ms thesis_vibration to electric energy conversion using a mechanically varied capacitor

7/31/2019 MS Thesis_vibration to Electric Energy Conversion Using a Mechanically Varied Capacitor

1/134

Vibration-to-Electric Energy Conversion Using aMechanically-Varied Capacitor

byBernard Chih-Hsun Yen

Bachelor of Science in Electrical Engineering and Computer ScienceUniversity of California at Berkeley, 2003Submitted to the Department of Electrical Engineering and Computer Sciencein partial fulfillment of the requirements for the degree of

Master of Scienceat the

MASSACHUSETTS NSTITUTE OF TECHNOLOGYFebruary 2005

Bernard Chih-Hsun Yen, 2005. All rights reserved.The author hereby grants to MIT permission to reproduce and distribute publiclypaper and electronic copies of this thesis document in whole or in part.

A thor............. . ................... ' .. ....... .............................Department of Electrical Engineering and Computer ScienceJanuary 14, 2005

Certifiedy ... .......... .......// ) Jeffrey H. LangAssociate Director, Laboratory for Electronic and Electromagnetic SystemsThesis Supervisor

Acceptedy ............. .............Arthur C. SmithChairman, Departmental Committee on Graduate Students

LIBRARIESARCHVES

MASSACHUE WNsrTitEOF TECHNOLOGY

MAR 14 205


2/134


3/134

Vibration-to-Electric Energy Conversion Using aMechanically-Varied CapacitorbyBernard Chih-IIsun Yen

Submitted to the Department of Electrical Engineeringand Computer Scienceon January 14, 2005, in partial fulfillment of therequirements for the degree ofMaster of Science

AbstractPast research in vibration energy harvesting has focused on the use of variable capac-itors, magnets, or piezoelectric materials as the basis of energy transduction. How-ever, few of these studies have explored the detailed circuits required to make theenergy harvesting work. In contrast, this thesis develops and demonstrates a cir-cuit to support variable-capacitor-based energy harvesting. The circuit combines adiode-based charge pump with an asynchronous inductive flyback mechanism to re-turn the pumped energy to a central reservoir. A cantilever beam variable capacitorwith 650 pF DC capacitance and 347.77 pF zero-to-peak AC capacitance, formed bya 43.56 cm2 spring steel top plate attached to an aluminum base, drives the experi-mental charge pump near 1.56 kHz.

HSPICE simulation confirms that given a maximum to minimum capacitance ratiolarger than 1.65 and realistic models for the transistor and diodes, the circuit canharvest approximately 1 lW of power. This power level is achieved after optimizingthe flyback path to run at approximately 1/4 of the mechanicalvibration frequencywith a duty ratio of 0.0019. Simulation also shows that unless a source-referencedclock drives the MOSFET, spurious energy injection can occur, which would inflatethe circuit's conversion efficiency if the harvester is driven by an external clock.

A working vibration energy harvester comprising a time varying capacitor with acapacitance ratio of 3.27 converted sufficient energy to sustain 6 V across a 20 MQload. This translates to an average power of 1.8 pW. Based on a theoretical harvestinglimit of 40.67 luW, the prototype achieved a conversion efficiency of 4.43 %. Additionalexperiments confirm that the harvester was not sustained by clock energy injection.Finally, the harvester could start up from a reservoir voltage of 89 mV, suggestingthat the circuit can be initiated by an attached piezoelectric film.

Thesis Supervisor: Jeffrey H. LangTitle: Associate Director, Laboratory for Electronic and Electromagnetic Systems3


4/134

-


5/134

AcknowledgmentsI owe a huge intellectual debt to numerous individuals working at the Laboratoryfor Electronic and Electromagnetic Systems for their help during the developmentof this thesis. Professor Dave Perreault provided excellent suggestions on the diodeselection as well as alternative energy flyback techniques. The vacuum chamber forthe variable capacitor and the surface mount PCB used in the final stage of testingwere produced at lightning speed by Wayne Ryan, whose knowledge on prototyping istruly amazing. Jose Oscar Mur-Miranda, Joshua Phinney, Lodewyk Steyn, MatthewMishrikey, and Yihui Qiu helped me ease the transition into LEES early on andprovided unwavering support whenever I ran into difficulties. Professor Thomas Keimsecured my internship at Engineering Matters, Inc., which allowed me to continueresearching during the summer.

The redesign of the variable capacitor occurred with plenty of guidance fromboth Professor Alex Slocum, Alexis Weber, and Gerry Wentworth. Alexis stayedovertime on numerous occasions to help me run the Pro/Engineer Wildfire finiteelement analysis in order to optimize and correct the out-of-plane resonant frequency.Gerry provided much help during the final prototyping on the waterjet and made theprocess as painless as it could be.

Schmidt Group Laboratory provided the necessary equipment to excite the pro-totype variable capacitor, which was crucial to the collection of experimental data.In particular, I want to thank Professor Martin Schmidt and Antimony Gerhardt forcoordinating the effort that allowed the shaker table and amplifier to remain checkedout for extended amounts of time. Your generosity will not be forgotten.

I also want to extend a warm thank you to Professor Charles Sodini for spendingtime to work out the clock power injection issue in the energy harvesting circuit.

5


6/134

Without the insight of using a source-referenced gate drive, the research would nothave been able to move past the simulation stage. Someday, when I find a coin worthyof this knowledge, it will be promptly deposited into your money jar.

My parents, Gili and Eva Yen, provided much guidance and moral support duringmy educational career and allowed me to reach where I am today. Their care andunderstanding go way beyond the norm, and I am forever grateful. This thesis belongsto them as much as it does to me.

Professor Jeffrey Lang deserves my deepest gratitude, not only as my thesis ad-viser but as someone who truly cares about me in every possible way. He offeredme a research position at a time when I felt extremely stressed because no otheropportunities existed. Throughout this research, he provided countless suggestionsfor overcoming difficult theoretical and experimental barriers. Without these criticalinsights, this thesis would not exist. I will never forget all the time he spent withme both during and after research meetings, even when he already had many otherbusinesses to attend to. Furthermore, he never hesitated to remind me to rest whenI had exams in the courses I was taking, or when my teaching assistant load grew toohigh. Thank you! I cannot possibly repay all this kindness and care.

6


7/134

Contents1 Introduction

1.1 Concept of Energy Harvesting .......1.2 Reasons to Research ............1.3 Previous Works.1.4 Chapter Summary.

1415171821

2 Foundations of Energy Harvesting 232.1 The Q-V plane ................ ......... .... 242.2 A Synchronous Charge-Constrained Circuit ............... 262.3 The Asynchronous Topology: An Overview ............... 282.4 Limitations Without Flyback ...................... 292.5 Energy Flyback Technique ........................ 362.6 Bucket Brigade Capacitive Flyback ................... 392.7 Relevant Measuring Techniques ................... .. 442.8 Chapter Summary ............................ 46

3 Circuit Simulation and Design3.1 Creating the Variable Capacitor .....................3.2 Inductor Modeling ............................3.3 Power Devices.

48485051

7


8/134

3.4 Oscilloscope Probes ..........3.5 Gate Drive Modeling .........3.6 Simulating the Two Diode Circuit . .3.7 Two Diode Circuit with Energy Flyba,3.8 Gate Drive, A First Attempt .....3.9 Corrected Gate Drive .........3.10 Parameter Optimization .......

3.10.1 Effect of Inductor Parasitics3.10.2 Effect of Clock's Duty Ratio3.10.3 Effect of Capacitance Variation3.10.4 Effect of Capacitor Values . .3.10.5 Effect of Initial Voltage Level3.10.6 Effect of Diode Leakage . . .3.10.7 Effect of Rise and Fall Time .

3.11 Chapter Summary.

. . . . . . . ... .. ... .. . .. 52...... ........... . ..53

. . . . . . . . . . . . . . . . . . 53ck ................ 57. . . . . . . . . . . . . . . . . . 61................. . ..66................. . ..68.. .............. . ..69................. . ..70................... . 71. . . . . . . . . . . . . . . . . . 72. . . . . . . . . . . . . . . . . . 73................. . ..74. . . . . . ... . .. .. ... . 75.. .............. . .75

4 Experimental Results4.1 Aluminum Block Capacitor Characterization .....4.2 Energy Harvesting with Aluminum Capacitor ....4.3 Design of a Cantilever Beam Capacitor ........

