Low Frequency Low Voltage Vibration Energy...

Johan Henning Pedersen, s052402

Low Frequency Low VoltageVibration Energy HarvestingConverter

Master’s Thesis, November 2011

Low Frequency Low Voltage Vibration Energy Harvesting Converter,

Report written by:Johan Henning Pedersen, s052402

Advisors:Arnold KnottOle Cornelius ThomsenThomas AndersenThomas Sørensen (DELTA)Peter Spies (Fraunhofer IIS)

Project period: April 26th, 2011 - November 1st, 2011

ECTS: 30 points

Education: Master of Science

Field: Electrical Engineering

Class: Public

Remarks: This report is submitted as partial fulfilment of the require-ments for graduation in the above education at the TechnicalUniversity of Denmark.

Copyrights: c©, Johan Pedersen, 2011

Department of Electrical EngineeringElectronics Group (ELE)Technical University of DenmarkØrsteds Plads, Building 349DK-2800 Kgs. LyngbyDenmark

Website: www.elektro.dtu.dkTel: (+45) 45 25 36 03E-mail: [email protected]

and

Energiemanagement undMikroenergietechnikFraunhofer IISNordostpark 9390411 NurnbergGermany

Website: www.iis.fraunhofer.deTel: (+49) 911 58061-6363

In cooperation with

DELTAVenlighedsvej 4DK-2970 HørsholmDenmark

Website: www.delta.dkTel: (+45) 72 19 40 00E-mail: [email protected]

Abstract

This thesis explores the feasibility of a non-linear switching circuit for optimizing lowfrequency low voltage vibrational energy harvesting from a Macro Fiber Composite piezo-electric generator powering a sensor node. This analysis shows that, compared to othercommonly used topologies, the Synchronized Switch Harvesting on Inductor topology issuperior in output power at small vibrations at 2 Hz. The power levels explored in theproject is in the microwatt range, which makes even a small component power loss impor-tant to take into account.

The performance of the topology at a frequency of 2 Hz and output power levels around10 µW was found to rise and fall with the peak detection control circuit performance. Anactive control circuit based on ultra low power ICs was proposed and a prototype of theSynchronized Switch Harvesting on Inductor was implemented and tested. The prototypeshowed to increase the output power by a factor of two, compared to the standard fullbridge rectifier, but when accounting for the control circuit power consumption of 15.4µW the gained output power was lost. The control circuit showed to be more of a limitingfactor than expected and a set of requirements for a new control circuit was made. Athigher energy levels the prototype is expected to increase the output energy by up to 8times and to extend the range of feasible low frequency energy harvesting sources andapplications. This project emphasizes the need for a passive control circuit at power levelsin the microwatt range.

vii

Resume

I dette speciale udforskes anvendeligheden af et ulineært switching kredsløb til at optimereenergihøst af lavfrekvent vibrationsenergi ved lav spænding fra en piezoelektrisk generatoraf makrofiber kompositmateriale, der skal drive en sensornode. I sammenligning med andreudbredte topologier viser SSHI (Synchronized Switch Harvesting on Inductor) topologiensig at have en overlegen udgangseffekt ved sma vibrationer omkring 2 Hz. De undersøgteeffektniveauer er i mikrowatt-omradet, hvilket gør det nødvendigt at tage hensyn selv tilsma effekttab i komponenterne. Ved en frekvens pa 2 Hz og udgangseffekt omkring 10 µWviste topologiens potentiale sig at være stærkt afhængig af kontrolkredsløbets performance.

Derfor blev et aktivt kontrolkredsløb baseret pa ultra low power IC’er foreslaet og en pro-totype af SSHI topologien implementeret og testet. Prototypen viste sig at øge udgangsef-fekten med en faktor to i forhold til en almindelig diodebrokobling, men ved modregn-ing af kontrolkredsløbets strømforbrug pa 15, 4 µW forsvandt den vundne udgangseffekt.Kontrolkredsløbet viste sig at være mere begrænsende end forventet sa et sæt krav tilet nyt kontrolkredsløb blev opstillet. Ved højere energiniveauer forventes prototypen atøge udgangseffekten med op til en faktor 8 og derved at udvide det brugbare omrade aflavfrekvente vibrationskilder til energihøst og dets anvendelser. Dette projekt fremhæverbehovet for et passivt kontrolkredsløb nar der arbejdes med effektniveauer i mikrowatt-omradet.

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Preface

This report is a Master’s Thesis in Electrical Engineering at the Department of ElectricalEngineering at the Technical University of Denmark.

The project has been carried out in cooperation with DELTA in Hørsholm, Denmark andFraunhofer IIS in Nurnberg, Germany.

Many people have supported me during the writing of this thesis and I would herebylike to thank all of you. A special thanks to my supervisors Arnold Knott, Ole Cor-nelius Thomsen, Thomas Andersen, Thomas Sørensen, and Peter Spies for great supportand to Loreto Matheu from Fraunhofer IIS for solid guidance and inspirational discussions.

Additionally, I would like to thank my colleagues from DELTA, Mickael Lallart from INSAin Lyon, France for his helpful correspondence, Rasmus Trock Kinnerup, Stig Hogberg,and Johan Musaeus Bruun, as well as my family for their consistent support.

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Contents

1 Introduction 11.1 Energy Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Standard Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Energy Generating Material . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Energy Harvesting Applications . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 WindSpear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2 Running Tights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.2 Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.3 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Vibrational Energy Harvesting 72.1 Vibrational Energy Harvesters . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 Electrostatic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Electromagnetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.3 Piezoelectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 The Piezoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Equivalent Electrical Circuit of Piezo Generator . . . . . . . . . . . . . . . . 11

2.3.1 Macro Fiber Composite Impedance . . . . . . . . . . . . . . . . . . . 122.4 Spring Mass Damper Mechanical Model . . . . . . . . . . . . . . . . . . . . 12

2.4.1 Force Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.2 Power Delivered to Resistive Load . . . . . . . . . . . . . . . . . . . 15

2.5 Macro Fiber Composite Output Power . . . . . . . . . . . . . . . . . . . . . 162.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Circuit Topologies for Piezo Harvesting 193.1 Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.1 Standard Full Bridge Rectifier . . . . . . . . . . . . . . . . . . . . . 203.2.2 Voltage Doubler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.3 Synchronized Switched Harvesting on Inductor . . . . . . . . . . . . 213.2.4 Synchronous Electric Charge Extraction . . . . . . . . . . . . . . . . 253.2.5 Output Power Comparison . . . . . . . . . . . . . . . . . . . . . . . 26

4 Synchronized Switch Harvesting on Inductor Analysis 314.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

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4.1.1 SSHI waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.2 Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3 MOSFET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.4 Quality Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4.1 Inductor Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.4.2 Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.4.3 MOSFET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.5 Peak Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.5.1 Simple Differentiator . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.5.2 Differentator based on opamp . . . . . . . . . . . . . . . . . . . . . . 404.5.3 Comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.6 Time Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.7 Analysis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5 Prototype 455.1 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.1.1 MOSFETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.1.2 Differentiator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.1.3 Comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.1.4 Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.1.5 Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.2 Bill of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.3 Control Circuit Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.3.1 Opamp and Comparator Power Supply . . . . . . . . . . . . . . . . 495.3.2 Differentiator Feedback . . . . . . . . . . . . . . . . . . . . . . . . . 495.3.3 Comparator Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3.4 MOSFET gate charge . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.4 Loss Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.5 Synchronized Switch Harvesting on Inductor Prototype Performance Eval-

uation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.5.1 Time Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.5.2 Prototype Evaluation Summary . . . . . . . . . . . . . . . . . . . . . 54

6 Results 556.1 WindSpear Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.1.1 Parallel-SSHI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.1.2 Series-SSHI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.2 RLC Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2.1 Inductor Oscillation with MOSFET Output Capacitance . . . . . . 596.2.2 RLC Loss Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.3 Peak Detection Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.4 Power Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.4.1 Theory Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626.4.2 Total Power Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.5 Prototype Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.5.1 Peak Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

7 Conclusion 697.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

References 71

Appendix 75A DELTA Greenlab Mote . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

A.1 Power Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . 76B Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77C Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79D LCR Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

D.1 PSMcomm Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . 81E Electromechanical Coupling Factor . . . . . . . . . . . . . . . . . . . . . . . 82F MFC Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

F.1 Capacitive load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83G Technical Low Power Laboratory Challenges . . . . . . . . . . . . . . . . . . 84

G.1 Measuring Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84G.2 Measuring Low Current . . . . . . . . . . . . . . . . . . . . . . . . . 84

H Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85H.1 MOSFETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85H.2 Opamps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85H.3 Comparators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

I Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86J Half-wave Rectifier Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89K Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

K.1 Self Wound Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . 90K.2 Build Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91K.3 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

L WindSpear Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93L.1 P-SSHI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94L.2 S-SSHI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

M Envelope Breaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

List of Figures

1.1 Visualizing the energy in a wireless sensor node system powered by a batteryor powered by energy harvesting [14]. . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Piezoelectric vibration harvester with commonly used rectifying circuit [11] . . 31.3 WindSpear with MFC piezelectric material for harvesting wind energy [18] . . 41.4 Running tights with MFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 MFC placed inside tights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.6 Block diagram describing a vibration energy harvesting system. This project

deals with optimizing the power extraction of a piezoelectric generator with aconverter rectifying the AC generated voltage to DC. . . . . . . . . . . . . . . . 6

2.1 Vibrational energy is apparent everywhere. One method to harvest the vibra-tional energy is to mount a piezoelectric material in the vibrating environment.The piezoelectric material will generate an AC voltage when in motion. . . . . 7

2.2 Electromagnetic conversion device from [7]. Vibrations will make the springattached mass move inducing a magnetic field with the magnet thus creatingenergy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Power density for the 3 different vibrational harvesters vs. frequency [13] . . . 92.4 Directional definition for piezoelectric coefficients [33]. . . . . . . . . . . . . . . 112.5 Norton electrical equivalent of piezoelectric generator [24]. . . . . . . . . . . . . 112.6 MFC on WindSpear impedance compared with the theory. . . . . . . . . . . . 122.7 Equivalent mechanical model of the piezo generator structure excited at its

resonance frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.8 Macro Fiber Composite output power load sweep at 5 different frequencies.

Theoretical power output is shown for f = 3 Hz f = 2 Hz and f = 0.5 Hz anda PSpice simulation of the equivalent circuit fits the measurement results. . . . 17

3.1 Complex conjugate impedance match for maximum power transfer [39]. . . . . 193.2 Standard full bridge rectifier [29]. . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Simple voltage doubler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4 Voltage doubler with synchronous rectification from [17]. . . . . . . . . . . . . . 223.5 Ideal parallel Synchronized Switched Harvesting on Inductor topology [29]. . . 223.6 Synchronized Switched Harvesting on Inductor waveforms: piezo voltage, V,

displacement, u, and velocity, u [29] . . . . . . . . . . . . . . . . . . . . . . . . 233.7 Example of P-SSHI circuit from [24] . . . . . . . . . . . . . . . . . . . . . . . . 243.8 Ideal series SSHI topology [29]. Here the inductor is switched in series with the

piezo capacitance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.9 Synchronous Electric Charge Extraction converter topology [31] . . . . . . . . . 253.10 Synchronous Electric Charge Extraction - piezo voltage, V, and piezo displace-

ment, u, waveforms [31] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

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3.11 SECE control circuit from [46] . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.12 Comparison of the 5 different topologies. Output power vs. load. . . . . . . . . 273.13 Comparison of the maximum output power as a function of the inversion coef-

ficient / converter efficiency, γ. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1 Simplified PSpice simulation circuit for analyzing the P-SSHI topology. . . . . 314.2 Piezo output voltage and piezo capacitor current waveform with no load. t1

and t2 indicates voltage maxima and minima - instances where an inductor willbe switched in parallel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3 PSpice sim: Control signal to N- and PMOS gate . . . . . . . . . . . . . . . . . 334.4 PSpice simulation - Key waveforms of SSHI. Left column shows the 2 Hz signals

and right column shows a ZOOM in on the switching instance tZOOM. . . . . . 344.5 Peak detector square output signal for control of SSHI switching. The peak

detector switches at the voltage peaks (maxima or minima) of the piezo element. 394.6 Simple differentiator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.7 Peak detection circuit consisting of differentiator based on opamp and a Schmitt

Trigger comparator. The waveforms from each part is shown and p and ndenotes positive and negative peak. . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.8 Bode plot of transfer function for modified differentiator (eq. 4.31). . . . . . . . 424.9 SSHI piezo voltage and piezo displacement [29] with delay. . . . . . . . . . . . . 43

5.1 P-SSHI Prototype Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.2 Solution to make the circuit self-supplying (not implemented). Half-wave rec-

tifiers for supplying the active components from the piezo voltage. The piezovoltage is connected to the AC input IN and the component positive and neg-ative supply pin to V+ and V−. . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.3 Power loss in the peak detection control in the SSHI circuit. The total loss is15.4 µW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.4 Maximum power output increase of the P-SSHI topology subtracted its lossesand the energy harvested with the standard full bridge. The dark parts arenegative, meaning that here the SSHI does not give a net power increase dueto the consumption of the control circuit. . . . . . . . . . . . . . . . . . . . . . 52

5.5 Maximum power output increase of the S-SSHI topology subtracted its lossesand the energy harvested with the standard full bridge. The dark parts arenegative, meaning that here does the SSHI not give a net power increase dueto the consumption of the control circuit. . . . . . . . . . . . . . . . . . . . . . 53

6.1 WindSpear open circuit piezo voltage. . . . . . . . . . . . . . . . . . . . . . . . 556.2 P-SSHI piezo voltage with an output load of R = 2.7 MΩ. The voltage peak is

at t1 and the actual inversion happens at t2. The inversion factor is estimatedto be γ = −V g+

V g− = 0.47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.3 P-SSHI inductor inversion voltage when PMOS turns ON. The load connected

is R=2.7 MΩ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.4 S-SSHI piezo voltage and comparator output with load R = 1.6 MΩ. . . . . . . 586.5 S-SSHI inductor inversion voltage when PMOS turns ON. . . . . . . . . . . . . 586.6 Comparison of the component losses in the RLC oscillation path. The MOS-

FET RDS and Coss are both < 1 % and are thus hard to see. . . . . . . . . . . 60

6.7 Piezo generator vibrating at 2 Hz and SSHI circuit with 2 Hz external controlsignal slightly off sync. Shows dependence on when the switching is done andthat it needs to be a bit after the voltage peak due to reduced phase shift whenresistive loading of the piezo. Red arrow indicates voltage bump after switchingdirectly on the voltage peak. The missing time/voltage scale is 250 ms/div and2 V/div and the figure is two merged oscilloscope screenshots. . . . . . . . . . . 61

6.8 Measurement results of the Parallel-SSHI and Series-SSHI prototype along withthe standard full bridge, STD. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.9 Test - Load sweep when harvesting energy from WindSpear with simple topolo-gies for evaluating the theory in use. . . . . . . . . . . . . . . . . . . . . . . . . 64

6.10 Prototype test results - Load sweep when harvesting energy from WindSpear. . 646.11 Prototype test load sweep. The output power subtracted the expected power

loss in the SSHI is plotted as a function of the load and compared with thestandard full bridge, STD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.12 Theoretical maximum output power of P-SSHI (γ = 0.47) and S-SSHI (γ =0.21) with the estimated control power consumption subtracted. Comparedwith the maximum output power of the standard full bridge for vibrations at2 Hz as a function of the piezo open circuit voltage, Vp. . . . . . . . . . . . . . 66

B.1 Vibrational acceleration [g] vs frequency [Hz] [35] . . . . . . . . . . . . . . . . 78C.1 Definition of the neutral axis, ie. the broken line, X . . . . . . . . . . . . . . . 79C.2 Arc with marked sagita and cord in bending beam. Sagita is the vertical line

orthogonal on the horizontal line. tegn ny tegning? . . . . . . . . . . . . . . . . 80E.1 Comparison of SSHI and SECE output power dependence on electromechanical

coupling factor and mechanical quality factor. From [15] . . . . . . . . . . . . . 82F.1 Measurement setup for characterizing the MFC piezoelectric material. DC

motor is seen on the right mounted on a stand. This rotates a rod in connectionwith the MFC which is mounted on a thin plastic plate. The rotations causesthe plastic sheet and the MFC to bend. . . . . . . . . . . . . . . . . . . . . . . 83

F.2 Energy produced by MFC vs capacitive load . . . . . . . . . . . . . . . . . . . 83I.1 Parallel Synchronized Switch Harvesting on Inductor Prototype Schematic . . . 86I.2 Series Synchronized Switch Harvesting on Inductor Prototype Schematic . . . . 87I.3 Implemented P-SSHI prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . 88K.1 Impedance-phase measurement of the inductor in use in the prototype of 180mH.

