting and scavengingsystems according to the application, the amount of environmental energythat can be converted into electricity, the kind and efficiency of the envi-ronmental energy transducer. However, hybrid solutions where a storageelement, which could be a battery as well as a capacitor or supercapacitor,can be adopted.

The study of the state-of-art of vibration-based generators (VBG) - i.e.electrostatic, electromagnetic and piezoelectric - must first be addressed inorder to identify the suitable VBG to be used to convert ambient mechanical

10

vibrations to electricity and hence powering the embedded units of the sys-tem in Fig. 1.4. A comparison among the advantages and disadvantages ofvibration-based generators - which will be discussed in the Chapter 2 - ad-dressed us to explore the possibility of using piezoelectric bender generator(PBG) as harvester (scavenger) to convert mechanical vibrations to elec-tricity. Therefore, the focus of this thesis work is on the optimal design ofintegrated power management electronics for a piezoelectric generator droveby vibrations.

A feasibility case study - which will be reported and discussed in theChapter 3 - has the goal to explore and study the use of PBG has powersource for wireless sensor systems, in particular for a wireless tire pressuremeasurement system embedded on the wheel of a car. The wheel of thecar is a very extreme environment where mechanical vibrations and radialaccelerations magnitude can reach values three order of magnitude largerthan those ones of common ambient vibrational sources. In fact, it is con-sidered - according to Cantatore et al. - the only one environment whichcould excite a vibration-based generator scaled to micro sizes so that it cangenerate enough power density for the power supply of a state-of-art wire-less sensor microsystem with on-board radio and sufficient processing power[Cantatore and Ouwerkerk, 2006]. In regard to the integration of the systemdepicted in Fig. 1.4, knowing if a VBG scaled at micro/nano sizes couldstill be able to power a wireless sensor system and their limits is an im-portant aspect that an electronic designer should know. By this knowledgethe electronic designer can design and optimize the electronic circuits in or-der to adapt them to the energy made available by the micro/nano harvester.

Another important aspect that must be addressed and that is also use-ful for an electronic designer is the development of a realistic model of thepower source, which in this case is the vibration-based generator. Thecharacteristic equations of the general model of a vibration-based genera-tor [Williams and Yates, 1996] - as will be introduced and discussed in theChapter 2 - can give to the designer the knowledge of a roughly estimationof the maximum power that a VBG can produce. Moreover, those character-istic equations do not take into account neither the geometrical and physicalparameters of the generator, nor the kind of the vibration-based genera-tor. The power output can be roughly estimated given only the magnitudeand frequency of input vibrations, the overall size (and therefore mass) ofthe device, and knowledge of the mechanical and induced electrical damp-ing ratios. Moreover, the general model is well suited for electromagneticgenerators rather than for piezoelectric generators. The electromechanical

11

model of the PBG developed by Roundy et al. [Roundy et al., 2004] cangive the designer a more accurate estimation of the power and voltage thatthe generator can produce, because based on an analytical mathematical ap-proach which takes into account both geometrical and physical parametersof the generator itself. Anyway, for an electronic designer it is useful tohave available a SPICE model of the power source above all in the contextof the integration of the electronics on chip and the possibility to simulatethe overall system - SPICE model of source and integrated electronic - withSPICE. The power sources which SPICE makes available (i.e. AC voltageindependent sources) are not suited to represent a vibration-based genera-tor, in particular a PBG. Moreover, a SPICE model of the VBG can givethe designer the possibility of studying the reciprocal interaction among themechanical and electrical parameters, that the use of the only power sourcesavailable in SPICE cannot offer. Therefore, based on the electromechanicalmodel of the PBG reported in [Roundy et al., 2004], which is suited to beimplemented in SPICE the first objective of this thesis work to be pursuedwill be the implementation in SPICE of the electromechanical model of thePBG - which will be discussed in the Chapter 4.

Vibration-based generator produces AC voltages that need to be con-verted, regulated and stabilized in DC before being used to power electronicsystems. A diode bridge rectifier is the common and simplest approach fol-lowed in literature to perform the AC-DC conversion. However, integratingonly passive devices as diodes on chip does not take advantage of the flexi-bility of the use of active devices with optimized control circuit which couldgive the possibility to manage in a smart way the power, and voltage gener-ated by VBGs. Performance, efficiency and low-power consumption can beimproved, and this is an important aspect above all in the context of energyscavenging applications, where the available energy may be poor. However,a fully active solution for the bridge rectifier, might need a more complicatedcontrol circuit to drive the active devices, which can increase the complex-ity and power consumption of the system. Therefore, a compromise amongsimplicity, efficiency, flexibility and performance is necessary. In this work asemi-active approach for the bridge rectifier is proposed. The design of thesemi-active bridge rectifier is the second objective of this work and it will bediscussed in Chapter 5.

The voltage regulator is a basic unit of the power management system. Itcan be used to regulate and adapt the diverse voltage levels needed to powerthe electronics belonging a system and also for optimizing the power transfertoward the final load, which could be a battery [Ottman et al., 2002] or the

12

Figure 1.5: Block diagram of the wireless power autonomous sensor systemwith semi-active bridge and DC-DC switching voltage regulator blocks.

units embedded in the wireless sensor system shown in Fig. 1.4. A LowDrop Out (LDO) linear voltage regulator can be used [Leland et al., 2006]in a store-and-release power management strategy to allow or not allow thepower transfer from a storage element to the load. This energy harvestingstrategy is adopted when the power generated by the harvester is not enoughto power the circuit for continuous operation. The power management circuitshould then store the energy generated by the harvester into a capacitor orbattery, till sufficient energy is stored and hence it can be released to powerthe electronic circuit. When the energy level decreases to a minimum value,the power management stops the energy flow toward the load and startsagain to store the energy by charging the capacitor. The use of LDO linearvoltage regulators, however, has the drawback of the low conversion efficiency- around the 40% - being dependent on the ratio between the output voltageand input voltage.

DC-DC switching converter having high conversion efficiency - aroundthe 90% - can be used to perform more efficient power management strate-gies for the energy harvesting from vibrational sources. Suitable adaptivecontrol algorithms can be implemented by using DSP [Ottman et al., 2002]or built by using suitable circuits which implement the algorithm relations[Ottman et al., 2003] in order to control the switches of the DC-DC switch-ing converter by varying the duty-cycle to optimize the power stored by thebattery. Maximum power transfer from energy harvester to the load cantherefore be performed by means of smart control switch strategies.

13

Figure 1.6: Block diagram of the power management blocks realized asASIC and PCB.

In the case which both vibrational source and VBG can allow the con-tinuous operation of the electronic system to be powered, e.g. a wirelesssensor, energy scavenging systems are better suited, as aforementioned, andDC-DC switching converter can be used to perform two tasks which are themaximum power transfer toward the load and/or regulation of the voltagegenerated by the scavenger at the useful level in order to adapt it to theright level needed by the circuit to be powered. In this last case, if differ-ent circuit blocks need different voltage levels, hence, more DC-DC switchingregulators can be present in the power management block. DC-DC switchingconverters are well suited to be used for energy harvesting and scavenging ap-plications, thanks to their high efficiency and flexibility which allow them tobe controlled by different switching control strategies. Therefore, the DC-DCswitching converter as voltage regulator for energy scavenging applicationswill be used also in this work. Because of a PBG generates high level voltages,the use of a step-down DC-DC switching converter - i.e. a buck converter -is needed.

The major effort in the development of the power management circuitis the design of the driver circuit, which controls the switches of the con-verter. In this work, the voltage regulated by the buck converter is usednot only for being compared with a reference voltage in order to performthe regulation, but, also is used to power the control circuits of the powermanagement system - i.e. the rectifier control circuit and the driver circuit.

14

The block diagram shown in Fig. 1.5 illustrates the proposed architecturefor the power management system powered by the PBG. Therefore, the thirdobjective of this thesis work is the design of an integrated, power/current-aware and self-sustaining voltage regulator. The issues addressed to makethe voltage regulator self-powered will be discussed in the Chapter 5, wherea SPICE analysis and simulation results of the whole system comprising ofthe SPICE model of the PBG, the semi-active bridge and voltage regulatorwill be presented.

The last part of this work concerns the design, development, fabricationof a prototype ASIC, a test printed circuit board and a PBG prototype.Fig. 1.6 shows the diagram block with the parts of the power managementcircuit which have been integrated and those ones realized with discrete com-ponents on printed circuit board. As it can be seen, only the rectifier and theswitching part of the step-down buck converter have been integrated. Thecontrol circuits and the LC filter of the buck have been inserted in the testPCB. This hybrid solution - ASIC and PCB - has been adopted in order tohave more flexibility in the design and for the experimental tests, integratingthe key components - rectifier and switching part of the DC-DC converter -in the ASIC, while, the other components - control circuits and LC filter -left outside the ASIC. Chapters 6, and 7 will present the design of the ASICtest chip and test board, and the experimental validation test results.

In order to validate the SPICE equivalent model of the PBG is necessaryto compare it with a realistic PBG. By performing experimental tests withthe prototype PBG and hence comparing the measured results with the sim-ulated ones, would allow understanding what are the limits of the developedSPICE model and hence, through the study and understanding of the resultsobtained, optimizing the developed SPICE model in order to make it closerto the realistic counterpart. The concluding chapter of this work presentsthe preliminary experimental tests realized with a fabricated PBG prototype,either tested alone or connected to the ASIC and test board.

Moreover, in the context of the future trends, an analytical mathematicalanalysis of a vibration-based hybrid generator, realized joining a PBG withan electromagnetic generator is also presented.

15

Chapter 2

Vibration-based energyharvesting

2.1 Introduction

The subject of this chapter are vibration-based energy generators, whichconvert kinetic energy in the form of mechanical vibration present in theenvironment where the generators are used, into electricity. Vibrations aretypically converted into electricity by means of electrostatic, electromagneticor piezoelectric transducers. The amount of energy/power that can be gen-erated by these transducers depends fundamentally upon the quantity ofvibrations available in the application environment, the efficiency of boththe transducer and power management electronic.

Following sections illustrate the general model used to describe vibration-based generators, based on a one-degree-of-freedom mass-spring-damper sys-tem, and the state of art of the three kind of vibration-based generatorsreported in the literature. A summary of the three vibration-based genera-tors performances is given at the end of the chapter.

2.2 General model of a vibration-based gen-

erator

In the literature vibration-to-electricity converters are described like a one-degree-of-freedom second order spring-mass-damper system connected to aninertial frame, which acts as fixed reference forced by a vibration source.Fig. 2.1 shows the equivalent system model in which there is an inertialmass m, a spring of stiffness k and a damper of damping coefficients ce and

16

cm, named electrically induced damping coefficient and mechanical damp-ing coefficient, respectively. The spring and the damper are both connectedbetween the inertial frame and the inertial mass. In Fig. 2.1, y(t) is theabsolute motion of the frame and that one of the proof mass is denoted asx(t) = y(t) + z(t), where z(t) represents the displacement of the mass withrespect to its rest position relatively to the frame. The inertial frame isuseful for transmitting vibrations to the suspended inertial mass with theresult of producing the relative displacement z(t) between the inertial massand the frame. The relative displacement can then be used to generate en-ergy by causing work to be done against the damping force. The nature ofthis damping force realized by an electric or magnetic field, or by strain-ing a piezoelectric material defines the type of vibration-based generator(VBG) [Mitcheson et al., 2004]. Besides, such a system possesses a naturalresonant frequency, therefore vibration-based generators can be designed inorder to match the fundamental frequency of the environmental vibrationsource. Matching the two frequencies allows to magnify the environmentalvibration amplitude by the quality factor of the resonant system.

With respect to the general model depicted in Fig. 2.1 the transduceris described by the damper, because the conversion mechanism damps themass. The expression for the electrically induced damping coefficient, ce isdifferent for each kind of VBG [Beeby et al., 2006b, Mitcheson et al., 2004].The inertial frame (who acts as a fixed reference) is excited by a sinusoidalvibration source modeled as y(t) = A sin(ωt− φ). Through the frame vibra-tions are transmitted to the suspended inertial mass, producing the relativedisplacement z(t) between them. This relative displacement is sinusoidal inamplitude, so that it can drive a suitable transducer to generate electricalenergy [Williams and Yates, 1996].

Consider the mass-spring-damper system as shown in Fig. 2.1. Appli-cation of the Newton’s law to the free-body diagram of Fig. 2.1 (b) yields

mg − k (x+ ∆st − y)− cT (x− y) = mx (2.1)

ormx+ cT x+ kx = cT y + ky (2.2)

where cT = ce + cm. In (2.1) and (2.2) the static deflection of the springdenoted as ∆st = (mg)/k cancels the gravity term mg because of the static-equilibrium position condition of the system [Kelly, 2000]. Define

z(t) = x(t)− y(t) (2.3)

as the displacement of the inertial mass relative to the displacement of the

17

(a) (b)

Figure 2.1: General model of the linear mass-spring-damper system repre-senting the resonant inertial generator (a). Free-body diagrams at an arbi-trary instant including effects of the absolute motion of the frame, y(t) (b).

frame. Equation (2.1) is rewritten using z as the dependent variable

mz + cT z + kz = −my. (2.4)

Dividing equation (2.4) by m yields

z + 2ζTωnz + ω2nz = −y (2.5)

where cT/m has been replaced by 2ζTωn, with ζT defined as the equivalentdamping ratio and ωn =

√k/m defined as the natural frequency of the

system. If the absolute motion of the frame is given by a single-frequencyharmonic of the form

y(t) = Y sinωt (2.6)

equation (2.5) becomes

z + 2ζTωnz + ω2nz =

(ω2Y

)sinωt (2.7)

where ω can be defined as the fundamental frequency of the vibration source,and (ω2Y ) is the acceleration amplitude, denoted as A, of the vibrationalsource. The standard steady-state solution of (2.7) for the inertial massdisplacement is given by

z(jω) =

(ω

ωn

)2

[1−

(ωωn

)2]+ j2ζT

(ωωn

)Y sin (ωt− φ) . (2.8)

18

The square of the module of (2.8) is given by

|z|2 =

(ωωn

)4

[1−

(ωωn

)2]2

+

[2ζT

(ωωn

)]2Y2 (2.9)

and the phase φ is given by

φ = tan

2ζT

(ωωn

)1−

(ωωn

)2

. (2.10)

The mechanical power converted into electrical is equal to the power removedfrom the mechanical system by the electrically induced damping coefficient,ce. The electrically induced force is then, Fe = cez, and the related power isdefined as

Pe =

∫ v

0

Fedv = ce

∫ v

0

vdv (2.11)

where v = z, then, the expression for the power becomes

Pe =1

2cez

2 = ζeωnmz2 (2.12)

where ce = 2ζeωnm. Knowing that z = jωz and that |z| = ω|z|, substitutingthis last one relation into (2.12) and considering equation (2.9), it yields[Williams and Yates, 1996]

Pe =

mζeY2ω2ωn

(ωωn

)4

[1−

(ωωn

)2]2

+

[2ζT

(ωωn

)]2 (2.13)

where ζT = (ζp + ζm + ζe) is the total damping ratio. The term ζp representthe parasitic damping caused by undesirable effects such as air resistance.If the fundamental mode of the vibrational source matches the resonancefrequency, ω = ωn, of the system, the maximum power can be generated bythe system and it is given by

Pe,max =mζeY

2ω3n

4ζ2T

(2.14)

19

or in terms of the acceleration amplitude of the vibrational source

Pe,max =mζeA

2

4ωnζ2T

. (2.15)

Equation (2.15) shows that the system must be designed so that its resonancefrequency (or natural frequency of the system) matches the lowest fundamen-tal frequency of the vibrational source, due to the fact that the maximumpower at resonance is inversely proportional to frequency.

Equations (2.14) and (2.15) are steady-state solutions and are valid onlyat resonance. From (2.13) it can be noted that the damping factor controlsthe selectivity of the device, i.e. for applications where the vibration fre-quencies are well known and concentrated around one point, a low dampingfactor would give a more peaked response and power. According to (2.14)or (2.15), if the damping factor reduces up to zero it is possible to obtain aninfinite generated power at resonance.

However, the damping factor cannot be equal to zero and so the electri-cally induced power that can be generated has a finite value. Reducing thedamping factor, however, increases the displacement of the mass - z(t) - upto a maximum limit value at resonance. At resonance, equation (2.9) givesthen, the maximum displacement of the mass

zmax =Y

2ζT(2.16)

which should be taken into account when designing vibration-based generator(VBG) if the mass can move out the frame - limited in size and geometry- where the generator itself is inserted. The maximum power that can begenerated by a VBG in terms of maximum displacement, is therefore

Pe,max = mζTω3nz

2max. (2.17)

As it has been said in the introduction, the characteristic equations of thegeneral model of a vibration-based generator [Williams and Yates, 1996] re-ported above can give to the designer the knowledge of a roughly estimationof the maximum power that a VBG can produce. The characteristic equa-tions of the general model as illustrated do not take into account neitherthe geometrical and physical parameters of the generator, nor the kind ofthe vibration-based generator. The power output can be roughly estimatedgiven only the magnitude and frequency of input vibrations, the overall size(and therefore mass) of the device, and knowledge of the mechanical and in-duced electrical damping ratios, by using equations (2.13), (2.14), (2.15) and

20

(2.17). Moreover, the general model is well suited for electromagnetic genera-tors rather than for piezoelectric generators [Williams and Yates, 1996]. Thegeneral model, moreover, is not suited to be used as reference model fromwhich developed a SPICE model for a VBG. Then, Chapter 4 will introducea better model, based on an analytical electromechanical model, which de-scribes better the behavior of a real VBG, it introduces better expressionsfor the estimation of the power which can be generated by the VBG, but,also, being based on an electromechanical model - described with equivalentelectrical elements of those ones of the general model - can be used as refer-ence model from which deriving a SPICE equivalent version. The followingsections give the reader an overview of the state-of-the-art of vibration-basedgenerators, in order to understand what VBG is better suited to be integratedwith CMOS-based electronics and microfabricated. .

2.3 State-of-the-art of vibration-based gener-

ators

Transduction mechanisms used to convert vibrations into electricity can ex-ploit the mechanical strain or the relative displacement, depending on thekind of transducer. Anyway, the characteristic shared by vibration-basedgenerator is that they generate an AC output voltage, which needs to beprior converted into DC before to be used to power electronic devices. Thebasic and common vibration-based generators usually reported on literatureand used to perform the mechanical to electrical conversion are piezoelectric,electrostatic and electromagnetic.

Piezoelectric materials subjected to mechanical strain induced by me-chanical stress applied by vibrational source become electrically polarized.The degree of polarization is proportional to the applied strain. The piezo-electric material subjected to strain exhibits a creation of a negative chargeon the compressed piezoelectric surface and a creation of a positive one inthe tensed piezoelectric surface, resulting in a negative and positive voltages,respectively, across the piezoelectric material. Therefore, if two electrodesare sputtered onto the top and bottom surface of the piezoelectric materiala differential open circuit voltage can be obtained across the piezoelectricmaterial.

Electromagnetic vibration-based generators exploit as transduction mech-anism the relative displacement in terms of velocity. They can consist of afixed coil and a mobile permanent magnet, or vice versa. The relative mo-tion between the permanent magnet and the coil induces the creation of an

21

electromotive force into the coil proportional to the velocity of the movingpart according to the Lorentz’s Force and Faraday’s Law of induction. If aresistive load is connected to the coil output terminals, a current starts toflow into the coil.

Electrostatic vibration-based generators are practically a variable capaci-tor, consisting of two conductors (one fixed and the other one movable) withusually the air as dielectric. In this case is the relative motion between con-ductors to allow converting vibrations in electricity and the generated voltageis a function of the relative position between conductors.

Following sections give the reader a summary of the state-of-the-art ofthe three kinds of VBGs.

2.3.1 Electrostatic generators

A vibration-based electrostatic generator is simply a variable capacitor, whoseplates are electrically separated from each other by a dielectric that can beair, insulator or vacuum. In order to allow the beginning of the harvestingprocess the capacitance needs to be previously charged by a priming volt-age. The work done against the electrostatic force between the two plates ofthe capacitor, made moving relatively from each other by vibrations providesthe harvested energy. Electrostatic generators are principally fabricated withMEMS techniques. There are three basic types of MEMS vibration-basedelectrostatic generators, which are the in-plane overlap converter, in-planegap-closing converter and the out-of-plane gap-closing converter (see Fig.2.2) [Roundy et al., 2002]. The operating principle of the electrostatic gen-erator bases its working on the variation of the electrostatic force between thetwo plates. The electrostatic force variation depends on the structure of theelectrostatic generator and if the charge (i.e. charge constrained electrostaticgenerator) or the voltage (i.e. voltage constrained electrostatic generator)between the plates is held constant.

In-plane overlap converters can be operated only charge constrained, be-cause the electrostatic force varies with inverse proportionality with respectto the square of the displacement of the mass if the charge is held constant andthe voltage made varying. On the contrary, if the in-plane overlap converteris operated voltage constrained the electrostatic force remains constant.

In-plane gap closing converters can be operated either in charge and volt-age constrained. If operated charge constrained the electrostatic force variesproportionally with the mass displacement, while, if operated voltage con-strained the electrostatic force varies with inverse proportionality with re-spect to the square of the mass displacement.

22

Figure 2.2: Electrostatic generators structures: in-plane overlap converter(left), in-plane gap closing converter (center), out-of-plane gap closing con-verter (right)

Out-of-plane gap closing converters can be operated only voltage con-strained because the electrostatic force varies with inverse proportionalitywith respect to the mass displacement, while, it remains constant if operatedcharge constrained.

Among the three structures the optimization of the design parameters ofthe in-plane gap closing converter could allow obtaining a generated powerdensity higher than the other two structures and equal to about 116 µW/cm3

at the frequency of 120 Hz and acceleration amplitude of 2.25 ms−2. Thedrawback is that it needs a priming voltage of 5 V. Out-of-plane gap clos-ing converter is the following second structure for which, with an optimizeddesign, a high power density can be obtained [Roundy et al., 2002].

Miao et al. have designed an electrostatic vibration-based generatornamed Coulomb Force Parametric Generator (CFPG) whose principal char-acteristic is to be non-resonant. Therefore, it can operate over a wide rangeof excitation frequencies and amplitudes. According to the operating fre-quency and amplitude it can generate voltages up to 220 V. The dimensionsof this device are about 11x11x0.4 mm3 with a proof mass of 0.12 g. Theauthors have predicted a generated power of 80 µW at 30 Hz and 10 ms−2

of acceleration amplitude [Miao et al., 2006].Ryoichi et al. have designed an electrostatic generator named Honeycomb-

type variable capacitor (HVC) that harnesses heart ventricular motion withthe aim of driving a cardiac pacemaker permanently in place of the commonbattery. This electrostatic generator has generated a power of 36 µW, whichhas been enough to drive a cardiac pacemaker in order to perform a con-tinuous electric generation and cardiac pacing for more than 2 hours in theanimal experimental test performed with canine heart [Ryoichi et al., 2002].

23

(a)

(b)

Figure 2.3: Electromagnetic generators: (a) MEMS-based by Beeby et al.,Wang et al., respectively; (b) Millimeter scale by Torah et al., by Glynne etal., respectively

2.3.2 Electromagnetic generators

Electromagnetic vibration-based generators bases their operation on relativemotion between a coil and a permanent magnet. The best design consists ofto keep the coil fixed and to have a mobile permanent magnet, mounted onthe free tip of a cantilever beam, so that it can be used as an inertial mass.Designs with mobile coil and fixed permanent magnet has been proposed inthe literature, but they do not allow generating high output power values.For example, Fig. 2.3 shows the laterally vibrating silicon microgenerator re-ported in [Beeby et al., 2006a] which exhibits a power density of 1.8nW/mm3

- in a volume of about 68 mm3 - and generates only 122 nW of power at theresonance frequency of 9.5 kHz into a 110 Ω load and acceleration amplitude

24

of 3.5 m/s2. The laterally vibrating silicon microgenerator had the woundcopper coil placed into the moving proof mass connected to the wafer bulkby a supporting cantilever beam. Therefore, coils move in the plane of thewafer relative to the fixed permanent magnets. Adhesively bonding the wiresalong the cantilever, increases the mechanical damping and then it decreasesthe generated power.