4.3.1 Qualitative Description .............4.3.2 Setting the EffectiveSpring Constant .....4.3.3 Dimensioning the Cantilever Beams ......4.3.4 Gap Engineering ..............4.3.5 Calculating the Capacitance Variation ....4.3.6 Second-Order Spring Constant Consideration

8

77..... . .78. . . ..... 82. . . ... . 85...... .. 86...... . 87. . . ... . 88. . . ... . 89. . . ... . 89. . . ..... 92


9/134

4.3.7 Design Verification Using FEM ................. 954.3.8 Additional Design Considerations ................ 97

4.4 Characterizing the Cantilever Beam Capacitor . ............ 984.5 Energy Harvesting with Steel Capacitor . . . . . . . . . . . . ..... 1004.6 Starting Up the System ......................... 1044.7 Sensitivity to Frequency Variation . ................... 1054.8 Simulation Revisited ........................... 1064.9 Energy Conversion Verification .......... ......... .. 1104.10 Energy Conversion Efficiency . . . . . . . . . . . . . . . . . . .. 1154.11 Chapter Summary . . . . . . . . . . . . . . . . . ......... 119

5 Summary, Conclusions, and Possible Future Work 1205.1 Chapter Summaries ............................ 1205.2 Important Conclusions .......................... 1235.3 Future Improvements . . . . . . . . . . . . . . . . . ........ 1245.4 Interfacing with the Load . . . . . . . . . . . . . . . . . ..... 1265.5 Final Words . . . . . . . . . . . . . . . . . . . . . . . . ...... 127

A HSPICE Simulation Code 128A.1 Complete Simulation Deck . . . . . . . . . . . . . . . . . ..... 128A.2 Device Models ............................... 130

9


10/134

List of FiguresTwo typical electric energy conversion cycles.. .............Charge-constrained energy harvesting circuit using two MOSFETs.Block diagram of capacitive energy harvester .............Charge-pump portion of energy harvesting circuit. ...........Equivalent circuit diagram of one idealized energy harvesting cycle.Charge-constraining portion of non-ideal energy harvesting circuit..Equivalent circuit diagram of one non-ideal energy harvesting cycle.Idealized inductive energy flyback circuit diagram. ...........Idealized capacitive energy flyback circuit diagram..........A possible bucket brigade energy flyback circuit. ............Flyback efficiencyversus number of bucket brigade capacitors ....Op-amp based network to extract capacitance variation magnitudes..Circuit to accurately determine the DC value of a capacitor .....Subcircuit for simulating a variable capacitor. ...Two-port input current of variable capacitor.....Inductor modeled with core loss and winding loss..Charge pump portion of the energy harvester. ...Voltage waveforms for energy harvesting circuit. . .Current waveforms for charge pump circuit . ...

10

2-12-22-32-42-52-62-72-82-92-102-112-122-13

3-13-23-33-43-53-6

25262829303334373840434445......... . .49......... . .50

.......... ....51

......... . .54......... ..54......... ..56


11/134

3-7 The complete energy harvesting circuit without gate drive ....... 583-8 VRES as a function of time for an ideally driven circuit . ...... 593-9 WVAR and vs as a function of time for an ideally driven circuit ..... 603-10 iD1 and iD2 as a function of time for an ideally driven circuit ...... 613-11 vRESas a function of time for a ground-referenced CLK drive. .... 633-12 Cycle of circuit operation that results in energy injection from CLK.. 653-13 Energy harvesting circuit with source-referenced flyback clocking. . . 663-14 vs as a function of time for slow energy flyback clocking. ...... 683-15 vs as a function of time for Cs = 10 nF. ................ 734-1 Energy harvesting PCB attached to an auxiliary breadboard ...... 784-2 Side-view of the aluminum block capacitor (not to scale) ........ 794-3 Ling Dynamic System V456 shaker table ................. 804-4 VOUTs a function of shaking strengths. ................ 824-5 CACas a function of shaking strength. ................. 834-6 Frequency sweep used to determine variation in quality factor .... 844-7 Waveform of vs for aluminum capacitor with VAMp,p-p 100 mV. . 854-8 HSPICE waveform of vs for CDC= 752.4 pF and CAC = 10.33 pF... 864-9 Waveform of vREsfor aluminum capacitor with different shaking . 874-10 Equivalent mechanical model of the top capacitor plate ......... 904-11 Cantilever beam when the proof mass is at maximum vertical travel.. 934-12 Pro/Engineer Wildfire finite element analysis results. ......... 954-13 Final design for the new variable capacitor, completely assembled. .. 974-14 Frequency sweep for the spring steel variable capacitor . ........ 994-15 CAC as a function of shaking strength. ................. 1004-16 Amplifier VOUTas a function of shaking strengths . ........... 101

11


12/134

4-17 Baseline experiment to gauge first order decay at VRES ........ 1024-18 First order decay at VRES for increasingly heavy shaking. ....... 1034-19 Plot of VRES as VAMP,p-p changes from 250 mV to 380 mV. ...... 1044-20 Rising curves at VRES for increasingly heavy shaking. ......... 1054-21 Plot of VRES as circuit starts up from VINIT = 200 mV. ......... 1064-22 Plot of VRES as a function of frequency with VAMp,p-p= 320 mV. ... 1074-23 LC network used to characterize the nonlinear inductor core loss. . 1084-24 Plot of Dc and Xc as a function of VDR,p-p at f = 865 Hz.. 1084-25 LC network used to model the nonlinear core loss in HSPICE. .... 1094-26 Comparison of the piecewise linear functions modeling Rc . ..... 1104-27 VRES as a function of time with nonlinear core loss. . ....... 1114-28 VRES as a function of time with nonlinear core loss. . ....... 1124-29 VRES as a function of reservoir loading with VAMP,p-p = 0 mV . . 1134-30 VRES as a function of reservoir loading with VAMp-,,,p 100 mV ... 1144-31 VOUT for both top and bottom plate grounding strategy ......... 1154-32 VRES as a function of clocking voltage . .................. 1164-33 Q-V plane trace representing theoretical harvesting maximum ..... 117

12


13/134

List of Tables3.1 Ideal converted power as a function of fCLK ............. . 623.2 Converted power as a function of VG ................... 643.3 Converted power as a function of fCLK................. 643.4 Converted power as a function of VGS ................... 673.5 Converted power as a function of fCLK................ . 673.6 Converted power as a function of RC and Rw .............. 693.7 Converted power as a function of D. ................... 703.8 Converted power as a function of CAC ................. . . . . . . . . 713.9 Converted power as a function of CRESand Cs. ............ 723.10 Converted power as a function of VINIT .................. 743.11 Converted power as a function of Is. .................. 743.12 Converted power as a function of tRISE and tFALL .......... . 754.1 CAC of aluminum block capacitor as a function of shaking strength. . 81

13


14/134

Chapter 1

IntroductionMore than two thousand years ago, Greeks and Romans used waterwheels, placedstrategically along streams, to mechanically rotate gears that helped grind corn. Thissimple idea spread around the world, and over the centuries, people built upon theoriginal design in hopes of improving the conversion efficiencybetween flowing waterand useful energy. In 1862, turbines situated in Wisconsin managed to produce12.5 kW of power based solely on water gushing through the equipment when thedam doors opened. The above development serves to illustrate that the concept ofenergy harvesting is nothing new. Rather, the methodology and principles of creatingan efficient system evolves.

Scavenging the energy of ambient vibrations constitutes one such methodology,and this will be the focus of the present thesis. Broadly speaking, vibration energyharvesting involves the creation of some physical structure that can couple in kineticenergy from small vibrations and convert it into storable electric energy. Due tothe growing demand of autonomous sensors that must function without the need forhuman intervention, interest in this topic has burgeoned in recent years. Althoughother methods of energy scavenging, such as those involving thermal and chemicalgradients, tidal waves, and photons, are also being actively researched, the wideavailability of vibration energy makes it a very good candidate, and this thesis will

14


15/134

show that the parts necessary to carry out such energy harvesting are relatively simple.This chapter presents a broad overview of the current affairs in vibration energy

harvesting, including the different methods presently employed as well as the reasonsbehind the continual interest in this topic. Furthermore, important achievementsdocumented in the literature will be summarized and categorized.

1.1 Concept of Energy HarvestingFundamentally, energy harvesting involves the conversion of ambient energy such aslight, heat, or mechanical motion into electrical energy that can directly power anexternal system or be stored in battery cells for future use. If the energy sourceis further limited to mechanical kinetic energy, or vibrations, three main strategiesof conversion dominate: piezoelectric, magnetic, and electric. Magnetic conversioncan be further subcategorized into systems with varying inductance and systemsthat employ moving permanent magnets. Likewise, electric conversion uses either atime varying capacitor or a permanent electret, where a fixed charge distribution isintroduced in the dielectric layer between the capacitor plates. Although the scope ofthis thesis covers variable capacitor electric energy harvesting only, all three strategieshave their own merits.

Piezoelectric materials, such as quartz and barium titanate, contain permanently-polarized structures that produce an electric field when the materials deform as aresult of an imposed mechanical force [1]. Such a mechanically excited element canbe modeled as a sinusoidal current source with a capacitive source impedance [2] wherethe amplitude of the current depends on the amount of force applied. Therefore, ifthis structure is placed near a constantly vibrating source, such as office walls near aconstruction site, it can harvest the vibration energy and generate electric power.

Magnetic energy harvesting, on the other hand, seeks to convert vibrational kineticenergy into an induced voltage across coils of wire, which then can deliver power to an

15


16/134

appropriate load. This is typically done by attaching either a permanent magnet, suchas that made from Neodymium Iron Boron, or a coil of wire onto a cantilever beamthat is vibrationally actuated [3]; the other one remains fixed. In either scenario,the coil will cut through magnetic flux as the cantilever beam vibrates, creating aninduced voltage in accordance to Faraday's law. Vibration energy can also be coupledinto the system through the use of a variable inductor, although no studies have beendone on this to date due to inherent advantages of using permanent magnets. Whilethis method of energy harvesting possess very high conversion efficiency, magnets,bulky in nature, make these type of systems difficult to integrate with the load it isdriving.

Finally, electric energy harvesting couples vibration energy into the system byhaving it perform work on charges via the electric field between parallel plate capac-itors. In a typical scenario, charges are injected onto capacitor plates when they areclosest together, meaning that the capacitance is at its maximum. Because chargesof opposite polarity reside on the separate plates, the plates tend to collapse when noexternal force is applied. Therefore, as vibration energy separates the two plates, itperforms positive work on the charges, which are then drained from the plates whenthe capacitor voltage is highest and harvested using power electronics. Besides thevariable capacitor, one can also employ a layer of embedded charge, or electret, in thedielectric to carry out electric energy harvesting [4]. Such a distribution of permanentcharges induces a voltage on the capacitor plates, polarizing them. As external vi-bration moves the capacitor plates and alters the capacitance, charge transport alongthe plates delivers power to the load. Most state of the art electret systems currentlyhave power densities inferior to those found in variable capacitor systems, so the vari-able capacitor is preferred until further advances are made in the use of embeddedcharges.