Measured on a phase sensitive multimeter described in app. D. The bump inthe green graph corresponds to 50Hz and is due to equipment noise. Could beremoved with larger test signals. . . . . . . . . . . . . . . . . . . . . . . . . . . 90

L.1 WindSpear mounted in hanging configuration for the prototype test. . . . . . . 93L.2 DC motor is in connection with the end of the WindSpear via the green stick

and makes it vibrate at frequency of 1.8 Hz. . . . . . . . . . . . . . . . . . . . . 93L.3 P-SSHI inductor inversion voltage when NMOS turns ON . . . . . . . . . . . . 94L.4 S-SSHI inductor inversion voltage when PMOS turns ON - FDV301N/304P . . 94L.5 Comparison of resonance between inductor and MOSFET output capacitance

for S-SSHI circuit with small signal FET FDV301N/304P and IRF7307. . . . . 95M.1 Electronic breaker for peak detection in SSHI. From [26]. . . . . . . . . . . . . 95

List of Tables

1.1 Examples of energy harvester output levels [37]. These numbers are made from thefollowing assumptions: Solar : the photovoltaic cell has 15 % efficiency, Thermal : thetemperature difference between human skin and ambient air is 5 K, Vibration: thehuman is in walking motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2.1 Vibration Levels of different sources [42] [49] . . . . . . . . . . . . . . . . . . . . . . 82.2 Definition of the piezoelectric energies from equation . . . . . . . . . . . . . . . . . 14

3.1 Output power expressions of topologies . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Parameters for theoretical power output in fig. 3.12 . . . . . . . . . . . . . . . . . . 273.3 Topology maximum output power from fig. 3.12 . . . . . . . . . . . . . . . . . . . . 28

4.1 PSpice simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Differentiator component values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.1 MOSFETs used in prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Opamp used in prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.3 Comparator used in prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.4 Bill of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.5 Time delay in the control circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.1 P-SSHI Test Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.2 S-SSHI Test Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.3 RLC Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.4 Theory parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

A.1 Energy consumption of sensor node in different operating modes running Aslak OS. . 76C.1 Different material Young modules [8] . . . . . . . . . . . . . . . . . . . . . . . . . . 80H.1 Low power operational amplifiers from different commercial manufacturers . . . . . . 85H.2 Low power comparators from different commercial manufacturers . . . . . . . . . . . 85

xviii

Nomenclature

EH Energy Harvesting

MFC Macro Fiber Composite - piezoelectric material

SSHI Synchronized Switch Harvesting on Inductor

SECE Synchronous Electric Charge Extraction

STD Standard Full Bridge Rectifier

VD Voltage Doubler

α Force factor [N/V]

ε Dielectric permittivity [F/m]

γ Inversion factor

γC Converter efficiency [%]

D Electric displacement [C/m2]

d piezoelectric charge coefficient [pC/N]

dn.axis Distance to the neutral axis [m]

E Electric field [N/C]

F Force [N]

fres LC resonance frequency [Hz]

L Inductor [H]

Q Electrical quality factor

Ropt Optimum load resistance [Ω]

S Mechanical strain [1/m]

T Mechanical Stress [N/m2]

tinv SSHI voltage inversion time [s]

Vinv Piezo voltage after SSHI inversion [V]

Y Young’s modulus, elasticity [Gpa]

xix

1

Introduction

This chapter introduces the project and explains the concept of energy harvesting alongwith applications of the harvested energy. Afterwards follows the description and scope ofthe project.

1.1 Energy Harvesting

Ambient energy is all around us. In all kinds of light, in the radio signals in the air,in kinetic movements (wind and vibration), and in heat flows. All these energies can beharvested in several ways. Energy Harvesting (EH) is in this project defined as harvestingof ambient energy in small-scale. These transducers can be photovoltaic cells, thermalgenerators, and vibrational generators. The ambient levels are in general small and willnot be able to supply a household with power, but there is plenty of applications wherethere is energy enough to supply small electronic devices within the areas of ambient intel-ligence, condition monitoring devices, implantable and wearable electronics, and wirelesssensor networks [36]. Table 1.1 shows a rough comparison on the energy produced bythree different energy harvesting sources to give an idea of the energy levels.

Table 1.1: Examples of energy harvester output levels [37]. These numbers are made from thefollowing assumptions: Solar : the photovoltaic cell has 15 % efficiency, Thermal : the temperaturedifference between human skin and ambient air is 5 K, Vibration: the human is in walking motion.

EH Technology Setting Output µWcm2

Solar Outdoor 15000Indoor 10

Thermal Human 20Machine 5000

Vibration Human 4Machine 200

A key challenge of energy harvesting is that the output power from the harvester is notnecessarily in the form required. Loading applications often demand specific voltage andimpedance characteristics. They also require energy to transfer and convert the power inan already energy-sparse system, and these are some of the converter challenges withinenergy harvesting that this project will investigate.

1

1. Introduction

Energy harvesting has yet to be commercialized at a large scale but the energy consump-tion of microcontrollers and sensory electronics has now decreased down to the level ofmicrowatts-milliwatts. Combined with improved energy conversion techniques, several en-ergy harvesting solutions have started to become feasible. Meanwhile there is a demandfor long lasting sensors in small form factors placed in hard-to-reach locations which makecables and batteries unfit as illustrated in fig. 1.1. Batteries will eventually deplete whereenergy harvesting in theory can generate energy indefinitely.

Figure 1.1: Visualizing the energy in a wireless sensor node system powered by a batteryor powered by energy harvesting [14].

The goal of this project is to increase the feasibility of harvesting vibrational energy whichis commonly available in many environments where the harvesting material can be inte-grated with the vibrating structure.

1.1.1 Standard Approach

The most common method of harvesting vibrational energy from piezoelectric elementsis shown in fig. 1.2. A piezoelectric generator has a blocking output capacitance whichis connected to a diode full bridge rectifier. This is throughout the project known asthe standard full bridge, and abbreviated STD. When the piezoelectric output voltageis greater than the output capacitor voltage + diode bridge forward voltage, energy isharvested.

1.1.2 Energy Generating Material

The piezoelectric material used in the project is of the type Macro Fiber Composite (MFC),which is a flexible material and thus capable of resonating at low frequencies. The outputAC voltage amplitude of the MFC is dependent on the mechanical setup and the vibrationamplitude and frequency and can be from 0 V to > 50 V. The vibration level explored inthis project is however low, and the focus is on voltages around 8 V.

2

1.2. Energy Harvesting Applications

Figure 1.2: Piezoelectric vibration harvester with commonly used rectifying circuit [11]

1.2 Energy Harvesting Applications

The vibrational energy harvested in this project is supplying a sensor node, but can ingeneral be used wherever there is low frequency vibrations and low power electronics.

The sensor node being developed at the danish company DELTA, is a small computingdevice capable of collecting data, joining a mesh network and through this transmitting itsdata to a base station. A mesh of such nodes is known as a sensor network. Such sensornodes are usually supplied with power from batteries, but these require maintenance. Toavoid this, the nodes can be made energy self-sufficient by means of energy harvesting.The sensor node needs an energy amount of 680 µJ to perform a cycle of start up, sensormeasurement and data transmit. A detailed description of the sensor node can be seen inappendix A.

1.2.1 WindSpear

One application is the WindSpear developed at DELTA [18]. This consists of a plexiglassrod stuck into the ground with a circular plate on the top which increases the air resistanceand makes the rod bend in the wind as illustrated in fig. 1.3. A Macro Fiber Compositepiezoelectric material is mounted on the sides of the spear. When the wind blows, just agentle breeze around 1 m/s, the spear bends and vibrates around its resonance frequencyof 2 Hz and energy is generated in the piezoelectric material. The top end of the Wind-Spear is in this case vibrating with a displacement amplitude ∼ 1 cm and this correspondsto a displacement of the piezoelectric element ∼ 1 mm. This generates an open circuitvoltage of 8 V, which is used as example throughout the project. The generated energy isharvested to supply the sensor node. The sensor node will in this application monitor cli-mate and environmental data. The power level at this vibration amplitude and frequencyis however very low, e.g. in the microwatt range. Thus there is a need for optimizing theoutput power.

The MFC piezoelectric material mounted on the WindSpear has a capacitance measured tobe Cp = 42 nF. This capacitance is an important parameter which will be used throughoutthe whole project. The WindSpear will in the end of this project serve as test applicationfor evaluating the implemented prototype.

3

1. Introduction

Figure 1.3: WindSpear with MFC piezelectric material for harvesting wind energy [18]

1.2.2 Running Tights

Another possible application for the circuit made in this project is a pair of running tightsas shown in fig. 1.4 and 1.5. Here a piezoelectric material is sewn into the fabric and whena person, wearing these tights, is moving, energy is generated [45]. This application hasmany perspectives regarding the concept of intelligent clothing where sensors are buildinto clothes.

Figure 1.4: Running tights with MFC

Figure 1.5: MFC placed inside tights

In the running tights an MFC piezoelectric material is mounted. This MFC has an outputcapacitance of Cp = 204 nF.

4

1.3. Project Description

1.3 Project Description

The feasibility of a switching topology for optimizing vibration energy harvesting at lowfrequency low voltage levels is investigated. The project deals with analysis of differenttopologies and design and implementation of a prototype circuit. The converter is designedfor low frequency energy generated by a Macro Fiber Composite piezoelectric generator.It will be determined if the circuit optimizing the energy transfer is feasible at a low fre-quency low voltage level compared with the standard full bridge rectifier. The applicationconsuming the harvested energy is a sensor node.

1.3.1 Problem Definition

The aim of the project is to clarify whether a switching circuit topology is feasible for lowfrequency vibrations instead of a simple passive rectifying circuit, when the power level isin the microwatt range.

The main challenges when developing a low frequency low voltage vibration energy har-vesting converter are:

• Characterizing piezoelectric generator

• Choice of topology and analysis

– Full bridge rectifier

– Voltage doubler

– Synchronized Switch Harvesting on Inductor (SSHI)

– Synchronous Electric Charge Extraction (SECE)

• Circuit design

– Switching components

– Control

• Implementation of prototype

1.3.2 Project Scope

To power a sensor node from vibrational energy, the whole system including a generator,a rectifying circuit, a load matching and storage control circuit is needed. As shown in fig.1.6, this project is limited to deal with the rectifying circuit which will be shown capableof optimizing the harvested power. The output power will have to be managed by a loadmatching circuit, which is another power management circuit and is beyond the scope ofthis project.

Key definitions in the project scope are:

Converter - Rectifying circuit, which rectifies the piezoelectric AC voltage into a DCvoltage while optimizing the output power.

Low voltage - Piezoelectric output voltages around 8 V.

5

1. Introduction

Low frequency - Mechanical vibrations around 2 Hz.

Power level - The generated power level is in the microwatt range.

When analyzing the electrical output power resulting from an mechanical vibration inputto a piezoelectric generator, a deeper mechanical analysis of the mechanical structure isneeded to directly link the applied mechanical vibrational energy to the generated electricalenergy. The mechanical analysis is not within the scope of the project. Thus the exactinput mechanical vibrational energy will in this project not be known. Instead the energylevel is stated as the open circuit piezo voltage as this is dependent on the input energy.

AC-DC Converter DC-DC Converter Storage Capacitor/Battery

Sensor Node

Mechanical Vibrational Energy

Piezoelectric Generator

Figure 1.6: Block diagram describing a vibration energy harvesting system. This projectdeals with optimizing the power extraction of a piezoelectric generator with a converterrectifying the AC generated voltage to DC.

1.3.3 Thesis Structure

The thesis introduces the reader to the basic concepts of vibrational energy harvesting andexplains the piezoelectric energy harvesting generator and theory behind the generatedoutput power. Different vibrational harvesting conversion topologies will be analyzed andcompared and a topology is chosen to be implemented and tested. The thesis rounds offby discussing the results and stating the further work needed. Abbreviations are listed inthe nomenclature placed immediately after the table of contents.

1. Introduction introduces the reader to energy harvesting and what the harvestedenergy is being used for.

2. Vibrational Energy Harvesting covers the mechanical and electrical aspects ofharvesting energy with piezoelectric materials. A theoretical expression for outputpower from the piezoelectric material is derived.

3. Circuit Topologies describes the common circuit topologies for harvesting piezo-electric energy. The topologies output power are compared and one is chosen to beanalyzed further and implemented as a prototype.

4. Analysis of Synchronized Switch Harvesting on Inductor analyzes the chosentopology via simulations and circuit loss considerations.

5. Prototype describes the details about the implemented prototype.

6. Results presents the harvesting results from the test of the implemented prototype.

7. Conclusion rounds off the thesis and discusses the challenges of vibrational energyharvesting in the microwatt range.

8. Further Work with the results of this project, what is to be done from here.

6

2

Vibrational Energy Harvesting

This chapter will describe the physics behind vibrational energy harvesting along with thedescription of energy harvesting with piezoelectric material. A theoretical expression forthe piezo output power is derived and the piezoelectric material is characterized and tested.

When harvesting mechanical energy one important factor is that the mechanical energy isnot free. The harvesting will convert the mechanical energy to electrical energy and thismeans that the mechanical motion will be dampened or altered.

Vibrational harvesting can be done wherever there is a movement. It can be harvested withelectromagnetic harvesters consisting of a core and a coil, electrostatic harvesters utilizinga material capacitance change, and piezoelectric harvester made with piezoelectric ceramicutilizing the piezoelectric effect, when the material is flexed.

Figure 2.1: Vibrational energy is apparent everywhere. One method to harvest the vi-brational energy is to mount a piezoelectric material in the vibrating environment. Thepiezoelectric material will generate an AC voltage when in motion.

Table 2.1 shows some examples of what vibration levels can be found in the ambient envi-ronment. Examples of vibration harvesting applications can be kinetic watches, industrialmotor monitoring, structural/bridge health monitoring, kinetic powered light switches,muscle powered implants and helicopter tracking nodes [36].

In this project the piezoelectric output voltage amplitude generated by the WindSpear insec. 1.2.1 is around 8 V. The energy level at 2 Hz is in the microwatt range. In appendixB a description of the mechanical theory of vibrations can be seen. It is shown that theinput energy, W , is proportional to the frequency, f , squared and the displacement, u.This is an important fact when looking at low frequency energy, as the energy gets verylow when the frequency decreases.

W ∼ f2 · u (2.1)

7

2. Vibrational Energy Harvesting

Table 2.1: Vibration Levels of different sources [42] [49]

Vibration Source Peak Acc. [m/s2] Freq. of Peak [Hz]

Walking 1 1Jogging 2 2Ventilation vents in office building 0.2-1.5 60Notebook computer while CD is being read 0.6 75External windows next to a busy street 0.7 100Washing Machine 0.5 109Door frame just after door closes 3 125Small microwave oven 2.25 121Refrigerator 0.1 240Wooden deck with people walking 1.3 385

2.1 Vibrational Energy Harvesters

2.1.1 Electrostatic

Electrostatic harvesters convert mechanical energy into electrical energy by the variation inthe separation distance/overlap area of the plates in a MEMS1 capacitor. Changes in thecapacitance produces energy when keeping the charge or voltage constant, Q = C · V [36].

2.1.2 Electromagnetic

Electromagnetic harvesters transform kinetic energy into electrical by moving a coil acrossthe magnetic field of a stationary magnet, thereby inducing a voltage across the coil.The electromagnetic generators can generate high output-current levels but the voltageis very low (typically < 1 V ). Macro-scale devices are fabricated using high-performancebulk magnets and multi-turn coils. Electromagnetic harvesters are heavy and bulky dueto their large magnetic components [42].!

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Figure 2.2: Electromagnetic conversion device from [7]. Vibrations will make the springattached mass move inducing a magnetic field with the magnet thus creating energy.

1Microelectromechanical System

8

2.2. The Piezoelectric Effect

2.1.3 Piezoelectric

Piezoelectric generators are made of a dielectric material where charge builds up when thematerial is stressed. Piezoelectric generators have the advantages of simple structure andeasy fabrication. It is also easy to be integrated into silicon devices and further fabricatedwith the microelectronic circuits on the same chip [36]. The piezoelectric effect and ma-terial will be explained further in sec. 2.2. The piezoelectric element produces a voltagewhen a strain/deformation is applied in a vibrating environment.

2.1.4 Comparison

Fig. 2.3 shows the power density for the 3 different vibrational harvesters. None of themare in the area of 2 Hz which is a sparsely explored frequency.

Figure 2.3: Power density for the 3 different vibrational harvesters vs. frequency [13]

2.2 The Piezoelectric Effect

The piezoelectric effect is a material property where an applied mechanical strain intro-duces an electric field across the material (direct effect) and conversely an applied electricfield introduces deformations in the material (converse effect).

The most common material is the piezoelectric ceramic. The materials consist of severalcrystallites (a dielectric material) with local charge separations (electric dipoles), initiallyrandomly ordered and in this state the material has no piezoelectric effect. The piezoelec-tric effect in piezo ceramics arises after the material has been applied a poling high DCvoltage electric field which aligns the orientation of the crystal polar domains. After thisprocess all the crystals will maintain their orientation and create a common electric dipolein the same direction and the ceramic will exhibit the piezoelectric effect [1].

The piezoelectric material used in this project is of the type Macro Fiber Composite [9].It consists of thin piezoelectric fibers glued together in epoxy. Due to this it is a flexiblematerial making it possible to flex with large deformations in comparison to rigid ceramics.

9


The flex is similar to flexing a regular cardboard playing card.

When applying an electric field in the direction of the crystal polar orientation the mate-rial will elongate or contract. Vice versa when the material is strained or compressed inthe direction of poling - the mechanical strain will be transformed into electrical charge.

The direct effect is the material property making it possible to harvest mechanical energyand use them as sensors and the converse effect makes the piezoelectric materials feasiblefor use as actuators [1].

The piezoelectric energy conversion from mechanical to electrical energy can be describedby two linearized constitutive equations of the electrical field, originating from Maxwell’sequations. These contain two mechanical variables and four electrical variables. Equation.2.2 is originates from Gauss’ law and is added the mechanical coupling term describing thedirect piezoelectric effect2. Equation 2.3 is Hooke’s law added the piezoelectric couplingwhich describes the converse piezoelectric effect [42] [11].

The piezoelectric coupling provides the medium for energy conversion. The electric fieldacross the material affects its mechanics, and the stress in the material affects its dielectricproperties.