The second microgenerator design proposed always by Beeby et al., de-veloped to overcome the problems raised with the lateral design (above alldesigned to avoid electrical connections to moving parts) has been realizedattaching four magnets mounted in turn onto a tungsten proof mass at thefree end of a steel cantilever beam, clamped at the other end as shown in Fig.2.3. The magnets in this case move relative to the coil, that is fixed. Thetotal volume of the device was 60 mm3 and the generated power deliveredto a resistive load of 100 Ω at the frequency of 350 Hz, and acceleration am-plitude of 3 m/s2 was about 2.85 µW [Beeby et al., 2006a]. The optimizeddesign of this generator, consisting of the optimization of the magnet size forthe same cantilever structure of the prior design, produced an output voltageof 87 mVrms across a resistive load of 9 MΩ from 0.6 m/s2 vibrations at thefrequency of 60 Hz, and a generated power of about 17.8 µW across a resis-tive load of 150 Ω. This optimization had the aim to increase the generatedoutput voltage that however it still remained too low, even if the generatedpower is increased of almost an order of magnitude, with respect to the priordesign [Torah et al., 2006].

A vibration-based linear electromagnetic micro-generator suitable to powerwearable body sensor nodes, consisting of a stator coil and a flexible stacktranslator of alternately magnets and spacer, succeeded to generate an outputpower of 2-25 µW, depending on the generator position on the human body.A two-stage procedure has been conducted by authors in order to optimizethe generator design. The optimization has consisted of firstly, the opti-mization of the geometric parameters of stator and translator for maximumelectromagnetic force capability, by magnetostatic finite element simulations.Secondly, the optimization of mechanical resonance frequency and load re-sistance in order to maximize the output power, by using lumped-parametersimulations and measured acceleration data from human walking motion.The designed linear electromagnetic micro-generator has a volume of 0.25 cm3

when worn on the body during walking [von Buren and Troster, 2007].Wang et al. presents a micro electromagnetic energy harvester which can

convert low level vibration energy to electrical power. The microgenerator,as shown in Fig. 2.3 consists of an electroplated copper planar spring, a per-manent magnet and a copper planar coil with high aspect ratio. Mechanicalsimulation have shown that the natural frequency of the magnet spring sys-

25

tem is 94.5 Hz. Electromagnetic simulations have shown that the line widthand the turns of the coil can influence the induced voltage. The optimizedvibration-based electromagnetic generator can generate 0.7 µW of maximumoutput power with output voltage of 42.6 mVpp at resonance and input accel-eration amplitude of 4.94 m/s2 (i.e low level environmental vibration source).The not-optimized prototype, fabricated using MEMS micromachining tech-nology have shown from experimental tests to be able to generate inducedvoltage of 18 mVpp and output power of 0.61 µW for 14.9 m/s2 (i.e. not lowlevel environmental vibration source) external acceleration amplitude in cor-respondence of its resonant frequency of 55 Hz . The measured output powergenerated by the prototype has shown to have a value close to the value ofthe simulated power of the design model. However, the strength of the inputvibration (i.e. 14.9 m/s2) used to excite the prototype has resulted muchhigher than that one (i.e. 4.94 m/s2) used to excite the optimized model.The input vibration source used to excite the prototype does not belong tocommon low level vibration amplitude presents in the environment. Excit-ing the prototype with input acceleration and input vibration amplitudes -which have been used in simulation - the output voltage and power that theprototype can generate reduce to very small values. Therefore the fabricatedmicro electromagnetic generator proposed by Wang et al. has resulted to benot suitable for harvesting low level vibration energy [Wang et al., 2009].

Serre et al. have designed a vibration-based electromagnetic inertial mi-crogenerator for energy scavenging applications, named Velocity DampedResonant Generator (VDRG), consisting of a fixed micromachined coil anda movable permanent magnet (that operates as an inertial mass) mountedon a resonant structure (Kaptonr membrane). This generator in a volumein the range of 0.6-0.7 cm3 if optimized could generate a power of 280 µW[Serre et al., 2007].

Glynne-Jones et al. have designed and fabricated a cantilever-based elec-tromagnetic generator, with overall volume of 3.15 cm3, as shown in Fig. 2.3,based on a moving coil between four magnets capable of generating usefullevel of power of average value of 157 µW when mounted on the engine blockof a car with peak of power of 3.9 mW [Glynne-Jones et al., 2004].

Beeby et al. have also reported about a macro vibration-based elec-tromagnetic generator - the Perpetuum PMG7 generator - designed to res-onate at 50 Hz, able to produce an AC output power of about 3 mW ifmade vibrated by a vibration acceleration amplitude of 0.5 m/s2. Themass of the generator was 85 g and with a overall volume of 41.3 cm3

[Beeby et al., 2006a].

26

Figure 2.4: Illustration of the two modes of piezoelectric conversion frominput mechanical stress (denoted as σ1). In the figure the strain is denotedas S1.

2.3.3 Piezoelectric bender generators

Vibration-based generators which exploit the piezoelectric effect in order toconvert the mechanical energy from vibrations into electrical energy, usuallyare formed as layer-based cantilevers. The number of layers define the kind ofpiezoelectric generator - usually unimorph structures composed by a piezoce-ramic layer attached to a metal layer or bimorph structures where two piezo-ceramic layers are attached to a central metal layer. A proof mass attachedon to the free end of the bimorph complete the vibration-based piezoelectricgenerator, usually called Piezoelectric Bender Generator (PBG). Accordingto how the electrodes are placed onto the surface of the piezoelectric mate-rial, as shown in Fig. 2.4, the cantilever beam transducer can operate eitherin the 31 mode (also called transverse mode) - electric field perpendicular tothe stress/strain direction - or in the 33 mode (also called thickness mode)- electric field parallel to the stress/strain direction. In the 31 mode theelectrodes are deposited on the top and bottom surface of the piezoelectricmaterial , while, in the 33 mode the electrodes are interdigitated. The ad-vantage of the 33 mode with respect to the 31 mode is that with the 33mode it can be generated a voltage 20 times than that one generated by thePBG in the 31 mode. At microscale sizes interdigited PBGs are preferredbecause the advantages of the 33 mode over the 31 mode in order to increasethe generated voltage and power. Scaling down the dimensions of the PBG,the power that it can be generated decreases, while the resonance frequencyof the PBG increases. Vibrational sources as reported in the introductionhave a frequency spectrum range of 10-500 Hz. Scaling the PBG at microscale sizes increases the resonance frequency of the PBG system, then, it be-

27

comes difficult to design it to match the fundamental mode of the vibrationalsource.

In [Leland et al., 2006] is reported about a millimeter scale PBG of bi-morph dimensions 31.5x12.7x0.51 mm3 by Piezo Systems, Inc., with a tung-sten proof mass of 52 g attached onto the free end, which has been excited byvibrations generated by continuous traffic on a staircase. This PBG, shownin Fig. 2.5 produced an instantaneous power of 30 µW in the time interval of816 ms (time required by the sensor and radio hardware to turn on, initialize,and transmitting the measure), after 50 minutes of continuous traffic duringwhich sufficient energy has been stored onto a capacitor allowing powering atemperature sensor and radio - a MICA2dot by Crossbow, Tech - to transmitthe measured temperature.

Choi et al., have designed a MEMS PBG device (see Fig. 2.5) based onthin film PZT/SiNx with proof mass placed onto the free end of bimorphdimensions 170x60x1 µm3 and total volume, comprising of proof mass, of2.2e-3 mm3. the Pt/Ti interdigitated electrodes are patterned onto the toppiezoelectric in order to employ the d33 mode. The MEMS PBG is ableto generate 1 µW of continuous electrical power to a 5.2 MΩ resistive load(in condition of impedance matching) at 2.4 V DC and at the resonancefrequency of 13.9 kHz [Choi et al., 2006].

Fang et al. have reported of a MEMS PBG - as shown in Fig. 2.5 -with a proof mass that allows transferring 2.16 µW of power to a 21.4 kΩ ofresistive load in condition of impedance matching, at a resonance frequencyof 608 Hz. A first prototype of this MEMS PBG resulted in about 0.89 V ACpeak to peak output voltage to overcome germanium diode rectifier towardenergy storage. This MEMS PBG operates with the 31 mode with can-tilever dimensions of 2000x600x13.64 µm3 and that ones of the proof mass600x600x500 µm3. The total volume was 0.615 mm3. It is a composite can-tilever made up of an upper piezoelectric thick film, sandwiched between apair of metal (Pt/Ti) electrodes, and with a lower non-piezoelectric element[Fang et al., 2006]. The same authors reported in [Liu et al., 2008b] about adesign and fabrication of an array of piezoelectric bender generators basedon thick-film piezoceramic materials connected in series. The PBGs arrayare fabricated with micromachining techniques on bulk silicon. The charac-teristic of the designed array of series-connected PBGs is that each PBG hasa different width and length (same thickness) in order to cover a frequencybandwidth in the range of 200-400 Hz. The design of a vibration-basedgenerator is strictly dependent on the knowledge of the vibrational sourcefundamental frequency mode of the application where the VBG will operate.The VBG should be in fact designed in such way that its natural frequencymatches the fundamental frequency mode in order to generate the maximum

28

(a)

(b)

Figure 2.5: Vibration-based piezoelectric generators: (a) Micromachinedcantilever by Marzencki et al., Choi et al. and Fang et al., respectively; (b)Millimeter scale by Roundy et al. and Leland et al., respectively.

power. The knowledge of this fundamental mode could be sometime not priorknown or the frequency could change or be random. The prototype gener-ator designed and fabricate by Liu et al. hence wanted to have a measuredperformance of 3.98 µW effective electrical power and 3.93 V DC outputvoltage to resistive load. This device is promising to support networks ofultra-low-power, peer-to-peer, wireless nodes.

Marzencki et al. have proposed a MEMS PBG with a seismic mass (seeFig. 2.5) with dimensions 800x1200x525 µm3 comprising of the seismic mass(the thickness of the cantilever is equal to 5 µm). The resonance frequencyof the MEMS PBG is equal to 1.3 kHz. The reported experimental resultsstated the possibility of exploiting very low amplitude signals produced bythe PBG in order to charge a storage capacitor. It is shown that power of2 µW at 1.6 V can be obtained from this MEMS PBG at 4g (g = 9.8 ms−2)excitation [Marzencki et al., 2007].

At macro and micro scale gravitation force plays the major role for driv-

29

Figure 2.6: Piezoelectric nanogenerator based on Zinc Oxide nanowire ar-rays by Wang, Z. L. et al..

ing the oscillation induced by vibrations of the inertial mass attached ontothe free end of the cantilever beam. However, scaling the PBG at nanosizes the gravitation not influences the motion of the mass anymore. There-fore, other approaches need to be found. Piezoelectric bender generatorsat nano scale have been investigated by Liu et al. [Liu et al., 2008a] (seeFig. 2.6). The nano generator made of nanowires of ZnO with diametersof ∼ 100 nm and lengths of 5 µm made growing on polymer substrate withan effective area of 6 mm2, this piezoelectric nano bender generator can pro-duce a continuous current (of about 500 nA) and voltage (of about 10 mV).Besides, considering the effective area it results in an effective current den-sity of 8.31 µA/cm2 and a power density of 83 nW/cm2. From the sameauthors in [Wang et al., 2008] it is estimated that if every nanowire spreadedin an effective area of 1 cm2 were involved in generating electricity the outputpower could reach 10 µW/cm2, which with the newly 3D integration tech-nology1 could be also improved. Fig. 2.6 shows also the package fabricatedto contain the nanowires using the 3D integration technology with the zigzag

1The 3D integration technology consists of stacking integrated circuits, heterogeneousdevices and technologies and connecting them vertically.

30

top electrode drove by an external ultrasonic wave or mechanical vibrations.Through the relative deflection/displacement between the nanowires and thezig zag electrode mechanical energy can be converted into electricity.

2.4 Summary

Vibration-based electrostatic generators have the advantages to be easily in-tegrated in silicon-based microsystems, because they can be realized withMEMS technology. Besides, miniaturization is facilitate because of the gen-erated energy density increases by reducing the gap between conductors ofthe capacitor. On the contrary, the generated energy density decreases whendecreasing the surface area. Further, high transduction damping at low fre-quency can be achieved only incorporating small capacitor gaps and highvoltages, rising the risk of capacitor electrodes shorting and ’stiction’ whenwafer-scale implemented. However, electrostatic generators - being variablecapacitor - need to be prior polarized by a priming voltage, that could be veryhigh (> 100 V). Other drawbacks regard the high output impedance (orderto GΩ), generated low output current and very high level output voltages(order of hundreds of volts).

The voltage (and so the power) that it can be generated by a vibration-based electromagnetic transducer depends of the length and thickness of thewire of the coil. The greater the length of the coil (and so the number ofturns) is, the greater the voltage and the power which can be generatedare. The problem is that the greater the number of turns, the greater theself-inductance of the coil. A high self-inductance needs a long conductionperiod to reach the value of current corresponding to optimal damping, andthis can lead to high resistive losses. Furthermore, adding more conductormaterial to the coil 1) increases the area or the length over which flux mustbe supported in the air gap between the magnetic materials and 2) requires alarger volume of permanent magnet [Mitcheson et al., 2007]. The request of alarge length of the coil to achieve high voltages and the wafer-scale integrationis quite difficult to achieve because of the poor properties of planar magnetsand the limited number of turns which can be achieved. Electromagneticgenerators can offer a wide variety of configurations and can be realizedwith various type of materials. They can generate high output current andpower. However, the major drawback of the electromagnetic generators isthat even if the power that they can generate can be comparable with thepower generated by piezoelectric generators, as will be illustrated in the nextsection, the voltage values they can generate are lower than 1 V. Therefore,the voltage generated by vibration-based electromagnetic generators needs to

31

be prior increased in order to be suitable to power practical wireless sensorapplications. Anyway, charge pumps, or voltage multipliers can be suitablefor increasing the low voltage generated by electromagnetic generators, andbesides, they operate also as rectifiers.

Piezoelectric generators offer the simplest approach for converting vibra-tions into voltage by exploiting the piezoelectric effect which allows obtainingvoltage by straining the material directly. Piezoelectric bender generators arecapable of producing relatively high output voltages, powers and power den-sities. However, because of the high output impedance - greater than 100 kΩ- they are able to produce relatively small currents and in order to pro-duce voltage and power the materials with which PBG are made require tobe directly strained, limiting performances and lifetime because of subject towear. The design of a PBG does not require complex geometries and it is thesimplest Vibration-Based Generator to fabricate. Several existing processesfor piezoelectric material deposition exist and can be exploited to fabricatemicromachined PBG to be integrated with silicon technology and then withCMOS-based circuits. Moreover, PBG can be well miniaturized by usinghigh quality piezoelectric thin layers, whose properties are recently improvedand made close to that ones of bulk materials [Ledermann et al., 2003] inorder to allow the piezoelectric device working efficiently. It has been de-cided therefore to explore the possibility of building the energy scavengingintegrated system employing the Piezoelectric bender generators as powersource because the most suitable among vibration-based generators to beintegrated with CMOS-based circuits.

32

Table

2.1

:Summaryofvibration-base

delectrostatic

generators

Refe

ren

ce

Pow

er

Volt

age

FA

Volu

me

Ch

aracte

ris

tics

(µW

)(V

)(H

z)

(m/s2

)(m

m3)

[Rou

nd

yet

al.,

2002]

11

N.A

.120

2.2

51000

In-p

lan

eover

lap

conver

ter;

pri

min

gvolt

age

of

5V

isre

qu

ired

[Rou

nd

yet

al.,

2002]

50

(@d

iele

ctri

cgap

0.2

5µ

m)

N.A

.120

2.2

51000

In-p

lan

egap

closi

ng

conver

ter;

pri

min

gvolt

age

of

5V

isre

-qu

ired

[Rou

nd

yet

al.,

2002]

20

(@0.0

01

atm

osp

her

es)

N.A

.120

2.2

51000

Ou

t-of-

pla

ne

gap

closi

ng

con

-ver

ter,

Pow

erin

the

use

ful

ran

ge

for

use

inso

me

ap

plica

-ti

on

s;p

rim

ing

volt

age

of

5V

isre

qu

ired

1e-

3(@

1atm

osp

her

es)

N.A

.120

2.2

51000

Pow

erto

olo

wto

be

use

dfo

rany

ap

plica

tion

[Mia

oet

al.,

2006]

80

220

30

10

50

Cou

lom

b-F

orc

eP

ara

met

ric

Gen

erato

r;p

rim

ing

volt

age

of

100

Vis

requ

ired

[Ryoic

hi

etal.,

2002]

36

2.4

6N

.A.

>10,0

00

Hon

eyco

mb

-typ

evari

ab

leca

-p

aci

tor;

ener

gy

harv

erst

ing

gen

erato

rfo

rh

arn

essi

ng

hea

rtven

tric

ula

rm

oti

on

for

card

iac

pace

maker

;p

rim

ing

volt

age

of

45

Vis

requ

ired

33

Table

2.2

:Summaryofvibration-base

delectromagnetic

generators

Refe

ren

ce

Pow

er

Volt

age

FA

Volu

me

Ch

aracte

ris

tics

(µW

)(V

)(H

z)

(m/s2

)(m

m3)

[Bee

by

etal.,

2006a]

0.1

22

3.7

e-3

(@110

Ω)

9.5

e33.5

68

Mob

ile

coil,

fixed

magn

ets,

mi-

crom

ach

ined

[von

Bu

ren

an

dT

rost

er,

2007]

2-2

5>

1N

.A.

N.A

.250

Lin

ear

gen

erato

r,M

ob

ile

stack

magn

ets

(tra

nsl

ato

r),

fixed

coil

(sta

tor)

,b

od

y-w

orn

[Wan

get

al.,

2009]

0.7

42.6

e-3

94.5

4.9

4

Mic

rom

ach

ined

,el

ectr

o-p

late

dco

pp

erp

lan

ar

spri

ng

wit

hp

er-

man

ent

magn

et(m

ob

ile)

,co

p-

per

pla

nar

coil

(fixed

)

[Bee

by

etal.,

2006a]

2.8

517e-

3(@

100

Ω)

350

360

Canti

lever

-base

d,

not-

op

tim

ized

[Tora

het

al.,

2006]

17.8

52e-

3(@

150

Ω)

60

0.6

N.A

.C

anti

lever

-base

d,

op

tim

ized

[Gly

nn

e-Jon

eset

al.,

2004]

157-3

.9e3

<1

106

N.A

.3150

Canti

lever

-base

d,

fou

rm

ovin

gm

agn

ets,

fixed

coil

[Bee

by

etal.,

2006a]

3e3

N.A

.50

0.5

41300

Com

mer

cial

dev

ice

-P

er-

pet

uu

mP

MG

7

34

Table

2.3

:Summaryofvibration-base

dpiezoelectric

bendergenerators

Refe

ren

ce

Pow

er

Volt

age

FA

Volu

me

Ch

aracte

ris

tics

(µW

)(V

)(H

z)

(m/s2

)(m

m3)

[Wan

get

al.,

2008]

12.4

(@5.4

MΩ

)13.9

e3N

.A.

2.2

e-3

Nan

ogen

erato

rbase

don

Zin

cO

xid

en

an

ow

ires

[Ch

oi

etal.,

2006]

12.4

(@5.4

MΩ

)13.9

e3N

.A.

2.2

e-3

Mic

rom

ach

ined

;In

terd

igit

ate

del

ectr

od

es;

exp

loit

d33

mod

e

[Fan

get

al.,

2006]

2.1

60.8

9A

C(@

21.4

kΩ

)608

N.A

.0.6

15

Mic

rom

ach

ined

;ex

plo

itd

31

mod

e

[Marz

enck

iet

al.,

2007]

21.6

1.3

e339.2

0.5

04

Mic

rom

ach

ined

;ex

plo

itd

31

mod

e

[Rou

nd

yet

al.,

2004]

210

>10

120

2.5

1000

PZ

T-5

H/B

rass

;Tu

ngst

enm

ass

;ex

plo

itd

31

mod

e

[Rou

nd

yet

al.,

2003]

375

>10

120

2.5

1000

PZ

T-5

H/B

rass

;T

un

gst

enm

ass

;ex

plo

itd

31

mod

e

35

Chapter 3

Case Study: PiezoelectricBender Generator for WirelessTire Pressure MeasurementSystems

3.1 Introduction

Usually Piezoelectric Bender Generators (PBG) are used to convert mechan-ical energy into electrical energy from common ambient vibrational sourceswith acceleration amplitudes in the range of 1-10 m/s2. In the case of a cartire, the acceleration amplitude that a PBG can experience can be greaterthan 1000 m/s2. The tire of a car is a very extreme ambient in which a PBGcan be used to convert vibrational energy into electricity, and hence power-ing an electronic device (e.g. pressure sensor). The extremely high values ofacceleration amplitude that are created inside of the tire of a car might notbe obtained through the common sources of vibration in the environment.Further, the accelerations created inside the tire of a car are radial and notlinear as those ones which are created due to the common vibrational sourcespresent in the environment.

The characteristic of the radial acceleration amplitude versus time in caseof tire tread application, in fact, does not match with that one of the vibra-tional common sources, which is practically sinusoidal in time [Roundy, 2003].The characteristic of the acceleration amplitude versus time is more similarto an inverted pulse, which passes from a high amplitude value to zero dur-ing a very brief time interval corresponding to the brief moment for whichan imaginary point situated on the wheel touches the ground. This extreme

36

environment is, according to [Cantatore and Ouwerkerk, 2006], the only onefrom which is possible obtaining enough energy to power a state-of-the-artwireless microsensor with on-board radio and sufficient processing capability(about 100 µW of power consumption) in case of a vibration-based generator(PBG in our case) is scaled from millimeter scale to micrometer scale, thatis, a MEMS harvester.

The estimated powers that vibration-based generators can produce andreported in [Cantatore and Ouwerkerk, 2006] have been computed using thegeneral formula (2.17), which will be introduced in the next chapter. How-ever, this formula gives an optimistic value for the power generated by ageneral vibration-based generator, i.e. supposing the resonance frequencyof the generator matches perfectly the fundamental mode of the vibrationalsource and optimal damping (i.e. without any losses). A more accurate for-mula to estimate the power generated by a PBG based on geometrical andphysical parameters will be reported on the Chapter 4, where, a SPICE ver-sion of the PBG electromechanical equivalent model by [Roundy et al., 2004]will be presented and developed.

This chapter presents the results of the experimental tests realized witha millimeter scale Piezoelectric Bender Generator (PBG) mounted on a testboard, in turn, mounted onto the outer wheel rim of a car. The conductedfeasibility study has been realized in order to validate the hypothesis of useof a PBG to replace a battery for the power supply of a Wireless Tire Pres-sure Measurement System (WTPMS) by exploiting the huge accelerations towhich the PBG can be subjected inside the tire of the car. Further, an esti-mation analysis about the power and energy consumption of three differentwireless sensor systems, is presented and used as reference to understand ifboth a millimeter and micrometer scale PBG can be able to power them, ifused in this extreme environment.

3.2 Wireless smart sensors energy/power re-

quirements estimation

For comparison only an estimation of the energy and power consumption ofthree wireless sensor systems - a state-of-the-art wireless microsensor as re-ported in [Cantatore and Ouwerkerk, 2006], a commercial wireless tire pres-sure measurement system (ATMEL ATA6285/6), and a wireless sensor nodeMICAz - is reported in this section. The energy and power consumptionestimations are evaluated considering the time needed to perform a pressuremeasure and a transmission of the measured data.