16


17/134

1.2 Reasons to ResearchAlthough the method of harvesting energy varies vastly, the ultimate goal of all vi-bration energy harvesters is to deliver the converted electrical energy to an attachedload that requires power. One might question the necessity of expunging proventechniques of expending electrochemical energy stored on batteries in favor of energyharvesting circuits, some of which cannot perform nearly as efficiently compared tobatteries. In reality, while batteries can painlessly power common household itemsincluding alarm clocks, radios, and wireless keyboards, many scenarios require ex-tended lifetime a typical battery cannot provide. Batteries are also limited to certaintemperature ranges; beyond those ranges, they begin to malfunction.

Consider the difficulty of powering an RF sensor network that must operate inharsh environments for prolonged periods of time, perhaps a couple years. In militaryapplications, motion sensors used for tracking enemy movement might be droppedinto enemy territories from low-flying planes. Or, seismological sensors could bedeployed in uninhabited areas accessible only by helicopters. As a final example,wildlife researchers tracking the behavior of rare bird species might need RFID chipsplaced on birds; trying to replace the batteries on these radio frequency tags afterreleasing the birds back into nature is difficult and time consuming. Even when theresearch can be completed within the battery lifetime, poisonous mercury pollutionfrom battery corrosion can occur if they are not ultimately recovered.

In all these cases, the sensors must be autonomous as far as energy supply goes,since physical access to the units is costly, if not impossible. Even if battery replace-ment were possible, trying to switch out batteries from thousands of sensor unitssimultaneously require a tremendous amount of manpower, which can be just as, ifnot more, infeasible. With an energy harvesting circuit powering these sensor units,the above problems can be solved.

Applications of energy harvesting are not limited to sensor networks. In the

17


18/134

army, for example, standard issue equipment such as night vision goggles and radiotransmitters require power supplies. However, carrying excess batteries increases theload on the soldiers, so it is preferable that the electronics be powered off availableambient energy sources. This might include recoil energy from a rifle or parasiticcompression energy from the sole of a soldier's boot striking the ground [5].

Of course, in order to successfully maintain power delivery to its load, an energyharvesting circuit needs to fulfill two requirements: efficiency and the ability to storeconverted energy. Vibrations in nature, although common, usually do not occur atvery high frequencies. Typical frequencies might range from a few hertz to a couplekilohertz. High conversion efficiency insures that as much energy as possible canbe extracted from these slow vibrations. Furthermore, because there are often deadtimes between the occurrence of vibrations, the system must be capable of storingunused energy efficiently in anticipation of later times when power demand exceedsthe amount harvested.

These two requirements are difficult to meet using traditional energy harvestingtechniques. As a baseline of comparison, solar panels are often only 10-20 % efficient,whereas the goal of energy harvesting circuits lie around 70-80 % efficiency. Sendingthe harvested energy into a capacitive or electrochemical source usually requires theuse of DC/DC converters, a circuit topology falling in the regime of power electronis.Being able to maintain high efficiency in this energy flyback portion of the system asthe amplitude and frequency of harvested energy change requires careful design.

1.3 Previous WorksA careful literature survey of recent developments in the field of energy harvesting isappropriate for placing the current thesis in context. However, due to the wide rangeof techniques used for energy harvesting, some as unusual as exploiting chemicaland thermal gradients, this thesis will limit the survey to vibrational kinetic energy

18


19/134

harvesting only.Numerous research groups have focused on piezoelectric energy harvesting due to

its potential of achieving the highest converted power per unit volume [6]. Kymissiset al employed unimorph strip made from piezoceramic composite material and astave made from a multilayer laminate of PVDF foil inside sport sneakers to harvestthe parasitic kinetic energy generated during walking [5]. An input signal of 1 Hz,similar in frequency to a person walking briskly, produced 20 mW peak power for thePVDF and 80 mW for the unimorph; this translates to roughly 1-2 mJ per step.

In order to maximize the amount of energy harvested from piezoelectric materials,Ottman et al developed a DSP-controlled, adaptive DC-DC converter that accuratelydetermined the duty ratio of the active devices as a function the instantaneous me-chanical excitation amplitude [7]. They showed that as the mechanical excitationincreasespast a certain point, the optimal duty ratio becomesessentiallya constant.A prototype circuit demonstrates a 325 % increase in harvested power using thistechnique.

As part of Berkeley Wireless Research Center's (BWRC) goal of making an au-tonomous 1.9 GHz chip-on-board RF transmit beacon, Roundy et al explored theuse of a two layer piezoelectric bender mounted as a cantilever beam that harvestedvibration energy [8]. They showed that with a driving vibration of 2.25 m/s2 at60 Hz, a maximum of 375pW can be transferred into a purely resistive load. On theother hand, if a capacitive load is attached to store the harvested energy for lateruse, the maximum delivered power drops to 180/uW. In this paper, the authors alsoimplement a shutdown control as part of the power circuitry that prevents the loadfrom consuming energy stored on the capacitor when the capacitor voltage falls belowa certain threshold.

In the area of magnetic energy harvesting, Williams and Yates derived an equa-tion relating the amount of generated power as a function of the damping factorfor a generator that consists of a permanent magnet attached to a micromachined

19


20/134

spring-mass system [9]. Barring physical limitations of the system, the magnet trav-els a longer distance near resonance due to peaking in the system's transfer function;this directly translates to increased harvested energy. They note, however, that lowdamping factor made the system more frequency selective, so if the ambient vibrationcovers a larger frequency spectrum, the resistive load attached to the inductor coilcan be changed to make the harvesting broadband.

Glynne-Jones et al made two actual prototypes of electromagnetic generators usedfor powering intelligent sensor systems [3]. In these prototypes, coils were hand woundonto a cantilever beam attached to a shaker table and immersed in magnetic fieldsgenerated from permanent magnets. When mounted on the engine block of a car, thesecond prototype device produced an average power of 157 IuW and a peak power of3.9 mW.

Research in capacitive electric energy harvesting focuses on two general areas:the variable capacitor itself and the power electronic circuitry that processes theconverted energy. Miao et al fabricated and conducted tests on a micro electro-mechanical system (MEMS) capacitor that can vary its capacitance from 1 pF to100 pF [10]. In a single charge-constrained cycle (refer to Chapter 2), this variablecapacitor is capable of producing 24 JuWof power using a 10 Hz vibration. However,they do not show results from actual supporting power electronics circuitry, so theoverall energy harvesting ability of the system is unknown.

Mur-Miranda conducted extensive research, using both a variable capacitor macromodel machined from blocks of aluminum and a MEMS capacitive comb drive trans-ducer, on an electric energy harvesting circuit topology that exploited the charge-constrained cycle [11]. Using a bread-board prototype that implemented both thepower electronics and the gate driver control circuitry for the active devices, hedemonstrated energy conversion from the vibrational source and showed that outputwaveforms matched theoretical calculations. Due to the inefficiencies of the powerelectronics circuit used, however, the converted energy could not be translated back

20


21/134

as a gain in voltage at a storage capacitor.Recetntly, Miyazaki et al reported a prototype vibration-to-electric variable capac-

itor energy converter that exhibited a measured power generation of 120 nW [12]. Thepower electronics used in this experiment resembled that used by Mur-Miranda; twocomplementary MOSFET switches regulate the flow of current through an inductorto charge and discharge the variable capacitor during specific portions of a mechanicalcycle. The measured conversion efficiency of this prototype comes out to 21 %. AsSection 3.8 will show, however, the clock signal driving the MOSFET switches caninadvertently inject energy into the system, and because measurements relating tosuch injection are not available within this paper, it is unknown what fraction of the"harvested" energy actually came from the vibration source.

From the above literature search, one sees that most fully functional state ofthe art energy harvesting systems fall into the piezoelectric and magnetic regimes.The only working prototype for a capacitive electric energy scavenging system comesfrom Miyazaki et al as described in the preceding paragraph, but because possibleclock injection issues did not receive attention there, a more thorough investigationis warranted. This reason, added to the fact that piezoelectric film can harm theenvironment and magnetic systems are relatively bulky, paves way for further researchinto the capacitive electric energy harvesting scheme.

1.4 Chapter SummaryThis chapter served both as an introduction to the world of energy harvesting as wellas motivation for the rest of this thesis. As noted, numerous techniques exist for har-vesting energy from the environment that otherwise would have been lost. Potentialenergy sources include solar power, thermal and chemical gradients, acoustic noise,and vibration. Vibrational energy harvesting can be furthered divided into piezoelec-tric, magnetic, and electric, depending on how vibration energy is coupled into the

21


22/134

system. All are active areas of research, but this thesis will focus on the variablecapacitor electric conversion process. Emphasis will be placed on the electronics andcircuit topologies as opposed to the implementation of the variable capacitor usingMEMS.

Chapter 2 provides the reader with a review of capacitive electric energy harvest-ing, sufficient to understand the theoretical, simulation, and experimental results thatfollow. Related laboratory measurement techniques will also be discussed. Chapter 3outlines critical HSPICE simulation results that lead directly to a final design ofthe energy harvesting circuit topology, one of the main goals of this thesis. Then,in Chapter 4, experimental data based on a fabricated circuit board is presentedand compared with computer simulations. Chapter 5 summarizes the thesis and itsconclusions, and presents possible directions for future work in this area of research.