D = dT + εE (2.2)

S =T

Y+ dE (2.3)

where:

D is the electrical displacement (charge density)

T mechanical stress

ε is the dielectric constant of the piezoelectric material (electric permittivity)

Y is Young’s modulus

S mechanical strain

d is the piezoelectric charge coefficient / elastic permittivity

E is the electric field

When the material is strained an electric charge is seen on the surface of the material viaelectrodes. Thus the piezoelectric properties has a sign convention making it possible todescribe properties in three directions. Often the piezoelectric coefficient d can be definedas d33 or d31. The first subscript denotes the electrode direction, the second the directionof poling. This means the d31 describes the piezoelectric property when the material isstrained in direction 3, the electric charge is generated in direction 1, perpendicular to thepoling direction. In fig. 2.4 the directions are defined.

2It is assumed that the mechanics take place along a single axis, and therefore, each variable or constantis treated as a single scalar rather than a tensor

10

2.3. Equivalent Electrical Circuit of Piezo Generator

In this case it is assumed that the piezoelectric material is used as a bender, which can besimplified to only imply one of the piezoelectric coefficients.

The strain applied in the piezoelectric material is very dependent on the structure it ismounted on. How to calculate the strain is shown in appendix C. It is noted that theneutral axis of the whole structure should be outside the piezoelectric material to getuniform strain through the piezoelectric material, which will generate more power. If theneutral axis is inside (e.g. both stress and strain at the same time inside the material) thematerial will work against ”it self” [9].

Figure 2.4: Directional definition for piezoelectric coefficients [33].

2.3 Equivalent Electrical Circuit of Piezo Generator

A simplified electrical equivalent circuit of a piezo generator is shown in fig. 2.5 wherethe Norton equivalent circuit is shown, consisting of an alternating current generator inparallel with a capacitor.

Figure 2.5: Norton electrical equivalent of piezoelectric generator [24].

The piezoelectric impedance is highly capacitive at lower frequencies, causing a phase shiftbetween the generated voltage and current [5].

The impedance of the equivalent circuit can be expressed as

Z =1sCp

(2.4)

and this is plotted along with the measured impedance in the following section in fig. 2.6.

11


2.3.1 Macro Fiber Composite Impedance

The impedance-phase measurements of the MFC mounted on the WindSpear, introducedin sec. 1.2.1, is shown in fig. 2.6 together with the impedance from the equivalent circuit.The equivalent circuit is seen to be matching the MFC measurements up until 300 kHz,and the equivalent circuit in fig. 2.5 is thus concluded to be applicable at the low frequen-cies in this project. See appendix D for the measurement setup.

100

101

102

103

104

105

106

100

105

1010

Impe

danc

e [Ω

]

Impdance Sweep − WindSpear MFC

100

101

102

103

104

105

106

−100

−50

0

50

100

Pha

se [

° ]

MeasurementEquivalent Circuit

Figure 2.6: MFC on WindSpear impedance compared with the theory.

2.4 Spring Mass Damper Mechanical Model

When the piezo generator structure is excited with a sinusoidal force around its resonancefrequency, with small displacements where the movements remain linear, e.g. linear elas-tic, it can be modelled as a structure with: A rigid mass, M , spring, K, damper, C, andthe piezoelectric element as shown in fig. 2.7, having only one degree of freedom [3].

The spring, K, corresponds to the mechanical structure stiffness and the damper, C, cor-responds to the mechanical loss. F is the external force applied to the mass and thedisplacement of the rigid mass is u, and I and V are the generated piezoelectric currentand voltage.

According to Newton’s second law of motion3, the sum of the forces applied to the massis described by the mechanical differential equation in eq. (2.6). The sum of the forces is

3The acceleration, a, of a body is proportional to the net force, F , and inversely proportional to themass, m, i.e. F = ma.

12

2.4. Spring Mass Damper Mechanical Model

Figure 2.7: Equivalent mechanical model of the piezo generator structure excited at itsresonance frequency.

denoted as the total force, FT =∑F . The structural displacement is denoted as u, and

hence u and u, is the speed and acceleration of the motion, respectively.

Mu = FT −Ku− Cu (2.5)Mu+ Cu+Ku = FT (2.6)

The total force acting on the mass can also be described by eq. (2.7), where α is the forcefactor of the piezoelectric element, and V is the output voltage.

FT = F − αV (2.7)

The force factor α describes the piezoelectric elements ability to convert mechanical forceto electrical energy.Combining eq. (2.6) and eq. (2.7) leads to eq. (2.2):

Mu+ Cu+Ku = F − αV (2.8)

To describe the energy balance in the system with the vibrating piezoelectric element, theenergy in the system can be described by the time integral of the force multiplied withthe velocity. Taking the time integral of both sides in eq. (2.2) and multiplying with thevelocity, u, leads to the energy balance in eq. (2.9)

∫ t0+∆t

t0

Fu dt =12M [u2]t0+∆t

to +12K[u2]t0+∆t

to + C

∫ t0+∆t

t0

u2 dt+ α

∫ t0+∆t

t0

V u dt (2.9)

The left side of eq. (2.9) is the provided energy and the right side is the kinetic energy +potential energy + dissipated mechanical losses + transferred energy over the time range[t0; to + ∆t] [28] [6] [3]. The energies are listed in table 2.2.

From the constitutive equations of piezoelectricity, the current flowing out of the piezo-electric element, I, can be expressed as eq. (2.10) [42].

13


Table 2.2: Definition of the piezoelectric energies from equation

Energy Equation

Provided∫ t0+∆tt0

Fu dt

Kinetic 12M [u2]t0+∆t

to

Potential 12K[u2]t0+∆t

to

Dissipated C∫ t0+∆tt0

u2 dt

Transferred α∫ t0+∆tt0

V u dt

I = αu− CpV (2.10)

where Cp is the piezoelectric capacitance. The transferred energy can then be describedby eq. (2.11)

α

∫ t0+T

t0

V u dt =12Cp[V 2]t0+∆t

to +∫ t0+∆t

t0

V I dt (2.11)

where the transferred energy is the sum of the electrostatic energy stored on the piezoelec-tric element and the energy delivered to the connected load, i.e. the harvested electricalenergy.

The job of the circuit in this project is to maximize the harvested power:

Eharvest =∫ t0+∆t

t0

V I dt (2.12)

Pharvest =1

∆t

∫ t0+∆t

t0

V I dt (2.13)

2.4.1 Force Factor

When the piezo is in open circuit the piezo current in eq. (2.10) is zero when the piezodisplacement is at its maximum, u, and corresponding the piezo voltage is at maximumV . Thus the force factor can be described as in eq. (2.15) [3].

αV = Cpu (2.14)

α =Cpu

V(2.15)

Eq. (2.13) describes the output energy in the piezoelectric element. In order to enhancethe conversion abilities of the system three ways can be explored:

1. Increase the force factor α.

14

2.4. Spring Mass Damper Mechanical Model

2. Increase the voltage V .

3. Decrease the time delay between V and the speed u.

1. is related to the piezoelectric material and 2. is related to the mechanical forces, but 3.is electrically related and corresponds to decreasing the phase shift between the voltageand the current. A topology for optimizing this factor will be explored later in sec. 3.2.3.

2.4.2 Power Delivered to Resistive Load

A theoretical expression of the power delivered to a purely resistive load connected inparallel with the piezoelectric element output is derived.

The piezoelectric element creates an AC voltage when vibrating. Eq. (2.10) is used, forsimplicity, when assuming the piezoelectric element displacement is at its maximum, u,and corresponding the piezoelectric voltage is at maximum V . These are used togetherwith the load resistance R to express the loaded piezoelectric output voltage in the fre-quency domain as a function of R [4].

I = αu− CpV (2.16)

V

R= αu− 1

jωCpV (2.17)

V = αuR− R

jωCpV (2.18)

αu

V=

R

jωCp+ 1 (2.19)

V =R

jωCp+ 1

αu(2.20)

V =αR

1 + jωRCpjωu (2.21)

Then the average power delivered to the resistive load, PR, can be described by the fol-lowing:

PR =V 2RMS

R=

(V/√2)2

R=V V ∗

2R(2.22)

V ∗ = −jωu αR

1− jωRCp(2.23)

V V ∗

2R= ω2u2 α2R2

2R|1 + jωRCp|2(2.24)

PR =α2Rω2u2

2(1 + (ωRCp)2)(2.25)

The optimum load resistance, Ropt is in eq. (2.26) and at this load the maximum power,PR−max, eq. (2.27), will be dissipated.

15


Ropt =1

ωCp(2.26)

PR−max =α2ωu2

4Cp(2.27)

Eq. (2.25) is used in the next section compared with measurements of the power outputof the MFC piezoelectric element vibrated at low frequencies.

Based on the theory just presented, expressions for output power of the standard fullbridge, voltage doubler, SSHI and SECE are calculated in the literature [2] [3] [4] [26] [29][31] [38]. These topologies along with their theoretical output power expressions will bepresented in next chapter and used to evaluate the different topologies to aid in the choiceof which to implement as a prototype.

2.5 Macro Fiber Composite Output Power

The MFC piezoelectric material to be used as vibration energy generator in this projectis tested for its output power dependence on frequency.

In fig. 2.8 a load sweep of the MFC output power at 5 different frequencies is seen. Thetheoretical power output at 3 of these frequencies are showed along with a PSpice simula-tion of the equivalent circuit. It shows that the power and the optimum load are frequencydependent and the theory corresponds to the measurements.

The practical setup can be seen in appendix F. The voltages was measured with a highinput impedance voltage follower [21] described in appendix G. If the measurements weremade with a regular oscilloscope probe with 1 MΩ impedance, the probe would dampenthe signal significantly as the piezoelectric current is in the range of 1− 10 µA.

The load sweep was done up to 3 MΩ. It is noted that the RC time constant of the loadand the output capacitor of 10 µF becomes very high at these loads. With τ = RC =3 MΩ · 10 µF = 30 s. This resulted in a low measurement accuracy of ∼ ±0.2 V.

The energy harvested from the MFC connected to a full bridge with varying capacitiveloads is shown in appendix fig. F.2. This is also described in [2] where the findings arethat there is an optimum capacitive load, as the results in appendix F.1 shows. This willnot be explored further in this project as the topologies to be examined are assumed tohave a fixed output capacitance and an optimum resistive load, but it is noted that thereis an optimum capacitive load to be further explored.

2.6 Summary

The theory describing the generated piezoelectric energy was derived and found to beapplicable for describing the power output of the Macro Fiber Composite piezoelectricgenerator. The presented theory is the foundation for the power expressions presentedin the next chapter where different circuit topologies for vibration energy harvesting aredescribed and compared.

16

2.6. Summary

104

105

106

0

0.5

1

1.5

2

2.5x 10

−6

Load [Ohm]

Pow

er [W

]

MFC output power vs. load

f=3HzTheory 3Hzf=2HzTheory 2HzPSpice 2Hzf=1.5Hzf=1Hzf=0.5HzTheory 0.5Hz

Figure 2.8: Macro Fiber Composite output power load sweep at 5 different frequencies.Theoretical power output is shown for f = 3 Hz f = 2 Hz and f = 0.5 Hz and a PSpicesimulation of the equivalent circuit fits the measurement results.

17

3

Circuit Topologies for Piezo Harvesting

This chapter describes the different topologies used throughout the literature to harvest en-ergy from piezoelectric material. The topologies are compared based on their theoreticaloutput power and one is chosen for further analysis.

To harvest the energy produced by a piezoelectric element, conversion electronics areneeded. It produces an alternating current which needs to be rectified. This can be donesimply via a rectifying bridge or other more complex ways that optimizes the output power.These will be described in this chapter [15] [39] [42].

Piezoelectric generators have a high internal impedance, especially at low frequencies, dueto their capacitive behaviour. This limits the amount of output current to the range ofmicroamperes. Thus the current consumption of the converter circuit is required to bevery low.

3.1 Impedance Matching

For maximum power transfer the piezoelectric impedance must be matched by its complexconjugate [5]. To describe the power transfer from the piezoelectric generator to a load,ZL, the piezogenerator can be seen as a Norton equivalent of a voltage source, VP , with aninternal impedance, ZP . From the maximum power transfer theorem [16] the maximumpower will be transferred when the load is the complex conjugate of the equivalent Nortonimpedance.

Figure 3.1: Complex conjugate impedance match for maximum power transfer [39].

In this project the MFC material on the WindSpear (sec. 1.2.1) has a capacitance ofCp = 42 nF. The complex conjugate load inductor is calculated to be L = 31.7 kH at afrequency of 2 Hz. This is not physically possible to implement and thus other means hasto be considered.

19

3. Circuit Topologies for Piezo Harvesting

RL = Rp (3.1)

L =1

ω2pCp

(3.2)

L =1

(2 · π · 2 Hz)2 · 42 nF= 151 kH (3.3)

3.2 Topologies

The topologies presented are all compared on output power vs. resistive load. And theirdependence on the mechanical coupling and circuit complexity is evaluated.

A weak coupling between the electrical and mechanical system is assumed, implying thatthe resistive load has no effect on the mechanical displacement.

3.2.1 Standard Full Bridge Rectifier

The standard full bridge rectifier is the most common and simple used circuit for vibra-tional energy harvesting. It simply consist of 4 diodes forming a rectified signal across acapacitance smoothing the DC voltage. The standard full bridge is in the project abbre-viated STD. To describe the output power from STD, eq. (3.4) from [29] can be used. Itis later seen that the other circuit topologies maximum output power can be expressed asa function of the STD maximum output power. Thus the expressions are later normalizedwith respect to eq. (3.6).

PSTD =Rα2

(RCpω + π2 )2

ω2u2 (3.4)

RSTD(opt) =π

2Cpω(3.5)

PSTD(max) =α2

2πCpωu2 (3.6)

Figure 3.2: Standard full bridge rectifier [29].

20

3.2. Topologies

3.2.2 Voltage Doubler

The voltage doubler is very similar to the standard full bridge. In the ideal case the max-imum power output is the same as STD, just at double the voltage and half the current,implying that the optimum load for the voltage doubler is twice the optimum load ofSTD. When the diode forward voltage drop, VD, is included the voltage doubler shows togive more output power, than STD, due to two less diodes voltage drops in the circuit [38].

PVD =4ω2Rα2u2

(CpωR+ 2π)2(3.7)

RVD(opt) =2πωCp

(3.8)

PVD(max) =α2

2πCpωu2 (3.9)

Figure 3.3: Simple voltage doubler

A voltage doubler with synchronous rectification from [17], is illustrated in fig. 3.4 wherethe diode voltage is minimized. It is although noted that the power consumption of thecomparators are 2.28 µW, so the power loss in the diodes has to be larger than this con-sumption before this solution becomes feasible.

3.2.3 Synchronized Switched Harvesting on Inductor

The Synchronized Switch Harvesting on Inductor (SSHI) topology optimizes the poweroutput of a piezoelectric element [2].

As seen in the electrical equivalent circuit, the piezoelectric element has a capacitancewhich will cause a −90 phase shift between the voltage and the current.

The topology can be configured both in a series and a parallel version. The main idea ofthe technique is to eliminate the phase shift between the piezo current and voltage by mak-ing the voltage self commutate and thus optimize the energy output. The SSHI methodutilizes an inductor to remove this phase shift, by temporarily switching it in parallel orseries with the piezoelectric capacitance and letting it oscillate with the capacitance onlyfor half a period, i.e. until the piezoelectric voltage is inverted. The inductor has to be

21


Figure 3.4: Voltage doubler with synchronous rectification from [17].

sized primarily to the output capacitance of the piezo and the frequency of operation.Usually within 1-200 mH. The dissipated and transferred energy described in sec. 2.4are respectively minimized and increased by the SSHI, as the sinusoidal voltage acrossthe piezo capacitance does not have to be build up from 0 V, but from a higher leveldependent on the inversion capability of the circuit (explained later in this section). Thusthe energy generated in the piezo generator going into the capacitance is lowered and theoutput energy is increased.

As seen in see fig. 3.5 the inductor is connected in parallel with the piezo element whenthe switch S is closed. The switch is open until maximum displacement in the transduceroccurs, which correspond to a maximum bend in the material and to the maximum voltagegenerated. At this instance the switch gets closed briefly and the inductor will oscillatetogether with the capacitance of the piezo. The switch opens again after half a period ofthe oscillation frequency between the inductor and piezoelectric capacitor. Then the piezovoltage is reversed. See the waveforms in fig. 3.6.

Figure 3.5: Ideal parallel Synchronized Switched Harvesting on Inductor topology [29].

The voltage of the piezo output capacitance will shift polarity due to the resonant currentin the LC oscillating network when the switch is closed. Thus current is not needed tocommutate/charge the capacitance and the current is transferred to the output and in-creases the output power.

22

3.2. Topologies

Figure 3.6: Synchronized Switched Harvesting on Inductor waveforms: piezo voltage, V,displacement, u, and velocity, u [29]

The resonance between the output piezo capacitance, Cp, and the inductance, L, is at thefrequency, fres calculated using eq. (3.10). The switch will only be closed for half of theperiod, corresponding to the inversion time tinv1 in eq. (4.1) [3].

fres =1

2π√CpL

(3.10)

tinv = π√CpL (3.11)

The switching would ideally invert the piezo voltage fully from the peak piezo voltage V toa negative peak voltage of same amplitude, −V . Due to switching losses the real inversioncan be described by eq. (3.12), where Vinv is the voltage after inversion, γ is the inversionfactor, and Q is the electrical quality factor.