37

Table 3.1: ATA6285/6 parameters.

Voltage supply 2 V≤ V cc ≤ 3.6 V

Current consumption

0.6 µA (sleep mode)

200 µA (measurement mode)

8.5 mA (transmission mode)

Data rate 0 kbps 315 MHz

Start-up time(∗) 0.85 msec

Note: (∗) Time occurring between enabling of theATA6285/6 and beginning of transmission

1st case: commercial wireless sensor system - ATMELATA6285/6

Referring to the technical data reported in Table 3.1 it is possible to esti-mate the power and energy consumptions required by a commercial TPMS(ATA6285/6) by ATMEL, Corp. Considering the minimum value of 2 V forthe voltage supply of the ATA6285/6, the following power consumptions canbe estimated:

• PMeas,mode = 200e-6 * 2 = 400 µW = 0.4 mW

• PTx,mode = 8.5e-3*2 = 17 mW

• PSleep,mode = 0.6e-6 * 2 = 1.2 µW

The total power consumption is then

• PATA6285/6 = 0.4e-3 + 17e-3 + 1.2e-6 = 17.4 mW

The transmission bit time (TBT) at a bit rate of 20 kbps is

• TBT = (1/20e3 bps) = 50 µs

If we want, for instance, to transmit 64 bits the overall transmission time is:

• ttx = 64 * 50e-6 = 3.2 ms

The total time requested by the ATA6285/6 to transmit a measurementpressure value (for example 64 bits) supposing a measurement time of 1 ms,is then:

• ttot = 1e-3+0.85e-3 + 3.2 e-3 = 5.05 ms

Therefore, the estimated energy consumption to realize one measurementand transmission is

• EATA6285/6 = 17.4e-3*5.05e-3 = 87.87 µJ

38

Table 3.2: Summary of the energy/power consumption estima-tions to perform a sensor sampling and transmission for powerautonomous wireless sensors.

Device AuthorPower Energy

Consumption Consumption

WMS(∗) [Cantatore and Ouwerkerk, 2006] 100 µW 505 nJ

MICAz [Barboni and Valle, 2008] 89.22 mW 5.57 mJ

ATA6285/6 ATMEL Corp. 17.4 mW 87.87 µJ

Note: (∗) Theoretical device whose performances are based on the state of the art of wirelesssensor systems.

2nd case: Wireless Micro System

From [Cantatore and Ouwerkerk, 2006] a realistic target power consumptionfor autonomous operation of state of the art wireless microsensors (WMS)with on-board radio and sufficient processing power is 100 µW. Supposingto use the same total time requested by ATA6285/6 to perform a measureand a transmission of the measured data, the estimated energy consumptionis therefore

• EWMS = 100e-6*5.05e-3 = 505 nJ

3rd case: Crossbow MICAz

From [Barboni and Valle, 2008] using a MICAz (by Crossbow, Tech.) thefollowing measured energy consumption values are given: 5.616 mJ (sensorsampling in 300 ms), 0.454 mJ (radio transmission of 25 bytes in 6.44 ms).The total power consumption is therefore:

• EMICAz =5.116e-3 + 0.454e-3 = 5.570 mJ

• PMICAz = (5.116e-3 / 300e-3) + (0.454e-3 / 6.44e-3) = 89.22 mW

A summary of the power and energy consumption estimations are reportedin Table 3.2. According to the values of the ideal maximum power gener-ated by a vibration-based generator, for different applications and reportedin [Cantatore and Ouwerkerk, 2006], if they are compared with power andenergy consumption values reported in Table 3.2, it can be noted that incase of a millimeter scale PBG (100 mm3) it is possible to produce enoughpower or energy to power a wireless sensor system. A micrometer scale PBG,instead, could provide enough power only if the vibrational source is the tiretread.

39

(a) (b)

(c)

Figure 3.1: (a) Centripetal force progress during the roto-translational mo-tion of an automobile tire, and its action onto Piezoelectric Bender Generator.(b) Schematic of the energy harvesting circuit. (c) Set up of the experimentwith the test board mounted on the outer rim of the wheel of an automobile.

3.3 Experimental results

A PBG placed inside a tire is subjected to the radial acceleration (and then,to the centripetal force) [Roundy, 2003]. The same thing can happen if thePBG is clamped in the outer rim of the wheel so that its upper surfaceis perpendicular to the radius of the wheel. During the roto-translationalmotion of the moving wheel of the car, the surface of the free end of thePBG is therefore subjected to the radial acceleration, making bending thePBG towards the center of the wheel. When the PBG is in correspondenceof the point of contact with the ground, the radial acceleration goes to zero,and therefore as well the centripetal force. Therefore, the generator not beinganymore subjected to the centripetal force starts to oscillate for the very brief

40

Figure 3.2: Measured Voltage and computed energy curves for different carspeeds.

Figure 3.3: Measured Voltage and computed energy curves for differentPBG thicknesses.

time interval in which the centripetal force is zero (see Fig. 3.1).The charge generated because of the strain induced in the piezoceramic

material and by bending and oscillation of the PBG can be transferred to a

41

Figure 3.4: Measured Voltage and computed energy curves for differentdistances of PBG from the wheel center.

storage capacitor and then it can be used to power a wireless TPMS.A test board with a PBG, a diode bridge rectifier circuit and a storage

capacitor of 220 µF has been set up and clamped on the outer rim of a wheelof a car (see Fig. 3.1). The dimensions of the PBGs (by Piezo systems, Inc.)used during the experimental tests were 31.8x3.2x0.66 mm3 (PBG1) and31.8x3.2x0.32 mm3 (PBG2). Both PBGs have been used without attachinga heavy proof mass on the free tip. The unclamped length of both PBGs wasabout 2.5 cm. In order to stress with the maximum centripetal force the freetip of the PBG, the stick with the PBG clamped inside it has been mountedin such a way that the surface of the free tip was perpendicular to the radiusof the wheel (see Fig. 3.1). During the experiments the voltage across thecapacitor has been measured in order to estimate the produced energy.

From the obtained experimental test results it is possible to derive somereference parameters that to a first extent have influenced the value of thevoltage measured across the capacitor. The reference parameters are: thedistance of the PBG from the wheel center, the car speed and the PBGthickness. Keeping constant the width and length of the PBG and makingvarying the PBG thickness, the car speed and the distance of the PBG fromthe center of the wheel the experimental results shown in Fig. 3.4, in Fig.3.2 and in Fig. 3.3, respectively, have been obtained.

The estimated power and energy consumption in order to perform a pres-

42

sure measurement (considering a 1 ms as measurement time) and transmis-sion of the measured data with 64 bytes at a bit rate of 20 kbps, have beencomputed to be about 17 mW and 88 µJ, respectively (see Table 3.2). Thesevalues of power and energy should be used in 5.05 ms, time required by theWTPMS to perform a pressure measurement and the subsequent transmis-sion of data.

With the car moving at 50 km/h, the energy stored on the capacitor hasbeen about 518 µJ (see Fig. 3.2). The stored energy (i.e. 518 µJ) used in5.05 ms allows transferring a power of 103 mW to the ATA6285/6. Thisvalue of transferred power is higher than the required one by the ATA6285/6and reported in Table 3.2. Then, with the millimeter scale PBG, denoted asPBG1, of size 31.8x3.2x0.66 mm3 (67 mm3 of device volume) it seems to bepossible to power the ATA6285/6 in order to perform a measurement andtransmission every 5 minutes, if the PBG is used for car tire applications.

However, according to [Cantatore and Ouwerkerk, 2006] scaling the di-mensions of the PBG from millimeter to micrometer scale (MEMS), a scalefactor of 100 must be applied to the generated power. Therefore, the trans-ferred power reduces to 1.03 mW, that it seems to be not enough to powerthe ATA6285/6 anymore (see Table 3.2), but it would be enough, theoreti-cally, to power the estimated state-of-the-art wireless microsensor reportedin [Cantatore and Ouwerkerk, 2006].

Considering a MEMS PBG from literature as reference, the next sectionillustrates a scenario in which this MEMS PBG is supposed to be embeddedinside the car wheel, and it is supposed to be used as power source for theATA6285/6. Further, it is illustrated also that not the whole energy thatcan be stored into the capacitor can be used to power the sensor, and alsothat, the percentage of the energy used is function of the minimum inputvoltage required by the sensor to still work. If the voltage decreases belowthe minimum value the sensor does not succeed to work any more.

3.4 Discussion

The MEMS PBG reported in [Choi et al., 2006] is used in this section asreference device in order to illustrate a scenario of use of a MEMS PBG aspossible power source for WTPMS embedded inside a car wheel. As referenceWTPMS has been considered the ATA6285/6.

The energy collected by the storage capacitor used in the experimentaltests described above, can be only partially used due to the finite value ofthe minimum supply voltage needed to power the sensor and radio blocks.The minimum voltage required by the ATA6285/6 is 2 V. Therefore, if for

43

Figure 3.5: Power flow from PBG to sensor and radio block in case ofnot considering and considering the minimum supply voltage required by thesensor and radio block to operate.

example, the TPS72501 Low Drop Out (LDO) linear voltage regulator, byTexas Instruments, Inc, was used and considering a drop out voltage (denotedas ∆VDO) equal to 170 mV (see the datasheet of the TPS72501), to powerthe sensor and radio blocks with a Vo,min equal to 2 V (i.e. minimum voltageof the ATA6285/6) the minimum input voltage in input to the LDO (denotedas Vin,min,LDO) should be at least 2.17 V.

Considering to charge a capacitor till the voltage value of Vstor,in = 5.5V ,which is the maximum input voltage value of the TPS72501, considering alsothat the MEMS PBG transfers to the storage capacitor a power equal to 1µW [Choi et al., 2006], it is possible to estimate the required value of thecapacitance to be used to reach 5.5 V in 300 sec (i.e. 5 minutes). Knowingthat in 5 minutes the Estor = PPBG,MEMS ∗ 300sec = 300 µJ), then therequired capacitance have a value of

• Cstor = (2Estor/V2stor,in) = 20 µF

The effective energy that can be used to power supply the sensor and radioblock is equal to

• Eeff = 12Cstor(V

2stor,in − V 2

in,min,LDO) = 255 µJ

44

where Estor,in = 1/2CstorV2stor,in is the energy collected by the storage capac-

itor.Considering the ATA6285/6, and the estimated time (5.05 ms) to perform

a measure and transmission, as previously estimated, the power transferredto the sensor and radio block, before that the voltage across the storagecapacitor reaches the minimum voltage value, is therefore

• P1 = Eeff / 5.05e-3 = 50.5 mW

Due to the fact that the LDO has an efficiency of about 40 % (as reportedin [Leland et al., 2006]), the effective power that can be transferred to thesensor and radio blocks is therefore

• Peff = P1 ∗ 0.4 = 20.2 mW

This value of the effective and instantaneous power is comparable with thepower consumption of the ATA6285/6 (see Table 3.2). Fig. 3.5 shows thepower flow from PBG to the sensor and radio blocks in case of it is consideredand not considered the minimum voltage value required by the sensor andradio blocks to work properly.

3.5 Summary

An energy and power consumption estimation of three different wireless sen-sors - state of art wireless microsensor from [Cantatore and Ouwerkerk, 2006],the commercial WTPMS from ATMEL, Corp, and the wireless sensor nodeMICAz from Crossbow - have been reported. The experimental results ob-tained from the experimental tests realized with two different PBGs fromPiezo System, Inc, mounted onto the outer rim of a wheel of a car haveshown that exploiting the very high values of radial acceleration amplitudeswhich are created by the moving wheel it is possible to power at least theWTPMS and state-of-the-art wireless microsensor, while the power consump-tion required by the MICAz is to high in the context of autonomous mi-crosystems. This extreme environment can also be suitable in case of use ofMEMS PBG to power tire pressure measurement system. In fact, accord-ing to [Cantatore and Ouwerkerk, 2006] the tire tread application was theonly one capable to excite a MEMS PBG in order to power the state-of-the-art wireless microsensor. The experimental results have also shown thatthe PBG thickness, the distance of the PBG from the wheel center, and thespeed of the car, influence both the voltage generated by the PBG and thestored energy into the capacitor. The stored energy into the capacitor in caseof the car moving at the speed of 50 km/h, using the PBG with the greater

45

thickness and greater distance from the center of the wheel has shown tobe enough for the power supply of the ATA6285/6. However, the value ofthe generated power if the PBG is scaled to the micrometer dimensions, hasshown to be enough only for the power supply of the state of art wirelesssensor reported in [Cantatore and Ouwerkerk, 2006].

Anyway, with the last example reported in this chapter it has been shownthat the MEMS PBG by [Choi et al., 2006] used in the scenario of the tiretread application could generate enough instantaneous power - during thetime interval (i.e. 5.05 ms) in which the storage capacitor discharges fromthe maximum to the minimum input voltage values - to power the ATA6285/6in order to perform a pressure measure and transmission. This example haveshown that if enough energy is stored in the storage capacitor it is possibleto transfer enough power in the very brief time interval to succeed to powera commercial WTPMS, even if the scavenger (PBG in this case) is MEMS-based.

46

Chapter 4

SPICE model of PiezoelectricBender Generator

4.1 Introduction

Energy harvesting devices that can scavenge the normally lost energy fromsurroundings and convert it into usable form have gained much attention inrecent years. A major source of the wasted energy from surroundings is theambient vibrations present around most machines and biological systems. Vi-bration based generators (VBG) have thus been explored extensively. VBGsare essentially second order mass spring damper system that are made tovibrate by an external vibration source - indicated in terms of accelerationy [Williams and Yates, 1996]. Three types of VBGs are usually reportedin literature, i.e. electrostatic, electromagnetic and piezoelectric. However,the piezoelectric materials based VBGs are preferred as they efficiently con-vert mechanical strain to an electrical charge without any additional power.Among piezoelectric materials based VBGs, the piezoelectric bender genera-tors (PBG), formed as cantilever beams such as bimorphs (two piezoceramicthin layers attached to a central metal shim) with a heavy proof mass placedon the free end (see Fig. 4.1), have received particular attention. Due tothe design simplicity, high voltage and power outputs, and the possibilityto be fabricated with MEMS technologies and integrated with CMOS-basedelectronics, the PBG has been used in this work.

A mathematical model of a PBG, taking into account its geometrical andphysical parameters, as described in [Roundy et al., 2004], allows better es-timation of the amount of power that the PBG is able to generate from avibration source. Describing such a model in terms of circuit elements, asshown in Fig. 4.2, gives a designer the tool to study the PBG as an electrical

47

circuit using the Kirchoff’s Voltage and Current Laws. The SPICE imple-mentation of this model, presented in this chapter, further allows a designerto simulate overall circuit (i.e. PBGs and the conditioning electronics) ofthe energy harvesting (scavenging) system. The SPICE implementation ofPBG, presented in this work, is a better alternative to the simpler models(e.g. comprising of sinusoidal current generator in parallel with the bendercapacitance) utilized in past [Ottman et al., 2002]. With SPICE-like soft-ware, it would be easier to evaluate the performance of the overall circuit,from PBG to load, both in time and frequency domains. The optimum waysof transferring maximum power, from PBG towards the load, too can bestudied by directly simulating the overall circuit in SPICE.

This chapter presents the SPICE implementation of the electromechanicalmodel of PBG reported in [Roundy et al., 2004]. A comparison of the SPICEsimulation results with those obtained with MATLABr is also presented anddiscussed in this chapter.

4.2 Theory

4.2.1 Analytical model

In the chapter 2 has been reported the mathematical analysis of the vibration-based generator, represented by a resonant second-order mass-spring-dampersystem. This general model is suitable for vibration-based electromagneticgenerators, but, to be applied to the piezoelectric case, it must be changedand adapted.

The electromechanical model of a PBG described in [Roundy et al., 2004]is based on the electromechanical piezoelectric transformer as reported on[Flynn and Sanders, 2002]. A piezoelectric transformer works by using thedirect and converse piezoelectric effects to acoustically transform power fromone voltage and current level to another. Hence, the power is converted elec-tromechanically through a vibrating piezoelectric structure rather than elec-tromagnetically as in an inductive transformer. This last one considerationis very important and it will be the base from which the electromechanicalcoupling will be modeled in SPICE by not using inductively elements, as willbe explained in the next sections. Electromechanical coupling, in one dimen-sion, is described by the the two linear piezoelectric constitutive relations[ANSI/IEEE, 1987]

S1 = sE11T1 + d31E3 (4.1)

D3 = d31T1 + εT3E3 (4.2)

48

Figure 4.1: (a) Piezoelectric bender generator with a proof mass placed onthe free end of the bender. (b) Piezoelectric bender generator wired for seriesand parallel operation mode.

Figure 4.2: (Bimorph electromechanical circuit model.

where S1 is the strain, T1 is the stress, D3 is the electrical displacement(surface charge density), sE11 is the compliance (equal to the inverse of thepiezoelectric Young modulus or elastic constant, Yp) evaluated at constantelectric field, εT3 is the piezoelectric dielectric constant evaluated at constantstress, and d31 is the piezoelectric strain coefficient. In our case it is assumedthat the piezoelectric layers are poled along the 3 axis, and the electrodesare placed on the top and bottom surfaces of the piezoceramic layers of thebimorph. Driving vibrations are assumed to be present along the 3 axis insuch a manner that the piezoceramic material experiences a one-dimensionalstate of stress, T1 along the 1 axis. A uniform width of the PBG has beenassumed. The proof mass is assumed to be a point mass located at centerof mass. The piezoelectric losses are assumed to be negligible. Dielectriclosses in piezoelectric materials can be explained using a complex dielectricconstant [Dahiya et al., 2009], when computing the capacitance between theelectrodes, Cb. This behaviour can be modelled with a frequency-dependent

49

resistance in parallel with the bender capacitance Cb [Dahiya et al., 2009].The dielectric losses are higher if piezoelectric polymers are used in PBG.Dielectric loss factor in polymers are around 0.25, while in piezoceramic ma-terials are in the range of 0.002-0.02. As piezoceramic based PBG is assumedin this work, the dielectric losses are negligible [Puttmer et al., 1997].

The hereafter T1, S1, D3, sE11, and εT3 , will be written as T , S, D, and εT ,for the sake of simplicity.

The electromechanical transformer described in [Flynn and Sanders, 2002]can be changed as shown in Fig. 4.2 in order to be adapted to describe aPBG, as reported in [Roundy et al., 2004]. Mechanical and electrical blocksthen, are treated as uncoupled mechanical and electrical systems. Due to thefact that the mechanical side is treated as an uncoupled system, the stressvariable is not T , but σ, and the relation between stress and strain is theHook’s Law, σ = cpS. The mechanical elements of the general model of avibration-based resonant generator [Williams and Yates, 1996], that is, mass,spring and damper are represented by their electrical analogous quantitiesi.e. equivalent inductance Lm, resistance Rb and capacitance Ck, respectively.Further, the piezoelectric coupling is modeled as an equivalent transformer -with transformer ratio n, as shown in 4.2.

4.2.2 Mechanical side and electrical block equations

Considering the current as analogous to the strain rate S, and voltage asanalogous to the stress σ, and applying the Kirchoff’s Voltage Law (KVL)across the mechanical block in Fig. 4.2, results in the following expression[Roundy et al., 2004]:

σin − LmS −RbS −S

Ck= nV (4.3)

Similarly, applying Kirchoff’s Current Law (KCL) to node ’A’ in Fig. 4.2,results in:

i = −CbV −V

R(4.4)

In 4.3, σin = K1my is the equivalent input stress, due to the input force(i.e. Fin = my) exerted by the proof mass, m - when vibrations are ap-plied at its base (see Fig. 4.1). Stress and force are related to through thegeometrical constant K1 [Roundy et al., 2004]. The acceleration is definedas y = ain sinωt, where ain is the acceleration magnitude and ωin is thefrequency of the acceleration.

The equivalent inductance, Lm = K1K2m which relates the second deriva-tive of strain to stress, represents the inertia of the proof mass. The geomet-

50

rical constant K2 can be derived from the relation between the displacement,z, and strain [Roundy et al., 2004].

The equivalent resistance, Rb = K1K2mbm which relates stress to strainrate, takes into account the mechanical losses due to damping. In this equa-tion, bm is the damping coefficient. The equivalent capacitance, Ck, whichrepresents the compliance, relates stress and strain, and it is simply equal tothe inverse of the Young’s modulus, Yp of the piezoelectric material.

In 4.4, the capacitance between the electrodes can be written as

Cb =a2wleε

2tp. (4.5)

In 4.5, ε, le and w are the absolute piezoelectric dielectric constant, lengthand width of the electrode respectively and a is a constant which takes intoaccount how the bimorph is wired (a = 1, if the bimorph is wired to operatein the series operation mode, or a = 2, if the bimorph is wired to operate inthe parallel operation mode, as shown in Fig. 4.1).

4.2.3 Piezoelectric coupling equations

The electromechanical conversion block, relating input stress on mechanicalside to the voltage on electric block, is depicted by means of a transformer,as shown in Fig. 4.2. The equation for the transformer is given below:

σ =

(−ad31Yp

2tp

)V = nV (4.6)

where d31, is the piezoelectric strain coefficient, and n is the equivalent voltagetransformer ratio.

The current i flowing through the electrical block of the electromechanicalbimorph model in Fig. 4.2, is generated as result of the mechanical stressapplied to the bimorph under the conditions of zero electric field. The currenti, can be related to strain rate S as:

i = (awled31Yp) S = AiS. (4.7)

The term between brackets is referred - in the following sections - to as theequivalent current transformer ratio Ai.

4.2.4 PBG model transfer function with resistive load

Equations (4.3), (4.4) and (4.7) can be used to obtain the transfer functionof the electromechanical model of the PBG with the Laplace Transform of

51

the output voltage, V , as output variable and the Laplace transform of thevibration in terms of acceleration, Ain as input variable. Taking the Laplacetransform of (4.3), (4.4) and (4.7) it yields

(s2 + 2ζωns+ ω2n)∆ =

ω2nd31a

2tcV +

AinK2

(4.8)

∆ = − aε

2tcd31cp

1

s

(s+

1

RCb

)(4.9)

where ∆ is the Laplace transform of the strain, ωn =√Yp/(K1K2m), which

is the resonance frequency of the system, ζ = bm/(2mωn), which is the me-chanical damping ratio. Substituting (4.9) into (4.8) and rearranging terms,the following transfer function of the system, represented a PBG with a re-sistive load connected across the PBG output can be obtain

V =− 1

K2

2tcd31Yp

aε[s3 +

(2ζωn +

1

RCb

)s2 +

(ω2

n

(1 + K2

31

)+

2ζωn

RCb

)s+

(ω2

n

RCb

)]sAin(4.10)

where K231 = (d2

31Yp)/ε is the piezoelectric coupling coefficient. The transferfunction (4.10) will be used in MATLABr and the results obtained by simu-lating the system in MATLABr will be compared with those ones obtainedby simulating the equivalent SPICE circuit model and those one reported in[Roundy et al., 2004], in order to validate the SPICE version, from the pointof view of the simulative results.

4.3 SPICE implementation

Modeling of the piezoelectric coupling is an important task when the ana-lytical model, discussed in previous section, is implemented in SPICE. Theequivalent transformer, used to depict piezoelectric coupling in Fig. 4.2, isdifferent from the usual electrical transformer whose equations are related tothe electromagnetic effects between the coils in the primary and secondaryof the transformer. Usually, an electrical transformer is described as twoinductances or inductively coupled conductors related by means of the trans-former ratio. An ideal electrical transformer can be described by means ofthe following equations:

V1 =

(N1

N2

)V2 = nV V2 (4.11)

52

Figure 4.3: SPICE schematic subcircuit of the Piezoelectric Bender Gen-erator model.