If the reader has access to HSPICE and wishes to modify certain design parametersand observe the effect they have on conversion efficiency, refer to Appendix (A) forthe complete set of HSPICE decks. The model files of all the active components,which were downloaded off the Internet, are also included.

22


23/134

Chapter 2Foundations of Energy HarvestingAs explained in Chapter 1, there exists a broad array of techniques for energy harvest-ing, of which piezoelectric, electric, and magnetic are perhaps the most prominent.Based on the specific harvesting strategy used, electric and magnetic energy scaveng-ing can be further divided into two subcategories each. Capacitive electric energyharvesting, the main focus of this thesis, usually relies on either charge-constrainedor voltage-constrained cycles, both of which will be fully explained below. Althoughmethodologies that fall between these two are also theoretically possible, power elec-tronics, switch-like in nature, rarely permit them.

In this chapter, the fundamentals behind electric energy harvesting will be ex-plored. Mathematics relating contours in the Q-V plane to the amount of harvestedenergy per cycle are covered first, followed by a direct application of the formulatedconcepts to a charge-constrained circuit topology presented in [11]. An alternativetopology based on self-synchronous diodes, which forms the centerpiece of this the-sis, is shown next, along with detailed equations that model the charge flow on thevariable capacitor and explain the impact of parasitic diode capacitances. Once thecharge pump portion of the capacitive energy harvester has been developed, an en-ergy flyback mechanism will be added and analyzed, and the pros and cons for variousflyback techniques will be discussed. The chapter concludes with important labora-

23


24/134

tory concepts relevant to the characterization of energy harvesting circuits, includingmethods of measuring the AC capacitance of a variable capacitor.

By the end of the chapter, an idealized capacitive energy harvesting circuit withinductive flyback will have been developed, although decisions on the specific com-ponent values will be left for Chapter 3. The chosen topology forms the basis uponwhich the simulations carried out in the next chapter will be based; further improve-ments to the circuit will curb the problem of clock energy injection, but the maintopology will not change.

2.1 The Q-V planeConsider a single capacitor with capacitance C and voltage vc. At any given time,the energy stored on the capacitor can be expressed as

I 21Wc = Cvc = Qvc, (2.1)where Q = Cvc from fundamental physics. In a physical system, Q, vc, and C canvary as a function of time. For argument purpose, assume that the distance betweenthe capacitor plates is variable, implying that C can change. If we plot Q and vcvalues parametrically over time in a Q-V plane as C goes from a maximum value toa minimum value and back up, a graph similar to Fig. 2-1 will result. Note that thetwo contours shown in this figure represent typical cases; numerous circuit topologiesproduce contours dissimilar to both.

Notice that the slope of lines A and C in both diagram represents the capacitancevalue in that duration of the cycle. In drawing these figures, an implicit assumptionis made that the capacitor charging (path A) and discharging (path C) occur muchfaster than the rate at which the capacitance changes. Were this not true, path Aand C would not be straight lines. Finally, note that a "short" path does not imply

24


25/134

CEnclosed rearepresentingetconverted nergy a

V V(a) Charge-constrained (b) Voltage-constrainedFigure 2-1: Two typical electric energy conversion cycles.

that the time duration associated with that path is short; in fact, path B in bothcases takes the longest time to traverse.

The distinction between the two cycle, one charge-constrained and one voltage-constrained, depends on which variable, Q or V, is held fixed during the time when thecapacitance value drops from maximum to minimum. For circuits where the variablecapacitor is disconnected when the circuit traverses path B, Fig. 2-1(a) shows thatthe charge on the capacitor plates remains fixed as the capacitance decreases. On theother hand, for circuits that connect the capacitor to a voltage source during path B,Fig. 2-1(b) illustrates the capacitor voltage remains fixed as the capacitance drops.

Now-,consider the area enclosed by path A-B-C in each case. For the charge-constrained cycle,

WCHARGE 2QoAVC (2.2)2where Qo represents the amount of constrained charge on the capacitor plates whenthe plates move apart. For the voltage constrained cycle,

1WVOLTAGE AQVC,O (2.3)2

25


26/134

CVAR M2L ControlEledronics

CRES- M1

Figure 2-2: Charge-constrained energy harvesting circuit using two MOSFETs.

where vc,o represents the constrained voltage when the plates move apart. ComparingEq. (2.2) and Eq. (2.3) with Eq. (2.1), it is seen that the enclosed area exactlyrepresents the net energy gained by the capacitor in one cycle [13]. Therefore, theprimary goal of a well designed energy harvesting circuit is to increase the amountof area surrounded by path A-B-C while retaining high conversion efficiency and theability to operate asynchronously.

2.2 A Synchronous Charge-Constrained CircuitFig. 2-2 shows an example of a circuit topology that employs the charge-constrainedenergy harvesting technique described earlier [11]. Assume that the current throughthe inductor starts at 0 A and that CVAR, nitially at its maximum value CMAX, suncharged. At the beginning of a cycle, M1 turns on, resulting in iL, the current inthe inductor, ramping up according to VL= L d . When iL reaches a desired value,M1 is turned off by the control circuitry and M2 is simultaneously turned on. Becauseof the continuity of iL, CVAR egins to charge up all the while staying at a capacitancevalue of CMAX;he mechanical cycle is assumed to be much longer than the electricalcharging and discharging.

Once iL reaches 0 A, the control circuitry turns M2 off, resulting in CVAR eingisolated from the rest of the circuit. Therefore, as vibrational force causes CVARo

26


27/134

move apart and reach CVAR CMIN, n energy harvesting cycle is carried out. Theharvested energy can be transferred back to CRES hrough a reverse cycle of inductorcharging and discharging.

There are several disadvantages to this topology, however. Perhaps the most im-portant are the need for accurate transistor turn-on and turn-off, power consumptionin the control electronics, and excessive conduction loss. Preliminary simulations inHSPICE not presented in this work indicate a necessityto hit the turn-on and turn-off points precisely in order to convert energy efficiently. For example, during thecharging phase of CVAR,M2 must turn off as soon as iL reaches 0 A, or else it ispossible for resonance between the capacitors and inductor to ring VAR own again.However, if M2 turns off too early, parts of the charge extracted from CRES o rampup iL will be wasted. There are similar considerations for the second half of the cyclein which the harvested energy is transferred back to CRES. Such precisions in the gatedrive signals are difficult to achieve due to the delay between the detection of zerocrossing points in iL and the toggling of the MOSFET switches, which can result inlimited conversion efficiency.

Power consumed in driving the MOSFET switches of this topology can be quitelarge, due to the complexity of accurately controlling two active devices. In an au-tonomous sensor IC, this power consumption would directly lower the amount ofstored energy available to drive the energy harvester load. A circuit topology thatrequires only one active device is preferred since its gate drive electronics can beimplemented with much less complexity, resulting in decreased power usage.

Finally, there is a severe disadvantage when conduction loss is considered. Inthe two transistor topology, current flows through M1 , M2, M2 , and M1 respectively,amounting to 4 transistor conduction losses every scavenging cycle. Given that suchconduction losses are comparable in magnitude to the amount of energy harvested,this charge-constrained circuit topology is not desirable.

To overcome these flaws, an asynchronous capacitive electric energy harvesting27


28/134

Figure 2-3: Block diagram of capacitive energy harvester.

circuit based on diodes, the topology this thesis examines in-depth, will be presentednext. Using uncontrolled devices such as diodes ameliorate stringent clocking require-ments because they turn on and off synchronously with the movement of the variablecapacitor without the need for current sensors. Therefore, cycle-to-cycle variation will,in a sense, be automatically tracked. Furthermore, the removal of sensing electronicsdecreases the complexity of the overall circuit, resulting in lower power consumptionand hence increased efficiency.

2.3 The Asynchronous Topology: An OverviewFig. 2-3 illustrates the building blocks of an asynchronous energy harvesting cir-cuit. The heart of this circuit lies in the charge pump, formed from two diodes anda variable capacitor, that converts vibration energy into electric energy by movingcharges from reservoir onto the variable capacitor and pushing energized charges intoa temporary energy storage. Both the reservoir and temporary storage consists of asingle capacitor. The flyback mechanism insures that the voltage at the reservoir ismaintained while the load draws power from the reservoir.

First, the charge pump block, connected to the reservoir and temporary storagecapacitors, is examined alone. Consider the circuit shown in Fig. 2-4, which includes3 capacitors and 2 diodes. In Chapter 3, the precise operation of this circuit will beexplored. For now, an intuitive understanding is developed. Assume that the capaci-tor starts at its maximum possible value and that all three capacitors are charged to

28

Load

8:


29/134

CRES VS

Figure 2-4: Charge-pump portion of energy harvesting circuit.

voltage vo. Because all the node voltages are equal, diodes D1 and D2 are both off.Now, through an external means such as vibrational motion, the capacitor plates aremoved apart, causing CVARo drop. Because the charge on the middle capacitor isconstrained by two diodes that are off, a drop in capacitance implies that VVAR ustrise to keep Q = CV satisfied; this corresponds to path B in Fig. 2-1. This rise involtage turns on D2, resulting in CVARpartially discharging. Unlike path C, CVARdoes not completely discharge into Cs but stops when VVAR vS. At this point, D2turns off.