Vinv = γV = V e−π/2Q (3.12)

γ = e−π/2Q (3.13)

With an ideal SSHI implementation, the sensing and switching control units do not bringany influence to the output piezo voltage amplitude, switching phase delay, or voltage gapto the circuit. It is important to note, that the SSHI increases the extracted energy of thepiezoelectric element, but also introduces switching losses. As long as these switching lossesare smaller than the energy increase, the SSHI is improving the vibrational energy harvest.

Parallel Synchronized Switched Harvesting on Inductor

The ideal parallel SSHI circuit is seen in fig. 3.5. The switch S, turns ON at every voltagepeak, creating an oscillation path between the piezoelectric capacitor and the inductor,inverting the piezo voltage. When the piezo voltage is larger than the output voltage(including the rectifying bridge) energy is harvested.

The rectified output voltage Vout is considered constant, and thus the output capacitor Crin fig. 3.5 has no effect on the output power. This assumption is valid as long as the timeconstant t = RCr is far greater than the charge transfer time period.

1Assuming high Q-factor - lower Q-factor would lead to a smaller inversion time because the inversionwill be smaller.

23


The theoretical power output for the P-SSHI is stated in eq. (3.14) from [29]. Theexpression is derived on the same basis as the calculations for power delivered to a resistiveload in sec. 2.4.2. So are the maximum power output, PP−SSHI(max) at the optimum loadRP−SSHI(opt).

PP−SSHI =4Rα2

(RCpω(1− γ) + π)2ω2u2 (3.14)

RP−SSHI(opt) =π

(1− γ)Cpω(3.15)

PP−SSHI(max) =1

1− γα2

πCpωu2 (3.16)

In fig. 3.7 a P-SSHI circuit from [24] is seen. This is later used as basis for the prototypemade in this project.

Figure 3.7: Example of P-SSHI circuit from [24]

Series Synchronized Switched Harvesting on Inductor

The ideal series SSHI circuit is seen in fig. 3.8. It is very similar to the parallel SSHI.The inductor is switched in series with the piezoelectric capacitor creating an oscillationwhich causes the piezo voltage to invert, but the load is also in this path. Due to this,the matched load is lower than the P-SSHI and the maximum power output of the S-SSHIshows to be slightly smaller than the corresponding maximum power output of the P-SSHI.Energy is harvested at every switching instance, i.e. at every voltage peak. The rest ofthe time, the piezoelectric element is left in open circuit [26].

The theoretical power output for the S-SSHI is stated in eq. (3.17) from [29]. Theexpression is derived on the same basis as the calculations for power delivered to a resistiveload in sec. 2.4.2. Along with the maximum power output, PS−SSHI(max) at the optimumload, RS−SSHI(opt).

24

3.2. Topologies

Figure 3.8: Ideal series SSHI topology [29]. Here the inductor is switched in series withthe piezo capacitance.

PS−SSHI =4Rα2(1 + γ)2

(RCpω(1 + γ) + π(1− γ))2ω2u2 (3.17)

RS−SSHI(opt) =π(1− γ)

(1 + γ)2Cpω(3.18)

PS−SSHI(max) =1 + γ

1− γ· α2

2πCpωu2 (3.19)

3.2.4 Synchronous Electric Charge Extraction

The SECE converter topology [31] [46] [51] is seen in fig. 3.9 and corresponding waveformsare seen in fig. 3.10. At every voltage peak, the switch T turns ON and all the energystored in the piezoelectric capacitor is transferred as magnetic energy to the transformerL. When the piezoelectric capacitor voltage reaches zero, the switch T turns OFF and theenergy flows from L to the load.

It can be argued that this technique is less efficient than the SSHI due to the fact thatwhen the output capacitance is 0 V and needs to be charged again this charging dampensand extract energy from the vibration and thus dampens the piezo movement, where theSSHI helps the movement in letting the charge flow out easier.

Figure 3.9: Synchronous Electric Charge Extraction converter topology [31]

SECE power output is independent from the load and the performance then only dependon the converter efficiency, γC [31].

25


Figure 3.10: Synchronous Electric Charge Extraction - piezo voltage, V, and piezo dis-placement, u, waveforms [31]

PSECE = 2γCα2

πCpωu2 (3.20)

[46] shows that the SECE control circuit is more complex than the SSHI control. Thisis due to a zero current detector needed to turn OFF the switch when the piezoelectriccapacitance has been discharged. See fig. 3.11. This control is although only valid for asmall power range. One has to adjust the resistance R21 to set the correct switch OFFtime. For making the switch turn OFF dynamically it requires a zero-crossing voltagedetection circuit which is described in [51].

Fig. 4. Block diagram of piezoelectric energy harvesting using synchronous charge extraction technique for powering wireless RF transmitter

Fig. 6. Circuit design of PCU

comparator (MAX981) and pulse generator (MAX919). Todetect the peak magnitude of the voltage across the piezo-electric generator, the control circuit tracks the rate ofchange of voltage, rather than the magnitude. Hence, theinstance a negative rate of change of voltage is detected,the differentiating op-amp and comparator trigger the pulsegenerator to generate a pulse with duty cycle and period fixedby passive resistors. The purpose of the comparator after thedifferentiating op-amp is to amplify its small output. Thetotal power consumption of the control circuit is 300 µWat supply voltage of 5 V. The output waveforms of the 3components are shown in Fig. 8.

Fig. 7. Schematic diagram of control circuit for the synchronous chargeextraction circuit

B. Synchronous Charge Extraction Circuit

Although the synchronous charge extraction (SCE) circuitis built upon established circuits [1] [10], its implementation

Fig. 8. Waveforms of synchronized switch control circuit

and optimization still require much attentions. This includesthe diodes and the flyback transformer used in the SCEcircuit. The choice of the diodes for the SCE circuit designought to have fast reverse recovery time, small leakagecurrent and low forward voltage drop. This is because duringthe energy harvesting interval, the magnitude of current flowcould be in the range of few hundred mA. In addition,any leakage or reverse current will reduce the amount ofgenerated charges that can be harvested by the SCE circuitand thus increase the amount of power loss in the circuit.The main function of the flyback transformer is to storeenergy, which is very different from the standard transformer,which only couples energy from the primary windings to thesecondary windings. For the flyback transformer, the storagecapability comes in the form of an air gap within its core. Forthe constructed flyback transformer, energy is stored in theair gap of length about 110 µm, which is inserted betweenthe 2 ED half cores of grade 3C90. Grade 3C90 is used forthe highest value of saturation flux density easily available.

V. EXPERIMENTAL RESULTS

A. Output Power Harvested Using Synchronous Charge Ex-traction Technique

Using an AC voltage source parallel to a capacitor of 250nF to emulate a piezoelectric generator, the implementedsynchronous charge extraction technique is tested for itsharvested power output and the results are plotted in Fig.9.

1126

Figure 3.11: SECE control circuit from [46]

3.2.5 Output Power Comparison

To be able to choose a topology, the theoretical output power is compared. The outputpower expressions are listed in table 3.1.

The 5 different topologies are compared in fig. 3.12. Table 3.2 shows the used parametersfor the theoretical expressions. The inversion factors are based on results from [15].

26

3.2. Topologies

Table 3.1: Output power expressions of topologies

Topology Output Power

STD Rα2

(RCpω+π2

)2ω2u2

VD 4Rα2

(CpωR+2π)2ω2u2

P-SSHI 4Rα2

(RCpω(1−γ)+π)2ω2u2

S-SSHI 4Rα2(1+γ)2

(RCpω(1+γ)+π(1−γ))2ω2u2

SECE 2γC α2

πCpωu2

Table 3.2: Parameters for theoretical power output in fig. 3.12

γ 0.74γc 0.86Cp 42 nFVp 7.6 Vα 0.00032 N/V

105 106 107 108

1

2

3

4

5 x 10−5

Load [Ω]

Pow

er [W

]

Topology Comparison

STDVDP−SSHIS−SSHISECE

Figure 3.12: Comparison of the 5 different topologies. Output power vs. load.

27


In table 3.3 the maximum power outputs from the graph in fig. 3.12 shows that theParallel-SSHI is theoretically able to give ∼ 8 times more power than the STD and theSeries-SSHI ∼ 7 times.

Table 3.3: Topology maximum output power from fig. 3.12

Topology Max output power [µW ]

STD 5VD 7SECE 15S-SSHI 38P-SSHI 43

The expressions used are ideal and thus does not include diode voltage drops. Thus it isnoted that this favors the STD and SSHI because they will in real life include 4 diodesin their rectifying bridge, where the voltage doubler will only include 2 and the SECE none.

Since all the topologies can be normalized with respect to the standard full bridge out-put power, this can be used to visualize how each topology depend on the coefficient,γ. For the SSHI topologies it represents their ability to invert the piezo voltage and forthe SECE it represents the circuit efficiency. In fig. 3.13 a comparison of the maximumoutput power as a function of γ is seen. In an ideal case the efficiency of the SECE isassumed to be 100 % (γ = 1). Here it has a maximum output power of double the out-put power of the standard full bridge. Then when looking at fig. 3.13, (the dotted lineindicates the maximum power output of SECE at γ = 1), it can be estimated that inorder for the P-SSHI and S-SSHI to produce a larger power output than the SECE, the P-SSHI needs to have a γ < 0.3 and the S-SSHI needs to have γ < 0.5. This looks promisingas the inversion coefficients found in the literature are in the range of γ = 0.6−0.8 [38] [15].

Due to the complex control of the SECE and the output power comparison above, theS-SSHI and P-SSHI are chosen to be further examined and simulated with the goal of im-plementation due to their large output power increase. The S-SSHI has a lower matchedload than the P-SSHI, but slightly lower power output as seen in the end of this chapter.It is noted that for the SSHI topology to give optimal performance in a fully operationalenergy harvesting system, it would need a DC-DC converter capable of matching their highoptimum load. A lower matched load can be desired when designing a matching DC/DCconverter that will manage the output power of the SSHI circuit. This is although not inthe scope of this project. Both the SSHI topologies are chosen as they are very similarand the same control circuit can be used for both.

In appendix E it is further shown that the output power of SSHI is independent on theelectromechanical coupling factor and mechanical quality factor where SECE has a de-creased output power for higher coupled systems. The mechanical coupling is not withinthe scope of this project, but it can be argued that the SSHI will be less dependent on themechanical setup as opposed to the SECE and is therefore a topology that fits a broaderrange of mechanical structures.

28

3.2. Topologies

10−1 10010−1

100

101

102

103

γ

P/P ST

D [W/W

]

Topology Comparison − Normalized Output Power vs. γ

P−SSHIS−SSHISECESTD

Figure 3.13: Comparison of the maximum output power as a function of the inversioncoefficient / converter efficiency, γ.

29

4

Synchronized Switch Harvesting on InductorAnalysis

This chapter analyses the function and performance of the SSHI topology. To explain thefunction a simulation is made in PSpice and key waveforms are discussed. Based on thesimulation, design constraints for the different circuit parts will be made.

The SSHI circuit consists of an inductor switched in parallel or series with the piezo ca-pacitance via a switch as explained in sec. 3.2.3.

To describe the functioning a simulation model has been build in PSpice. A simplifiedcircuit schematic is seen in fig. 4.1. The switch in the SSHI simulation consists of a NMOSand a PMOS, where the diode, Dn, blocks in the NMOS body diode conduction directionand Dp blocks in the PMOS body diode direction. The inductor used in the simulation is1 mH and the piezo capacitance Cp = 204 nF.

Figure 4.1: Simplified PSpice simulation circuit for analyzing the P-SSHI topology.

4.1 Simulation

The SSHI circuit simulated is the parallel version described in sec. 3.2.3. In the P-SSHI,the inductor is shortly switched in parallel with the output capacitance of the piezo, Cp,and these will start to oscillate. In this short time period current flows in the oscillation

31

4. Synchronized Switch Harvesting on Inductor Analysis

path consisting of the inductor L, the piezo capacitance Cp, a diode and a MOSFET. TheMOSFET is ON only for a short time interval, long enough for the piezo voltage to beinverted. This means half a quasi period of the oscillation (T2 = 1

2 ·1fres

). Assuming a highQ-factor, this time can be calculated as [2] [24] [32]:

tinv = π√L · Cp (4.1)

tinv is the maximum time needed for the voltage inversion. If the Q-factor of the oscilla-tion path is low, the inversion will occur faster, the signal will be more dampened and theinversion will end at a lower voltage level.

4.1.1 SSHI waveforms

Through the simulated circuit in PSpice, the SSHI principle is explained and main voltageand current waveforms are shown.

The piezo voltage and current waveform is seen in fig. 4.2, where the piezo is in opencircuit. Here it is seen that the current lags the voltage by 90 due to the capacitivebehaviour of the piezoelectric element.

t1 t2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

−2

0

2

Time [s]

Volta

ge [V

]

Piezo voltage and current

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7−2

−1

0

1

2x 10−5

Cur

rent

[A]

VpIp

Figure 4.2: Piezo output voltage and piezo capacitor current waveform with no load. t1and t2 indicates voltage maxima and minima - instances where an inductor will be switchedin parallel.

Every time the piezo voltage reaches a peak, maxima or minima, an inductor is switchedin parallel with the piezo output and thus in parallel with the output capacitance of thepiezo. This makes the inductor and capacitance resonate for a short period which willcause the piezo voltage to be inverted. The piezo voltage is inverted because current runsfrom the inductor into the piezo capacitance which causes the voltage inversion. Thecurrent does not flow back due to the blocking diode (Dp or Dn) in the circuit. Thismethod can both be made in a parallel and series version and the functioning is the same -

32

4.1. Simulation

invert the piezo voltage at every peak by creating an oscillation path between the inductorand the capacitor. This increases the power transfer by removing the phase shift.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−4

−2

0

2

4

Time [s]

Volta

ge [V

]

N− and PMOS gate voltages

VGS−NVGS−P

t1 t2

Figure 4.3: PSpice sim: Control signal to N- and PMOS gate

The control signal for the switches can be seen in fig. 4.3 and the resulting key SSHIwaveforms in fig. 4.4. When there is positive piezo voltage the NMOS is OFF and PMOSON. This means that there is no connection to ground as the potential across DP makes itblock. Then when the voltage peaks, NMOS is turned ON - meaning there is a connectionto ground - so current starts running through L and back to Cp - hence they are oscillatingtogether. But only in one direction as the diode Dn is blocking the other direction. Socurrent can only flow one way and thus the voltage is inverted.

The N- and P-MOS are ON for half a period one at a time. Due to the body diode, fromsource to drain in the NMOS and from drain to source in the PMOS, the diodes Dn andDp are placed in opposite direction to prevent connection when the MOSFETs are OFF.When ON Dn and Dp also serves the purpose of only letting current flow in one directionand are thus an essential part of the SSHI functionality.

The parameters used in the simulation model in fig. 4.1 can be seen in table 4.1. Here Cp isthe piezoelectric capacitance, Igen and fgen are the sinusoidal current generator amplitudeand frequency, L is the inductor, tr and tf are the rise and fall time of the control signalsseen in fig. 4.3. These control signals are provided by an external square wave source.Cout is the output capacitance at the load.The waveforms of a simulated P-SSHI circuit with a piezo vibrating at 2 Hz is seen in fig.4.4. The voltage is inverted at every peak and thus it has a steep slope at every peak. Howthese voltage peaks will be detected is explained later in section 4.5. In this simulationthe control signals for the NMOS and PMOS are depicted in fig. 4.3.

The graphs in the left column are measured over 1 s. The graphs in the right column area ZOOM in on the switching instance, tZOOM , marked with the red dotted line. Whenfocussing on the left column, the 2 Hz voltage and current signals from the piezo capacitorand the inductor are seen. Every time switching occurs (e.g. in tZOOM ) current flowsfrom the capacitor to the inductor or the other way around.

33


0 0.2 0.4 0.6 0.8 1

−5

0

5

Time [s]

Volta

ge [V

]

Piezo voltage

0 1 2 3 4 5 6x 10−5

−5

0

5

Time [s]

Volta

ge [V

]

Piezo voltage ZOOM

0 0.2 0.4 0.6 0.8 1−0.1

−0.05

0

0.05

0.1

Time [s]

Curre

nt [A

]

Piezo capacitor current

0 1 2 3 4 5 6x 10−5

−0.1

−0.05

0

0.05

0.1

Time [s]

Curre

nt [A

]

Piezo capacitor current ZOOM

0 0.2 0.4 0.6 0.8 1

−5

0

5

Time [s]

Volta

ge [V

]

Inductor voltage

0 1 2 3 4 5 6x 10−5

−5

0

5

Time [s]

Volta

ge [V

]

Inductor voltage ZOOM

0 0.2 0.4 0.6 0.8 1−0.1

−0.05

0

0.05

0.1

Time [s]

Curre

nt [A

]

Inductor current

0 1 2 3 4 5 6x 10−5

−0.1

−0.05

0

0.05

0.1

Time [s]

Curre

nt [A

]

Inductor current ZOOM

tzoom

Figure 4.4: PSpice simulation - Key waveforms of SSHI. Left column shows the 2 Hzsignals and right column shows a ZOOM in on the switching instance tZOOM.