I2 =

(N2

N1

)I1 =

(1

nV

)I1 (4.12)

where, N1, N2, nV and nI are the number of turns in the primary andsecondary, and voltage and current transformer ratio, respectively. It canbe noted that for an ideal electrical transformer the current transformerratio is the reciprocal of the voltage transformer ratio. However, the currenttransformer ratio Ai, obtained from (4.6) and (4.7), is not the reciprocal ofthe voltage transformer ratio n. This is an important difference between theelectrical transformer and the equivalent transformer used to describe thepiezoelectric coupling, which convert the power, electromechanically and notelectromagnetically as do the inductive electrical transformer.

To describe and model the piezoelectric coupling by means of a trans-former, the only voltage transformer ratio n is not enough. The currenttransformer ratio Ai is also needed for a complete model of the piezoelec-tric coupling and hence to describe the equivalent transformer. Accordingto (4.6) and (4.7), controlled sources, available in SPICE, can be used todescribe a complete model of the electromechanical piezoelectric coupling. Asimilar approach is used in [Dahiya et al., 2009] to model the electromechan-ical conversion in the SPICE model of the piezoelectric polymer.

In fact, (4.6) can also be modeled like a voltage controlled voltage source,(E5 in Fig. 4.3), with voltage across Cb (equivalent to the voltage across thesecondary of the transformer) as the controlling parameter. The mechanicalstress, σ (analogous to the voltage across the primary of the transformer) is

53

the controlled analogous voltage in this case.Similarly, 4.7 can be implemented in SPICE like a current controlled

current source (F5 in Fig. 4.3). In this case, the con-trolling current is theanalogous current flowing in the mechanical side i.e. the strain rate S and thecontrolled current is the current flowing in the secondary of the transformeri.e. i. The gain of E5 is the equivalent voltage transformer ratio n and thegain of F5 is equivalent current transformer ratio Ai. The mechanical stress,σin, is modeled in SPICE like a sinusoidal voltage source (V0 in Fig. 4.3).

An important characteristic of the proposed SPICE circuit implementa-tion is its applicability to bimorph wired in both series and parallel operationmodes (the differences between the two operating modes is due to the dif-ferent wiring, as shown in Fig. 4.1). The parameters that depends on theoperation mode are the values of the equivalent voltage and current trans-former ratios, n and Ai respectively and the value of the capacitance Cbbetween the electrodes of the bimorph. This is due to the dependence ofthese parameters on the constant a - which defines the operation mode. Fig.4.3 shows the SPICE implementation of the electromechanical model of bi-morph, discussed in previous section. The netlist for the equivalent circuitof Fig. 4.1 is given in Appendix B.

4.4 Simulation results

To evaluate the model, the SPICE simulated plots of powers and voltageswere compared with corresponding plots presented in [Roundy et al., 2004].For the comparison only, the physical parameters of the bimorph were as-sumed to be same as those used in [Roundy et al., 2004]. The bimorph pro-totype used in [Roundy et al., 2004], is made of two layers of PZT-5H witha brass center shim (from Piezo System, Inc). The bimorph has a lengthof 6.5 mm, width of 3.2 mm, thickness of each piezoceramic layers of 0.14mm, and the thickness of the center metal shim is 0.1 mm. The proof mass,made of tungsten and nickel alloy (density of about 17.6 gm−3), has lengthof 8.5 mm, width of 6.7 mm, and height of 7.7 mm. The bimorph is setto operate in parallel mode and a sinusoidal vibrational source of 2.5 ms−2

and frequency of 120 Hz (the bimorph was designed to resonate at 120 Hz),same as that used in [Roundy et al., 2004], is assumed to excite the system.The sinusoidal stress source, σin, has a magnitude of 1.1727 MNm−1 andfrequency of 120 Hz. A load resistance R, is assumed to be connected to theoutput of the bimorph model as in Fig. 4.2. The average output power is

54

(a)

(b)

Figure 4.4: Comparison among the MATLAB and SPICE (a) and theRoundy simulated and experimental measured (b) powers and voltages versusload resistance in case of bimorph wired for the parallel operation mode.

55

(a)

(b)

Figure 4.5: SPICE and MATLAB powers (a) and voltages (b) versus loadresistance in case of bimorph wired for the series operation mode.

computed using the following formula,

P = V 2eff/R =

(VM/√

2)R = VM/ (2R) (4.13)

where Veff is the rms voltage across the load resistance.Fig. 4.4 compares the powers and rms voltages versus load resistance

plots obtained both by means of MATLABr and SPICE. The MATLABr

simulations, performed by solving the transfer function of the system, havebeen useful to validate the SPICE model of the PBG. It is important to setthe same solver method both in SPICE and MATLABr (i.e. trapezoidal

56

method) and the same simulation time step, to obtain similar results. Asshown in Fig. 4.4, the powers and rms voltages versus load resistance agreewell with each other.

The plots shown in Fig. 4.4 are also in agreement with the correspondingplots presented in [Roundy et al., 2004] and reported in Fig. 4.4 for compar-ison only.

As mentioned earlier, the SPICE implementation can also be used to eval-uate the response of bimorph operating in series mode; only by changing thevalue of the constant a. The plots in Fig. 4.5, give the power and rms voltageof bimorph, operating in series mode, at various load conditions. ComparingFig. 4.4 and Fig. 4.5, it can be noted that the power is maximum at differentload values, according to the different bimorph wiring. The bimorph oper-ating in series mode shows maximum at an optimal load resistance greaterthan that of bimorph operating in parallel mode. For greater values of theoptimal load resistance, the generated power varies more slowly in the caseof the bimorph operating in series mode with respect to the power generatedby the bimorph operating in parallel mode.

4.5 Summary

A SPICE implementation of a vibration-based piezoelectric bimorph gen-erator for energy harvesting or scavenging applications has been presented.Comparing simulated voltages and powers, obtained with MATLABr andSPICE, show a good agreement with each other and with the results reportedin [Roundy et al., 2004]. The MATLABr and SPICE simulated powers andvoltages of a bimorph, wired for the parallel and series operation modes, havebeen presented. The two operation modes have different generated power andoptimal load resistance.

57

Chapter 5

Design and analysis of aVibration-Based EnergyScavenging System

5.1 Introduction

This chapter presents the SPICE design and analysis of a vibration basedenergy scavenging system that comprises of the SPICE model of the PBGpresented in the Chapter 4 and a self-powered voltage regulator circuit. Inthis chapter, an integrated semi-active bridge rectifier is presented. Thesemi-active bridge rectifier is used in place of the traditional full-wave diodebridge rectifier to perform the AC-DC conversion. Somewhat similar semi-active bridge rectifier has been prior proposed in [Wong, 1996]. However,the rectifier presented here differs in the control circuits used to drive the ac-tive devices. Other differences include using power MOSFETs, in particularVertical Double-diffused MOS (VDMOS) transistors as active devices. Theuse of active devices, like MOS transistors for the bridge rectifier, instead ofdiodes, helps overcoming drawbacks such as higher voltage drop and powerdissipation across diodes. Moreover, due to the fact that active devices can becontrolled it gives the designer the possibility to implement a smart control.

However, active devices need to be controlled by suitable circuits, whichshould be also designed in order to maintain the advantages gained by sub-stituting diodes with active devices. Keeping this in view, an optimizedcontrol circuit of the voltage regulator too has been implemented. The re-ciprocal interaction between PBG and the scavenging system with respect tothe load (in terms of stress, strain rate, mechanical and electrical powers) isalso presented in this chapter.

58

Figure 5.1: Block diagram of vibration based energy scavenging systemwith PBG (excited by a vibration source), the voltage regulator system andcontrol circuit (supplied by the output of the DC-DC voltage regulator).

5.2 Vibration-Based Energy Scavenging Cir-

cuit

A vibration-based energy scavenging system, using a PBG as scavenger, isillustrated in Fig. 5.1. The block diagram represents a voltage regulator,consisting of a voltage rectifier, a DC-DC converter and their control circuits.The load and the control circuits of the voltage regulator are powered by thesame regulated output voltage, realizing a complete self-powered vibration-based energy scavenging system.

PBG generates AC voltage, as a result of the mechanical vibration toelectrical energy conversion. To power the electronic circuits, the AC volt-age must be converted in to DC. Among various alternatives available forthis purpose, full-wave bridge rectifiers are the most commonly used circuitsin energy scavenging systems [Roundy et al., 2004, Ottman et al., 2002]. Asthe voltages greater than 10 V can be easily generated by PBGs the powerdevices are more suitable for this type of application. Therefore, high voltagediodes and power MOSFETs are used for the design of the bridge rectifierand the DC-DC converter. The AMIS I3T50 process technology (from Eu-ropractice IC Service) has been used to design the system.

5.2.1 Semi-Active Bridge Rectifier

In Fig. 5.2 is illustrated the schematic of the proposed integrated semi-activebridge rectifier used as interface circuit between the PBG and the followingDC-DC converter. The dimensioning of the devices belonging the rectifier isillustrated in Appendix D. In order to reduce the power consumption of therectifier, it has been chosen to dimension the rectifier devices, both VDMOS

59

Figure 5.2: Schematic of the semi-active bridge rectifier with the ZCCcontrol circuit inside the dashed rectangle.

and high voltage diodes, so that when they are in the on-state, they havethe smaller on resistance. In particular, that means to have a lower voltagedrop across the devices and hence a lower dissipated power - which meansdecreasing the power consumption of the circuit when in the on-state. SW1and SW2 are n-channel VDMOS transistors and D1 and D2 are high voltagediodes. The use of only two active devices in place of two of the four diodesof the bridge rectifier aimed to develop a simple and power efficient circuit.In fact, in the case of a full-active bridge rectifier another couple of powerMOSFETs (p-channel type, in particular) should be used to substitute theother couple of diodes of the bridge rectifier (i.e. D1 and D2 in Fig. 5.2).A full-active bridge rectifier, however, would need a more complex controlcircuit. In order to know which one of the two power p-channel MOSFETsshould be turned on and off, the control circuit should check not only thevoltage level of the AC1 or AC2 nodes, but also, it should check the voltagelevel at node VO1, which does not constitute a fixed reference. Moreover,the control circuit should generate the right source-gate voltage referred toVO1 - which is not a fixed reference - and this may constitute another issueto be overcome and could increase the complexity of the circuit.

The SW1 and SW2 transistors of the bridge rectifier in Fig. 5.2 have theirsource terminal connected to ground. Therefore, the control circuit has togenerate only the source-gate voltage referred to ground - which representsa fixed reference - when one of the two transistors has to be turned on. Toturn off and on SW1 and SW2 alternately, according to the polarity of thevoltage generated by the PBG, a Zero Crossing Comparator (ZCC) with

60

two output terminals (one the complement of the other one) constitutes thesimple control circuit (see Fig. 5.2). DMOS devices are realized with a gateoxide of only 7 nm of thickness, therefore special care is needed to avoidoperation above 3.6 V. A greater value of the gate to source voltage couldtake the gate oxide of SW1 and SW2 to break down. The voltage divider,realized by means of the couple of resistances R1 and R2 has been necessaryto lower the AC differential voltage from PBG to the suitable voltage valueof at maximum 3.3 V in input to the ZCC. The bd1 and bd2 in Fig. 5.2are the bulk-drain parasitic diodes, which are an intrinsic characteristic ofVDMOS transistors.

The semi-active bridge rectifier proposed here is self-starting. At theonset of the scavenging process the ZCC is not powered yet, and hence, SW1and SW2 cannot be driven yet and hence, being off, the rectification processcould not start. Anyway, this issue is overcome by exploiting the two parasiticdiodes of the VDMOS transistor. At the onset of the scavenging process,these two diodes assume the role of the diodes replaced by the VDMOStransistors, allowing the initial phase of the rectification process. When theZCC starts to be powered, it starts driving SW1 and SW2, according to thepolarity of the AC differential voltage generated by the PBG, and parasiticdiodes turn off, being reverse biased.

5.2.2 Voltage regulator

The DC voltage rectified by the semi-active bridge rectifier is not stabilizedand regulated. Stabilization and regulation of the rectified voltage can beperformed by DC-DC switching converters. The use of PBGs as source im-plies the need to step down the rectified voltage before powering electroniccircuits. On purpose, a buck converter (see Fig. 5.3) can be connected to therectifier output and it can be used to step down, regulate and stabilize thevoltage generated by the PBG. A power MOSFET, in particular a p-channelVDMOS is used in place of the standard MOS transistor as high side switch(SW3 in Fig. 5.3) of the buck converter, due to the fact that a commonMOS transistor might have problems to withstand the high level voltage am-plitudes generated by the PBG at the terminal source. The control circuit ofthe DC-DC converter, illustrated in Fig. 5.3, consists of a driver block anda voltage level shifter circuit.

Driver block

The driver block consists of a comparator, a rising-edge triggered monos-table circuit (denoted as Oneshot in Fig. 5.3), an OR gate and an inverters

61

Figure 5.3: Schematic of the voltage regulator circuit with the semi-activebridge rectifier and the SPICE model of the PBG.

chain. The CMOS inverter has been dimensioned in order to have an al-most symmetrical characteristic. The following dimensions have been set:Wp = 2.25 µm, Lp = 0.5 µm as width and length, respectively, in case ofthe PMOS and Wn = 1 µm (minimum width), Ln = 0.5 µm of width andlength, respectively, in case of the NMOS. The other CMOS logic gates (i.e.NAND, NOR, OR) have been dimensioned referring to the inverter tran-sistors dimensions. The transistors used for the driver circuit are standardMOS devices. The internal view of the monostable circuit, is depicted in Fig.5.4, while in Fig. 5.5 is depicted the internal view of the CMOS-based flipflop D Master Slave with the inputs of SET (denoted as SDN) and RESET(denoted as CDN). The SDN input as well as the D input are always atthe high level state, being connected to Vdd, as shown in Fig. 5.4. Whenthe output voltage of the buck converter is lower than the reference voltage,the output of the comparator is at the zero level, therefore CP = 0. Thetransmission gates are in the following states:

T1−→ ON, T2−→ OFF, T3−→ OFF, T4−→ ON.

Therefore, the slave is isolated from the Master and its feedback is closed,allowing the Slave to hold its previews state (Q = 0, Q = V dd, CDN = 0),which, hold the output of the Oneshot to the zero level. In the meanwhile,the feedback of the Master is opened and its output, denoted as Q′, is equalto the D input, that is V dd. When the output voltage of the buck converterbecomes greater than the reference voltage, the output of the comparatorgoes to its high level, therefore CP = V dd. The transmission gates assume

62

Figure 5.4: Internal schematic view of the monostable circuit.

Figure 5.5: Internal schematic view of the flip flop D master slave.

the following states:

T1−→ OFF, T2−→ ON, T3−→ ON, T4−→ OFF.

The results is that the Master is disconnected from the complement of theinput D and its feedback is closed. When the transmission gate T3 closes,the high state of the output of the Master propagates in input to the slavewhich implies the output Q to commutate at the low state. The low stateof the Q output allow the capacitance Cx in Fig. 5.4 to be charged at Vdd,and the output of the NOR gate goes in its high state. Therefore the CDNinput is held at the high state, and it remains in this state for a time intervalequal to the time constant RxCx. With the CDN input in the high state, itimplies that the NAND gate U4 has its output at the low state, therefore,

63

the Q output is held in the high state for a time instant equal to the timeconstant RxCx. When the capacitance discharged, the CDN input goes inthe low state. Therefore, the Q′ output of the Master goes in the low state,Q goes in the high state, and the Q output in the low state.

The energy scavenging system is thought to be self-powered, that is, itshould be able to harvest the energy from the ambient and use it to poweritself. The voltage regulator has the goal to regulate the voltage at thesuitable level required by the circuits that it should power. The loop of thevoltage regulator, however, works only if the output voltage can be comparedwith a fixed reference voltage. Therefore, an important issue to address inthe design of the voltage regulator is how can be generated the referencevoltage to give in input at the comparator. This is one of the issues thatshould be still studied and addressed in order to find a solution.

The comparator is the only circuit of the system which should be stilldesigned at transistor level because it requires a careful study, being a circuitwhich needs to consume power in order to work properly. Fig. 5.6 shows aninternal schematic view of the comparator used during the simulations withSPICE. It is composed of a CMOS inverter and a Voltage Controlled VoltageSource (VCVS). The RC filter models the dynamic of the comparator for asingle pole response (R = 10 kΩ, C = 1 pF). The VCVS1 sets across itsterminals a voltage equal to +3.3 V, if the reference voltage is greater thanthe DC-DC converter output voltage, while, if the reference voltage is lowerthan the DC-DC converter output voltage, the voltage drop across VCVS1is set to be equal to zero (those values have been set for the 3.3 V voltageregulation).

Voltage level shifter circuit

The voltage level shifter is driven by the driver block according to the resultof the comparison between the regulated voltage and reference voltage ininput to the driver comparator.

The voltage level shifter has been designed in order to hold SW3 in theon-state as default. This strategy has been adopted because during the initialphases of the scavenging process the voltage in input to the voltage regulatoris still low. With SW3 in the on state the current flows towards the loadand hence the output capacitance, C of the buck converter can be charged,allowing the output voltage to increase. The transistors of the voltage levelshifter, M1, M2, M3 and M4 are VDMOS devices.

The VDMOS available in the AMIS I3T50 process technology used todesign the system can hold a voltage source-gate drop of about 3.6 V atmaximum, before to be damaged. The voltage level shifter circuit has the

64

Figure 5.6: Internal schematic view of the SPICE model of a one-polecomparator.

aim to step up the voltage at the terminal gate of SW3 (see Fig. 5.3) andalso keeping the switch in the on-state. When SW3 has to be turned off, thevoltage at the terminal gate is stepped up to be almost equal to the voltage atthe terminal source, by the voltage level shifter, allowing then, to turn SW3off. To turn off quickly the switch SW3, in the node ’A’ should be injected alarge current value, in order to step up the voltage at node ’A’ at the valuealmost equal to the source terminal voltage, therefore, short circuiting SW3.Therefore, the current mirror M1 (W = 10 µm) and M3 (W = 80 µm) hasbeen dimensioned to have an aspect ratio of about 1:K, to amplify of aboutK times the current flowing on M1, M2, M3 when at the gate terminal of M2the high level state is present. When at the gate terminal of M2 is presenta low level state (Vout,DC−DC < Vref ), M4, M5 and R4, realize a voltagedivider. In order to draw a low current when M4, and M5 hold SW3 in theon-state, R4 should have a large value (i.e. 1 MΩ). On the contrary, R3 hasa lower value (i.e. 4 kΩ) in order to draw a large current when SW3 shouldbe turned off.

The following sections describe the behavior of the driver circuit duringthe transient and steady-state phases.

5.2.3 Transient and steady-state

Transient state

At the onset of the scavenging process, the output voltage across the loadresistance is lower than the reference voltage. With the output voltage lowerthan the reference voltage value the comparator output voltage is zero andthe monostable output is not triggered - keeping the driver output voltageat the zero logic level. A zero logic level at the terminal gate of M2 implies

65

that also M1 and M3 are turned off and hence SW3 is kept in the on-state byM4, M5 and the resistance R, which set the source-gate voltage at the rightvoltage drop to allow SW3 to be switched on. With SW3 in the on-statethe input vibrations, converted by the PBG in electrical voltage, charge thecapacitance C during the initial transient phase (interval τ1 in Fig. 5.8),hence, allowing the output voltage to increase.

During the transient phase the voltage that can be measured across theload resistance is, in fact, the rectified voltage at the output of the rectifier”shifted” across the load resistance.

After the transient phase, according to the value of the current generatedby the PBG two different cases can happen in the case of the driver circuitpowered by the output of the DC-DC converter. The first case is when thecurrent generated by the PBG (denoted as Iout,PBG) is equal or greater thanthe sum of the current requested by the load (denoted as ILoad) and the drivercircuit (denoted as IV dd,Driver) allowing the driver to commutate from low tohigh and vice versa. The second case is when the current generated by thePBG is lower than the sum of the current requested by the load and drivercircuit. The following sections describe the two above mentioned cases.

Steady-state: case of Iout,PBG < (IV dd,Driver + ILoad)

The non-optimized driver circuit requires a current of about 850 µA (in caseof 3.3 V voltage regulation) in order to commutate from the low state tothe high state and vice versa. This value of current consumption has beenfound by performing a SPICE transient analysis simulation of the wholevoltage regulator circuit, with the control circuits (driver and ZCC) poweredby an external ideal source voltage of 3.3 V, and hence, measuring the driversupply current. The use of an ideal source to power the control circuitsallowed having an idea of the amount of current needed by the driver towork properly. When some simulations were performed using the driver withdimensions as said above, trying to power the control circuits of the voltageregulator with the regulated output voltage of the buck converter, (i.e. tohave a self-powered system) it has been noted that even if the output voltageresulted regulated in some way, the driver circuit was not working at all. Infact, as it can be seen in Fig. 5.7 the control output voltage (Vctrl in Fig.5.7) resulted always equal to zero (i.e. the driver did not commutate).

However, as it can be seen in Fig. 5.7, the output voltage, Vout, seemsto be regulated at 3.3 V with a ripple of about 60 mV. In fact, the driverdoes not commutate because the buck output voltage does not overcome the3.3 V voltage value. The voltage difference between the buck output voltageand the 3.3 V reference voltage in input to the driver comparator (denoted

66

Figure 5.7: Voltage regulator control circuit cycle timing diagram in caseof Iout,PBG < (IV dd,Driver + ILoad).

as (Vout - Vref) in Fig. 5.7), resulted to be or equal to zero or lower thanzero. Having the output of the driver always at the zero logic level meansthat the high-side witch, SW3 of the buck converter is never turned off.Usually, if that happens, the DC-DC converter output voltage would resultwithout control and then it would start oscillating and increasing, becauseSW3 would result never turned off. This behavior does not happen in thecase of the voltage regulator circuit powered by the PBG, as it can be seenin Fig. 5.7 (notice the Vout curve). When the buck output voltage reachesthe 3.3 V voltage reference and overcomes it, the output driver comparatorshould go high for the whole time interval during which the buck outputvoltage is greater than the reference voltage.

The edge-triggered monostable circuit of the driver would sense the changedstate of the driver comparator output and then, it should trigger a positivepulse, which is added to the inverters chain output voltage through the ORgate. Then, a positive impulse from the OR gate output should go in inputto the voltage level shifter turning off SW3. However, as it can be noted inFig. 5.7, Vout does not overcome the 3.3 V, but it results clamped to thatvalue, for a certain time interval (τ2 in Fig. 5.7), hence, it decreases (fromabout of the half of τ3 and the whole interval τ4, as it can be seen in Fig.5.7) and after another time interval (τ1 in Fig. 5.7) it starts again to increaseup to 3.3 V. When Vout increases the voltage difference between Vout andVref tends to zero (see Fig. 5.7, (Vout - Vref) curve). This fact is sensed

67

by the driver comparator and when the difference becomes equals to zero,the driver comparator starts to commutate. However, the driver comparator,when it commutates, consumes current, but, the amount of current neededby the driver comparator to commutate to the high logic level is not enough,and then, the commutation process results not completed. This is due to thefact that, as said above, the driver circuit needs about 850 µA of current, tocomplete the commutation, but, the effective current generated by the PBGis about 150 µA (in case of the 3.3 V regulation), hence, not enough to allowthe driver to commutate.