Now, as the capacitor plates move back towards each other, again due to anexternal force, the cycle is also charge-constrained because both D1 and D2 are off. AsCVAR ncreases, VVARrops, forcing D1 to turn on and resulting in a partial chargingof the variable capacitor. This corresponds roughly to path A. The charging of thecapacitor causes VVARo rise, eventually turning off D1 and returning the circuit toits starting point. Thus, this circuit acts as a charge pump from CRES o Cs, addingnet stored energy to the capacitor over time.

2.4 Limitations Without FlybackAs more and more energy conversion cycles are carried out, Cs in Fig. 2-4 begins toaccumulate large amounts of charge. Eventually, vs rises so high that the variationin CVAR s unable to pump more charge to Cs; equivalently, charge can no longerflow from CRES onto CVAR. The maximum vs given a certain variation in CVARwill

29


30/134

D1 D2 D1 D2

VRES CMAX VRES CS VSn-1 VRES CMIN vsn Cs Van

(a) First half of cycle (b) Second half of cycleFigure 2-5: Equivalent circuit diagram of one idealized energy harvesting cycle.

now be explored using a cycle-to-cycle iteration process. For the first pass of thederivation, ideal diodes are used, meaning that the forward voltage drop is VD= 0 V,the parasitic diode capacitance is CD = 0 F, and the reverse bias leakage currentcoefficient is Is = 0 A.

Assume that the variation limits of CVAR re such that CMIN< CVAR< CMAX ndthat VVAR= VRES (i.e. diode D1 has just equalized the voltage between the reservoirand the variable capacitor). Define a complete energy harvesting cycle as the time inwhich CVAR ndergoes one capacitance variation from maximum to minimum back tomaximum; take vs,i, where i is an integer index starting at 0, to represent the voltageon Cs when CVAR= CMAX.Finally, since the variation on CRES s so small, representthe reservoir capacitor as a constant voltage source.

Fig. 2-5(a) shows the equivalent circuit diagram at the start of cycle n - 1. Atthis point, the total capacitor charge on CVAR nd Cs is

Qtotal = CMAXVRES+ CSVS,n-1 (2.4)

Now consider the variable of interest in the next cycle, namely vs,,. It is easy to seethat vs does not change once D2 stops conducting, so analyzing this portion of thecircuit operation when CVAR rops in value and VVARncreases in value is sufficient.The point where CVAR CMIN s shown in Fig. 2-5(b).

Because D1 does not conduct when VvAR> VRES,charge-constrained operation

30


31/134

dictates that QT = QVAR+ Qs is constant, giving

(2.5)s CMAXVS,n= CS Sn- + MAX VRESCNIIN+ CS CMIN+ CSwhen CVAR = CMIN. Furthermore, initial condition gives vs,0 = VRES.

Define a = C+C and = CMAX RES.Eq. (2.5) can then be written asCMVIIN+CS CMIN-CSVS, = CVS,n-+ , (2.6)

which is a recurrence relation in variable vs,i. Such a recurrence relation can be solvedby determining the homogeneous and particular solution for the associated recurrenceequation

rn = rn- 1 + , (2.7)which is obtained by substituting ri = vs, into Eq. (2.6). The homogeneous solutionmust satisfy

rn = arn-l (2.8)and therefore by inspection,

v(h)= KanS,nFrom Eq. (2.7), one particular solution that works is

(p) -S,n 1-- C )

(2.9)

(2.10)

which, when combined when the homogeneous solution and simplified, results in

(h) Cp)= K ( Cs ) nVS,n = VS,n -US,n -

Now, using the initial condition vs,o = VRES,

K = VRES - CMAX)CMIN

31

CMAXCMI VRESMIN (2.11)

(2.12)


32/134

and so the cycle-to-cycle variation of the storage node voltage is

Cs CM(2.13)S,n= VRES(1C- MAX) cMI C (2.CM13)

To check that Eq. (2.13) makes sense, substitute the extreme case of n = 0 toobtain

vs,O = VRES (2.14)as expected from the initial condition. To determine the voltage limit on the storagecapacitor without the flyback block illustrated in Fig. 2-3, plug in n = oo to obtain

CMAXVS, CMI VRES (2.15)CMIN

Eq. (2.15) interestingly indicates that the maximum storage on Cs depends on theratio of CMAXo CMIN.Because the efficiency of the energy harvester will inevitablyhinge upon the maximum temporary energy storage capacity, it is reasonable toexplore Eq. (2.15) in more detail. Writing out the terms, the equation becomes

CDC + CACVS,oo CDC - AvRES (2.16)

where CAC ndicates the positive zero-to-peak magnitude of the capacitance variation.From Eq. (2.16), it is apparent that given a fixed CAC, a smaller CDC will allow vsto reach a higher ultimate value. Hence, minimizing parallel parasitic capacitancesbecomes a design goal for this particular circuit topology.

Having worked out the circuit behavior using ideal diodes, now consider the sit-uation when the diode's junction capacitance Cj is included. The modified circuitdiagram is shown in Fig. 2-6. In order to understand the behavior of this non-idealcircuit, one cycle needs to be divided up into five stages: D2 closed, D1 and D2opened, D1 closed, D1 and D2 opened, and D2 closed again. For the equivalent cir-cuit diagram of each stage, refer to Fig. 2-7. Note that the ordering of the stages is

32


33/134

CJ1

CRES VS

Figure 2-6: Charge-constraining portion of non-ideal energy harvesting circuit.

slightly different compared to the ideal case analysis. Here, the cycle begins with D2on instead of D1 on. In Stage 1, the amount of charge stored on Cs is

Qs,n-1 = CSVS,n-1 (2.17)

Now, as the capacitance begins to increase from CMIN,assume, without loss ofgenerality, that D2 turns off first before D1 turns on; this brings the circuit intoStage 2. From Stage 1 to Stage 2, the amount of charge at node X is conserved.Paying attention to the polarity of charge on CJ2and Cs carefully, one can write that

QS - QJ2 = CSVS,n-1 - (2.18)

As the capacitor plate moves apart and CVAR = CMAX, D1 turns on and the circuitenters Stage 3. At this moment, vVAR VRES, SOby Kirchhoff's Voltage Law,

VS + VJ2QS QJ2Cs CJ2

= VRES- VRES

(2.19)(2.20)

Multiplying Eq. (2.18) through by Cs,

QsCs - QJ2CS= CVS,n-1

33

(2.21)


34/134

CMIN VSn-1

(a) Stage 1CJ2

I I(~~+ V2-1I I + VJ2-

CJ1+ -VJi+ + VJ2-

Cs n VRES CS = =

(b) Stage 2

TSs(c) Stage 3

CJ1-vjl +

V1+VRES

(d) Stage 40VS.n

(e) Stage 5Figure 2-7: Equivalent circuit diagram of one non-ideal energy harvesting cycle.

which, when substituted into Eq. (2.20), gives

QSCJ2 + QSCS - CSVSn-1 = VRSCSCJ2 (2.22)

Hence, Qs, the amount of charge on the storage capacitor during Stage 3, is

Qs = VRESCsCJ+ CsVS,-iCs + CJ (2.23)At the same time, the amount of charge on CVAR s

QVAR = CMAXVRES (2.24)

Now, again without loss of generality, assume that D1 opens before D2 turns on,resulting in charge conservation for both node X and Y in Fig. 2-7(d). This is Stage 4

34

CJ111-----,VRES

CJ2 ()

VS

VRES( CMAX vs

i i ,.

1C


35/134

of the circuit operation. Defining QJ 2 as the amount of charge on CJ2, the total chargeon all capacitors sums to

QTOT = (Qs - Q2) + (QVAR + Q2) = QS + QVAR, (2.25)

where Qs and QVAR re defined in Eq. (2.23) and Eq. (2.24).Finally, D2 turns on as CVAR rops to its minimum value once more. The charge at

node Z is equivalent to the sum of the charges at node X and Y in Stage 4. Therefore,by distributing QTOT across the 3 capacitors and solving for vs,,, one obtains that

VS=~CS!~CJ +CMAXCJCS(CJ2+CS VRES (2.26)(S + CJ2) (CJ1 + CMIN+ CS) CJ1 + CMIN+ CSDefining c2a- CS (2.27)(C + CJ2) (C1 + CMIN+ CS)and

CJ1 + CMAX+ CJ2CSCJ2 +CS VRES ,(2.28)CJ1 + CMIN + CSEq. (2.26) can be rewritten as

vs, = avS,n-l + / , (2.29)which is similar to Eq. (2.6) except for the definition of a and P. The technique forsolving recurrence relation used earlier in the ideal energy harvesting cycle can bedirectly applied here. In the end,

K (CS+CJ2)CJ1 CMIN CS).30)V(P) _ (CS + CJ2) (CJ1 + CMAX QCJ2+CS)Sn (CJ1 + CJ2) Cs + (CJ2 + CS) CMIN+ CJ1CJ2 (2.31)

35


36/134

Using the initial condition and defining(C J 1c+ CMAXCJ2CS

(CJ1 + CJ2) CS + (CJ2 + CS) CMIN+ CJ1CJ2 ' (2.32)the full cycle-to-cycle variation in the storage capacitor voltage is

Vs,n = [(1 - y) an + 7] vREs (2.33)

Again, check the derived equation with an extreme case of n = 0. Here, Vs,OvREs,which is consistent with the initial condition. Since a < 1, substitute n = ooto yield

VS,oo= ?vREs (2.34)Grouping terms on the numerator and denominator of Eq. (2.34) makes it apparentthat the voltage limit on the storage capacitor is significantly smaller compared tothe ideal case. Hence, energy harvesting efficiency goes down with increasing C1 andCJ2, which indicates that diodes with small parasitics are preferred. As CJ1and CJ2approaches 0, vs,,o approaches CX vRES; this makes sense because diodes withoutparasitic junction capacitance are ideal diodes.