34

4.2. Inductor

Table 4.1: PSpice simulation parameters

Function Value

Cp 204 nFIgen 10 µAfgen 2 HzL 1 mHtr, tf 1 µsCout 10 µF

In the right side of fig. 4.4 the zoomed in waveforms of switching event at tZOOM areshown. Here an inversion of the piezo voltage from negative to positive occurs. The risetime can be read from the piezo voltage ZOOM graph and it is noted that this time istinv = 45 µs and is decribed by eq. (4.1). This corresponds to a frequency of 1

2·45µs = 11.1kHz which is the resonance frequency of L and Cp.

f =1

2π√

1 mH · 204 nF= 11.1 kHz (4.2)

In the inductor voltage ZOOM, second lowest graph to the right, it is seen that L atfirst resonates at 11.1 kHz, but after the inversion, when the Dp is blocking, L startsresonating at a higher frequency. This resonance frequency is measured to be 2.5 MHzand corresponds to L = 1 mH resonating with a MOSFET output capacitance of 4 pF.This resonance energy is lost and will be described later in this chapter.

4.2 Inductor

The LC oscillating circuit consisting of the inductor and the piezo output capacitanceneeds to have a time constant a lot smaller than the period of the vibration frequency tobe able to invert the voltage:

τLC 1fvib

(4.3)

Since the piezo capacitance in this project, is in the order of 40-200 nF, and the frequenciesaround 2 Hz this will not be an issue.

The inductor size sets the time for the inversion, tinv. This time is critical for the con-trol circuit and the switches as they need to be able to switch faster than tinv. If theswitches+control rise/fall time, tsw is longer than, tinv the switches will be in the activeregion when the inversion occurs and there will be losses and low inversion. Therefore doesa small inductance need very fast switches, and very fast switching leads to large voltagespikes1. Thus a large inductance is desirable.

The inductor size also influences the amount of current flowing from the inductor to thepiezo capacitance when switching. This current flows through the diode Dn or Dp whichwill introduce losses, corresponding to the product of diode forward voltage drop and thecurrent.

1As the voltage across the inductor is proportional to the derivative of the current.

35


4.3 MOSFET

As explained earlier, an NMOS and PMOS are used as switches in the SSHI circuit. TheON resistance of the MOSFETs, RDS(ON) introduce losses when the L Cp oscillationoccurs and after the inversion, the output capacitance Coss resonates with L as seen in fig.4.4, in the figure Inductor voltage ZOOM. The charge for rising the MOSFET gate, QG,is also desired to be small in order to use little energy in the switching process.

Thus both a small RDS(ON) and a small Coss and QG is desired. But the ON resistanceis inverse proportional to the capacitances.

A low ON resistance requires a broad channel inside the MOSFET. But a broad channelmeans larger surface area of the gate and thus larger capacitances.

This relation can be seen by looking at the MOSFET formula’s of input capacitance,Cgs + Cgd and ON resistance rds in the saturation region [19]:

Ciss ∼ WLCox (4.4)

rds =1λID

∼ L

WCox·X (4.5)

In eq. 4.5 for simplicity X denotes the rest of the variables2.

It is seen in above equations that the input capacitance (and the same holds for the outputcapacitance) is proportional to the channel length (separation between drain and source)L, gate width W and gate capacitance per unit area3 Cox and the ON resistance is in-versely proportional to W and Cox. Thus there is compromise to be found in order to findthe optimal switch.

The MOSFETs also have to be able to withstand the voltage spikes, arising when switchingthe inductor ON and OFF. This sets a requirement for the MOSFET maximum VDS rating.

4.4 Quality Factor

The inversion factor, explained earlier in eq. (3.13), is a measure of how good the circuitsability to invert the piezo voltage is. This depends on the Q-factor of the oscillation cir-cuit. The components that affects this are the inductor, the MOSFET, the conductingdiode and the piezo capacitor, constituting an RLC circuit. Each of their contributions tothe total Q-factor will be analyzed in this section. A large Q-factor in the circuit leads toclose to ideal inversion.

Q-factor is defined as the ratio of the reactance to the ratio of the resistance in the circuitor Q-factor of an RLC circuit is defined as the resonance frequency divided by the band-

2Ciss = Cgs + Cgd where Cgs = 23WLCox +WLovCox and Cgd = WLovCox

λ = krds

2L√VDS−Veff +Φ0

and ID = µnCox2

WL

(VGS − Vtn)2(1 + λVDS − Veff )

3Gate capacitance per unit area is given by Cox = Koxε0tox

, where Kox is the relative silicon (SiO2)permittivity and tox is the thickness of the thin oxide layer under the gate

36

4.4. Quality Factor

width: Q = ω0∆ω .

In an ideal series RLC circuit the Q-factor is eq. (4.6) [16]:

Q =1R

√L

C(4.6)

In the Parallel-SSHI the piezo capacitance, Cp, will be switched in parallel with the in-ductor, L and the total series resistance of the oscillation path, Rosc. This consists ofthe series resistance of the inductor, the ON resistance of the MOSFET, on the diodeequivalent resistance and parasitic losses4.

The larger the resistance, Rosc, the lower Q-factor in the RLC circuit. The resonancefrequency and the period are defined as:

f =1

2π√LCp

(4.7)

T = 1/f = 2π√LCp (4.8)

4.4.1 Inductor Loss

The voltage across L is assumed to be sinusoidal as in eq. (4.10). The voltage amplitudeacross the inductor VL is, as explained in eq. (3.12), a function of the inversion factorγ. It is assumed that the inductor voltage will be the difference between the piezo peakvoltage, Vp, and the inverted voltage, γVp, subtracted the diode forward voltage, VD inthe oscillation path. This leads to eq. (4.9):

VL = Vp(1 + γ)− VD (4.9)

The inductor current seen in the inductor current ZOOM graph of fig. 4.4 is calculated tobe able to estimate the losses in the oscillation path5. Ires is the peak resonance current.The time period when the current flows is half the resonance period, T

2 .

vL(t) = VL sinωt (4.10)

Ires =1L

∫ T/2

0vL(t) dt (4.11)

Ires =VLL

1− cosπ2πfres

=VLL

2√LCp (4.12)

IRMS =

√VL

2CpL

(4.13)

The RMS inductor current in eq. (4.13) is used to evaluate the different parts losses tobe able to evaluate which components has the largest influence on the total loss in theoscillation path. This will set the limits of the inversion factor, and this analysis is thus

4The loss from the oscillation between L and Coss contributes here.5To calculate the RMS value of the sinusoidal pulse appendix A.16 in [10] is used.

37


used to clarify which components are vital for achieving a high inversion factor.

The energy and power loss in the inductor series resistance, Resr, is shown below. Theenergy lost at every switching instance, Eloss−L, is calculated. This energy is lost twotimes in every vibration period. Thus the power lost is eq. (4.15).

Eloss−L = I2RMS ·Resr ·

T

2(4.14)

Ploss−D =2Eloss−D

T(4.15)

4.4.2 Diode

The diode is a part of the resistance in the RLC circuit. Power is lost through the blockingdiode (DN or DP ) in the resonating circuit due to the diode forward voltage drop, VD.This corresponds to a loss described by eq. (4.20), dependent on the inversion current,IRMS , running in the oscillation path. The current is present in half of the resonanceperiod:

Eloss−D = VDIRMST

2(4.16)

Eloss−D = VD ·2VLL

√LCp · π

√LCp (4.17)

Eloss−D = VD2VLLLCp · π (4.18)

Eloss−D = 2πVDVLCp (4.19)


T(4.20)

4.4.3 MOSFET

Both the ON resistance, RDS(ON), and the output capacitance, Coss, contributes to thetotal RLC loss.

ON Resistance

The MOSFET ON resistance power loss is expressed below.

Eloss−Rds = I2RMSRDS

T

2(4.21)


T(4.22)

It is important to note that the value of the resistance highly depend on the gate-sourcevoltage of the MOSFET. If it is not fully saturated the ON resistance will be high.

Output Capacitance

The output capacitance does however not depend on the inversion current, IRMS , and isthus not that simple to compare theoretically with the other losses. The value is insteadcalculated later in the results in chapter 6, and then compared with the above losses.

38

4.5. Peak Detection

4.5 Peak Detection

To control the S-SSHI and P-SSHI peak detection is used. The SSHI topologies are highlydependent on the peak detection of the piezo voltage.

It is desired to have a control circuit capable of sensing the piezo voltage peaks and turna switch ON precisely at this instance. It should only detect the desired low frequenciesand only detect global peaks6. Fig. 4.5 shows the piezo voltage and the desired squareswitch control signal from the peak detection.

p n p p n pPiezo Peak Detector

Figure 4.5: Peak detector square output signal for control of SSHI switching. The peakdetector switches at the voltage peaks (maxima or minima) of the piezo element.

To sense the maximum and minimum peaks, the piezo voltage can be differentiated. When-ever the differentiated signal crosses zero, there is a peak.

The peak detection circuit will be dependent on the vibration frequency and the operationbandwidth will be limited as seen later in this section. The peak detection circuit is de-sired to draw very little current to not dampen the piezo voltage, and to limit the energyflow to the peak detection circuit as this energy will not be harvested. The piezo currentis in the range of microamperes so the input impedance of the peak detection should be 1 MΩ.

4.5.1 Simple Differentiator

A simple method of differentiating the piezo voltage is using a capacitor and a resistor asin [24] (also shown in fig. 3.7). The current through the capacitor is proportional to thederivative of the voltage, so this is a simple way to make a differentiated signal.

Figure 4.6: Simple differentiator.

6A global peak means when a signal at one frequency has a large amplitude where it might also haveother components with smaller amplitude and higher frequency local peaks.

39


Vdiff = iR ·R = C · dVdt·R (4.23)

This is however with a low gain, as seen in next section, so another solution is proposed.

p n p p n p p n p

Figure 4.7: Peak detection circuit consisting of differentiator based on opamp and aSchmitt Trigger comparator. The waveforms from each part is shown and p and n denotespositive and negative peak.

4.5.2 Differentator based on opamp

The differentiated signal can be made with an opamp coupled as an inverting differentiatoras seen in fig. 4.7. This will provide a larger gain than the simple differentiator and as theinput signals are low, due to the desired high input impedance, the gain will be importantfor the control.

The differentiator is designed based on a regular opamp differentiator with an input ca-pacitor, Cin, and feedback resistor, Rfb. Without Rin and Cfb the differentiator would besusceptible to higher frequencies as the gain at higher frequencies would be high. Thusthe differentiator is modified with Rin and Cfb which introduces an integrating behaviorat higher frequencies dampening higher frequencies and increases the stability.

To limit the high frequency gain, Rin, placed in series with Cin, introduces a high fre-quency limiting impedance as the input impedance of the differentiator without Rin wouldbe Zin = 1

sCin, which would be very low at high frequencies and thus susceptible to insta-

bility. Rin and Cfb introduces a pole in the frequency response at f = 1RinCfb

.

The input capacitor and feedback resistor sets the lower bandwidth limit, fl. The ratioof the feedback resistance and the input resistance will set the gain shelve in the band fland fh.

40

4.5. Peak Detection

fl =1

Cin ·Rfb(4.24)

fh =1

Cfb ·Rin(4.25)

gain =−RfbRin

(4.26)

The transfer function of the modified differentiator seen in fig. 4.7 is derived by equatingthe current running through the input, via Rin and Cin, and through the feedback, viaRfb and Cfb.

iin =Vin

Rin + 1sCin

(4.27)

ifb =Vo

Rfb ‖ 1sCin

(4.28)

iin + ifb = 0 (4.29)Vin

Rin + 1sCin

= −Vo(

1Rfb

+ sCin

)(4.30)

VoVin

=−1(

Rin + 1sCin

)(1Rfb

+ sCin

) (4.31)

This transfer function results in the bode plot seen in fig. 4.8 with component valuesfrom table 4.2. Here it is seen that the phase shift is −90 at frequencies < fl. So thedifferentiating behaviour is only within a bandwidth of 0 and up to ∼ 10 Hz dependingon how low the minimum required gain is and what phase shift tolerance there is. Thesefactors will be evaluated later in the project.

Table 4.2: Differentiator component values

Function Value

Cin 1 nFRfb 10 MΩfl 1 kHz

Cfb 1 pFRin 2 MΩfh 450 kHz

41


−60

−40

−20

0

20M

agni

tude

(dB

)

100

101

102

103

104

105

90

135

180

225

270

Pha

se (

deg)

Differentiator bode plot

Frequency (Hz)

Opamp differentiatorPassive differentiator

Figure 4.8: Bode plot of transfer function for modified differentiator (eq. 4.31).

4.5.3 Comparator

To produce the square wave control signal for the MOSFETs, a comparator is needed.In order not to be sensitive to higher frequency signals, hysteresis is added as a SchmittTrigger. This can be achieved with the comparator seen in fig: 4.7. Here the resistorsR1 and R2 creates a voltage divided reference with the below thresholds, where V+ is thepositive supply voltage and V− is the negative supply voltage for the comparator:

Vl = V− ·R1

R1 +R2(4.32)

Vh = V+ ·R1

R1 +R2(4.33)

To keep the power consumption as low as possible high impedance resistors are used.

Later in sec. 4.6 it is shown that the hysteresis-threshold-to-signal ratio in the compara-tor should be < 0.1 in order not to create a too long time delay in the output square signal.

A ratio of 0.05 is achieved with R1 = 2 MΩ and R2 = 40 MΩ. The resistor values arechosen to be this large to minimize the current and avoid large losses as seen later insection 5.3.

4.6 Time Delay

The vibration frequencies in this project are very low and the time periods are long. Al-though time delays through the control circuit might influence the circuit performanceand this is examined in this section.

42

4.6. Time Delay

In [28] it is shown that the output power of the SSHI depend on the switching precision.If the inductor is switched ON before the optimum timing, e.q. the piezo voltage peak,it has the effect of creating a voltage inversion less than the maximum possible and withthe same result when switching after the optimum time. The deviation from the optimumswitching time can be denoted both as a phase shift, σ, and a time delay, τ . See fig. 4.9.

Figure 4.9: SSHI piezo voltage and piezo displacement [29] with delay.

In [28] it is shown that the output power is decreased to ∼ 80 %7, when the phase shift /time delay ratio, d, is larger than 0.18.

d =τ

T=

σ

360(4.34)

The time period of a 2 Hz signal is T = 0.5 s.

td = 0.1 · 0.5 s = 0.05 s (4.35)σ = 0.1 · 360 = 36 (4.36)

This means that the phase shift is desired to be σ < 36 and the time delay td < 50 ms.The components that contribute to a delay is the peak detection control consisting of thedifferentiator, comparator and switches. Here the time delays are, as seen in the nextchapter, though all in the order of nanoseconds to microseconds, which will thus not be aproblem. The differentiator phase shift might not be precise −90 as desired, but as the tol-erable margin is within ±36 it should be acceptable with the bode plot in fig. 4.8 in mind.

The comparator hysteresis thresholds will also introduce a time delay. If the switchingthreshold is 10mV with a 1V signal, giving a ratio of 0.01 it will introduce a time delayof 10 mV

1 V · 0.5 s = 5 ms. If the hysteresis threshold to signal ratio was > 0.1, it would makea large contribution to the time delay and decrease the power output.

Later, in sec. 6.3, a test of the inversion factor dependence on the peak detection timingis shown.

7Value also depending on the mechanical coupling8These results are although obtained around 100 Hz, but the theory should apply for 2 Hz as well.

43


4.7 Analysis Summary

In this chapter it was shown how the Synchronized Switch Harvesting on Inductor topologyoperates, key components were discussed and theoretical expressions for each componentspower loss where stated. A peak detection circuit was proposed and the time delay limit,td, to achieve at least 80 % maximum power output was found.

td > 0.05 s

The next chapter will describe the implemented prototype and it will in chapter 6 be seenif the prototype operates as expected.

44

5

Prototype

This chapter describes the implemented prototype based on the SSHI topology. Both theP-SSHI and the S-SSHI are implemented. It will be stated which components the prototypeconsists of and how it operates. The losses in the circuit are estimated and in the end ofthe chapter the expected performance of the circuit is presented.

Based on the theoretical comparison in sec. 3.2.5 it is chosen to implement a prototype ofthe SSHI topology and test the topology potential in practice as it shows great theoreticalpotential if a high inversion factor, γ, can be achieved.

With inspiration from the parallel SSHI circuit in fig. 3.7 the prototype is designed withthe peak detection circuit described in sec. 4.5. The full schematic can be seen in fig.5.1 (large version in appendix I along with the Series-SSHI schematic and a photo of theprototype). The schematic includes the inductor, MOSFETs, blocking diodes, peak detec-tion control circuit, consisting of the differentiator and comparator and an output rectifier.

Figure 5.1: P-SSHI Prototype Schematic

The prototype is used in both parallel and series configuration. The difference betweenthese is the placement of the load. The control circuit is for simplicity chosen to be ex-ternally supplied. It could be supplied by the piezo voltage with a half wave rectifier, asdescribed later in fig. 5.2, but to be able to compare the performance with the theoretical

45

5. Prototype

expression presented in sec. 3.2, it is chosen to be externally supplied. In the end theexpected power consumption of the external supplies are subtracted from the results toget a clear image of the total power output.

5.1 Components

The specific component choices are discussed here. The main challenge is to find activecomponents with very small current consumption for the control circuit. A table withpossible choices from different IC manufacturers can be seen in appendix H.

5.1.1 MOSFETs

The MOSFETs chosen can have influence on the circuit performance. As explained inthe analysis in chapter 4, it needs to have a small output capacitance to limit resonancebetween the MOSFETs and the inductor. The gate charge is desired to be low to drawas small as possible current from the output of the comparator as this is limited by thecomparator power supply. A third parameter is the ON resistance that is also desired tobe low as it affects the circuit Q-factor.