The current generated by the PBG in part goes to the load resistance,and in part is distributed among the different circuits which constitute thevoltage regulator. The most of current generated by the PBG, however isconsumed by the driver circuit. Fig. 5.7 shows the current flowing into SW3,denoted as Isd,SW3, and the current consumed by the driver when it starts tocommutate, denoted as Ivdd,Driver. As it can be noted, the difference betweenthe two current values remains constant for the whole time interval for whichthe driver tries to commutate. The difference of the two currents is equal tothe current that goes into the load. The plots of Fig. 5.7 have been obtainedusing a load resistance of 60 kΩ and for the 3.3 V regulation, hence, it resultsthat the current flowing into the load resistance is about 55 µA. This valueof current is about equal to the resulting value of the difference betweenIsd,SW3 and Ivdd,Driver. Referring to Fig. 5.7, during interval τ1 the outputvoltage, V out, and the current, Isd,SW3, flowing into SW3 increase. WhenV out reaches the value of 3.3 V (at the beginning of interval τ2 in Fig. 5.7),the driver comparator begins to commutate and hence consuming current.But the current, Ivdd,Driver that arrives to the driver is only the 12 % of thewhole current needed by the driver to complete the commutation.

The voltage across the load is kept at 3.3 V, because as it can be seenin Fig. 5.7, the difference between the current that goes into the driverand the current flowing into SW3 remains constant and about equal to theratio between the 3.3 V and the load resistance value. During interval τ2,the current flowing into SW3 starts to decrease after to have reached thepeak of maximum at the beginning of interval τ2. Then, the current flowinginto the driver decreases as well, so that the difference between Isd,SW3 andIvdd,Driver remains constant, keeping clamped to the 3.3 V value the DC toDC output voltage. When Isd,SW3 is equal to the current flowing into theload, Ivdd,Driver becomes equal to zero, and so it is the output voltage of thecomparator (the end of interval τ2). During interval τ3 the current Isd,SW3,decreases up to become zero, and hence, the DC-DC converter output voltagestarts to decrease (interval τ4) as well. The phase when the current Isd,SW3 isequal to zero is the phase during which all the devices of the bridge rectifiers

68

are in the off-state because the PBG capacitance, Cb (see Fig. 5.3) is in thelast part of the discharging phase and in the beginning part of the chargingphase, hence, the voltage generated by the PBG has a value lower than thethreshold voltage for which the bridge devices can be kept in the on-state.

Steady-state: case of Iout,PBG ≥ (IV dd,Driver + ILoad)

The control circuit has been optimized to allow the system to be self-powered.The inverters have been dimensioned to have 1.25 µm of width and 2.2 µmof length for the PMOS and 0.5 µm of width (minimum width dimensionfor the standard MOS devices of the AMIS I3T50 process technology) and2.2 µm of length for the NMOS. The other CMOS logic gates have been di-mensioned referring to the inverter transistors dimensions. The dimensionsof the transistors of the logic gates have been chosen to reduce the currentconsumption during the commutation. The current consumption of the con-trol circuit is an important issue to overcome. The control circuit in fact isthe most consuming part of the system - in terms of current - and due tothe fact that PBG does not generate high level current values, it should bedesigned current-aware.

The timing diagram of Fig. 5.8 illustrates the cycle-by-cycle regulationprocess when the driver circuit works properly. When the voltage across Creaches the reference voltage value, the output comparator goes high andthe monostable triggers a positive pulse. The monostable guarantees thatSW3 is always switched off for a fixed time interval when the comparatorreaches and overcome the reference voltage, then, avoiding the control loopstarts to oscillate. The monostable is non-re-triggerable, and hence, if theoutput voltage overcomes the reference one during the time interval whenthe monostable triggered pulse is still high the monostable does not triggera new pulse. The monostable positive pulse and the delayed output voltageof the comparator by the inverter chain, propagate in input to the OR gate.Then, the OR gate generates a positive pulse which switches M2 on, andhence, a current starts flowing through M1.

The current flowing into M1 is mirrored into M3 and goes into the sumnode A (see Fig. 5.3). The voltage drop across R4 increases (during intervalτ2). As results M4 and M5 are turned off. When the voltage at node Ais equal to the rectifier output voltage (i.e. the voltage source), SW3 turnsoff and the capacitance C starts discharging over the interval τ3. When thevoltage across the load reaches the reference voltage, the output voltage ofthe driver comparator goes low, the monostable holds the zero logic level atits terminal output, and the driver output is set to the zero logic level. Asresults, the level shifter M2, M3 and M4 transistors turn off. During interval

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Figure 5.8: Voltage regulator control circuit cycle timing diagram in caseof Iout,PBG ≥ (IV dd,Driver + ILoad).

τ4 the voltage at node A starts decreasing, hence allowing the source-gatevoltage across SW3 to increase. When the source-gate voltage across SW3overcomes the threshold voltage of SW3, the transistor turns on (interval τ5

in Fig. 5.8), and then, the charging cycle starts again.

5.3 SPICE simulation results

Using SPICE and considering the circuit in Fig. 4.3, it is possible to computethe average of the product between the stress and strain rate in the PBGmechanical side. The average of the product computed in the mechanical sideusing SPICE, in fact, is a power density (W/m3). To express the average ofthe product between stress and strain rate as power instead of power density,it is possible to multiply it with the ratio between the equivalent current andvoltage ratio (which has the dimensions of m3).

In this way it is possible to express the average power densities computedwith SPICE in the mechanical side as average powers with Watt as unit andcomparing them with the electrical powers computed in the electrical side1.

1In formulas, considering equations (4.6) and (4.7), the average of the product betweenthe stress, σ and the strain rate, S in terms of power density (W/m3)

〈σ · S〉 = 〈(nV ) ·(i

Ai

)〉 =

n

Ai〈V · i〉

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The SPICE transient analysis reported in this section has been performedwith Spectrer, Cadencer simulation tools.

5.3.1 Semi-Active Bridge rectifier simulation results

The SPICE transient analysis simulation results of the comparison betweenthe semi-active and diode bridge rectifiers are shown in Fig. 5.9. The rectifiedoutput voltage of the two arrangements is obtained by connecting a 1 µFcapacitor and a load resistor at the output terminal of the bridge rectifiers.The R1 and R2 resistances of the voltage divider have the values of 10 MΩand 12.5 MΩ respectively (see Fig. 5.2). These large resistance values havechosen to lower the current that is drawn by the voltage divider.

Fig. 5.9 (a) shows the average rectifier input and load power with respectto the load resistance. The comparison between the two bridge rectifierarrangements reveals that the amount of power extracted from the PBG ispractically equivalent. Fig. 5.9 (a) shows also that an optimal load resistancefor which the power generated by the PBG has a maximum exists. However,the power transferred towards the load is slightly greater in case of semi-active than diode bridge rectifiers (i.e. 403 µW and 408 µW for the diodeand semi-active bridge rectifiers, respectively, see Fig. 5.9 (a)). This can bedue to the fact that the voltage drop across the VDMOS transistors, whenthey are in the on state, is lower than the voltage drop across the forwardbiased diode. Decreasing further the voltage drop across the VDMOS mayallow transferring more power to the load, improving the performances.

Fig. 5.9 (b) shows the rms voltage across the load resistance in case ofthe semi-active and diode bridge rectifiers. The voltage generated by thePBG can be greater than 10 V, as it can be seen in Fig. 5.9 (b), and thisjustifies the use of power devices in place of standard devices for designingthe bridge rectifier. At the increasing of the load resistance value the rmsvoltage generated by the PBG increases as well.

Fig. 5.9 (b) shows also the efficiency (computed as the ratio between theload power and the rectifier input power) of the two bridge rectifier arrange-ments at various load resistance values. The efficiency for both solutionstends to be 90 % at the increasing of the load resistance values, meaningthat most of the power generated by the PBG is transferred to the load.However, both voltage and efficiency values can be considered comparable.

and rearranging terms, as power in Watts

Ai

n〈σ · S〉 = 〈V · i〉

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(a)

(b)

Figure 5.9: (a) Simulated rectifier average input power (left) and load power(right) of the semi-active and diode bridge rectifiers vs. load resistance. (b)Simulated rms load voltage (left) and efficiency (right) of the semi-activebridge and diode bridge rectifiers vs. load resistance.

5.3.2 Voltage regulator simulation results

The self-powered voltage regulator circuit simulation analysis investigatesthe reciprocal interaction among the PBG and the system. The SPICEsimulation analysis has been conducted by varying the load resistance valuesconnected to the output of the DC-DC converter. Further, different values

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(a)

(b)

Figure 5.10: Simulated mechanical input power for the 3.3 V, 1.8 V and1.4 V regulated voltages versus load resistance (a). Simulated mechanicalinput power, PBG output power and load Power at various load resistancesin case of the 3.3 V regulation (b).

for the reference voltage (i.e. 3.3 V, 1.8 V and 1.4 V, respectively) in inputto the driver comparator have been used to vary the voltage value to beregulated by the circuit.

Fig. 5.10 (a) shows the mechanical input power produced by the inputstress source (σin in Fig. 5.3), as result of the vibration to mechanical conver-

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(a)

(b)

Figure 5.11: Efficiency (a) and simulated PBG output current curves (b)for the 3.3 V, 1.8 V and 1.4 V regulated voltages versus the load resistance.

sion - both in case of semi-active and diode bridge rectifiers - for various loadresistance values and for the three regulated voltage values. It can be notedthat for various regulated voltages the mechanical input power increases withthe increasing of the load resistance, reaches a maximum, and then decreaseswith further increasing of the load resistance. Fig. 5.10 (a) shows also thatthe load resistance value at which the mechanical input power has the max-imum value, changes with the regulated voltage value. The larger the value

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of the regulated voltage, the larger the optimal resistance value. However,the maximum of the mechanical input power does not significantly vary withthe regulated voltage, remaining almost constant. With respect to the useof the semi-active bridge or diode bridge there is not a meaningful differenceamong the mechanical input power curves, as it can be noted from Fig. 5.10.

In the following analysis even if the simulation results of the voltageregulator with the semi-active and diode bridge rectifiers can be consideredcomparable, for comparison only, the simulation results both for the semi-active and diode bridge rectifiers will be reported. For the sake of simplicityonly the comments referred to the simulation results of the voltage regulatorwith the semi-active bridge will be reported due to the fact that can beconsidered valid also for the case of use of the diode bridge rectifier. Whennecessary for comparison only the comments referred to the voltage regulatorwith the semi-active bridge rectifier will be completed with those ones of thevoltage regulator with the diode bridge rectifier.

Considering the 3.3 V regulation, Fig. 5.10 (b) shows how the powervaries from PBG to the load resistance. It can be noted that a large part(i.e. about the 57 %) of the mechanical power in Fig. 5.10 (b)), as resultof the vibration to mechanical conversion, is dissipated by the PBG itself.The electrical power produced by the PBG in input to the rectifier, as resultof the mechanical to electrical conversion (denoted as PBG output power inFig. 5.10 (b)) is in part dissipated by the rectifier and in part by the voltagelevel shifter, DC-DC converter, and control circuits before to be transferredto the load. In fact, of the electrical power produced by the PBG only abouta 56 % is transferred to Rload, as shown in Fig. 5.11 (a). This is due tothe fact that both the regulated voltage and the load resistance are fixed,and the maximum power that is transferred to the load resistance (i.e. 215µW) and reported in Fig. 5.10 (b) is almost equal to the load power (i.e.218 µW) computed as the ratio between the square of the regulated voltage(i.e. 3.3 V) and the optimal load resistance value (i.e. 50 kΩ).

Fig 5.11 (b) shows the output current generated by the PBG as result ofthe strain induced by the vibration source in the piezoceramic material. Theoutput current that a PBG can generate has a maximum in correspondenceof the optimal load resistance. The larger current (i.e. about 240 µA) isgenerated by the PBG for the 1.4 V voltage regulation and load resistance of20 kΩ, as it can be seen in Fig. 5.11 (b). On the contrary the current requestsby the driver to commutate is larger for greater values of the regulated volt-age. In particular from the pursued simulation analysis the driver requests apulse of current when it commutates of values equal to 100 µA, 23 µA and10 µA for the 3.3 V, 1.8 V and 1.4 V voltage regulations, respectively.

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(a)

(b)

Figure 5.12: Simulated strain rate curves for the 3.3 V, 1.8 V and 1.4 Vregulated voltages versus the load resistance (a). Simulated PBG outputvoltage curves for 3.3 V, 1.8 V, 1.4 V versus load resistance (b).

Fig. 5.12 (a) illustrates the strain rate curves with respect to the loadresistance, for different values of the regulated voltages. The PBG is sub-jected to strain at a rate that tends to lower when the load resistance valueincreases. The strain rate has an opposite behavior with respect to the stress,which tends to increasing with load resistance as depicted in Fig. 5.13 (a).In fact from Fig. 5.13 (a), it can be noted that for increasing load resistances

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(a)

(b)

Figure 5.13: Simulated stress curves for the 3.3 V, 1.8 V and 1.4 V regulatedvoltages versus the load resistance (a). Comparison among the three differentregulated voltage curves versus load resistance (b).

the magnitude of the stress σ across E5 (see Fig. 4.3) increases to valuesgreater than the magnitude of the input stress σin (which has a constant rmsmagnitude of 829.5 kNm−2 at vibrations of 120 Hz and 2.5 ms−2). A greaterstress across E5 (see Fig. 4.3) implies a greater VBD voltage magnitude, i.e.the PBG output as it can be seen in Fig. 5.12 (b).

Fig. 5.12 (b) shows the voltage generated by the PBG with respect to the

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Figure 5.14: Simulated load power for 3.3 V, 1.8 V, 1.4 V versus loadresistance (c).

load resistance. The larger the load resistance, the larger is the voltage thePBG generates. As it can be noted the larger values of the voltage generatedby the PBG correspond to the curve of the lower regulated voltage value.

Fig. 5.13 (a) shows the comparison of the three different regulated volt-ages. The load resistance value for which the voltage starts to be regulatedcorresponds at the load resistance value for which the load power (see Fig.5.14) is at its maximum value. For lower load resistance values the voltageacross the load is, in fact, the rectified voltage, which is reported across theload because the SW3 switch of the buck converter (see Fig. 5.14) is kept onby the driver circuit.

5.4 Discussion

The conducted simulation analyses of the semi-active and diode bridge rec-tifiers has shown that there is not a meaningful improvement with respect tothe use of active devices in place of passive devices. The electrical power thatcan be extracted from PBG of 1 cm3 of volume excited by a vibration sourceof acceleration magnitude of 2.5 ms−2 at 120 Hz has shown to be almostequivalent for the two arrangements (i.e. equals to about 450 µW). Of thepower generated by the PBG about the 90 % is transferred to the resistiveload, both in case of semi-active and diode bridge rectifiers (as it can be seenin Fig. 5.9).

The voltage divider used to lower the differential AC voltage from PBG

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to the suitable magnitude to be addressed in input to the ZCC becomes anissue in terms of current consuming and power dissipation. However, there isthe need to have large resistances to lower the current drawn by them, andincreasing the current transferred from the rectifier to the load. However,large resistances in case of an integrated solution means to have a largeroccupation area. To prevent these issues active loads - like diode-connectedtransistors - can be used in place of resistors.

An issue of use of PBGs as vibration-based generators to power self-powered electronic circuits is in the low current values that they can generate.Even if the power and voltage generated by PBG, can be enough to powerthe system, the current can be not enough to allow the digital part of thesystem to commutate. For this reason the analog part of the system shouldbe designed to allow that the most of the current that the PBG generatescan be made available for the digital part, and the digital part should bedesigned to be as much as possible current-aware. The voltage regulatorcontrol circuit has been then optimized to consume less current with respectto the prior design, for which the driver did not work, reducing the dynamiccurrent consumption from 850 µW to 100 µW, respectively, in case of the3.3 V regulation.

The current that can be obtained by PBGs can be increased also usingmore PBGs whose outputs connected in parallel, or using a hybrid vibration-based generator composed by a PBG and an electromagnetic generator. Theelectromagnetic generator can be obtained replacing the proof mass of thePBG with a magnet, which, moving along with the free end of the vibratedPBG, can cut the magnetic flux generated between the moving magnet anda fixed coil, properly mounted. The current induced in the coil can then beadded to the PBG current connecting the coil wires in parallel with the PBGoutput.

5.5 Summary

Power management circuits for energy scavenging applications should be sim-ple and current/power-aware designed. Further, in systems powered com-pletely by converting the scavenged energy from the ambient, the scavengershould generate the energy needed to power all the system, and with com-plex circuits this may be not practical. Then, both the proposed semi-activebridge and the self-powered voltage regulator circuits presented and describedaim to be simple, current-aware and low power consuming.

The presented SPICE simulation analysis of both the semi-active anddiode bridge rectifiers and voltage regulator circuit powered by PBG has

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shown the reciprocal interaction between PBG and the scavenging system, interms of stress, strain rate, mechanical and electrical powers at various loadsand regulated voltages. The analysis has shown that exists an optimal loadresistance for which powers and efficiency are at their maximum value, andthe regulation process begins. Simulated voltages, mechanical and electricalpowers for different load and reference voltages have shown also how boththe load and voltage to be regulated can influence the behavior of the stressand strain rate induced in the PBG by the vibration source. A large part ofthe mechanical power produced by the input stress source, as result of thevibration to mechanical conversion, is dissipated by the PBG itself, beforeto be converted in electrical and transferred to the load. Comparisons ofsimulated stress and strain rate have shown an opposite behavior of thestrain rate (which reaches a maximum value - for an optimal load - beforeto decrease) with respect to the stress (which continues to increase with theincreasing load). The simulation analysis has shown also that an optimalload resistance for which the power - mechanical and electrical - reach theirmaximum value exists.

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Chapter 6

Test chip design

6.1 Introduction

As mentioned in the introduction to the thesis work, the objective is tointegrate all the power management block on chip. But, before to do that,it is better to study the various circuits separately, in order to understandhow to optimize the system. In this context it has been chosen to integrateonly some circuit blocks and not the whole power management circuit. Inparticular, it has been chosen to integrate only the semi-active bridge rectifierand the switching part (high-side switch and low-side freewheeling diode) ofthe buck converter on chip. While, all the control circuits and the LC filterof the buck converter have been implemented with discrete components byrealizing a test board prototype - discussed in the next chapter.

Fig. 6.1 shows the SPICE test chip core schematic. As it can be seen,some dummy transistors (both for the pair of rectifier switches, SW1 andSW2, and for the DC-DC buck converter switch, SW3) have been insertedalong the semi-active bridge rectifier, in case of after the experimental teststhe need to have different areas (by connecting in parallel or series the tran-sistors) of the switches could raise. The dummy transistors in the layouthave been laid out in order to change the only METAL 2 mask to allowthe connection of the SW1, SW2 and SW3 switches with the correspondingdummy transistors, both in series or parallel connection.

The test chip makes available as external pins both the rectifier output,denoted as VO1, and the output of the switching part of the buck converter,denoted as VO2. Having the output of the rectifier available as externalpin, along with the gate and drain terminals of SW3, allows during theexperimental tests to isolate the rectifier from the switching part of the buckconverter. In this way it is possible to test only the rectifier by only short

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Figure 6.1: SPICE schematic of the test chip core.

Figure 6.2: Test chip connection diagram and top view of the Dual-In LinePackage pin out of the test chip.

circuiting the gate and drain terminals of SW3, therefore keeping turned itoff. Fig. 6.2 shows the test chip connection diagram and the top view of theDual-In Line Package pin out.

An overview of the AMIS I3T50u process technology devices used forthe test chip design is given in the appendix C. The dimensioning of therectifier devices can be found in the appendix D. Concerning the dimensioningof the p-channel VDMOS transistor (denoted as LFPDM50 in the AMISI3T50u process technology) it has been chosen to dimension it so that ithas the same on resistance of the n-channel counterpart (i.e. 16 Ω at 1 mA

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and 160 mV in correspondence of the linear region). By performing someSPICE simulations, of the ISD/VSD characteristic making vary the width ofthe p-channel VDMOS it resulted a width of 3600 µm for having the sameon resistance of the n-channel VDMOS transistor. In order to reduce theoccupation area of the device on the test chip, the p-channel VDMOS hasbeen set to have 36 fingers with width 100 µm each one.

6.2 ESD protections

The test chip core devices need to be protected against ElectroStatic Dis-charge (ESD) events. Only managing the chip with our hands we can infact damage irreparably it. Therefore, in this section it is discussed aboutthe ESD protection circuits, made available by the AMIS I3T50u technologyprocess as standard cells, which have been used to protect the different com-ponents of the test chip core. The ESD protections must be inserted betweenthe pads of the chip and pins of the test chip.

The test chip core has three LV input terminals, i.e. the two gates, G1and G2 of the two bridge switches SW1 and SW2, and one HV input pin,i.e. the gate terminal G3 of SW3. Besides, the test chip core has also twoHV output pins. The first one (VO1) is the output terminal of the SABrectifier, and the second one (VO2) is the drain terminal of SW3. The testchip, comprising of the test chip core and the ESD protections need also ofa LV supply line, denoted as VBAT in Fig. 6.3, which is necessary for thecorrect operation of the ESD clamp protections.

Fig. 6.3 shows, how the different ESD protections, both for Low Voltage(LV) and High Voltage (HV) have been connected among the test chip coreand pads in order to protect from damages caused by ESD events the test chipcore devices. Table 6.1 summarizes the specifications of the AMIS I3T50UESD protection cells used for the test chip design [DES-0076, 2006].

6.2.1 LV input pad protection

To protect the gate terminals of SW1 and SW2, denoted as G1 and G2 (seeFig. 6.3), LV input pad protections have been used. To protect the gateoxide of SW1 and SW2 against an ESD event, an input protection scheme,based on local ESD clamp protections has been used. The local protectionsare placed among the input pad (which are the gate terminal G1 (G2) ofSW1 (SW2), in Fig. 6.3) and the VSS (GND in the schematic in Fig. 6.3)and LVVDD (VBAT, equal to 3.3 V, in the schematic in Fig. 6.3) lines.

The LV input pad protections consist of a primary (ESD1 and ESD2 in

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Table 6.1: Summary of the ESD protection cells specifications.

Cell Name TypeVbd (V) Stdev (V)

TLP(∗) HBM(+)

(@ 25C) (@ 25C)

ESD IO LV 8.0 0.12.6A (IO to LVDD)

4.5kV6A (IO to VSS)

ESDGATE CLAMP LV 8.7 0.04 0.3A 0.75kV

ESDCGNMOS LV 8.6 0.18 6A 4.5kV

ESD40 SUP v1 HV 42.4 0.18 3.6A 4.5kV

ESD50 DIODE HV 50.7 — 6A —

Note: (∗) TLP (Transmission Line Pulse Tester). TLP can give a device’s I-V characteristics in transientmode TLP tester can give much more information than the ’pass’ / ’fail’ from a regular HBM tester,e.g. trigger voltage (Vt1), snap-back voltage, on-resistance, second break-down current (It2). Thecorrelation between HBM voltage and the second break-down current is V HBM(kV) 1.5*It2(A) (fromHyte Scientific).

(+)HBM (Human Body Model). HBM is one of the ESD models which represents a charged humanbody touching the IC. HBM discharge waveform has a fast rise (rise time: 2 to 10 ns) and slow decay(decay time: about 150 ns). The waveform is obtained by the discharge of a 100 pF capacitor with aninitial voltage (say 2 kV) through a 1.5 kΩ discharging resistor. 2 kV HBM ESD has a peak currentof 1.33 A (from Hyte Scientific).

Figure 6.3: Test Chip core SPICE symbol with ESD protections blocksdiagram.