2.5 Energy Flyback TechniqueSo far, the charge pump has been analyzed as a standalone block. However, as seenfrom the previous section, the energy harvesting cycle becomes less efficient as chargebuilds up on the storage capacitor Cs. Furthermore, referring back to Fig. 2-3, theload is attached to CRES nstead of Cs. In this thesis, the load comprises of a 10 MQscope probe measuring VRES n series with another 10 MQ resistor. Therefore, flyingthe converted energy back into a reservoir capacitor that satisfies CRES > Cs mustoccur as part of the circuit operation.

36


37/134

LFB

DFB

Figure 2-8: Idealized inductive energy flyback circuit diagram.

Broadly speaking, there are two main methods of energy flyback: inductive and ca-pacitive. Inductive flyback, shown in Fig. 2-8 without parasitic components, operatesby first ramping up the current in LFB using a voltage difference across the inductor.Then, at a later time, the inductive path is disconnected by means of a transistorswitch, forcing current to "freewheel" through DFB in the second half of the flybackcycle. Topologically, the inductive flyback portion of Fig. 2-8 looks remarkably sim-ilar to a DC/DC buck converter. The main difference stems from the fact that ina buck converter, the main objective is to maintain a constant output voltage VOUTwhile the circuit here deliberately tries to pull VRESup as efficiently as possible.

Theoretically, the efficiency of such a flyback system can reach 100 %, but due toparasitic core and wire loss in the inductor as well as conduction and switching loss inthe MOSFET and diodes, part of the energy is lost. For now, ignore the non-idealitiesof the inductor and focus on the conduction loss. Chapter 3 will provide justificationas to why inductor parasitics prove to be non-critical. Assume that the CLK signal ishigh enough to force the MOSFET into the triode region. In this case, the conductionloss is resistive:

(PFET,COND) = (iFETVFET) ZRMSRDS,ON (2.35)where RDS,ONis the equivalent on-resistance of the MOSFET in triode region. Onthe other hand, because a diode exhibits constant forward bias voltage drop across

37


38/134

Figure 2-9: Idealized capacitive energy flyback circuit diagram.

its terminals, the conduction loss can be represented as:

(PD,COND)= (iDVD) (iD) VD (2.36)

In summary, the root-mean-square current is important for a transistor while the av-erage current is important for a diode. The total energy lost per cycle of an inductiveflyback circuit is therefore

WLOSS = RMSRDS,ON- + (iD) VD fF(237)fFB fFBwith fFB representing the frequency at which the flyback portion of the energy har-vesting circuit operates and D representing the duty ratio of the MOSFET.

For a capacitive flyback strategy, such as that shown in Fig. 2-9, the storage andreservoir capacitor are simply shorted together through a transistor at regular timesduring the circuit operation. Energy flyback occurs by way of voltage equalizationbetween Cs and CRES;given that both D1 and D2 are off during the time of flyback,charge conservation along with the fact that vs > VREs esults in vRES ncreasing afterthe equalization. Mathematically, the total charge initially is

QTOT,O = CSVs + CRESVRES (2.38)

38


39/134

and the total initial energy is1 2WTOT,O =- CSV + -CRESVRES (2.39)

When the circuit reaches steady state operation after the MOSFET has been turnedon, the voltage on the capacitors equalizes to a final value VF. However, charge isconserved, leading to

QTOT,F = (Cs + CRES)VF = QTOT,O (2.40)1WTOT,F = (CS + CRES) (2.41)2

with VF determined from Eq. (2.38) and Eq. (2.40) to beCsvs + CRESVRESvF R (2.42)CS + CRES

Therefore, the amount of energy lost per capacitive flyback cycle is

WLoss WTOT,OWTOT,F Cs+ CRES (Vs VRES) , (2.43)which increases in magnitude as the voltage difference between the reservoir andstorage node increases. Note that in contrast with the inductive flyback loss, thecapacitive strategy energy loss is independent of the fFB. Despite this independence,inductive flyback is still superior to capacitive flyback given typical component values.

2.6 Bucket Brigade Capacitive FlybackThe reader might wonder whether using multiple capacitors in the flyback path willincrease the efficiency of energy flyback. An example of such a flyback circuit is shownin Fig. 2-10. In this diagram, WIN, the energy being fed into the system, comes fromthe vibrational source and WOUT, he energy being taken out, goes into the reservoir.

39


40/134

WIN Si.2 S2 .3

Figure 2-10: A possible bucket brigade energy flyback circuit.

Imagine C1 as the storage capacitor Cs and the voltage source VRES as the reservoircapacitor CRES.

In order to calculate the energy flyback efficiency of this setup, the periodic steadystate (PSS) condition must first be determined. PSS denotes the situation in whichall the circuit state variables (i.e. voltages and currents) return to the same valueafter every cycle of circuit operation. In this case, a complete cycle involves thevariable capacitor's capacitance going from maximum to minimum back to maximum,or equivalently, a single WIN njection.

The exact calculations involved in deriving the PSS condition of an n-capacitorbucket brigade is extremely involved and offers no additional insight into the circuitoperation. Therefore, a more intuitive approach is offered. First assume all capacitorsare equivalent, meaning that C1 = C2 = ... = Cn-2 = Cn-l = C. Consider anycapacitor Ci, 1 < i < n- 1, that is sandwiched between two other neighboringcapacitors. When the switch on its left, Si1_,i, closes,vi equalizes with vi-1 and reachessome intermediate voltage between the two original values. Then, when the switchon the right, Si,i+1 closes, vi equalizes with vi+1 and reaches a different intermediatevoltage. But these two operations are exactly equivalent to averaging the centervoltage with its two neighboring voltage, so one would expect that after many cycles,the progression of v1, v2 ,..., vn, 2, vn_1 becomes linear and evenly spaced.

In fact, that is exactly what happens for a bucket brigade of capacitors in PSS.

40

SR.n-1 Sn-.n WOUT


41/134

The PSS voltage on each capacitor can be expressed as

vi = vVl- (i - 1) VRE (2.44)

Having determined the PSS condition, the energy flyback efficiency analysis can pro-ceed. The steps in determining where 7 = W is as follows:

1. Begin with PSS capacitor voltages on the k-th energy flyback cycle of vl(k),V2(k),. . , Vn-2(k), and Vn-l(k).

2. Inject WIN into the system at C1.3. One at a time, turn switches S1,2, S2,3 ,..., Sn-2,n-l, and Sn-l,n on then off.

Denote this as the switch rippling stage.4. Determine Vl(k+l), 2(k+l),. , Vn-2(k+l), and Vnl(k+l) and require that Vi(k+l)

Vi(k) for all i such that 1 < i < n - 1.During Step 1, the amount of energy stored on C1 is

W1,0 2 CV1,o- 2C (2.45)

all the capacitance values are simply C since they are assumed to be equal, as men-tioned earlier. After Step 2, the total energy stored on C1 becomes

W ,o 2C + WIN= (2.46)2C 2Cwhich, when multiplied through with 2C and simplified, gives

Q1,F = V/Q1,o 2CWIN (2.47)Finally, this allows the change in Q1 o be calculated:

AQI = Q1,F - Q1,o Q1, o + 2CWIN - Q,O (2.48)41


42/134

Because all capacitor voltages must return to their original values vi(k)after Step 3and 4, the entire AQ1 must ripple all the way through and exit into the voltage sourceVRES.Therefore, WOUT an be determined as

WOUT AQ1VRES ( ,0 + 2CWIN - Ql,o) VRES (2.49)The only thing necessary before characterizing 7, the efficiency of a bucket brigadeenergy flyback circuit, is the value for Ql,o. This charge can be obtained by examiningthe voltage equalization between C1 and C2 more closely. From Eq. (2.44),

V2,PSS V ,0 VRES (2.50)

where vi,pss means the PSS voltage on Ci. Denote the voltage on C1 before Step 2as v1,O and the voltage after Step 2 as vl,F. This gives

2 12CV,F = 2CV1, 0 + WIN (2.51)2WINV1,F = V1, + C (2.52)

After Step 3 when the switch is closed, the final voltage is the average of V1,Fand v2,Psssince the capacitors are equal in value. But this final voltage will be the ultimatevoltage on C1 during this cycle since the switch opens after equalization occurs. Inorder to satisfy PSS,

1 1'o1 V, - RES) 1,0 (2.53)2 2 v n - 2Substituting Eq. (2.52) into Eq. (2.53) and simplifying,

-2 (n - 1) vREs 4 (n- 1) VEs - 4 (-2 n + 3)54Vl, = (2.54)-4n + 6

where a = (n - 2)2WIN - V2ES. Note that the negative solution for the quadraticequation was selected since vl, > 0. The required expression for QI,o is simply

42


43/134

0.918

0.8

0.6eta(n)

0.4

0.2

0.185 nu 0 20 40 60 80 1004 n 100

Figure 2-11: Flyback efficiency versus number of bucket brigade capacitors.

Q1,o = Cvl,o. Finally, referring back to Eq. (2.49), r isWOUT (Q1,o + 2 CWIN -Q1,o) VRES (2.55)

WIN WIN

Substituting in the expression for Q1,o into Eq. (2.55) and plotting the result inMathCAD, one obtains an efficiency versus n plot, which is shown in Fig. 2-11. Theefficiency decreases as the number of capacitors increases. Note that because thederivation is invalid for n < 3, the section of the curve with r7> 1 can be safelyignored.