The time delay in the MOSFET might also have an influence on the voltage inversion asexplained in sec. 4.6. And the saturation voltage needs to be low, for the MOSFET notto be in the active region when inverting the piezo voltage.

The prototype has been implemented with two types of MOSFETs. The IRF7307, whichis a package containing both an NMOS and PMOS, has a low ON resistance, but largecapacitance. The small signal MOSFETs FDV301N/FDV304P have a low capacitancebut higher ON resistance. Their properties can be seen in table 5.11. In the prototypetest results, in the next chapter, it will be evaluated whether the ON resistance and theoutput capacitance are factors of importance for the total circuit performance.

Table 5.1: MOSFETs used in prototype

Partnumber VDSS max [V] RDS(ON) [Ω] Coss [pF] QG [nC] Max delay [ns]

IRF7307 NMOS 20 0.07 310 20 51 (tf )IRF7307 PMOS -20 0.14 380 22 51 (tD(OFF))FDV301N 25 5 6 0.40 15 (tr)FDV304P -25 1.5 34 1.1 55 (tD(OFF))

5.1.2 Differentiator

The requirements for the differentiating opamp described in sec. 4.5.2 are low. It doesnot need to be fast, as it only has to differentiate a signal of a few Hz. The main param-eter to choose from is the power consumption along with the supply voltage range. The

1In the parameter max delays only the largest of the MOSFET turn ON delay, tD(ON), turn OFF,tD(OFF), rise time, tr and fall time, tf , is shown. RDS(ON) is at VGS = 2.7 V

46

5.1. Components

prototype will be implemented with external supplies, but on a later stage it should besupplied by the piezo voltage, as described in appendix J. The opamp should be able towithstand the piezo output voltage and on the other hand be able to operate from lowvoltages. Although as seen later in sec. 5.5, the feasibility of the circuit is limited at verylow voltages (< 5 V), as the energy level here is very small. In appendix H.2 a list ofopamps is shown. The LT6003 is chosen for implementation in the prototype.

Table 5.2: Opamp used in prototype

Part number LT6003

Supply voltage range [V] 1.6-18 VSupply current [µA] 1Input bias [pA] 90

The feedback and the input resistor and capacitor are described in table 4.2 in sec. 4.5.2.

The peak detection will be exposed to the high frequency components across L, whenswitching, but these are dampened in the differentiator feedback.

5.1.3 Comparator

The comparator drives the MOSFETs with a square wave signal. To provide the squarewave signal from rail to rail, the comparator needs to have a push-pull output. In appendixH.3 a list of comparators is shown. The LMC7215 is implemented. It is a low power pushpull comparator and some of its key specifications are listed in table 5.32 .

Table 5.3: Comparator used in prototype

Partnumber LMV7215

Supply voltage range 2-8 VSupply current 0.7 µAInput offset 8 mVRise time 1 µsFall time 0.4 µsPropagation delay 24 µs

The LMV7215 has an input offset voltage of VOS = 8 mV. In order not to switch ON andOFF due to high frequency signals, the comparator is implemented as a Schmitt Trigger,i.e. with the positive feedback described in sec. 4.5.3. This will introduce hysteresisand make the output voltage switch fast. The resistance values are R1 = 2 MΩ andR2 = 40 MΩ giving a hysteresis window of 0.05 · V+ to 0.05 · V−.

2The high-to-low propagation delay is equal to the low-to-high in this comparator.

47

5. Prototype

5.1.4 Diodes

The diodes used in the prototype are small signal silicon diodes 1N4148 which have lowleakage current and a forward voltage drop of 0.7 V. A schottky diode could provide lessvoltage drop, but with higher leakage current which would short the piezo voltage.

5.1.5 Inductor

An off-the-shelf inductor of 180 mH is used in the prototype. The impedance-phase mea-surement of it can be seen in appendix K. A large inductance is used to get a low oscillationcurrent. When switching occurs the inversion time will be long (compared to a smallerinductor) as the resonance frequency with the piezoelectric capacitance will be lower andthus the requirements to the MOSFET rise/fall time is low.

5.2 Bill of Materials

The bill of materials for the prototype is seen in table 5.4.

Table 5.4: Bill of Materials

Inductor 180 mH

MOSFET IRF7307 NMOS+PMOS

Diodes 1N4148

Output capacitor 10 µF

Control

Opamp LT6003

Cin 1 nFRfb 10 MΩCfb 1 pFRin 2 MΩ

Comparator LMV7215

R1 2 MΩR2 40 MΩ

5.3 Control Circuit Loss

This section describes estimates of power losses within the control circuit. This containsthe active component power consumption and the power lost in their surrounding feedbackcomponents.

The energy lost in the supply of the peak detection components is not accounted for inthe theoretical output power expressions mentioned earlier. Neither are the power foractivating the MOSFETs or the output capacitance resonance with the inductor. These3 factors are dealt with here below.

48

5.3. Control Circuit Loss

It is important to note that the prototype is externally supplied and thus are the opampand comparator power consumption not seen in the results. These has to be subtracted toget the real net result of how much power is increased with the SSHI topology. In the feed-back of the opamp and comparator the energy is also supplied from the external suppliesexcept the input on the differentiating opamp. The input impedance of the differentiatordetermines how much current will be drawn from the piezoelectric element. The energydissipated in the input impedance will not be harvested and therefore lost.

5.3.1 Opamp and Comparator Power Supply

The opamp used in the prototype has a current consumption of IS−opa = 1 µA and thecomparator IS−com = 0.7 µA.

Fig. 5.2 shows a half-wave rectifier solution that could be used to supply the opamp andcomparator. The supply voltage in the prototype is external, but if it were with internalsupply, with a half-wave rectifier as explained in appendix J, the supply voltage would bethe piezoelectric voltage subtracted the half-wave diode forward voltage Vs = ±Vp − VD.Therefore the calculations are made with Vs = 7.6 V − 0.7 V = 6.9 V .

Thus at a supply voltage of 6.9 V the active components consume, PICsup:

PICsup = V I = (1 µA+ 0.7 µA) · 6.9 V = 11.7 µW (5.1)

The assumed supply voltage and current are only rough estimates and can vary signifi-cantly. The calculations are made to be able to give an estimated power loss in the circuit.

Figure 5.2: Solution to make the circuit self-supplying (not implemented). Half-waverectifiers for supplying the active components from the piezo voltage. The piezo voltageis connected to the AC input IN and the component positive and negative supply pin toV+ and V−.

In appendix J a calculation example of the capacitor size for the half-wave rectifier is seen.

5.3.2 Differentiator Feedback

The differentiator is seen in fig. 4.7. The current running in the differentiator feedbackcomponents are very small due to the high input impedance at 2 Hz, which is:

Zin = ZRin + ZCin (5.2)

49

5. Prototype

The impedance of the capacitor is a lot higher than the resistor at 2 Hz, ZRin << ZCin,and ZCin = 1

j2π·2 Hz·1 nF so the AC current magnitude is calculated as

|ZCin| ≈ 80 MΩ (5.3)

Iin =Vp|ZCin|

= 0.1 µA (5.4)

So the resulting current amplitude at an input voltage amplitude of 8 V will be in theorder of Iin = 0.1 µA. The same current will be running in the feedback impedance Rfb3.

The resulting power loss in the differentiator resistors are

Pdiff−in = I2rmsRin =

(0.1 µA√

2

)2

· (2 MΩ) = 10 nW (5.5)

Pdiff−fb = I2rmsRfb =

(0.1 µA√

2

)2

· (10 MΩ) = 50 nW (5.6)

Even though the energies are small and will not count much in the total consumption itis noted that Pdiff−in is drawn from the piezo energy and Pdiff−fb is drawn from theexternal supplies.

Later in chapter 6.4 in the test of the prototype the differentiator opamp and the compara-tor are externally supplied. Here it is important to note that the current drawn from thepiezo by the peak detection control is equal to the input current in the differentiator, Iin,defined by the input impedance. The current flowing from the output of the differentiatorto the comparator input is defined by the input impedance of the comparator and suppliedby the external supplies. These considerations are important when evaluating the poweroutput results and subtracting the power consumption of the external supplies.

5.3.3 Comparator Feedback

The comparator is seen in fig. 4.7. The voltage level seen on the input of the comparatoris defined by the differentiator gain. As seen in the bode plot in fig. 4.8, the gain at 2 Hz is−20dB ∼ 1

104. With an input voltage amplitude of 8 V, the differentiator will output 0.8 V.

The current amplitude in the comparator feedback components are defined by input re-sistor R1 = 2 MΩ and will be:

Iin =0.8 V2 MΩ

= 0.4 µA (5.7)

The same current will be running in the feedback impedance R2 = 40 MΩ. The resultingpower loss in the differentiator components are:

Pcomp =(

1.6 µA√2

)2

· (2 MΩ + 40 MΩ) (5.8)

Pcomp = 3.36 µW (5.9)

3At 2 Hz the impedance of the feedback capacitor Cfb = 1 pF will be magnitudes larger than theimpedance of Rfb and will thus not have an influence at this frequency

4∼ −20dB = 20 log VinVout

→ Vout = 110Vin

50

5.4. Loss Summary

5.3.4 MOSFET gate charge

The total gate charge of the implemented MOSFETs, IRF7307, is Qg = 20 nC. The squarewave signal coming from the comparator is rail to rail, meaning ±6.9 V. An estimate ofthe energy lost when charging the gate is seen in eq. (5.11)

E =12QV (5.10)

EG =12· 20 nC · 6.9 V = 69 nJ (5.11)

At a 2 Hz frequency the power lost in the gate is:

Pgate =2 · EGT

=2 · 69 nJ

0.5 s= 276 nW (5.12)

5.4 Loss Summary

The losses/consumption described above will not be reflected by the prototype measure-ment results, as they are externally supplied. For an overview these are illustrated in thepie chart shown in fig. 5.3.

76%

< 1%2%

22%

External Power Loss

IC SupplyOpamp feedbackMosfet gateComparator feedback

Figure 5.3: Power loss in the peak detection control in the SSHI circuit. The total loss is15.4 µW .

It is seen that the consumption of the two ICs is the main consumer. The total controlcircuit loss, Pcontrol, is used to setup the expected net power increase of the SSHI circuit,with this power loss subtracted.

The total loss, which is not taken into account in the expression for the maximum poweroutput of the P-SSHI and S-SSHI ( eq. (3.16) and eq. (3.19)), can be summed up to be:

Pcontrol = PICsup + Pdiff−fb + Pcomp + Pgate (5.13)

In the prototype calculation example this is Pcontrol = 15.4 µW . This value will later showto be critical for the prototype performance at the tested vibration level.

51

5. Prototype

5.5 Synchronized Switch Harvesting on InductorPrototype Performance Evaluation

At a given energy input level the power consumption of the control circuit and the switchinglosses within the SSHI circuit becomes larger than the energy increase the SSHI provides.This describes the boundary of when this SSHI circuit becomes feasible.

To give an estimate of where that boundary lies fig. 5.4 illustrates the maximum poweroutput increase of the Parallel-SSHI topology subtracted its losses, eq. (5.14), and thepower output with the standard full bridge, eq. (3.6), as a function of the vibration fre-quency, f, and the inversion factor, γ. The dark areas are negative, showing that here willthe P-SSHI circuit will give less power than the standard full bridge5.

It is seen that at a frequency of 2 Hz the inversion factor has to be γ > 0.5 (the powerincrease is positive, aka. the graph color is white at γ > 0.5).

PSSHI−net−out = PSSHI(max)− Pcontrol − PSTD(max) (5.14)

0.10.3

0.50.7

0.9

12

34

56

78

9

−1

0

1

2

3

4

5

x 10−4

γ

Max net output power increase by P−SSHI in comparison to STD

Frequency [Hz]

Pow

er in

crea

se [W

]

Figure 5.4: Maximum power output increase of the P-SSHI topology subtracted its lossesand the energy harvested with the standard full bridge. The dark parts are negative,meaning that here the SSHI does not give a net power increase due to the consumption ofthe control circuit.

The same plot for S-SSHI is seen in fig. 5.5, where it is noted that at 2 Hz γ > 0.7.

5The same graph could have been made with the power increase as a function of γ and the open circuitpiezo voltage, Vp, instead of the frequency, f , and similar results would have been seen as both f and Vprepresents an input energy level.

52

5.5. Synchronized Switch Harvesting on Inductor Prototype Performance Evaluation

0.10.3

0.50.7

0.9

12

34

56

78

9

−1

0

1

2

3

4

5

x 10−4

γ

Max net output power increase by S−SSHI in comparison to STD

Frequency [Hz]

Pow

er in

crea

se [W

]

Figure 5.5: Maximum power output increase of the S-SSHI topology subtracted its lossesand the energy harvested with the standard full bridge. The dark parts are negative,meaning that here does the SSHI not give a net power increase due to the consumption ofthe control circuit.

5.5.1 Time Delay

The total expected time delay in the control circuit is the sum of the each parts delay.The differentiating opamp time delay is negligible as it is working around 2 Hz. Thecomparator has an internal delay and an external delay due to the Schmitt Trigger. TheMOSFET will also contribute with a time delay.

Instead of switching at a 0 V output of the differentiator (corresponding to a piezo voltagepeak), the comparator will first switch a bit later, when the differentiated signal crossesthe threshold set by the Schmitt Trigger. The Schmitt trigger has the thresholds ofVh = 0.05 · V+ and Vl = 0.05 · V− with the feedback resistance values stated in sec. 4.5.3.A supply voltage of ±3 V is assumed6: V+ = −V− = 3 V , and then the comparator willtrigger at ±0.15 V. At 2 Hz this corresponds to a time delay calculated as:

v(t) = V sinωt (5.15)0.15V = 1V · sin (2 · π · 2 Hz · t) (5.16)

→ t =12· arcsin (0.05 V)

π · 2 Hz= 0.012 s (5.17)

The control circuit time delays are listed in table 5.5. It can be seen that the SchmittTrigger introduced time delay is magnitudes larger than the other delays, but is stillbelow the time delay boundary of 50 ms discussed in sec. 4.6. The MOSFET time delayis negligible7.

6±3 V supply voltage is used in the test in the next chapter.7Not all MOSFET times are listed as they are insignificant.

53

5. Prototype

Table 5.5: Time delay in the control circuit

Part Delay

Schmitt trigger 12 msComparator propagation delay 24 µsMOSFET 51 ns

5.5.2 Prototype Evaluation Summary

The potential for both the Parallel-SSHI and the Series-SSHI prototype was estimated,and based on the calculations on peak detection control circuit, requirements for the circuitinversion factor was found. The P-SSHI is expected to be feasible and produce a largerpower output than STD if its inversion factor is:

P − SSHI : γ > 0.5 (5.18)

and the S-SSHI is expected to produce a larger power output than STD if:

S − SSHI : γ > 0.7 (5.19)

Here the estimated time delay of 12 ms, is however not included and might show influencein the end result, which will be determined in the next chapter.

54

6

Results

This chapter will describe the measurements of the implemented circuit tested with theWindSpear. The circuit can be configured both as Series-SSHI and Parallel-SSHI just byplacing the inductor in series or parallel with the piezoelectric element. The prototypeperformance is illustrated and compared with the expectations. The power consumption ofthe control circuit is estimated and the output power increase results are evaluated, statingwhich parts of the circuit could be optimized.

6.1 WindSpear Test

The prototype described in chapter 5 is tested with the WindSpear described in sec. 1.2.The spear is mounted upside down, hanging from a fixture and vibrated by a 1.8 Hz motioncreated by a DC engine, simulating a light wind breeze (photos of the hanging WindSpearcan be seen in appendix L).

Fig. 6.1 shows a measurement of the open circuit piezo voltage. This is estimated toVp = 7.6 V. The waveform is uneven due to the mechanical setup non-idealities.

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5−8

−6

−4

−2

0

2

4

6

8

Time [s]

Volta

ge [V

]

Protype TEST2 − Open Circuit Piezo VoltagePrototype TEST

Figure 6.1: WindSpear open circuit piezo voltage.

55

6. Results

6.1.1 Parallel-SSHI

The piezo voltage of the P-SSHI circuit in operation is seen in fig. 6.2. If it is assumedthat the voltage peak (optimum switch time) is just before the voltage starts to decrease,it is seen that the voltage inversion happens a short while after. It is estimated that thevibration period is T = 0.54 s ∼ f = 1.8 Hz and the inversion happens t2 − t1 = 0.07 safter the peak. Referring to the analysis of the delay influence in section 4.6, this timedelay is above the limit of 0.05 s, and might cause less power output.

The inversion factor is from fig. 6.2 estimated to be γ = −V g+V g− = − 1.8 V

−3.8 V = 0.47. Thiscould be higher and according to the expectations shown in the 3D graph in fig. 5.4 thisis just at the boundary of when the circuit increases the total output power.

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5−6

−4

−2

0

2

4

6

Time [s]

Volta

ge [V

]

Prototype TEST2 − P−SSHI Piezo Voltage

t1 t2

Vg-

Vg+

Figure 6.2: P-SSHI piezo voltage with an output load of R = 2.7 MΩ. The voltage peakis at t1 and the actual inversion happens at t2. The inversion factor is estimated to beγ = −V g+

V g− = 0.47.

Table 6.1 shows the main parameters of the P-SSHI circuit test.

Table 6.1: P-SSHI Test Parameters

MOSFETs IRF7307 (Coss = 310 pF)Inductor L = 180 mHLoad R = 2.7 MΩ

Inversion factor γ = 0.47Time delay td = 5 ms

Inversion

In fig. 6.3 the inductor inversion voltage is seen, where the PMOS turns ON and initiatesthe inversion.