Fig. 6.4) and a secondary protections (ESD3 and ESD4 in Fig. 6.4) with adecoupling resistor (R in Fig. 6.4) placed between the primary and the sec-ondary protections. The primary protections are directly placed at the bondpad, while, the secondary protections are an additional clamping structureplaced closer to the device to be protected against an ESD event and against

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Figure 6.4: LV input protection scheme based on local ESD clamp protec-tions and the path follow by the ESD event from the input pad to VSS orVDD, and viceversa. In the figure are also shown the AMIS I3T50u standardcells for the ESD1, ESD2, ESD3 and ESD4 blocks.

over-voltage. The secondary protections are useful for a better protectionof the gate oxides against CDM1 stresses. The decoupling resistor is usedto limit the fraction of the discharge current through the SW1 and SW2switches or the secondary protections (i.e. voltage clamp), by taking theexcess of voltage built up by the primary protections (i.e. current shunt).The decoupling resistor should have a value of more than 500 Ω, so that,the remaining ESD current through it will never exceed the destructive cur-rent level of the secondary protections. Fig. 6.4 shows, how an ESD eventstarting from a pad can be diverted through the ESD protections in such a

1CDM (Charged Device Model). CDM is one of the ESD models representing a chargedIC device to discharge to a different potential (usually ground). There are two kinds ofCDMs:

• CDM (or ns-CDM) - non-socketed CDM (ns-CDM, now simplified as CDM)

• SDM (or s-CDM) - socketed CDM (s-CDM, now called SDM).

CDM is a better representation of the real world ESD than SDM since SDM has parasiticsinvolved from the socket. CDM performance depends strongly on package types/sizessince the C (capacitance) in CDM is from the package itself (not like HBM and MM)(from Hyte Scientific).

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Table 6.2: NPOR electrical parameters.

Model Name Model Parameters Typical

NPOR

Rsh (Ω/sq) 292

Etch (m) 7.88e-9

Etchl (m) -2.33e-7

Tc1 (1/K) -1.97e-3

Tc2 (1/K2) 4.06e-6

way that the device to be protected is not damaged. For ESD1 and ESD2blocks, the ESD IO cell from the library amis350ubasea has been used. InFig. 6.4 is shown the ESD IO cell internal view. The ESD IO cell is con-stituted by two transistors, M0 and M2, which act as the ESD1 and ESD2protections and by the decoupling resistor, R. The decoupling resistor is an-type unsilicided poly resistor, called NPOR (amis350ubatxx library). In[I3T50uResModRep, 2006] an equation to compute the decoupling resistancevalue is given, and here is reported,

R = Rsh

(L− 2Etchl

W − 2Etchl

)[1 + Tc1 (T − TNOM) + Tc2 (T − TNOM)] (6.1)

Equation 6.1 can be approximated with the following equation, due to thefact that T = TNOM = 25C,

R = Rsh

(L− 2Etchl

W − 2Etchl

)(6.2)

In (6.2) Rsh is the sheet resistance, W and L are the resistor width andlength, respectively, Etch and Etchl are the width and length correctionterms respectively, Tc1 and Tc2 are the linear and quadratic temperaturecoefficients, respectively.

The typical electrical parameter values for the NPOR resistor are givenin Table 6.2. Referring to the values reported in Table 6.2, and substitutingthem into equation (6.2), with a W of 6 µm and L of 12 µm (dimensions ofthe NPOR resistor in the standard ESD IO cell), a value of 608 Ω for thedecoupling resistor R is obtained (a value greater than 500 Ω was suggestedas safe value in [I3T50uResModRep, 2006]).

For ESD3 and ESD4 cells, the ESDGATE CLAMP cell from the libraryamis350ubasea has been used. The VD terminal of the ESD3 (ESD4) cell isconnected to the LVVDD line. For ESD3 cell the terminal Z is connectedto LVVDD line, while the VS terminal is connected to the Z terminal of theESD4 cell. The VS terminal of the ESD4 cell is then connected to the VSS

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line. To protect from an ESD event the couple of LV supply lines - VSSand LVVDD - the Power supply clamp (ESDCGNMOS cell from the libraryamis350ubasea) has been used. In Fig. 6.4 and in Fig. 6.3 the Power supplyclamp is denoted as ESD5.

6.2.2 HV IO protections to protect the HV switches

The test chip has three HV input pads, which are AC1 and AC2, that corre-spond to the drain terminals of SW1 and SW2 and the gate terminal, G3 ofSW3. Besides, the chip has also two HV outputs, which are VO1 and VO2that are the source and drain terminals of SW3, respectively. The ESD pro-tections used to protect the three HV transistors against an ESD event aretreated in the AMIS I3T50u ESD documentation [DES-0076, 2006], and it isrelated to the 40V HV IO protections for the VFNDM50 (switches SW1 andSW2) in Low Side (LS) configuration and that one related to the 40V HV IOprotections for the LFPDM50 (switch SW3) in High Side (HS) configuration(see Fig. 6.5). These reference schemes have been used and adapted to ourcase.

Between the VO1 and VO2 and between VO2 and GND pads, two clamp-ing diodes (i.e. ESD50 DIODE in Fig. 6.5) have been connected to protectthose pads from ESD events and over-voltages greater than 45 V. A HV sup-ply clamp structure has been also connected between VO1 and GND (seeFig. 6.3). To protect the drain terminals of SW1 and SW2, connected tothe HV AC1 and to the HV AC2 input pads, an ESD clamp structure hasbeen used. In particular, the ESD40 SUP v1 cell (which can be found in theamis350ubasea library) has been chosen as clamp structure because of thehigh level voltage (open circuit voltage of 36 V) generated by the PBG in caseof series operation mode (from Piezo Systems, Inc. products catalog). TheESD40 SUP v1 must be connected between the HVVDD and VSS lines (seeFig. 6.5). Without the HVVDD line, the HV terminal of the ESD40 SUP v1has been connected to the AC1 (AC2) input pad of the test chip core, asillustrated in Fig. 6.3. With respect to the protection strategy scheme il-lustrated in Fig. 6.5 (right) between the source (connected to the VSS (i.e.GND) line) and drain (AC1 or AC2) terminals of the rectifier switches, SW1and SW2, the two clamping diodes (i.e. ESD50 DIODE) and the poly-diodestring connected between the gate (G1 and G2) and VSS (i.e. GND) linehave not been used, because considered not useful in the context of our case.

Due to the fact that the ESD clamp could be triggered by fast currentspikes, which can flow into the HV input line, an nMOS should be added toshunt the clamp gate (G in the schematic view in Fig. 6.5) to the groundline (VSS in Fig. 6.5) and then avoiding the false triggering of the ESD

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Figure 6.5: Test chip core with 40V HV IO ESD protection strategy bothfor the LFPDM50 in HS configuration (right) and for the VFNDM50 in LSconfiguration (left) schematic diagrams.

clamp. The nMOS transistor is part of the circuit dedicated to the reductionof the trigger sensitivity of the clamp circuit, as shown in Fig. 6.5 inside thedashed rectangle. To allow that the circuit for the reduction of the triggersensitivity works properly a LV supply line (LVVDD as shown in Fig. 6.5and VBAT in the schematic view in Fig. 6.3) have been added at the testchip. In correspondence of the gate terminal of the nMOS transistor a filtercomposed by a capacitor C and a resistor R has been connected. As capaci-tor C a n-channel-based MOS capacitor with a width of 80 µm and a lengthof 30 µm has been used (see [DES-0076, 2006]). During the layout designing,because of some problems related to the DRC check, raised from having aunique MOS capacitor with the dimensions said above, the MOS capacitoritself has been split in two MOS capacitors connected in series, each one witha width of 80 µm and a length of 15 µm, respectively.

In [DES-0076, 2006] for the R resistor a value of 200 kΩ is suggested. TheR resistor is a polysilicon resistor called HIPOR (amis350ubatxx library).The same equation (6.1) or (6.2) used to compute the resistance value ofthe NPOR resistor, as described previously, can be used to compute alsothe resistance value of the HIPOR resistor. Using the electrical parametersreported in Table 6.3 and using a W of 2 µm and a L of 420 µm, a value of223 kΩ for the R resistor is obtained. In [DES-0076, 2006] a reported valueof 200kΩ is suggested to use for this resistor. The same NMOS dimensions,250 µm of width and 0.4 µm of length, reported in [DES-0076, 2006] havebeen chosen for the NMOS transistor for reduction trigger sensitivity circuit.

To protect the gate of SW3 (i.e. the LFPDM50 p-channel DMOS) theprotection strategy illustrated in Fig. 6.5 (left) has been adapted to our case.

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Table 6.3: HIPOR electrical parameters.

Model Name Model Parameters Typical

HIPOR

Rsh (Ω/sq) 975

Etch (m) 7811e-8

Etchl (m) -4.54e-8

Tc1 (1/K) -1.42e-3

Tc2 (1/K2) 2.87e-6

The source and drain terminals of SW3 need to be protected against anESD event, because they are connected to the output pads, VO1 and VO2,respectively. The protection strategy used is the same illustrated in Fig. 6.5.The ESD protection is constituted of a clamping circuit (ESD40 SUP v1)among the VO1 pad (HVVDD as shown in Fig. 6.5) and the VSS line(GND as shown in Fig. 6.3). The reduction of the trigger sensitivity cir-cuit depicted in the previous section is connected to the G terminal of theESD40 SUP v1 cell. A cascoded poly diodes string (POLYD from the li-brary amis350ubatxx), between the gate (G3) and source (VO1) has beenconnected in order to clamp the gate voltage of SW3 because of the gatevoltage dependence of its snapback behavior (during an ESD event the cas-code poly diodes string allows to keep the voltage gate below 5 V). Besides,a decoupling resistor (NPOR resistor of 608 Ω, the same of the LV input padprotections decoupling resistor described in section 6.2.1)) between the G3pin of the test chip core and the gate pad (G3) of the test chip (see Fig. 6.4)has been connected.

6.3 Layout of the test chip

The overall layout and a SEM picture of the test chip are shown in Fig.6.6. The die area of the test chip is 1.4578 mm X 1.465 mm. All the ESDprotections have been arranged around the test chip core and among thepads. Fig. 6.6 (a) illustrates also the different layout of the devices and ESDprotection cells constituting the test chip. The layout of the test chip hasbeen realized using 3 METAL layers. The test chip has been fabricated bythe Europractice IC service. The package of the test chip is a DIL16 (Dual-InLine) package.

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(a)

(b)

Figure 6.6: Layout of the test chip with ESD protections (a). SEM pictureof the test chip (b).

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Chapter 7

Test board design andexperimental validation

7.1 Introduction

A test board prototype realizing a 3.3 V voltage regulator, comprising ofthe DC-DC buck converter with control circuits (i.e driver and zero crossingcomparator necessary to drive the switches of the test chip) has been designedand developed to characterize the test chip and to perform some experimentaltests. On the contrary of the integrated voltage regulator implemented inSPICE, that one implemented for the test board has the control circuitspowered separately.

Prior to connect a PBG to the test board, it has been necessary validatethe well working of both the test chip and control circuits. As referencefor the power source, the PBG T226-HA-303x by Piezo Systems, Inc, hasbeen chosen. This PBG is made of PZT-5HA piezoceramic material and hasdimensions of 31.8x12.7x0.66 mm3 and it is polarized for the series operationmode. This PBG generates a differential open circuit voltage of ±36 Vpp,and a short circuit current equal to ±1.6 mA at the resonant frequency of400 Hz. The differential open circuit AC voltage to be rectified by the testchip can not be generated by the function generator alone. The functiongenerator can generate a wave form with a maximum amplitude of ±10 Vpp.In order to step up the differential voltage to the value of ±36 Vpp theoutput of the function generator need to be prior stepped up. To performthis task the function generator can be followed by a power amplifier - inorder to realize a prior voltage amplification - and hence by a transformerwhich has the role to step up further the voltage and generating the requireddifferential voltage as well as the PBG. Besides, the frequency of the voltage

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generated by the PBG has a value of 400 Hz, then, discrete components foraudio applications have been chosen.

A TDA2030A power amplifier for audio applications and a general pur-pose audio transformer - A262A3E - with a turns ratio of 1:6.5 have beenchosen in order to step up and make differential the sinusoidal wave formgenerated by the function generator, as shown in Fig. 7.1. Considering thatthe transformer has a turns ratio of 6.5 from the primary to the secondary inorder to have a differential voltage of ±36 Vpp at the secondary of the trans-former the function generator could generate a sinusoidal voltage of ±1.8 Vppand the power amplifier should amplify 3.1 times the output of the functiongenerator. In fact, with those values it is possible to obtain a differentialoutput voltage of amplitude equal to Vin,chip = 1.8 ∗ 3.1 ∗ 6.5 = 36.3Vpeak atthe frequency of 400 Hz from the secondary of the transformer. With 36.3 Vat the secondary of the transformer at the primary results a voltage equal to5.6 V. To set the gain value of the power amplifier to 3.1, R2 and R1 havethe values of 10 kΩ and 4.7 kΩ, respectively. In case of parallel connectionof the terminals of the transformer, at the primary the impedance is equal to150 Ω. Then, a current of 37.3 mA flows into the primary of the transformer,while at the secondary it results a current equal to 5.7 mA. In case of se-ries connection of the transformer the impedance at the primary is equal to600 Ω. For the same primary voltage the current flowing into the primary istherefore equal to 9.3 mA and at the secondary results a current of 1.4 mA,which is close to the short circuit current generated by the reference PBG ifwired for the series operation mode.

The PBG T226-HA-303x, if polarized for the parallel operation mode hasan open circuit voltage equal to ±18 Vpp, while the short circuit currentis equal to 3.2 mA. In this case, to obtain ±18 Vpp at the secondary, theprimary voltage should be equal to 2.8 V and with the gain of 3.1 of thepower amplifier, the function generator should generate a sinusoidal voltageof ±0.9 Vpp. The current at the primary in case of parallel connection of thetransformer terminals is equal to 18.4 mA, while at the secondary it resultsa current of 2.8 mA, which is close to the short circuit current generated bythe PBG if wired for the parallel operation mode. It has been decided toconnect the terminals of the transformer for the parallel connection.

The test board components have required two different voltage supply inorder to work. The power supplier TTI EX752EM has used to power supplythe ±12 V requested by the Power Amplifier and INA101 instrumentationamplifier - used as current sense circuit. The ±3.3 V are generated by twoLDO linear voltage regulators, one with positive output (KF33BDT) andthe other one with negative output (LT1964ES5). The ±3.3 V is used topower supply the double comparator - LM393 - used as comparator of the

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(a) (b)

Figure 7.1: Schematic of the circuit comprising of the Power Amplifier andtransformer to step up the AC voltage magnitude of the Function Generatortill 36 Vpeak (a). Voltage level shifter circuit (b).

ZCC circuit and driver comparator, the NOR gate (74HC02N), the Inverter(74HC14), the ESD protections of the test chip.

7.1.1 Test board voltage level shifter

The voltage level shifter circuit designed for the integrated version has beenmodified in order to be realized with discrete components. Fig. 7.1 illustratesthe voltage level shifter architecture that has been adopted for the test board.The integrated version of the voltage level shifter, as shown in Fig. 5.3, isa non inverting circuit, in the sense that if the voltage signal in input tothe voltage level shifter (denoted as Vctrl in Fig. 5.3) is high the outputvoltage signal (denoted as Vctrlsw in Fig. 5.3) is equal to the higher voltagevalue of the output voltage range (about equal to the source voltage of SW3),therefore SW3 turns off. On the contrary, if the voltage signal in input tothe voltage level shifter is low the output voltage signal is equal to the lowervoltage value of the output voltage range, and SW3 turns on. The integratedvoltage level shifter turns off the switch SW3 of the DC-DC buck converterby imposing a source-gate voltage about equal to zero.

On the contrary, the test board voltage level shifter is an inverting circuitin the sense that when the input voltage signal is high, the output voltagesignal is equal to the lower value of the output voltage range, turning on theswitch SW3 of the DC-DC buck converter, while when the input signal is low

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Figure 7.2: Schematic internal view of the driver circuit.

the output of the test board voltage level shifter is equal to the higher voltagevalue of the output voltage range. The zener diode (MMSZ4678T1) in Fig.7.1 has the aim to impose - when reverse biased - a source-gain voltage equalto at maximum 3 V to allow the switch SW3 to be turned on. The resistanceR3 is necessary to discharge quickly the gate capacitance of SW3 when SW3is turned off. The n-channel MOS (BSN20), when in the on-state, connectthe resistance R4 to ground, lowering the voltage at node ’A’ and reversebiasing the zener diode, which impose a voltage of 3 V at maximum betweenthe source and gate of SW3, therefore, turning it on.

7.1.2 Test board driver

In order to drive the gate G3 of SW3 of the test chip, it is necessary the useof a driver circuit. The driver circuit, shown in Fig. 7.2 is similar to theintegrated one. Therefore, it is composed by a comparator, a multivibratormonostable circuit, an inverters chain, and a NOR gate. The use of a diversedesign for the level shifter circuit has required to invert the output level ofthe driver circuit. To perform this task a NOR gate in place of the OR gateof the integrated driver circuit has been used.

As monostable circuit the MC14528BCPG dual monostable multivibratorhas been chosen and configured non-retriggerable and in order to trigger incorrespondence of the rising edge of the input signal - output of the drivercomparator - as well the oneshot circuit of the integrated version. The pulse

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width triggered by the monostable circuit is the same used for the integratedversion, and equal to 5 µs (RX = 5 MΩ, CX = 1 pF).

The output voltage of the buck converter is compared by the driver com-parator with ground. Referencing the output voltage to be regulated withground has been necessary because the dynamic output range of the LM393comparator is limited by the power supply (i.e. ±3.3 V). The driver com-parator in fact is in the same package of the ZCC comparator. Due to thefact that the output voltage of the buck converter is 3.3 V or larger, thecomparator would not succeed to follow the variations of the input, there-fore, the comparator could not commutate in correspondence of an inputvoltage greater or lower than the reference voltage. To solve the problem,some resistors have been connected at the input and output of the drivercomparator, as shown in Fig. 7.2.

7.2 Test board experimental validation results

As explained in section 5.2.1 the semi-active bridge rectifier should be ableto start to work even if the two switches of the rectifier are not driven yet bythe zero crossing comparator, by exploiting the two bulk intrinsic parasiticdiodes of the VDMOS transistors. These diodes play the role of the twodiodes - replaced by the active devices - during the start up phase.

A prior test was then set up to verify if the semi-active bridge rectifier isable to start to work even with SW1 and SW2 are initially off. In order tohold SW1 and SW2 switched off, their gates have been connected to ground.The SW3 switch not being used, it can be switched off by connecting the G1pin to the VO1 pin. A schematic diagram of the set up of the test is shownin Fig. 7.3, while in Fig. 7.5 is shown a digital oscilloscope screen shot ofthe output VO1 (top wave form) and of the positive input AC1 (bottomwave form). As it can be noted in Fig. 7.5 the start up of the rectifier hasbeen verified and at the output of the semi-active bridge rectifier the classicalrectified voltage wave form is obtained.

The second validation test was related to the control of SW1 and SW2.In order to control the switches of the rectifier a Zero Crossing Comparatorhas bee used, as shown in Fig. 7.4. The ZCC is used to determine the zerocrossing instants of the test chip input voltage, in order to switch off and onSW1 and SW2, alternatively, to allow the correct operation of the rectifier.The voltage divider, constituted by the pair of resistances, R1 and R2, isnecessary to lower the differential input voltage to the maximum value of 3.3V in input to the ZCC. Fig. 7.5 shows the digital oscilloscope screen shotof the voltage measured at the output pin VO1 (top wave form) of the test

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Figure 7.3: Test board schematic circuit set for the start up verification.

Figure 7.4: Test board schematic circuit set for the control switches rectifierverification.

chip and the output pulse of the ZCC in input to the test chip (bottom waveform). At the output pin VO1 of the chip a 100 nF capacitance has beenconnected as load.

7.2.1 Efficiency of the test board voltage regulator

Fig. 7.6 shows the curves of the output voltage measured across the loadresistance connected at the output of the DC-DC buck converter. Each curvecorrespond to a different voltage value in input to the test chip. the voltageregulator realized with discrete components shows to have an optimal loadresistance value in correspondence of which the regulation process starts, as ithas been found for the integrated version. For the same value of the optimalresistance the output power transferred to the load is at its maximum value,

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Figure 7.5: (left) Rectified voltage measured at the output VO1 (top waveform) and single voltage wave form measured at the input AC1 (bottom waveform). (right) Rectified voltage measured at the output VO1 (top wave form)and pulse wave form applied at the gate G1 of the chip (bottom wave form).

as shown in Fig. 7.6. At the increasing of the voltage in input to the testchip the value of the optimal load resistance decreases.

The voltage curves in Fig. 7.6, highlight also that under a certain valueof the voltage in input to the regulator and for smaller resistance values theregulation process does not start at all. Due to the fact that the rectifiercontinue to work till the input voltage is enough to forward bias the rectifierdiodes, Moreover, due to the fact that the rectifier switches are driven bythe ZCC, which is powered separately, it means that the neck bottle is inthe level shifter circuit. The level shifter has a minimum voltage and currentvalue under which the zener diode cannot be reversed bias. Therefore, thelevel shifter implemented for the test board holds the high side switch ofthe buck converter always turned off. This fact, does not happen in theintegrated version, because the integrated level shifter has been designed inorder to hold the high side switch of the buck converter in the on-state, whenthe output voltage of the buck converter is lower than the reference voltage(i.e. low level input voltage or stated in other terms, low level of the inputvibrations). In this way, the output capacitance of the buck converter canbe charged.

In order to estimate the efficiency of the test board voltage regulator, ithas been necessary to measure the power in input to the test chip. Measuringthe power in input at the chip so that by the knowledge of the voltageregulator output power it could be possible to estimate the efficiency of thewhole circuit, it has been a difficult task, because it has been necessary tounderstand how to measure the input power. As definition the Effective

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(a)

(b)

Figure 7.6: Measured load voltage (a) and output power (b) with respectto the resistive load and for different input voltage values in input to the testchip.

Power is the average value of the instantaneous power, that is the product ofthe rms values of the input voltage and current and the Power Factor. If theinput voltage and current are both in a sinusoidal form, the Power Factor isthe cosine of the angle Phi, where Phi is the phase difference between thecurrent and voltage sine wave forms. In our case, the Power Factor is not

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Figure 7.7: Set up to estimate the effective input power.

the cosine of the angle Phi, because the wave form of the current is not ina sinusoidal form, being the current which flows into a rectifier. However aPower Factor exists, and its value reduces the value of the Effective Power.To measure the input Effective Power, it is not enough to measure with themultimeter the rms values of the input current and voltage and multiplyingthem to obtain the Effective Power, due to the fact the this product doesnot take in consideration the Power Factor (the product of the rms valuesof current and voltage only gives the value of the apparent power). To solvethe issue of computing the average value of the instantaneous power in inputto the semi-active bridge rectifier, a 10 Ω resistor (Rp) has been connectedbetween the ground and a terminal of the primary of the transformer (seeFig. 7.7). The voltage between the terminals of this resistor is

VRp = Rp · Ip. (7.1)

By measuring the primary voltage Vp of the transformer using the probe ofthe channel 1 (CH1) of the digital oscilloscope and the voltage VRp acrossthe resistor terminals using the probe of the channel 2 (CH2) of the digitaloscilloscope, it is possible to compute the product between the two measuredvoltage wave forms and then computing the average of the product using thefunction ”avg” of the digital oscilloscope. The average of the product of thetwo measured voltages is

〈Vp · VRp〉 = 〈Vp ·Rp · Ip〉 (7.2)

the effective power is therefore

Pin =〈Vp · VRp〉

Rp

=〈Vp ·Rp · Ip〉

Rp

= 〈Vp · Ip〉. (7.3)

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(a)

(b)

Figure 7.8: Measured input power (a) and efficiency (b) with respect to theresistive load and for different input voltage values in input to the test chip.

Fig. 7.8 shows the input power curves computed by using the methodillustrated above. As it can be noted, the input power shows an almostconstant trend till the optimal load resistance value for which the regulationstarts. Then, the input power starts to decrease.