From the above derivation, it is apparent that the use of a bucket brigade capaci-tive energy flyback is inferior to the solution of a direct flyback in which Cs is shortedto CRES hrough the MOSFET. Another disadvantage of using such a flyback schemeis the large number of switches involved. Because these switches will be implementedusing discrete transistors, each of them will exhibit conduction loss due to a finiteRONvalue. Therefore, the actual efficiency will be much smaller than that predictedby the previous calculation.

43


44/134

C = 100pF

iVAR

10T

Figure 2-12: Op-amp based network to extract capacitance variation magnitudes.

In summary, the best flyback topology out of the three possible candidates -inductor, direct shorting switch, and capacitive bucket brigade - is the inductor. Notonly does it possess the highest theoretical flyback efficiency relative to the other twomechanisms, the inductive flyback is also very simple to implement. The only majordrawback comes from the inherent bulkiness associated with inductors, but becausethe design goals do not include minimizing the overall system size, the remainder ofthis thesis will use the inductive flyback topology.

2.7 Relevant Measuring TechniquesThe AC variation of CVARconstitutes an important parameter to characterize accu-rately in the energy harvesting circuit. Such a circuit was proposed in [11] and willbe repeated here for convenience. Consider the op-amp network shown in Fig. 2-12.There are two additional power line bypass capacitors not shown in the schematic;one is a 0.22 F film capacitor connected between v+ and ground while the other isa 1 nF capacitor connected between v+ and v_.

If w < = 100 krad/s, the impedance in the flyback path can be approximatedby ZFB R = 100 kQ. Therefore, if the output voltage is approximately sinusoidal,

44

+


45/134

vssin(wt)

Figure 2-13: Circuit to accurately determine the DC value of a capacitor.

which is valid under the assumption that CAC < CDC, t can be expressed as

VOUT= -iVARR (2.56)

Taking (CVAR CDC+ CACsin (wt),

VOUT= (10 V) WRCAC Cos(wt) , (2.57)

which implies thatIvOUTICAC = (10 )R (2.58)

Hence, by measuring the output voltage at specific frequencies, CACcan be determinedas long as w


46/134

of both side,(rVCl VS (2.60)1 + (RCDC) (2.60)

Finally, solving for CDC,one gets

CDC = (2.61)wRAs will be documented in Chapter 4, the circuits shown in Fig. 2-12 and Fig. 2-13give CDC= 650 pF and CAC,MAX 317.36 pF for the variable capacitor used in thisthesis.

2.8 Chapter SummaryThis chapter mapped out the theoretical foundations behind energy harvesting cir-cuits, the most important one being the Q-V plane contours and their relationshipto scavenged energy. Two typical capacitive conversion cycles were given - charge-constrained and voltage-constrained - and the circuit topology explored in [11] wasgiven as an example employing charge-constrained cycles. However, due to the topol-ogy's synchronous nature, excessive power consumption for the gate drive, and highconduction loss, it is undesirable as an energy harvester. An alternative topologybased on an asynchronous diode charge pump connected to an energy flyback mech-anism was proposed instead.

In order to sustain the efficiency of energy harvesting and to power the loadconnected at the reservoir, three possible flyback circuits were analyzed, including theinductor, direct shorting switch, and the capacitive bucket brigade. Although bulky,the inductive flyback allowed for maximum theoretical flyback efficiency, 100 %, andrequired few components to implement. Hence, the topology chosen for this thesisuses inductive flyback.

46


47/134

Comparing Eq. (2.15) and Eq. (2.34), it is apparent that parasitic diode capaci-tances hurt the overall conversion efficiency by decreasing the maximum voltage levelCs can reach. This implies that diodes with low junction capacitance should beused for the charge pump. Furthermore, if the circuit is implemented on an IC, onemust observe careful circuit layout techniques to avoid creating excessive parasiticcapacitances.

The remaining chapters of this thesis builds upon the established foundations andexamine second-order effects that are difficult to characterize analytically. Chapter 3examines in greater details the effect of device parasitics through the use of HSPICE,a specialized circuit simulation program, and addresses energy flyback timing opti-mization. Chapter 4 presents experimental results from a PCB that was designedand optimized based on simulation results; the variable capacitor used will also becharacterized.

47


48/134

Chapter 3Circuit Simulation and DesignAlthough the theoretical foundations of electric energy harvesting laid out in the pre-ceding chapter are important, a computer-based simulation nonetheless is necessaryto pinpoint the most efficient circuit implementation. The discussion in Chapter 2lacked specific component values, maximum tolerable parasitic sizes, and other im-portant details necessary for the development of a successful prototype circuit board(PCB). In this chapter, results from various HSPICE simulations that comprehen-sively survey the effect of different design choices will be first presented; they willthen lead to the formation of the actual circuit schematic upon which the final set ofexperimental data presented in Chapter 4 is based.

3.1 Creating the Variable CapacitorBecause HSPICE inherently does not provide an easy way of simulating mechani-cal variable capacitors with moving plates, the first task involves creating a circuitequivalent that can represent the vibrating plates accurately enough. Based upon thediscussion in [14], a variable capacitor can be represented by a subcircuit consisting ofa fixed value capacitor in series with a dependent source whose voltage depends on the

48


49/134

jiN

CDCZIN

Figure 3-1: Subcircuit for simulating a variable capacitor.

voltage difference across the terminals of the subcircuit. Such a circuit configurationis shown in Fig. 3-1. The two-port impedance of this subcircuit is

VIN 1ZIN . (3.1)Z N SCDC (1 + A)Eq. (3.1) suggests that the subcircuit behaves equivalently to a capacitor that hascapacitance CDC 1 + A), which means that if A =-Aa sin (wt + b), the two-portCDCmodel is precisely a variable capacitor with frequency w, DC value CDC,AC amplitudeCAC,and angle 0. Given the desired value for A, the dependent voltage source AVINmust have the value

CACAVIN VIN- sin(wt+ ) , (3.2)CDCwhich is simply a multiplication of the two-port voltage, a sinusoidal excitation ofamplitude 1, and a constant CAC/CDC.

Such a dependent voltage source can be specified in HSPICE through the use of apolynomial function [15]; refer to Appendix (A) for the actual code implementing thevariable capacitor subcircuit. Verification of the variable capacitor implementationinvolves attaching the subcircuit to a fixed voltage source Vs and gauging the amountof current flowing into the subcircuit. Defining CVAR(t)= CDC + CAC(t), correctoperation requires

d d/IN= (CvAR(t)Vs)= Vs- (CAc(t)) . (3.3)dt ~~~dt49


50/134

/ 71perlods)=5.26e-04I L urrent (A)3.58e-0OI \I II ,

I/ I I/ I I II II II I/ I% // I /tI I

I/r IIr I

500u ImTime (ln) (TIME)

I II II II I

II I

II I.

1.5m 2m

Figure 3-2: Two-port input current of simulated variable capacitor for CDC = 1.22 nF,CAC= 300 pF, and Vs = 1 V. The vertical axis represents the input current plottedin amps and the horizontal axis represents time plotted in seconds.

As an example, if CDC = 1.22 nF, CAC = 300sin (2ir x 1900t) pF, and Vs = 1 V,the input current should be iIN = 3.58 cos (2ir x 1900t) i-A. Computer simulation ofthe two-port input current, shown in Fig. 3-2, confirms that the subcircuit behavescorrectly. Although shown with a sinusoidal variation, the capacitor model, throughadditional parameter fitting, can also accommodate non-linear mechanical effects.

3.2 Inductor ModelingA real wire-wound inductor will inevitably have parasitic losses associated with it.Because the success of electric energy harvesting hinges upon high power conversionefficiency, parasitic resistances associated with wire loss and core loss must be accu-rately modeled. Capacitive effects, significant for radio frequency applications, willnot be considered here since environmental vibration doing work on the electricalcharges occur at much lower frequencies.

50

3.5u3u

2.5u2u

1.5ulu

- 500n

-500n-1u

-1.5u-2u

-2.5u-3u

-3.5uo. . . . . . . . . . .


51/134

Rw L

Figure 3-3: Inductor modeled with core loss and winding loss.

Characterization of the energy flyback inductor has been performed in [11] usinga multimeter and a bridge instrument set at 300 kHz. The final model, with Rcrepresenting the core loss and Rw representing the winding loss, is shown in Fig. 3-3. Extracted parameter values are L = 2.5 mH, chosen to limit the rate of currentramping and prevent inductor saturation, Rc = 360kQ, and Rw = 8 Q for the exper-imental circuit. Note that by modeling the core loss as a linear resistor, one implicitlydisregards nonlinear loss mechanisms found in the inductor. Although not critical inthe simulation phase, these second-order effects turn out to be important when aclose fit between experimental data and simulation is desired. Refer to Chapter 4 formore details.

3.3 Power DevicesBecause the amount of energy harvested from the vibrational source is on the or-der of several pW, power electronic components in the circuit, including diodes andMOSFETs, also require accurate modeling to insure that the associated losses do notexceed the converted energy. To model the components with precision, they must firstbe selected. As with most circuits processing power, diodes exhibiting nearly idealbehaviors are desirable; this translates to a low forward bias voltage drop, small par-asitic resistance and capacitance, as well as low reverse bias leakage. Based on theselimitations, the 1N6263 Schottky barrier diode was selected. As will become evidentlater from simulation results, the best MOSFET for energy harvesting should havelow on-resistance, small parasitic gate capacitance, and a weak body diode. These

51


52/134

requirements lead to the selection of a 2N7002 n-channel MOSFET for use in thiscircuit.