56

6.1. WindSpear Test

−4 −3 −2 −1 0 1 2 3 4 5 6

x 10−4

−6

−4

−2

0

2

4

6

Time [s]

Indu

ctor

Vol

tage

[V]

WindSpear TEST − Inductor inversion voltage PMOS

Figure 6.3: P-SSHI inductor inversion voltage when PMOS turns ON. The load connectedis R=2.7 MΩ

It is seen that the MOSFET output capacitance, Coss, resonates with large amplitudewith L. The corresponding loss will be calculated in sec. 6.2. The same voltage inversionwhen the NMOS is turned ON is seen in appendix L.1.

6.1.2 Series-SSHI

The piezo voltage for the S-SSHI circuit test is seen in fig. 6.4. The test parameters areseen in table 6.2. The inversion factor is estimated to be γ = −−1.5 V

7 V = 0.21. This issignificantly lower than the P-SSHI inversion factor. The main reason is found to be theinductor series resistance. When the S-SSHI circuit is switching the inductor in series withthe piezo capacitor, power is delivered to the load. The rest of the time, the piezoelectricelement is in open circuit. This means that every time the power flows to the load, it hasto go through the inductor, and thus through the inductor series resistance, where poweris lost.

Table 6.2: S-SSHI Test Parameters

MOSFETs IRF7307 (Coss = 310 pF)Inductor L = 180 mHLoad R = 1.6 MΩ

Inversion factor γ = 0.21Time delay td = 5 ms

57

6. Results

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5−10

−5

0

5

10

Time [s]

Vol

tage

[V]

WindSpear TEST − S−SSHI Piezo Voltage

PiezoComparator

Figure 6.4: S-SSHI piezo voltage and comparator output with load R = 1.6 MΩ.

Inversion

In fig. 6.5 the inductor inversion voltage when NMOS turns ON is seen. To show theresonance dependency on the MOSFET output capacitance, the same voltage inversionwhen the PMOS is turned ON is seen in appendix L.2, where a MOSFET with smalleroutput capacitance (FDV304P) is used.

0 0.2 0.4 0.6 0.8 1 1.2

x 10−3

−6

−4

−2

0

2

4

6

Time [s]

Indu

ctor

Vol

tage

[V]

WindSpear TEST − Inductor inversion voltage NMOS

Figure 6.5: S-SSHI inductor inversion voltage when PMOS turns ON.

58

6.2. RLC Loss

6.2 RLC Loss

The RLC loss in the oscillating circuit consisting of the piezo capacitance, the induc-tor, the conducting diode and the conducting MOSFET is calculated to determine whichfactors influence the inversion factor obtained in the test. The theoretical expressionsfor the RLC losses derived in sec. 4.4 are used. The results from the prototype test ofthe P-SSHI circuit are used to evaluate which components makes the largest contributions.

The resonance frequency and time period is

f =1

2π√

180 mH · 42 nF≈ 1.83 kHz (6.1)

T =1f≈ 546 µs (6.2)

The P-SSHI circuit has γ = 0.47, the piezo voltage is Vp = 7.6 V and the diode forwardvoltage drop is VD = 0.7 V. This leads to a maximum inductor voltage of VL = 11.3 V byusing eq. (4.9). Eq. (4.13) is then used to calculate the oscillation RMS current, IRMS :

IRMS =

√VL

2CpL

=

√(11.3 V)2 · 42 nF

180 mH≈ 5.6 mA (6.3)

This current runs through each part in the oscillation path. With the current known, thelosses can be calculated. The losses are seen in table 6.3 together with the loss from theoscillation between the inductor and the output capacitance of the MOSFET.

6.2.1 Inductor Oscillation with MOSFET Output Capacitance

The loss in the oscillations between the inductor and the output capacitance of the MOS-FETs, Coss, will be estimated.

As seen in fig. 6.3 and fig. 6.5, the voltage amplitude of the resonance after inversionis around 2 V in both the P-SSHI and S-SSHI circuit. The resonance frequency seencorrespond to the resonance between L and Coss which is f = 1

2π√LC

= 12π√

180 mH·300 pF∼

30 kHz. The period is T = 1/f = 34 µs. This approximately correspond to the inductoraverage current in equation 6.4.

ICoss =1L· V√

2· T

2=

1180 mH

· 2 V√2· 34 µs

2= 0.13 mA (6.4)

The energy lost in this oscillation, ECoss, is then estimated in eq. (6.5) as it correspondsto the stored energy in the inductor within the first period of the oscillation.

ECoss = 0.5 · L · I2Coss = 0.5 · 180 mH · (0.13 mA)2 = 1.5 nJ (6.5)

This energy is present each time there is a switching event, e.g. 2 times per period. Whenthe vibration frequency is 2 Hz this is the 2 times per 0.5 s. Thus the power loss:

Ploss−Coss =2 · EoscT

=2 · 1.5 nJ

0.5 s= 6 nW (6.6)

59

6. Results

Table 6.3: RLC Losses

Part Power Loss [µW ]

Inductor 14.6Diode 3.81MOSFET RDS 0.004MOSFET Coss 0.006

6.2.2 RLC Loss Summary

Fig. 6.6 illustrates a comparison of the estimated losses of the different components in theoscillation path. It can be concluded that the diode has a large contribution as well as theinductor series resistance. It is also concluded that the MOSFET losses are in this casenegligible.

The total power lost in the oscillation path is estimated to be 18.42 µW. In a futureprototype the inductor series resistance should be lowered1 and it can be investigated howto reduce the diode loss by replacing it with a synchronous rectifier or similar circuit.

21%

< 1%< 1%

79%

RLC Components Power Loss Comparison

DiodeMOSFET C

ossMosfet R

DS

Inductor ESR

Figure 6.6: Comparison of the component losses in the RLC oscillation path. The MOS-FET RDS and Coss are both < 1 % and are thus hard to see.

1In this case it showed to be 500 Ω so this is easily reduced with another inductor.

60

6.3. Peak Detection Test

6.3 Peak Detection Test

To show the effect of switching the SSHI inductor ON before and after the optimal in-stance, a test was made where the piezoelectric element was vibrated at 2 Hz and anexternal square wave control signal controlled the MOSFETs slightly off-set at 2 Hz. TheP-SSHI circuit used was loaded with a resistive load.

This test shows in fig. 6.7 the inversion dependence of when the MOSFETs are switchedON. The inversion factor in the test is low, but the purpose is to show its dependence onthe peak detection. It shows the effect of switching ON the inductor before the capacitorcurrent has reached zero, i.e. there is still current flowing into the piezo capacitor chargingthe voltage again. This creates the small voltage bumps seen after the switching. Whenthe switching occurs at the moment where the current into the capacitor is zero, i.e. theoptimal time, the voltage bump is not seen. There are no bumps as well, when the piezois switched after the optimal time late but the inversion is reduced.

Figure 6.7: Piezo generator vibrating at 2 Hz and SSHI circuit with 2 Hz external controlsignal slightly off sync. Shows dependence on when the switching is done and that it needsto be a bit after the voltage peak due to reduced phase shift when resistive loading of thepiezo. Red arrow indicates voltage bump after switching directly on the voltage peak.The missing time/voltage scale is 250 ms/div and 2 V/div and the figure is two mergedoscilloscope screenshots.

Voltage bumps seen on the graph corresponds to the piezo capacitance getting chargedagain by the current left in the source but only up until a diode forward voltage dropdue to the blocking diode, Dn or Dp. The explanation for why the optimum switchinginstance in this test is after the voltage peak can be explained by the resistive load. Whenthe piezoelectric element is in open circuit it can be seen as only having a capacitive loadconsisting of its output capacitance. Here the phase shift between the current and thevoltage is −90. When applying a resistive load, this phase shift is decreased. That re-sults in shifting the optimum switching instance after the voltage peak, as shown in fig. 6.7.

The main challenge with the peak detection circuit used in the prototype is the balancebetween the phase shift and the gain. As seen in the frequency response of the differ-

61

6. Results

entiator in the bode plot in fig 4.8, the gain is -20 dB at 2 Hz. Adjusting the feedbackcomponent values can increase the gain but will decrease the phase shift. The optimalpoint for switching the inductor ON, is when the current in the piezo capacitor is zero.This happens when the piezoelectric element reaches its maximum displacement. Whenit is loaded with a resistive load, the phase shift between the current and the voltage willnot be exactly 90, but less. The piezoelectric generator does not only see its internalcapacitance as it does in open circuit, but the external resistive load makes the phaseshift decrease. This will only be an issue with the parallel SSHI circuit as the load isconnected to the piezoelectric element all the time. In the series-SSHI, the load is onlyintermediately connected, when switching, and the rest of the time the piezoelectric ele-ment is left in open circuit and the phase shift will thus not be affected by the resistive load.

For optimal control one would need a zero current detector. This is although not feasi-ble. The optimum switching instance shift in P-SSHI can instead be solved by using asmall secondary piezoelectric element only for the control. This will not be loaded andthe thus the voltage peak will precisely correspond to the extremum displacement, whichcorrespond to the instance with zero piezo capacitor current [38].

6.4 Power Results

The measurement results of the prototype output power are seen in fig. 6.8. Here theP-SSHI and the S-SSHI prototype results are shown together with measurements of astandard full bridge with 4 diodes (1N4148) and Cout = 10 µF . It is seen that the P-SSHIcircuit does increase the power output of the piezoelectric element in comparison to STDby up to a factor of 2. S-SSHI however does not and the reason for this is mainly the lowinversion factor.

6.4.1 Theory Evaluation

The theoretical power output expressions defined in sec. 3.2 are used with the parametersin table 6.4 to be compared with the real measurements.

Table 6.4: Theory parameters

Cp 42 nFVp 7.6 Vγs 0.21γp 0.47

Passive Circuits

To evaluate how well the theoretical expressions for the simple passive circuits match realmeasurements, the WindSpear test was also conducted with the following:

• Single resistive load, R

• Standard full bridge, STD

• Voltage doubler, VD

62

6.4. Power Results

105

106

107

0

0.2

0.4

0.6

0.8

1

1.2x 10

−5

Load [Ω]

Pow

er [W

]

WindSpear Test − Prototype

STDP−SSHI prototypeS−SSHI prototype

Figure 6.8: Measurement results of the Parallel-SSHI and Series-SSHI prototype alongwith the standard full bridge, STD.

These results are seen in fig. 6.9 along with the corresponding theoretical expected poweroutput. It is seen that the theory corresponds with the measurements, keeping in mindthat the theory applied is ideal has not included the loss through the diodes in the circuits.This explains that the measured VD output is higher than the measured STD output, dueto fewer diodes in the voltage doubler circuit.

The load sweep was done up to 10 MΩ. It is noted that, as in sec. 2.5, the measurementaccuracy was ∼ ±0.2 V due to the long time constants.

Synchronized Switch Harvesting on Inductor

Fig. 6.10 shows the results from the prototype P-SSHI circuit and S-SSHI circuit. Theresults do not fully comply with the theoretical expected power output.

The P-SSHI results look more like the expected theoretical power output at loads up to< 2 MΩ but hereafter the output is less than expected. The main reason for this is con-sidered to be the time delay in the control circuit. As previously described, the time delayof 7 ms seen in the piezo voltage of the P-SSHI circuit, can according to the time delaycalculations in sec. 4.6 be responsible for a ∼ 10-20 % power decrease.

It is noted that the theory applied is for a simplified system in one dimension, which is anapproximation of the actual real setup and mechanical parameters unaccounted for mighthave influence. Measurement inaccuracies, mainly due to the large time constants, mightalso have an influence.

63

6. Results

105

106

107

108

0

0.2

0.4

0.6

0.8

1

1.2x 10

−5

Load [Ω]

Pow

er [W

]

WindSpear Test − Theory Evaluation

RR theorySTDSTD theoryVDVD theory

Figure 6.9: Test - Load sweep when harvesting energy from WindSpear with simple topolo-gies for evaluating the theory in use.

105

106

107

108

0

0.5

1

1.5

2

x 10−5

Load [Ω]

Pow

er [W

]

WindSpear Test − Prototype

P−SSHI prototypeP−SSHI theoryS−SSHI prototypeS−SSHI theory

Figure 6.10: Prototype test results - Load sweep when harvesting energy from WindSpear.

64

6.4. Power Results

6.4.2 Total Power Output

In fig. 6.11 the expected total output power of the prototype circuits are plotted. Theapproximated power consumption of the control circuit is subtracted from the measure-ment results in fig. 6.10 to give a clear image of how the prototype SSHI compete withthe standard full bridge. The negative power increase means that the circuit is actuallyconsuming more energy than it outputs.

It is seen that the neither the P-SSHI prototype or the S-SSHI prototype can outperformthe standard full bridge at this energy level. The inversion coefficient is too low and thecontrol power consumption is too big.

105

106

107

108

−1.5

−1

−0.5

0

0.5

1

1.5x 10

−5

Load [Ω]

Pow

er [W

]

WindSpear Test − Prototype incl. control power loss

STDSTD theoryP−SSHI prototypeP−SSHI theoryS−SSHI prototypeS−SSHI theory

Figure 6.11: Prototype test load sweep. The output power subtracted the expected powerloss in the SSHI is plotted as a function of the load and compared with the standard fullbridge, STD.

The sensor node described in sec. 1.2 consumes 680 µJ in one cycle where it starts up,performs a sensor reading and transmits the data. Assuming an ideal case where no loadmatching circuit is needed between the rectifying circuit and the sensor node, and withideal storage, the required WindSpear energy harvest can be estimated. The tested outputpower level was ∼ 5 µW from the standard full bridge. Thus the time for harvesting energyfor one sensor node cycle is:

tharvest =680 µJ5 µW

= 136 s (6.7)

This time is naturally very optimistic and would in a real application be longer. An opti-mized SSHI circuit, with smaller losses and better inversion factor would aid in decreasingthis time.

65

6. Results

6.5 Prototype Evaluation

To evaluate the measurement results, the expected theoretical power output of the SSHIcircuits with the realized inversion factors from the test, are shown in fig. 6.12.

One has to keep in mind that the power levels are very low at 2 Hz. It was also notedin chapter 2, that the vibration acceleration, e.g. force applied, is dependent on the fre-quency squared. The WindSpear is operating around 2 Hz due to its structure. To give animpression of when the prototype in theory would produce more power than the standardbridge, fig. 6.12 shows a ”slice” of the 3D graph from fig. 5.4, only for f = 2 Hz.

1 3 5 7 9 11 13 15 17 19−2

0

2

4

6

8

10

12x 10

−5

Piezo Voltage [V]

Pow

er [W

]

Theoretical max output power incl. control consumption @ 2Hz

P−SSHI theoryS−SSHI theorySTD theory

Figure 6.12: Theoretical maximum output power of P-SSHI (γ = 0.47) and S-SSHI (γ =0.21) with the estimated control power consumption subtracted. Compared with themaximum output power of the standard full bridge for vibrations at 2 Hz as a function ofthe piezo open circuit voltage, Vp.

It is seen that the P-SSHI gives a net power output increase when operating with piezovoltages Vp > 7 V in comparison to STD, corresponding to an output power of 5 µW. TheS-SSHI inversion factor is very low and is thus not expected to deliver a power increase,before a piezo open circuit voltage Vp > 17 V, corresponding to an output power level of25 µW . At this level the P-SSHI circuit is expected to output 80 µW. This shows theimportance of the inversion factor.

The losses in the inductor and the diode was found to be the in order of the output power,and it is concluded that further optimization should focus on these parts. Especially theinductor loss should be simple to reduce by a lower series resistance inductor.

The theory applied did not fully match the measured results and the peak detection circuitwas found to prevent the prototype from operating as theoretically expected.

66

6.5. Prototype Evaluation

6.5.1 Peak Detection

The peak detection control circuit consumes too much power, and it has a too large timedelay.

The delay was not expected to be the measured 70 ms, as shown in the analysis in sec.5.5.1. Here the Schmitt Trigger was found to give a 12 ms delay. The control circuitwas expected to function with the differentiator feedback described in sec. 4.5.2. But thepractical gain showed to be too low and the control circuit did not output any square wavesignal signal at 2 Hz. Thus the differentiator feedback lower cutoff frequency was loweredto increase the gain around 2 Hz, but with the suffering of the phase shift, which endedup not being the wanted −90 leading to a non-optimal inversion of the piezo voltage.

It can be concluded that this control circuit is not capable of sensing the voltage peaks atthe low power level tested while maintaining a phase shift of −90. Additionally it con-sumes too much power. A set of requirements to an improved control circuit is thereforemade.

Improved Peak Detection Requirements

The active peak detection circuit used in the prototype was found not to be optimal forthe energy level tested. A circuit with lower power consumption and small time delay(−90 phase shift) is needed.

In the measurement results of the P-SSHI prototype without the control circuit powerconsumption subtracted, seen in fig. 6.8, it is seen that the difference between the STDand the P-SSHI maximum power output is ∼ 4 µW. Thus the power consumption of thecontrol should be less.

The time delay of 70 ms measured in the P-SSHI circuit on fig. 6.2 is considered as having abig influence on the inversion factor. The time delay should therefore be significantly lower.

The control circuit should have a high input impedance, not to draw power from the piezo-electric signal.

Requirements for a new control circuit is proposed:

• Power consumption: < 4 µW

• Time delay (phase shift) @ 2 Hz: <7 ms (< 5)

• Input impedance: > 5 MΩ

If the time delay is decreased, and thus the output power increased, there might be roomfor a larger power consumption than the proposed.