As it can be seen in Fig. 7.8, the efficiency of the test board voltageregulator is very low (about 32%) and under the 50%. The maximum of the

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Figure 7.9: Test board circuit and set up of the experimental tests.

efficiency is found in correspondence of the input voltage value of 7.95 V, andin correspondence of the load resistance value of 10 kΩ. At the increasingof the input voltage the efficiency of the system decreases as well. It canbe also noted that the efficiency shows to have a trend which increases forinput voltage values lower than 7.95 V. On the contrary the efficiency showsa decreasing trend for values of the input voltage greater than 7.95 V. In

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fact, as it can be seen the curve related to the input voltage of 5.95 V, hasan efficiency value smaller than the curve related to the input voltage of 7.95V, but, the curve is found to be on the right of the curve of the maximumefficiency, on the contrary of the curves of the efficiency for input voltagevalues greater than 7.95 V, which are on the left.

7.3 Summary

This chapter has presented the test board voltage regulator circuit design,and the experimental measurements performed to validate and characterizethe test chip. The experimental tests have also highlighted the low efficiency(about 32%) of the voltage regulator realized with discrete components. Theeffective input power in input at the chip (i.e. transformer effective outputpower) should be less than that one computed by using the formula (7.3),due to the transformer losses. The values of the effective input power usedto compute the efficiency of the test board do not take into account thetransformer losses. The losses in the semi-active bridge rectifier, in the DC-DC switching converter, and the fact that the driver is non-optimized, havereduced the performance and the efficiency of the whole system. Both anoptimized driver and an integrated level shifter circuit might improve theperformance of the whole system.

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Chapter 8

Conclusions and future trends

One of the major challenge in developing a wireless power autonomous mi-cro/nano sensor-based system - discussed in the introduction of this thesiswork - is the design and development of a low power/current consumingpower unit. The power unit should in fact be able to harvest the whole en-ergy needed for the power supply of the system from the ambient where thesystem itself operates, conditioning and delivering this energy to the variouselectronic units composing the system (sensors, signal conditioning circuit,elaboration unit, RF module). The renewable energy-based power unit ismade of two basic blocks - the ambient energy harvester (scavenger) and anintegrated power management circuit. The ambient energy harvester shouldreplace the need to have a battery - which is the most limiting factor for thelife time and size reduction of the wireless sensor system - as power source.

As discussed in the introduction of this thesis work, mechanical vibrationsources are the most promising one from which harvesting enough energyto make wireless sensor systems self-sustaining. Therefore, the study of thestate of art of vibration-based generators (VBG) - i.e. electrostatic, electro-magnetic and piezoelectric - discussed in the Chapter 2, have been pursuedin order to identify the suitable vibration-based generator to be used. Theelectromagnetic method offers the higher energy density, but in order to workefficiently it requires to be fabricated with high quality magnets and low resis-tance coils which is difficult to obtain in case of micro scale sizes, hence, theiruse in the context of the miniaturization and integration with CMOS-basedcircuits is difficult. Moreover, the voltage generated by vibration-based elec-tromagnetic generators is very low. Electrostatic generators even if suitableto be easily miniaturized require high priming polarizing voltages suppliedby special polarization circuits in order to start to operate. Piezoelectricgenerators can be simply miniaturized and integrated with CMOS-based cir-cuit thanks to the recent progress of piezoelectric material deposition of high

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quality piezoelectric thin layers, whose properties have been improved andmade closer to that ones of bulk materials [Ledermann et al., 2003]. There-fore, it has been decided to explore the possibility of building the energyscavenging integrated system employing the piezoelectric bender generatorsas power source because the most suitable among vibration-based genera-tors to be integrated with CMOS-based circuits for the power supply of thewireless micro/nano sensor based system described in the Chapter 1.

The feasibility study presented in the Chapter 3 about the use of a Piezo-electric Bender Generator - with volume of 67 mm3 - has illustrated the pos-sibility to power a commercial WTPMS (ATMEL ATA6285/6) to perform ameasurement and a transmission every 5 minutes with a PBG mounted onthe outer rim of a car wheel. Moreover, a scenario of use of MEMS PBGfrom literature [Choi et al., 2006] as power source for the WTPMS has shownthat if the MEMS-based PBG is used for tire tread application it could gen-erate enough instantaneous power - during the time interval (i.e. 5.05 ms)in which the storage capacitor discharges from the maximum to the mini-mum input voltage values required by the wireless sensor system to work -to power the ATA6285/6 in order to perform a pressure measure and trans-mission. However, in case of use of MEMS-based PBG excited by commonambient vibrational sources the power that the micro generator can produce,could be not enough to power a wireless sensor system, even if it is usedto power the state-of-the-art wireless microsensor with on-board radio andsufficient processing capability - with estimated power consumption of about100 µW - depicted by [Cantatore and Ouwerkerk, 2006]. Therefore, in caseof the PBG was miniaturized and integrated with CMOS-based electronicson-chip, in order to generate enough energy to power the wireless sensorsystem one possibility could be connecting more MEMS-based PBGs in anarray configuration.

The development of integrated circuits needs the use of SPICE-like tools,in order to design, simulate, check the circuit design and predict the circuitbehavior before creating the final layout of the integrated system to be fab-ricated. SPICE-like tools make available at the designer equivalent voltageand current sources to power electronic circuits, and hence, simulating thecircuit behavior. However, the power sources which SPICE makes availableare not suited alone to describe the behavior of the piezoelectric generator,which shows both mechanical and electrical behaviors. The electromechani-cal model of a PBG as reported in [Roundy et al., 2004] describes the PBGin terms of circuit elements, giving at the designer a tool to study the PBGas an electrical circuit using the Kirchoff’s Voltage and Current Laws. Inorder to be used in SPICE the equivalent transformer used to describe theelectromechanical coupling of a PBG has been modified to be suited in the

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context of the analysis in SPICE. The modeling of the electromechanicalcoupling depicted by a transformer in SPICE has been discussed in detailin the Chapter 4. The simulated voltages and powers generated by theSPICE model of the PBG have been compared with the simulated volt-ages and powers, obtained with MATLABr and with the results reportedin [Roundy et al., 2004], showing a good agreement with each other. How-ever, the results obtained by simulating the SPICE model of the PBG are ingood agreement with the simulated ones reported in [Roundy et al., 2004],but they have shown - as the simulated ones reported by Roundy et al. -only a sufficient agreement with the reported measured ones. Therefore, aneffort and a careful study must be carried out in order to improve the SPICEmodel of the PBG.

The SPICE model of the PBG discussed in the Chapter 4 has been usedas power source to perform the SPICE simulation analysis of the integratedenergy scavenging system presented in the Chapter 5 which comprised of thesemi-active bridge rectifier and the voltage regulator. The SPICE simulationresults of the analyses concerning the semi-active bridge rectifier proposedand described in the Chapter 5 connected to the SPICE model of the PBG,have shown that there is not a meaningful improvement with respect to theuse of active devices in place of passive devices, such as diodes for the bridgerectifier. The voltage divider used to lower the differential AC voltage fromPBG to the suitable magnitude to be drawn in input to the Zero CrossingComparator - which control alternatively the two switches of the rectifieraccording to the phase of the AC input signal - becomes an issue in termsof current consuming and power dissipation. However, as discussed in theChapter 5 there is the need to have large resistance values for the voltagedivider in order to lower the current drawn by them, and therefore increasingthe current transferred from the rectifier to the load. Further, large resis-tances in case of integrated solution means to have a larger occupation areaon the IC die. To prevent these issues active loads - like diode-connectedtransistors - can be used in place of resistors.

In regard to the voltage regulator circuit the conducted simulation anal-ysis - discussed in the Chapter 5 - has been useful in understanding how theload can influence the power, voltage and current generated and the PBG pa-rameters - like stress and strain rate - and vice versa. The use of the SPICEmodel of the PBG connected to the semi-active bridge rectifier and voltageregulator has been useful to understand the limits of the circuit and how toovercome the issues that a self-powered vibration-based energy scavengingsystem can present to a designer. The driver circuit, which is composed bylogic circuits, should be designed current aware. In fact, the SPICE analy-sis performed by connecting the SPICE model of the PBG has highlighted

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the issue of dimensioning the transistors which compose the logic gates inorder to reduce as much as possible the current consumption when the logicgates commutate. Even if the power and voltage generated by PBG, can beenough to power the system, the current generated, on the contrary, can benot enough to allow the digital circuits to commutate. For this reason theanalog part of the system should be designed in order to allow that the mostof the current that the PBG generate could be made available for the digitalpart. Further, the digital part should be designed in order to be as much aspossible current-aware.

Further, the SPICE simulation analysis presented in the Chapter 5 ofboth the semi-active and diode bridge rectifiers and voltage regulator circuitpowered by PBG has shown the reciprocal interaction between PBG and thescavenging system, in terms of stress, strain rate, mechanical and electricalpowers at various loads and regulated voltages. The simulation analysishas shown that a large part of the mechanical power produced by the inputstress source, as result of the vibration to mechanical conversion, is dissipatedby the PBG itself, before to be converted in electrical and transferred tothe load. Comparisons of simulated stress and strain rate have shown anopposite behavior of the strain rate (which reaches a maximum value - for anoptimal load - before to decrease) with respect to the stress (which continuesto increase with the increasing load). The simulation analysis has shownalso that mechanical and electrical powers reach their maximum value incorrespondence of an optimal load resistance.

Some aspects regarding to the design of the integrated voltage regulatorstill need to be addressed. The comparator used to perform the simulationanalysis was realized only in part at transistor level. The simulation anal-ysis has highlighted the need to have circuits with a very low power anddynamic current consumption. Therefore, a comparator designed to work inthe subthreshold region could be suited for this purpose, since it could haveoperating currents in the order of nA. Further, with the supply voltage of3.3 V supplied by the voltage regulator the comparator could have a powerdissipation in the order of nW. Other aspects to be addressed concern tosolve the issue regarding to the design of a stable reference voltage and thedesign and development of an integrated inductance for the buck converter.

Chapter 7 has presented the design of the voltage regulator circuit real-ized with discrete components, and some experimental measurements whichhave been performed to validate and characterize the test chip - whose designhas been discussed in the Chapter 6. The prototype IC has been designed inAMIS I3T50 process technology, for High Voltage applications, in particularto be used with PBG as power source. High voltage technology has neededbecause of the relatively high voltage generated by PBG. The test chip proto-

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type comprises of the semi-active bridge rectifier (described in the Chapter 5)and the switching part of the DC-DC buck converter. As discussed in theintroduction of this thesis work it has been decided to integrate on chip onlythe key components (i.e. those ones that not need to be changed) and re-alized a test board prototype with discrete components which comprises ofthe control circuits (ZCC and driver circuit) and the LC filter of the voltageregulator. This hybrid solution has been pursued because of the need to havefor that part of the circuit a design flexibility during the experimental tests.Design corrections and incremental design improvements can then be easilyand readily made. If a design error is found in the test board circuit, it isrelatively easy to modify each part of the system to fix the problem, evenunder warranty.

The pursued experimental tests have highlighted the low efficiency (about32%) of the 3.3 V voltage regulator realized with discrete components. Thelow value of the efficiency of the voltage regulator could depend on the lossesin the semi-active bridge rectifier, in the DC-DC switching converter, andthe fact that the driver circuit has non-optimized. Both an optimized driverand an integrated level shifter circuit might improve the performance of thewhole system. Future works could involve the possibility to realize the controlcircuits of both the rectifier and voltage regulator by means of an optimizedalgorithm made running on a microcontroller, or DSP, which at first, could berealized with discrete components, and then, integrated with the semi-activebridge rectifier and buck converter. Smart control algorithms or architecturecontrol circuits could therefore manage the power management circuits toimprove the power transfer from harvester to the load. The final aim in thecontext of the future trends could be in fact to have all the system integratedon chip and powered by PBG.

In order to verify and validate the simulated results obtained with theintegrated voltage regulator, next experiments will concern the tests of thediscrete components-based voltage regulator with control circuits poweredby the regulated output voltage as it is in the integrated circuit in SPICE.

The study of a macro model of the scavenging circuit realized with discretecomponents is necessary for understanding how to optimize both the SPICEmodel of the PBG and power management circuit designs. The SPICE modelof the PBG should be optimized so that when simulated in SPICE its elec-tromechanical behavior - modeled in SPICE by circuit elements - could becloser to the realistic one. Therefore, it is useful to have a prototype of aPBG in order to compare the measured results with the simulated ones. Areliable SPICE model of the PBG is therefore desired in order to be usedwhen the integrated system is simulated in SPICE. However, a careful studymust first be made.

107

Some preliminary experimental results regarding some tests carried outwith a PBG prototype have been realized and are presented in the nextsection of this concluding chapter.

8.1 Preliminary experimental results

This section reports the preliminary results obtained from the experimentaltests realized with a fabricated PBG prototype. The experimental tests areaddressed to validate the SPICE model of the PBG, and to characterizethe test chip and test board realized and described in the Chapters 6 and7 when powered by PBG. In order to validate the SPICE equivalent modelof the PBG - presented and developed in the Chapter 4 - is necessary tocompare it with a realistic PBG. By performing experimental tests with theprototype PBG and hence comparing the measured results with the simulatedones, it would allow understanding what are the limits of the developedSPICE model and hence, through the study and understanding of the resultsobtained, optimizing the developed SPICE model in order to make it closerto the realistic counterpart. In fact the developed model does not take intoaccount losses like dielectric, viscoelastic, hysteretic, and so forth. Thoselosses are frequency dependent, and hence they could be expressed as complexconstants rather than real constants.

Two PBG prototypes have been fabricated in order to pursue the exper-imental tests. The two prototypes are made by using two bimorphs fromPiezo Systems, Inc. (i.e. the T226-A4-503Y and T220-A4-103Y both polar-ized for the parallel operation mode) with steel proof mass attached to thefree end. The bimorphs are made of two layers of PSI-5A4E piezoceramic(with nickel electrodes) - attached to a brass center shim reinforcement - withdimensions of 31.8x3.2x.51 mm3 and 63.5x31.8x.66 mm3, respectively. Thebigger PBG prototype (the hereafter denoted as PBG1) has been designedto resonate at the frequency of ∼ 30 Hz, by attaching a steel proof mass of∼ 220 g and dimensions of 30x35x26 mm3 onto the top surface of the free endof the bimorph, as shown in Fig. 8.1. The smaller prototype (the hereafterdenoted as PBG2) has been designed in order to resonate at the frequency of80 Hz, with proof mass of 15.6 g attached to the free end. The dimensions ofthe proof mass for the two prototypes have been computed by using the ex-pression for the resonance frequency of the PBG [Roundy et al., 2004], herereported

ωn =

√Yp

(K1K2m)=

√6IYp

l2b(2lb + 1.5lm

)m

(8.1)

108

where Yp is the Young’s modulus of the piezoceramic, I is the second momentof inertia of the PBG1, m = ρmlmwmhm, is the inertial mass with length lm,width wm, height hm and density ρm (i.e. 7.85e3 kg/m3 for the steel). Inparticular the expression (8.1) has been used to compute the height of theproof mass, by setting the width and length of the proof mass according tothe dimensions of the bimorph and the length, lb of the bender - as definedin Fig. 4.1. The height of the inertial mass can be found rearranging termsof (8.1), and therefore, it yields

hm =6IYp

l2b(2lb + 1.5lm

)lmwmρmω

2n

. (8.2)

Therefore, from the knowledge of the height of the proof mass computed using(8.2) for the given resonance frequency, it has been computed the mass, mof the proof mass for the two PBG prototypes.

The mechanical Q of the PSI-5A4E is 80 (Piezo Systems, Inc, publishedvalue), which implies a mechanical damping ratio, ζ of ∼ 0.0125. In orderto calculate the damping ratio an impulse has been applied to the PBG1prototype and hence by measuring the damped open voltage amplitudes ofthe PBGs at two separated points (denoted as X1 and X2), n periods apartan average mechanical damping ratio of ∼ 0.0175 has been computed usingthe formula ζ = 1/(2πn) ln(X1/X2). This value of mechanical damping ratiowill be used when compute the parameters of the SPICE PBG model in placeof the computed one by using the published mechanical Q.

The preliminary experimental tests have been realized using one of thetwo non-optimized PBG prototypes which have been fabricated. In particu-lar, the piezoelectric generator, denoted as PBG1 has been used. In order tocompare the measured and the SPICE simulated results it is necessary theknowledge of the acceleration amplitude, to be able to compute the right am-plitude value for the input stress generator (i.e. σin = K1main sinωt whereain is the amplitude of the acceleration) of the SPICE model of the PBG.To pursue this task, it is necessary to measure the acceleration amplitude by

1The second moment of inertia is found by applying the parallel axis theorem to thecross-section area of the composite bimorph, and here reported [Roundy et al., 2004]

I = 2

(wt3p12

+ wtpb2

)+ η

wt3sh12

where w, tp, and tsh are the width, length, thickness of the bimorph, b is the distancebetween the center of the brass shim and the center of the piezoceramic layer, and tshis the thickness of the metal shim, and η = Ysh/Yp is the ratio between the Young’smodulus of the brass shim and piezoceramic, respectively. The term η is needed to madethe cross-section area of the bimorph as it was made only of piezoceramic.

109

Figure 8.1: The fabricated prototypes - PBG1 and PBG2 - made of PSI-5A4E with a steel proof mass attached to the free end, and clamped to asteel support.

Figure 8.2: The prototype generator (PBG1) mounted on the vibrometer(Tira TV50018) used to perform the experimental tests.

means of an accelerometer mounted on the surface of the PBG proof mass.For the time being, this task has not been pursued yet and it will be one ofthe next tasks to be addressed. Therefore, only the measured results from theexperimental tests with the PBG1, have been reported in this thesis work.

A first experimental test has concerned the measure of the open circuit

110

Figure 8.3: Schematic diagram of the test set up for the open circuit voltage(left) and resistive load voltage measurements (right) across the output ofthe PBG prototype.

Figure 8.4: Measured open circuit voltages (peak values) at various fre-quencies.

voltage (see Fig. 8.3) generated by the PBG1 for various frequencies in therange of 25-50 Hz, around the resonance frequency of the generator. ThePBG prototype has been mounted on a shaker (Tira TV50018) - as shownin Fig. 8.2 - which is controlled and made vibrated by means of LabView.As shown in Fig. 8.4 the PBG1 generates the maximum open circuit voltage

111

Figure 8.5: Measured open circuit voltages (peak values) and powers vs.load resistance at 32 Hz (resonance frequency of the PBG)

in correspondence of the resonance frequency of the generator. This test hasshown that the maximum of the voltage that the PBG is able to generate is incorrespondence of the resonance frequency of the PBG, given the dimensionsof the PBG and the magnitude of the vibrational source. When testing thePBG for values of the vibration frequency lower than the resonance frequency,in particular for values lower than 25 Hz, maybe the aluminum support, orthe structure of the shaker along with the aluminum support, influenced thefrequency behavior of the PBG, which showed another frequency mode forfrequency values around 12 Hz, with a peak of voltage of about 43 V (notreported in Fig. 8.4). This frequency mode is anyway not related to thePBG. Therefore, the set up for the experimental tests should be carefullyrevised. A new support, made of plastic instead of aluminum - in case of theheavy aluminum support were the structure which influenced the frequencybehavior of the PBG - is under construction, and new experimental tests willbe carried out.

Fig. 8.5, shows the voltage values (peak values) measured across diverseresistive loads - a schematic diagram of the test set up is illustrated in Fig.(see Fig. 8.3). As it can be noted the curve of the voltage tends to anasymptotic value near the 16 V, which should be the maximum voltage thePBG is able to generate in case of resonance, according to the maximum valueof the voltage found making vary the frequency of the vibrational source,

112

(a)

(b)

Figure 8.6: Measured PBG output voltage and rectified voltage with re-spect to time (a). Voltage regulator measured open circuit voltage and for a10 kΩ resistive load (b).

and reported in Fig. 8.4. Besides, with respect to the measured voltage datareported in [Roundy et al., 2004] which have shown a variability in the values,this variability has not been found when measuring the output voltages ofthe PBG1 prototype for various load resistance values, as it can be noted inFig. 8.5.

Some other preliminary experimental tests have concerned the connectionof the PBG1 prototype to the test board in order to pursue some measure-ments with the test chip and the discrete components-based voltage regula-tor. Fig. 8.6 shows the wave forms of the 21.3 Vpp output voltage of thePBG1 excited by vibrations at 32 Hz; the PBG1 output voltage rectifiedby the integrated semi-active bridge rectifier on-chip (at 32 Hz); the 3.3 Vregulated voltage across the output capacitance of the buck converter withno resistive load connected to, and with a 10 kΩ load resistance connected

113

to the output of the buck converter (at 32 Hz). The measured voltage acrossthe 10 kΩ load resistance is not regulated at the value of 3.3 V because, itis lower than the optimal load resistance for which the regulation at 3.3 Vstarts.

Future trends will involve the measurements of the regulated voltage,output power and input power, efficiency for various load resistance values,frequency of the vibration, connecting both PBG1 and PBG2. Further, ex-perimental tests will involve also the use of the two PBGs to power a newtest board energy scavenging system with the semi-active bridge rectifier(test chip), voltage regulator with discrete control circuits or substituted bya low power microcontroller, entirely powered by the PBG.

8.2 A proposal for a hybrid vibration-based

generator

An improvement of the simple PBG generator is the development of a hy-brid generator. PBG and electromagnetic generators can be joined to real-ize a vibration-based hybrid generator. PBG can generate high level powerand voltage values, but, low level current values, due to the high outputimpedance. Electromagnetic generator can generate high level power andcurrent values, but low level voltage values. Then, combining the two kindsof vibration-based generators into one hybrid vibration-based generator itcould be possible to exploit the advantages of the two generators alone andcompensate the disadvantages of each one.

8.3 Electromechanical analytical model of a

vibration-based piezoelectric and electro-

magnetic generator

Even if a PBG is able to generate high level voltages and powers, the fact ofhaving the bimorph a high output impedance does not allow the PBG gen-erating high current values. A way to increase the generated current fromthe PBG, which can be made available for the electronic system to be pow-ered, a vibration-based electromagnetic generator could be integrated intothe PBG design. In fact the proof mass attached on the free end of thebimorph can be substituted by a permanent magnet, which made moving bythe vibration source, can induce for the Faraday’s Law an electromotive forceinto a fixed coil against the time varying flux linkage Φ(B) of the magnetic

114

field B. Then, if a load resistance is connected across the coil terminals, acurrent starts to flow in the coil. A similar approach has been proposed in[Torah et al., 2006].

A representation of a linear vibration-based electromagnetic generatorsystem is depicted in Fig. 8.7. A permanent magnet of mass m, is attachedto a spring of elastic constant k made moving by a vibration source actingon the base of the spring. A fixed coil with a load RL connected to its ter-minals is set so that the magnet moves in its center. A current iB flows inthe coil because of the induced electromotive force which creates against thevariation of the circuit flux linkage.

An analytical analysis of the electromechanical circuit of the electromag-netic generator can be found in [Poulin et al., 2004] and it is the base of thefollowing analysis.