Buermen extracted the appropriate HSPICE parameters for the 1N6263Schottkybarrier diode in [16];Vishay, a company specializing in semiconductor devices, gen-erated the HSPICE model for the 2N7002 n-channel MOSFET. Briefly, the Schottkybarrier diode model contains two diodes, each with its own set of parameters, in par-allel; one of them serves as a parasitic component. The n-channel MOSFET modelaccounts for parasitic p-channel MOSFET, gate capacitance, and the body diode.For the complete model files, refer to Appendix (A).

3.4 Oscilloscope ProbesAs will be shown in simulations later during this chapter, the parasitic resistancepresented to the circuit due to the presence of oscilloscope probes can significantlyaffect the energy conversion efficiency. In an extreme case, a simulation that resultsin positive converted energy can see its reservoir voltage collapse when a 10 MQequivalent probe resistance is included as a load.

The significant problems posed by the scope probes arise because they form un-expected current paths through which charge that had work done on it can leak toground, greatly decreasing conversion efficiency. As an example, if the scope probeis attached to a point in the circuit with DC voltage VNODE 2 V, the parasiticresistance will on average dissipate

V2 22(PDIss)= R= 106 0.4 pW , (3.4)which could realistically exceed the amount of harvested energy.

In order to minimize probe loss, all probe points on the final PCB design require aseries 10 MlQ esistor in front of the scope probe entry point; this halves the consumed

52


53/134

power at the expense of voltage resolution on the oscilloscope. With this in mind,all simulations will have a 20 MQ parasitic resistance attached to probing nodes, themost prominent ones being VRES nd vs, in order to assure that measurements can betaken on the actual board.

3.5 Gate Drive ModelingIn order to feed the converted energy from the temporary storage capacitor Cs backinto the reservoir capacitor CREs, the n-channel MOSFET serving as a pass transistormust be driven on and off in a timely fashion. The actual choice of drive strength andfrequency will be discussed later in the chapter after simulation results are presented,but it is nonetheless important to discuss ways in which the clock signal can bemodeled with sufficient precision in HSPICE.

Based on the selection of an LMC555 CMOS timer configured in astable operationas the gate drive, two important limitations must be modeled: finite rise time andsaturation voltage limits from Vss, the bottom power rail, and VDD, he top powerrail. These nonidealities are important because both contribute to additional powerloss during the conversion - finite rise time incur switching losses while saturationvoltage limits give rise to leakage current at the low end and higher than expectedchannel on-resistance at the high end. From the LMC555 datasheet, the rise and falltime are both 15 ns and the saturation voltage limit is 0.3 V from either supply rail.

3.6 Simulating the Two Diode CircuitTo better understand the energy harvesting process, the first part of the circuit,namely the components of the charge pump, is simulated on its own. As a startingpoint, a reservoir capacitor of value CRES= 1 F and a storage capacitor of valueCs = 3.3 nF are chosen; the value of Cs insures that parasitic capacitance from the

53


54/134

+VsVsRES

Figure 3-4: Charge pump portion of the energy harvester.

9.5 -

9-

8.5 -

87.5-

7-

6.5 76 -

i . .. . i. . . - t .i .. i.. ' - ' I I i0 Im 2m 3m 4m 5m 6m 7m 8mTime (11n) (TIME)Figure 3-5: Voltage waveforms for energy harvesting circuit with CDC = 1.22 nF,CAC = 300 pF, RES = 1 F, Cs = 3.3 nF, and VINIT = 6 V. The vertical axisrepresents voltage plotted in volts and the horizontal axis represents time plotted inseconds.

oscilloscope probe and other sources do not dominate.Fig. 3-4 shows the schematic for this section of the energy harvesting circuit,

repeated from Chapter 2 for convenience. The schematic lacks any source of voltageexcitation; instead, before the simulation in HSPICE begins, all the individual nodevoltages, VRES, WAR, and vs are initialized to 6 V. This allows the system to beginwith some initial energy that is necessary to start the energy conversion process. Ina real circuit, a battery that can be disconnected would serve as this initial energyinjection source.

54


55/134

During each cycle of operation, within which CRESdecreases from its maximumvalue and goes back up, energy flows from both the reservoir capacitor and the vi-brational source into Cs, as shown earlier in Chapter 2. The voltage waveforms forVRES,vvAR,and vs plotted in Fig. 3-5 indicate the effects of these energy transfers. Asexpected, the energy transferred to Cs causes vs to rise in accordance to Ws = 2Csvs.At the same time, VRESdrops as charge is pulled out of CRESand placed onto CVAR orthe vibrational source to do work on. However, because CRES> CVAR,he decreasein VRES s insignificant, allowing VRES o be treated as a constant during this partof the simulation. Furthermore, vAR oscillates up and down as CVAR aries, also inagreement with the predicted behavior.

In each energy conversion cycle,1 1 1 1 1WCONV QOAVAR -Q ( C )(3.5)2 2 MIN MAX

where Qo is the amount of constrained charge and CMIN nd CMAX re the minimumand maximum capacitance value for the vibrating capacitor. As more and moreconversion cycles occur, Qo decreases due to increasing difficulty of placing additionalcharge on CVAR refer to Eq. (2.15)). This results in the decreasing step height forVS.

The theoretical maximum voltage that vs can obtain has been calculated in Chap-ter 2. Using the derived formula,

VS,MAX CMAX VS = 1.65 x 6 V = 9.9 V (3.6)CMINif we take CD = 1.22 nF and CAC = 300 sin (27rx 1900t) pF like in the earlierexample. Looking at Fig. 3-5, it is apparent that vs does not approach 9.9 V butinstead flattens out at around 9.5 V. This discrepancy stems from the fact that thetheoretical calculations presented in Chapter 2 ignored the forward bias voltage dropof the Schottky barrier diodes.

55


56/134

IAliii'Ii

Li

iiI

I1.

li

IIiIII,1ii1IIII

iIiI11Iii1.1I I

I I

i.I..Ii!iiI

.1.1..II1J

ilIi1Iii

Ii

ID1

Iii|'Ii 1

iD2

/

1 IIJ 1: ...., , i i . .. . - . . . . i0 I m 2m 3m 4mTime (ln) (TIME) 5m

.... I"i ikil6m ? m Sm

Figure 3-6: Current waveforms for charge pump circuit with CDC = 1.22 nF, CAC=300 pF, CRES= 1 1 F, Cs = 3.3 nF, and VINIT 6 V. The vertical axis representscurrent plotted in amps and the horizontal axis represents time plotted in seconds.

Fig. 3-6 shows the current passing through the two diodes. The simulated wave-forms shows that the diodes conduct in alternating fashion, in agreement with theory.However, theoretical calculation ignored the effect of leakage current during the timewhen diodes are reverse biased. Simulations later in this chapter confirms that diodeleakage has a detrimental effect on the efficiency of energy harvesting (due to thecareful selection of Schottky diodes with maximum Is = 0.15 MA, the reverse biasleakage current is not readily visible in the simulated waveforms).

Comparing the current and voltage waveforms, one finds that vs ramps up whenD2 is conducting and stays flat when D1 is conducting. This makes sense intuitivelybecause the only time when harvested energy can flow into Cs occurs while D2 con-ducts. Finally, notice the decreasing amplitude of conducted current; this shows thatas vs rises, CVAR ischarges less into Cs per cycle and therefore extracts fewer chargesfrom the reservoir.

For this part of the energy harvesting circuit to be considered successful, positive56

20u18u16u14u -12u -

i! IOu -

Su -6u -

4u

2u0

_________________________________

_ - -_ u ^ - L 11 L ,L-1',- U l!Y Iml I I . . . . . . .

/L

.. .................

LIIiIIa

"` - -AI

I 1-

I !

III

II

Ii iiIi

I I l II ~

I


57/134

net energy should result after a few cycles of vibrational motion. For any capacitor,the change in stored energy given an original voltage vo and a final voltage VF is

AW = C (VF-VO). (3.7)Using the same simulation parameters as above, the reservoir voltage droops fromVRES 6 V to VREs= 5.9923 V after 4 cycles. During the same period of time, thetemporary storage node rises from vs = 6 V to vs = 8.2268 V. Therefore,

CR (2 2+ 2 (3.8)2 (10- 6 F)(0.092 V2) + (33 x 10 - 9 F)(31.680V 2) (3.9)

2. (3.10)6 nJ. (3.10)

The net energy of the system is rising, indicating a success in injecting mechanicalvibration energy into the circuit.

3.7 Two Diode Circuit with Energy FlybackNow that the charge pump portion of the circuit has been shown to convert positiveenergy, the inductive energy flyback consisting of a pass transistor, freewheeling diode,and an inductor will be added. Their addition, along with a parasitic probe resistanceRp mentioned earlier, completes the entire circuit except for the transistor gate drive;the schematic is shown in Fig. 3-7.

As a first pass simulation, the gate of the MOSFET is driven in such a way that itis impossible for energy to be accidentally injected into the system. In HSPICE, thisamounts to modeling the transistor as a variable resistor, with resistance value varyingdiscontinuously from the MOSFET RONvalue to 1010Q as a controlling node voltagesweeps through vT, the threshold voltage of the MOSFET. Other relevant parametersare CRES = 1 F, CS = 3.3 nF, Rp = 20 MQ, LFB = 2.5 mH, RC = 360 kQ,

57


58/134

Rc

Rp

Figure 3-7: The complete energy harvesting circuit without gate drive.

Rw = 8 Q, CDC = 1.22 nF, CAC = 300 pF, and VINIT = 6 V, where VINIT repres

ms thesis_vibration to electric energy conversion using a mechanically varied capacitor

Documents