The fundamental mechanical law applied to the system depicted in Fig.8.7 is

mx = mg − k(x− y + ∆st)− bT (x− y)−BliB +my (8.3)

where mg is the weight, g = 9.81ms−2 is the gravitational acceleration, bT isthe damping coefficient, l is the coil length and ∆st is the static deflection.The static deflection of the spring equals to ∆st = (mg)/k cancels the gravityterm mg because of the static-equilibrium position condition of the system[Kelly, 2000]. The term BliB in (8.3) is the electromagnetic force. Defining

z(t) = x(t)− y(t) (8.4)

as the displacement of the magnet relative to the displacement of the supportdue to the vibration, equation (8.3) becomes

mz + bT z + kz = −BliB −my. (8.5)

The absolute displacement of the frame is y(t) and considering the vibrationsource as a harmonic source motion, the absolute displacement can be definedas y(t) = Y0 sinωt. Taking the first and second derivative of y(t) it yieldsy = ωY0 cosωt and y = −ω2Y0 sinωt. Substituting y in (8.5) it yields

mz + bT z + kz = −BliB +mω2Y0 sinωt. (8.6)

Defining the vibration source in terms of acceleration as y = ω2Y0 sinωt =ain sinωt, where ain is the acceleration amplitude, equation (8.6) becomes

mz + bT z + kz = −BliB +my. (8.7)

Applying the KVL to the coil circuit in Fig. 8.7 it yields

ε = VB +ReiB + LediBdt

(8.8)

115

Figure 8.7: Model of a linear vibration-based electromagnetic generator.

where ε = Blz is the induced electromotive force, Re and Le are the resistanceand self-inductance of the coil, respectively. Rearranging terms in (8.8) ityields

VB = Blz −ReiB − LediBdt. (8.9)

Equation (8.5) can be coupled to the electromechanical model of the PBGmaking some considerations which arises from the system depicted in Fig.8.7. In the analytical model of the electromagnetic generator the spring anddamping are general parameters. Considering that, the magnet is attachedto the bimorph, being in place of the proof mass, the spring in Fig. 8.7 can beconsidered as the bimorph itself with elastic constant k and equivalent damp-ing coefficient bT = bm + be (i.e. bm and be the equivalent electrically inducedand mechanical damping coefficients, respectively, and the displacement z isthe same of the PBG electromechanical model. Knowing that the relationwhich relates displacement and strain is z = K2S, from section above, andsubstituting it in (8.7) it yields

mK2S + bmK2S + beK2S + kK2S = −BliB +my. (8.10)

Then multiplying both members of (8.10) for K1 it yields

mK1K2S + bmK1K2S + beK1K2S + kK1K2S = −K1BliB +K1my (8.11)

Comparing (8.11) with (4.3) it yields

LmS +RbS + nV +1

CKS = −K1BliB +K1my. (8.12)

116

In (8.12) the term 1/CK can be substituted with the Young’s Modulus of thepiezoelectric material of the bimorph, denoted as Yp. In fact, as reported in[Roundy et al., 2004] the spring constant k is considered to be given by theratio

k =Yp

K1K2

(8.13)

which substituted in (8.11) it yields 1/CK = Yp as it has been definedin [Roundy et al., 2004]. Then, rearranging terms, equation (8.12) can berewritten in the form

LmS +RbS + YpS = −nV − nemiB +K1my (8.14)

where nem = K1Bl can be defined as the equivalent electromagnetic trans-former ratio, which relates the magnetically induced stress σem in the me-chanical side to the induced current iB flowing into the coil.

As reported in [Roundy et al., 2004], the term beK1K2S can be equatedto the term nV , from which in [Roundy et al., 2004] can be found the ex-pression for the electrically induced damping ratio.

ζe = − ωK231

2

(s+ 1

RLCb

) . (8.15)

The electrically induced damping ratio is a function of electrical parameters,and it can be designed to be equal to or greater than the mechanical dampingratio.

A magnetically induced damping ratio (i.e. ζem = bem/(2mωn), wherebem is the electromagnetic damping coefficient) as function of electrical andmagnetic parameters can also be derived using an approach similar to thatone used in [Roundy et al., 2004] to derive the electrically induced dampingratio. In fact equating the terms

bemK1K2S = K1BliB (8.16)

and rearranging terms it yields

iB

S=

2mωnζemK2

Bl. (8.17)

Taking the Laplace transform of (8.17)

IBs∆

=2mωnζemK2

Bl(8.18)

117

where s∆ is the Laplace transform of the strain rate, and taking that one of(8.9), in which the expression relating displacement and strain (i.e. z = K2S)is used, and substituting also the expression V = RLiB, it yields

RLIB = −BlsK2∆−ReIB − sLeIB. (8.19)

Then, rearranging terms

IBs∆

= − BlK2

(RL +Re + sLe). (8.20)

Equating (8.18) with (8.20) and rearranging terms it yields

ζem = − (Bl)2

2mωnLe

(s+ RL +Re

Le

) . (8.21)

In the case of use of the only PBG, the power output is optimized when theequivalent electrically induced damping ratio (i.e. ζe which is designable)is equal to the mechanical damping ratio, ζm. The designable equivalentelectrically induced damping ratio is a one-degree of freedom which allowsthe designer optimizing and maximizing the power generated by the PBG.Coupling the PBG and the ElectroMagnetic Generator a designable equiva-lent magnetic induced damping ratio can be derived, and hence, a one moredegree of freedom can be used by the designer to optimize the output powergenerated by the system PBG+EMG, by making the sum ζe + ζem = ζm.

8.3.1 PBEMG model with resistive load: coil connectedin parallel with the PBG output

Connecting the output of the coil in parallel with the PBG output (see Fig.8.9), hence, adding the current flowing into the coil with the PBG outputcurrent, to increase the total output current, applying the KVL and KCL tothe circuit in Fig. 8.8, it yields

LmS +RbS +1

CKS = −nV −K1BliB +K1my. (8.22)

VB = K2BlS −ReiB − LediBdt. (8.23)

i = iB − CbV −V

RL

. (8.24)

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Figure 8.8: Equivalent electromechanical Piezoelectric Bender ElectroMag-netic Generator model.

Figure 8.9: Equivalent electromechanical Piezoelectric Bender ElectroMag-netic Generator model, in case of parallel connection of the coil output withthe PBG output.

Taking the Laplace transforms of (8.22), (8.23) and (8.24), and rearranging

119

terms, it yields(s2 +

bmms+

YpK1K2m

)∆ =

(ad31

2Yp

)(Yp

K1K2m

)V −

(Bl

K2m

)IB +

1

K2

Ain.

(8.25)where with ∆ is denoted the Laplace transform of the strain, S. Equation(8.23) becomes

VB = K2Bls∆− ZeIB (8.26)

where Ze = Re + sLe and (8.24) becomes

I = IB − CbsV −V

RL

. (8.27)

Substituting in (8.27) the Laplace transform of equation (4.7) it yields

awled31Yps∆ = IB − Cb(s+

1

RLCb

)V (8.28)

and rearranging terms

V =

(2tc

a2wleε

)1(

s+ 1RLCb

)IB − (2tcd31Ypaε

)1(

s+1

RLCb

)s∆. (8.29)

The output voltage of the coil, denoted as VB becomes equal to the PBGoutput voltage V , because of the parallel connection between the output ofthe coil with the PBG output. Then, it is possible to equate (8.26) and(8.29), and rearranging terms, the following equation of the coil current IBrelated to the strain, it yields

IB =

(K2Bl

Ze

) (s+2tcd31YpaεK2Bl

+1

RLCb

)(s+

2tc

Zea2wleε

+1

RLCb

)s∆. (8.30)

Substituting (8.30) into (8.29) and rearranging terms, a transfer function ofthe Laplace transform of the strain, ∆, related to the Laplace transform ofthe output voltage, V , can be found

∆ =

(s+

2tc

Zea2wleε

+1

RLCb

)s

[2tc

Zea2wleε

(K2Bl)−2tcd31Ypaε

]V (8.31)

120

The transfer function of the whole system, in case of parallel connection ofthe coil with the PBG output, and resistive load, can be found substituting(8.30) and (8.31) into (8.25)

V =a0

(s3 + b0s2 + c0s+ d0)sAin (8.32)

where

a0 =1

K2

[2tc

Zea2wleε(K2Bl)−

2tcd31Ypaε

](8.33)

b0 =2tc

Zea2wleε+

1

RLCb+bmm− (Bl)2

mZe(8.34)

c0 =bmm

(2tc

Zea2wleε+

1

RLCb

)+

+Yp

K1K2m

1−

(ad31

2tc

)[2tc

Zea2wleε(K2Bl)−

2tcd31Ypaε

]+

−2tcd31YpBl

ZeaεK2m− (Bl)2

mZe

1

RLCb(8.35)

d0 =Yp

K1K2m

2tcZea2wleε

+Yp

K1K2m

1

RLCb. (8.36)

The transfer function (8.32) relates the total output voltage, V , of the systemwith the input vibration in terms of acceleration, Ain.

8.4 Combining piezoelectric and electromag-

netic SPICE models

To develop the equivalent electromechanical model of the PBG+EMG sys-tem, equation (8.12) can be rewritten as

LmS +RbS +1

CKS = −nV −K1BliB +K1my. (8.37)

Using also equations (8.8) and (4.4), which are reproposed here

VB = K2BlS −ReiB − LediBdt. (8.38)

and

i = −CbV −V

RL

(8.39)

121

Figure 8.10: Equivalent SPICE model circuit of the Piezoelectric BenderElectroMagnetic Generator.

Then, the equivalent electromechanical model of the PBG+EMG system canbe depicted as in Fig. 8.8. All terms in (8.37) are dimensionally a stress,which is, in the mechanical side of the electromechanical model, the analogousof the voltage.

The equivalent SPICE model of the electromechanical model depicted inFig. 8.8, can be derived using dependent controlled sources, as it has beendone when deriving the SPICE PBG model.

8.4.1 SPICE modeling of the mechanical and electricalsides

The mechanical to electrical coupling of the EMG is depicted by the termσ = nV , which can be modeled like a Voltage Controlled Voltage Source(VCVS), where the controlled voltage is the stress σ, while the controllingvoltage is the voltage V across the secondary of the transformer, and n isthe gain.

The term σem = K1BliB is dimensionally a stress, and can be modeledin SPICE like a Current Controlled Voltage Source (CCVS), where the con-trolled voltage is the stress σem, while the controlling variable is the currentiB flowing into the coil, and K1Bl is the gain.

The electrical side of the electromechanical model is depicted by two dif-ferent circuits. The PBG SPICE electrical side, as developed in the previous

122

sections, is coupled with the mechanical side by the Current Controlled Cur-rent Source (CCCS) in parallel with the bender capacitance, Cb, and withcontrolled variable the current flowing into the secondary of the transformer,i, and controlling variable the analogous of the current flowing into the me-chanical side, i.e. the strain rate S. The gain of the CCCS is Ai = awled31Yp.

Equation (8.38) can be used to model in SPICE the electrical side of theelectromagnetic part of the PBG+EMG system. The induced electromotiveforce is from (8.38) given by ε = K2BlS. It represents the electro-mechanicalcoupling between the electrical and mechanical sides of the equivalent model,and it can be modeled in SPICE like a CCVS. The controlled variable is theelectromotive force, ε, while the controlling force is the strain rate, S, andthe gain is −K2Bl. The complete equivalent SPICE model is illustrated inFig. 8.10.

123

Appendix A

Publications

The following list details the articles published in scientific journals and na-tional and international conferences dring the course of this thesis.

Journals:

1. Luigi Pinna, Ravinder S. Dahiya, Fabrizio De Nisi, Maurizio Valle,”Circuit simulation analysis of Self-Powered Vibration-Based EnergyScavenging System”, Microelectronics Journal, Elseviere, 2010. (sub-mitted)

National Conferences:

1. Luigi Pinna, Maurizio Valle, Gian Marco Bo, ”Experimental results ofpiezoelectric bender generators for the energy supply of smart wirelesssensors”, proceedings of AISEM 2008 - The XIII annual conferenceof Associazione Italiana Sensori E Microsistemi, Rome, 19th-21st ofFebruary, 2008.

International Conferences:

1. Luigi Pinna, Ravinder S. Dahiya, Maurizio Valle, ”SPICE model forpiezoelectric bender generators”, ICECS 2009, The 16th IEEE Interna-tional Conference on Electronics, Circuits, and Systems, Hammamet,Tunisia, December 13th-16th, 2009.

2. Luigi Pinna, Ravinder S. Dahiya, Gian Marco Bo, Maurizio Valle, ”Cir-cuit Simulation Analysis of Vibration-Based Energy Scavenging Sys-tem”, ISCAS 2010, The IEEE International Symposium on Circuitsand Systems, Paris, France, May 30th-June 2nd, 2010. (submitted)

124

3. Luigi Pinna, Ravinder S. Dahiya, Fabrizio De Nisi, Maurizio Valle,”Analysis of Self-Powered Vibration-Based Energy Scavenging System”,ISIE 2010, The IEEE International Symposium on Industrial Electron-ics, Bari, Italy, July 4th-7th, 2010. (submitted)

125

Appendix B

SPICE Netlist of thePiezoelectric Bender Generator

* source PBG Equivalent Circuit

Vsigmain 1 6 SINE(0 K1*m*ain fin)

V3 4 5 0

E5 5 6 B D n

F5 D B V3 Ai

Lm 1 2 Lm

Rb 2 3 Rb

Ck 3 4 Ck

Cb B D Cb

* source PBG Dielectric Losses Equivalent Circuit

Vsigmain 1 6 SINE(0 K1*m*ain fin)

V3 4 5 0

E5 5 6 B D n

F5 D B V3 Ai

Lm 1 2 Lm

Rb 2 3 Rb

Ck 3 4 Ck

Cb B D Cb

Rdl B D Rdl

126

Appendix C

AMIS I3T50u devices overview

C.1 Introduction

To design the chip the AMIS I3T50U technology process has been used. Thistechnology process provides a useful library, of high voltage devices, that hasbeen necessary to realize the project of the chip. The descriptions of devicesused can be found on the AMIS I3T50U process technology documentation[DES0035, 2008] and in this appendix a brief overview of the principal char-acteristic of the only HV devices is reported.

The I3T50U process technology features high voltage devices, such asVDMOS transistors, up to 40 V as well as analog operation at 3.3 V. TheI3T50U process technology includes also a complementary library of LowVoltage 0.35 µm CMOS devices. Both Low Voltage and High Voltage MOSdevices are realized with a gate oxide of 7 nm of thickness. Due to thischaracteristic it is necessary to avoid operation of the devices above 3.6 V.

Each high voltage device is isolated from each other and also from thelow voltage part of the circuit by means of the use of deep trenches. Anoverview of the benefits of the trench isolation in High voltage applicationscan be found in [Thiel and Stibila, 2007]. The trench isolation with the self-aligned n-type sinkers and blanket BLN - characteristic of the I3T50u processtechnology devices - are the ”walls” to completely isolate the devices, byrealizing a kind of pocket where the device can operate. With this approachthe isolation distance between two devices can be less than 5 µm, which incase of HV devices this isolation distance can be reduced to 1 µm.

Table C.1 reports an overview of the devices used to design the semi-active bridge rectifier, voltage regulator and for the design of the test chipprototype.

127

Table C.1: Summary of the AMIS I3T50-U devices used.

Category UDS name Description

HV DMOSVFNDM50 Vertical floating n-channel DMOS

LFPDM50 Lateral floating p-channel DMOS

LV MOSENM Standard LV n-channel MOS (four terminals)

EPM Standard LV p-channel MOS (four terminals)

DIODESFID50U High Voltage fully isolated diode

POLYD Poly diode for zener application (gate protection)

RESISTORSNPOR n+ poly resistor

HIPOR High ohmic poly resistor

C.2 n-type VDMOS transistor: VFNDM50

The version of the n-channel VDMOS transistor by AMIS I3T50U processtechnology can be used in high-voltage switching applications, where nodesfloating up to 50 volts with respect to the p-substrate. This characteristic isuseful in our case, because of the high output voltage levels the piezoelectricbender generators can generate due to the fact that using them as switchesof the semi-active bridge rectifier the voltage levels to which the drain can besubjected could rise up to 40 V. In Table C.2 are summarized the principalcharacteristics of the VFNDM50 device. To avoid that the intrinsic parasitic

Table C.2: VFNDM50 device parameters.

Floating NDMOS Typical Value Unit

Vth0 (W=40µm) 0.77 V

Vdsmax 40 V

Vgsmax 3.6 V

Ids (Vds=25 V; Vgs=3.6 V; 4 channels) 220 µA/µm

Ron*Area (20 channels) 52e-3 Ωmm2

Note: W=width of the channel

NPN bipolar turns on when the VDMOS is working the source and bulkterminals are always short circuited. That is indicated in the schematicsymbol of the VFNDM50 (see Fig. C.1) with a connection between thesource and bulk terminals. Referring to the Fig. C.1, a PBODY well hasbeen introduced to allow to have a channel self-aligned to the poly gate.Another characteristic of the VDMOS by AMIS is the introduction of anActive Junction Termination (AJT) that allows to have an increment of theoutput device current, that is an advantage in using smaller devices. The

128

AJT besides protect the PBODY bulk region to an increase of the electricfield at the curvatures. A PField ring is also added to the AJT in a way thatsurrounding the edge of the PBODY bulk it creates an additional channelthat participates in the delivery of the current, ideally the same amount asone PBODY VDMOS channel, in parallel with the core device.

C.3 p-type VDMOS transistor: LFPDM50

The version of high voltage pDMOS transistor by AMIS I3T50U technologyused in the project of the chip, it is called LFPDM50. This pDMOS, like then version, can be used in high-voltage switching applications, where nodesfloating up to 50 volts with respect to the p-substrate must be switched. Inrespect to the VFNDM50, the LFPDM50 has the source not circuit shortenedwith the bulk terminal, so, the body effect needs to be taken into account.

In the LFPDM50 the Ids current flows horizontally. In respect to thenDMOS device the LFPDM50 is not self-aligned. That is due to the factthat the channel is defined by the overlapping between the nWell and polygate, with a fixed nominal length channel of 1.0 µm (see Fig. C.1). Then,the length of the channel is susceptible to misalignment and besides, thecharacteristics of the device are orientation dependent. When we design thelayout to obtain a good matching it is better using LFPDM50 devices withsmall width and orienting them in the same direction. In Table C.3 aresummarized the principal characteristics of the VFNDM50 device.

Table C.3: LFPDM50 device parameters.

Floating PDMOS Typical Value Unit

Vth0 (W=40µm) -0.57 V

Vdsmax -40 V

Vgsmax -3.6 V

Ids (Vds=25 V; Vgs=-3.6 V -110 µA/µm

Ron*Area (20 channels) 150e-3 Ωmm2

Note: W=width of the channel

C.4 High Voltage diode: FID50U

The fully isolated FID50U high voltage diode bases its operational principleon an lateral bipolar device with shorted base-collector junction. The para-sitic vertical PNP (see Fig. C.1) with the blanket BLN layer as n-type base

129

and the p-substrate as collector. The widely and highly doped blanket BLNlayer allow to almost eliminate the contribute of the parasitic vertical PNP.in Table C.4 are summarized the principal characteristics of the VFNDM50device.

Table C.4: FID50U device characteristics.

Floating High Voltage Diode Typical Value Unit

Vbd -57 V

VKA at Ianode = 1µA 0.68 V

Note: K=cathode, A=anode

Figure C.1: Symbol and cross-section of the VFNDM50 and LFPDM50VDMOS transistors and cross-section of the FID50U diode, respectively.

130

Appendix D

Semi-Active Bridge rectifierdimensioning

The PBG T226-H4-303X (31.8x12.7x0.38 mm of dimension) by Piezo Sys-tem, Inc., has been used as reference source in order to dimension the SABrectifier devices. The reference PBG is able in case of series operation modeto generate an open circuit voltage of ±36 Vpp and a closed circuit currentof 1.6 mA at the resonance frequency of 400 Hz (those values of current andvoltage are valid in condition of impedance adaptation). The use of powerMOSFET devices allows the SAB rectifier to be used in high voltage ap-plications (up to 50 Volts in input [DES0035, 2008]). In order to designthe rectifier, three components have needed to be prior dimensioned. Theswitches SW1 and SW2 and the diodes D1 and D2 belonging the full bridgerectifier.

In order to reduce the power consumption of the rectifier, it has beenchosen to dimension the rectifier devices so that when they are in the on-state, they have the smaller on resistance. In particular, that means to havea lower voltage drop across the devices and hence a lower dissipated power -which means decreasing the power consumption of the circuit.

The AMIS I3T50u process technology makes available a n-channel VD-MOS transistor named VFNDM50, and a HV fully isolated diode, namedFID50U.

In order to dimension SW1 and SW2, a parametric analysis with SPICEhas been performed. As reference device, the standard device with W =160µm (Wch = 40µm in case of 4 channels), at the ambient temperature of25 C, has been taken and the width of the VFNDM50 has been varied incorrespondence of the three operating conditions, Typical, Worst Case Power(WCP), and Worst Case Speed (WCS). All the (Vds, Ids) characteristics of thedevice, obtained by performing the parametric analysis have been realized

131

Table

D.1

:Resu

ltsof

the

parametric

analy

sisin

case

of

Typical

(Typ),

Worst

Case

Speed

(WCS),

Worst

Case

Power(W

CP),

conditionsoperation.

Con

dit

ion

Vd

sR

on

Wid

th

(Vgs

=3.3V

)(V

)(Ω

)(µ

m)

Typ

75

75

160

Typ

37

37

320

Typ

25

25

480

Typ

19

19

640

Typ

15

15

800

Typ

12

12

960

Typ

11

11

1120

Typ

99

1280

Typ

88

1440

Typ

7.5

7.5

1600

Con

dit

ion

Vd

sR

on

Wid

th

(Vgs

=3.3V

)(V

)(Ω

)(µ

m)

WC

S91

75

160

WC

S46

46

320

WC

S31

31

480

WC

S23

23

640

WC

S18

18

800

WC

S15

15

960

WC

S13

13

1120

WC

S11

11

1280

WC

S10

10

1440

WC

S9

91600

Con

dit

ion

Vd

sR

on

Wid

th

(Vgs

=3.3V

)(V

)(Ω

)(µ

m)

WC

P65

65

160

WC

P32

32

320

WC

P22

22

480

WC

P16

16

640

WC

P13

13

800

WC

P11

11

960

WC

P9

91120

WC

P8

81280

WC

P7

71440

WC

P6.5

6.5

1600

132

Table

D.2

:Resu

ltsof

the

parametric

analy

sisin

case

of

Typical

(Typ),

Minim

um

(Min)and

Maxim

um

(Max)conditionsoperationobtained

byvarying

themult

iplierofthediode.

Con

dit

ion

Vd

Rd

Mu

ltip

lier

(V)

(Ω)

Typ

833

833

1

Typ

728

728

10

Typ

700

700

20

Typ

681

681

40

Typ

653

653

80

Typ

636

636

160

Con

dit

ion

Vd

Rd

Mu

ltip

lier

(V)

(Ω)

Min

868

868

1

Min

765

765

10

Min

736

765

20

Min

715

765

40

Min

690

765

80

Min

670

765

160

Con

dit

ion

Vd

Rd

Mu

ltip

lier

(V)

(Ω)

Max

809

809

1

Max

703

703

10

Max

688

688

20

Max

652

652

40

Max

632

632

80

Max

609

609

160

133

keeping the Vgs voltage to the value of 3.3 V, due to the fact that the deviceoperates as switch with a controlling voltage between 0 V and 3.3 V. Incorrespondence of a width of a single channel of 40 µm and for a numberof channels of 4, then, a 160µm as total width of the VNDM50, a 75 Ω ofRon has been found during the simulations, and this value is close to the76 Ωvalue given by the AMIS, for the same width and number of channels.In correspondence of the value of the drain to source current, Ids, equal to 1mA it has been extract the value of the drain to source voltage, Vds. Dividingthe value of the Vds for the value of the Ids of 1 mA it has been computedthe value of the on resistance of the VFNDM50. A device of 750 µm withan on resistance of about 16 Ω has been chosen for the VFNDM50.

In correspondence of the value of the forward diode current equal to 1mA it has been extract the value of the forward voltage diode. Dividing thevalue of the forward voltage for the value of the forward diode current of 1mA it has been computed the value of the on resistance of the diode. FromTable D.2(a) it can be noted that the values of the forward voltage of thediode are in the range of the common value of 0.7 V. A compromise betweenthe occupied area of the transistor and the minimum forward voltage valueand then of the on resistance, in order to have a lower voltage drop whenthe diode is on, take us to choose as diode that one with 653 mV of forwardvoltage and then 653 Ω of on resistance with a multiplier of 80.

134

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