The envelope breaker [41] shown in appendix M, could be a solution, but further analysisis needed.

67

7

Conclusion

In this project different circuit topologies for harvesting low frequency low voltage vibra-tional energy have been evaluated, and the theory behind conversion from mechanicalvibration energy to electrical energy via a piezoelectric generator has been described. Theexpected power increase of different vibration harvesting topologies were presented, andthe Synchronized Switch Harvesting on Inductor (SSHI) was theoretically found to beapproximately 8 times better than the commonly used standard full bridge rectifier, andwas thus further analyzed leading to the implementation of a prototype.

The analysis clarified the key parameters of the SSHI topology performance. The SSHIcircuit output power was shown to be dependent on its ability to invert the piezoelectricvoltage. The parameters limiting the inversion factor were found to be the componentlosses in the oscillation path and the control circuit time delay. The trade-off betweenMOSFET capacitance and MOSFET ON resistance was discussed, but was later foundto be an insignificant part of the total power loss. The inductor equivalent resistancealong with the loss introduced by the diode were found to be the main parameters in theoscillation path limiting the inversion factor of the circuit.

To control the switching of the SSHI circuit, a peak detection circuit was designed withtwo active ICs, an opamp and a comparator. The control circuit provided control of thesquare wave signal of the MOSFETs. It was estimated that the total power consumptionof the control circuit of 15.4 µW was dominated by the IC supplies. From the analysis ofthe control circuit it was also derived that some power was lost in the comparator feedback.With the control circuit power consumption in mind, an expected power increase with theSSHI topology in comparison to STD was shown and a required minimum inversion factorwas found. For the SSHI topology to produce a larger total power output, with the controlconsumption in mind, the minimum required inversion factor was found to be γ > 0.5 forParallel-SSHI and γ > 0.7 for Series-SSHI at the tested vibration level producing an opencircuit piezo voltage of 7.6 V.

A prototype was implemented both as a series and a parallel version of the SSHI topology.The prototype was tested with Macro Fiber Composite piezoelectric material mountedon a vibration harvesting device called the WindSpear, and the results showed that theprototype Parallel-SSHI circuit increased the power output of the piezoelectric materialto 11 µW compared with the standard full bridge rectifier of 5.9 µW. Though, since thepower consumption of the control circuit was higher than the prototype output power, thetotal net output power of the SSHI prototype was lower than the standard full bridge.

The power output from the prototype was lower than expected due to a low inversionfactor. The limiting components were evaluated and along with the losses in the oscil-

69

7. Conclusion

lation path, primarily the loss in the diode and the series resistance of the inductor, thepeak detection control circuit was found to be the main reason for the low inversion factor.

The control circuit was expected to make the circuit switch at every voltage peak witha time delay of 12 ms, but was found being incapable of this due to a low gain in thedifferentiator. The control circuit feedback was thus modified which caused an increasedtime delay to 70 ms. The time delay made the circuit perform the switch after the op-timal point, which is assumed to be the main factor decreasing the power output of theprototype circuit.

This work has investigated the SSHI topology potential at low frequencies, and it wasseen that low frequency vibration harvesting is challenging at power levels of microwatts,mainly since the power consumption of the control circuit also is in the microwatt area.When considering a full energy harvesting system another DC/DC converter is neededfor matching the load and this will introduce additional power consumption. At highervibration levels the prototype is expected to increase the power output significantly.

It was also seen that the optimal point of switching is not directly on the voltage peakbut after, depending on the resistive loading of the piezoelectric element. To increasethe output power at the tested vibration level, a new control circuit with lower powerconsumption and less time delay is desired. With an improved control circuit the SSHItopology could increase the power output of a vibration energy harvesting system, by upto 8 times, which would extend the range of feasible vibrational energy harvesting sources.A WindSpear-powered sensor node with a SSHI circuit could allow the sensor node tooperate at lighter wind speeds or at an increased duty cycle.

7.1 Future Work

Further work needs to be done before making a Synchronized Switched Harvesting onInductor circuit capable of increasing the power output at the tested energy level in com-parison to the standard full bridge.

The inductor should be replaced with one having a low equivalent series resistance and anew peak detection control circuit should be designed. It should have a power consumption< 4 µW and a time delay < 7 ms, along with a high input impedance. This control circuitshould be internally powered, making the circuit independent of external supplies. Whenhaving reduced the loss in the inductor, the diode has the largest loss. Synchronous rectifiersolutions could be investigated, while evaluating their power consumption compared to thereduced power loss.

• Implement inductor with low series resistance

• Design new peak detection control circuit

• Supply the control circuit from the piezoelectric element

• Investigate reduction of diode loss

70

References

[1] Claus Bo Andersen. Piezo technology course material. Course taken at Noliac AS inKvistgaard, Denmark february 2008, 2008.

[2] A. Badel, D. Guyomar, E. Lefeuvre, and C. Richard. Efficiency enhancement ofa piezoelectric energy harvesting device in pulsed operation by synchronous chargeinversion. Journal of Intelligent Material Systems and Structures, 16:889–901, 2005.

[3] A. Badel, G. Sebald D. Guyomar, M. Lallart, E. Lefeuvre, C. Richard, and J. Qiu.Piezoelectric vibration control by synchronized switching on adaptive voltage sources:Towards wideband semi-active damping. Acoustical Society of America, 2006.

[4] A. Badel, M. Lagache, D. Guyomar, E. Lefeuvre, and C. Richard. Finite elementand simple lumped modeling for flexural nonlinear semi-passive damping. Journal ofIntelligent Material Systems and Structures, 18:727–742, 2007.

[5] J. Brufau-Penella and M. Puig-Vidal. Piezoelectric energy harvesting improvementwith complex conjugate impedance matching. Journal of Intelligent Material Systemsand Structures, 2008.

[6] Edited by Mickael Lallart. Ferroelectrics - Applications. InTech, 2011.

[7] Anantha Chandrakasan, Rajeevan Amirtharajah, James Goodman, and Wendi Ra-biner. Trends in low power digital signal processing. Department of EECS, Mas-sachusetts Institute of Technology, Cambridge, 1998.

[8] Roger D. Corneliussen. Elastic modulus values - modern plastics encyclo-pedia 99. http://www.maropolymeronline.com/Properties/modulus_values.asp#ValueRanges.

[9] Thomas P. Daue, Jan Kunzmann, and Andreas Schoenecker. Energy harvesting sys-tems using piezo-electric macro fiber composites. Smart Material Corp., 2008.

[10] Robert W. Erickson and Dragan Maksimovic. Fundamentals of Power Electronics -2nd ed. Springer, 2001. ISBN: 0-7923-7270-0.

[11] Alper Erturk and Daniel J. Inman. Piezoelectric Energy Harvesting. Wiley, 2011.

[12] A. Kasyap et al. Energy reclamation from a vibrating piezoceramic composite beam.Proceeding of the 9th International Congress on Sound and Vibration, 2002.

[13] C.O. Mathuna et al. Energy scavenging for long-term deployable wireless sensornetworks. Tyndall National Institute, 2008.

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[14] Zhi Ang Eu, Hwee-Pink Tan, and Winston K.G. Seah. Design and performanceanalysis of mac schemes for wireless sensor networks powered by ambient energyharvesting. National University of Singapore, 2010.

[15] D. Guyomar, G. Sebald, S. Pruvost, M. Lallart, A. Khodayari, and C. Richard. Energyharvesting from ambient vibrations and heat. Journal of Intelligent Material Systemsand Structures, 20, 2009.

[16] Allan R. Hambley. Electrical Engineering - Principles and Applications - 3rd ed.Pearson Prentice Hall, 2005. ISBN: 0131277642.

[17] Jifeng Han, Annette von Jouanne, Triet Le, K. Mayaram, and T. S. Fiez. Novel powerconditioning circuits for piezoelectric micro power generators. School of ElectricalEngineering and Computer Science Oregon State University, 2004.

[18] J T Henckel, T Sørensen, D. Vuckovic, and J Madsen. Powering sensor node us-ing macro fiber composite. IWPMA 2011 Conference and the 6th Annual EnergyHarvesting Workshop, 2011.

[19] David A. Johns and Ken Martin. Analog Integrated Circuit Design. Wiley, 1997.ISBN: 0-471-14448-7.

[20] Alireza Khaligh, Peng Zeng, and Cong Zheng. Kinetic energy harvesting using piezo-electric and electromagnetic technologies - state of the art. Illinois Institute of Tech-nology, 2010.

[21] Rasmus Trock Kinnerup. Ultra low frequency infrasonic measurement system, 2011.

[22] Na Kong, Dong Sam Ha, Alper Erturk, and Daniel J. Inman. Resistive impedancematching circuit for piezoelectric energy harvesting. Journal of Intelligent MaterialSystems and Structures OnlineFirst, 2010.

[23] A Kovalovs, E. Barkanov, and S. Gluhihs. Active control of structures using macro-fiber composite (mfc). Functional Materials and Nanotechnologies, 2007.

[24] Natan Krihely and Shmuel (Sam) Ben-Yaakov. Self-contained resonant rectifier forpiezoelectric sources under variable mechanical excitation. IEEE Transactions onpower electronics, 26(2), 2011.

[25] Mickael Lallart, Lauric Garbuio, Claude Richard, , and Daniel Guyomar. Low-costcapacitor voltage inverter for outstanding performance in piezoelectric energy har-vesting. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency control,57(2), February 2010.

[26] Mickael Lallart and Daniel Guyomar. An optimized self-powered switching circuit fornon-linear energy harvesting with low voltage output. Smart Materials and Structures,2008.

[27] Mickael Lallart, Elie Lefeuvre, Claude Richard, and Daniel Guyomar. Self-poweredcircuit for broadband, multimodal piezoelectric vibration control. Sensors and Actu-ators: A. Physical, 143:377–382, 2007.

[28] Mickael Lallart, Yi-Chieh Wu, and Daniel Guyomar. Switching delay effects on non-linear piezoelectric energy harvesting techniques. IEEE Transactions on industrialelectronics, 59(1), 2012.

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[30] Elie Lefeuvre, David Audigier, Claude Richard, and Daniel Guyomar. Buck-boostconverter for sensorless power optimization of piezoelectric energy harvester. IEEETransactions on power electronics, 22(5), 2007.

[31] Elie Lefeuvre, Adrien Badel, Claude Richard, and Daniel Guyomar. Piezoelectric en-ergy harvesting device optimization by synchronous electric charge extraction. Journalof intelligent material systems and structures, 16, 2005.

[32] Junrui Liang and Wei-Hsin Liao. An improved self-powered switching interface forpiezoelectric energy harvesting. IEEE International Conference on Information andAutomation, 2009.

[33] E. Minazara, D. Vasic, and F. Costa. Piezoelectric generator harvesting bike vibra-tions energy to supply portable devices. SATIE (CNRS UMR 8029), PRES UNI-VERSUD, ENS Cachan, 2008.

[34] Thurein Paing and Regan Zane. Design and optimization of an adaptive non-linearpiezoelectric energy harvester. IEEE APEC, 2011.

[35] Bjorn Baruel Petersen. Apparatdesign til vibrations- og chokkrav. enkle overslags-beregninger, formler, eksempler og regler. DELTA, 1987.

[36] Shashank Priya and Daniel J. Inman (editors). Energy Harvesting Technologies.Springer, 2009. ISBN: 978-0-387-76463-4.

[37] Murugavel Raju and Mark Grazier. Ulp meets energy harvesting: A game-changingcombination for design engineer. http://focus.ti.com/lit/wp/slyy018a/slyy018a.pdf 2010, Texas Instrument.

[38] Yogesh K. Ramadass and Anantha P. Chandrakasan. An efficient piezoelectric en-ergy harvesting interface circuit using a bias-flip rectifier and shared inductor. IEEEJournal of solid-state Circuits, 45(1), 2010.

[39] Yogesh Kumar Ramadass. Energy processing circuits for low-power applications.Doctor of Philosophy in Electrical Engineering and Computer Science at the MAS-SACHUSETTS INSTITUTE OF TECHNOLOGY, 2009.

[40] Yuan Rao and David P. Arnold. An input-powered active ac/dc converter with zerostandby power for energy harvesting applications. Interdisciplinary MicrosystemsGroup, Dept. of Electrical and Computer Engineering, 2010.

[41] C. Richard, D. Guyomar, and E. Lefeuvre. Self-powered electronic breaker withautomatic switching by detecting maxima or minima of potential difference be-tween its power electrodes. Patent PCT/FR2005/003000, Publication number:WO/2007/063194, 2007.

[42] Shadrach J. Roundy. Energy scavenging for wireless sensor nodes with a focus onvibration to electricity conversion. Berkeley, 2003.

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[43] Adel S. Sedra and Kenneth C. Smith. Microelectronic Circuits, International StudentEdition. Oxford University Press, Inc., New York, NY, USA, 5th edition, 2004. ISBN:978-0-19-514252-5.

[44] Henry A. Sodano, Gyuhae Park, and Daniel J. Inman. An investigation into the per-formance of macro-fiber composites for sensing and structural vibration applications.Mechanical Systems and Signal Processing, 18:683–697, 2004.

[45] T Sørensen, J Pedersen, and D Vuckovic. Energy harvesting from clothes using macrofiber composites. 2011.

[46] Y.K. Tan, J.Y. Lee, and S.K. Panda. Maximize piezoelectric energy harvesting usingsynchronous charge extraction technique for powering autonomous wireless transmit-ter. ICSET, 2008.

[47] Lihua Tang, Yaowen Yang, and Hongyun Li. Optimizing efficiency of energy har-vesting by macro-fiber composites. School of Civil and Environmental Engineering,Nanyang Technological University, Singapore, 2008.

[48] G. W. Taylor, J. R. Burns, S. M. Kammann, W. B. Powers, and T. R. Welsh. Theenergy harvesting eel: a small subsurface ocean/river power generator. IEEE J.Ocean. Eng., 2001.

[49] R. Tiwaria, Nathan Buch, and E. Garcia. Battery modeling for energy harvestingsystem. Laboratory of Intelligent Machine Systems, Cornell University, 2011.

[50] Guojun Wang. Piezoelectric energy harvesting utilizing human locomotion. MasterThesis - The University of Minnesota, 2010.

[51] Shengwen Xu, Khai D. T. Ngo, Toshikazu Nishida, Gyo-Bum Chung, and AttmaSharma. Low frequency pulsed resonant converter for energy harvesting. IEEE Trans-actions on power electronics, 22(1), 2007.

[52] Yaowen Yang and Lihua Tang. Equivalent circuit modeling of piezoelectric energyharvesters. Journal of intelligent material systems and structures, 20, 2009.

74

Appendix

75

Appendix

A DELTA Greenlab Mote

The energy consumer in this project is a sensor node being developed at DELTA, calledDELTA Greenlab Mote. A sensor node is a small computing device capable of collectingdata, joining a mesh network and through this transmitting the data to a base station. Amesh of such nodes is known as a sensor network. These sensor nodes are usually suppliedwith power from batteries, but these require maintenance. To avoid this, the nodes canbe made energy self-sufficient by means of energy harvesting.

The Greenlab mote uses the Texas Instruments MSP430f1611 microcontroller, the Chip-con CC2420 radio and the Atmel AT45DB161D external flash.

The microcontroller is equipped with low-quality sensors for temperature and voltage. Themote has three on-board sensors:

• Temperature and humidity Sensirion SHT11

• Ambient Light OSRAM Opto Semiconductors SFH5711

• Infrared PIN Photodiode Fairchild QSB34

A.1 Power Consumption

The sensor node power consumption varies depending on what task the node performs.Table A.1 shows the energy consumption from different operating modes. It is clearlyseen that there is not enough power generated by the WindSpear (∼ 10 µW) to supplythe sleep current of the sensor node. Thus it will be fully OFF while harvesting energy,and when enough energy has been harvested, it will start up and perform a measurement,before transmitting the data and then turn OFF again.

Table A.1: Energy consumption of sensor node in different operating modes running Aslak OS.

Mode Energy

Sleep (1.8V) 2 mWStart up - measure ADC - Transmit 670 µJLight sensor ADC measurement 4 µJThermistor sensor ADC measurement 4 µJ

76

B. Vibrations

B Vibrations

The energy available in vibrations can be described by the work performed by the forceacting on the system, W = F · s. Newtons second law describes the force related to theacceleration level and mass. F = m · aThe acceleration level can also be described in an circular motion a = ω2 · r. A vibrationcan be seen as a one-dimensional circular motion. Thus the acceleration can also be relatedto frequency, f , and displacement, u:

a = (2 · π · f)2 · u (1)

From this equation it is seen that the acceleration level is very frequency dependent (byf2). This is shown in fig. B.1 where the displacement is related to the acceleration (y-axis)and frequency (x-axis). A 1 mm displacement vibrating at 100 Hz will have an accelerationof 45 g where the same displacement will at 10 Hz have an acceleration of 0.35 g. Themechanical work performed on the energy harvesting piezoelectric material is a functionof the acceleration. Thus vibrations at low frequencies need to have large displacementsin order to reach acceleration levels feasible for vibration energy harvesting.

An example with the acceleration level 0.01g and 1 Hz and 20Hz is made. That means adisplacement of:

u(f) =a

(2 · π · f)2(2)

u(1) =0.01g

(2 · π · 1Hz)2= 0.25mm (3)

u(20) =0.01g

(2 · π · 20Hz)2= 0.63µm (4)

Example: If a 1 kg mass is vibrating at 10 Hz with a displacement of 1 cm how much energyis available. (Here it is assumed that there is no damping introduced by the harvestinggenerator, i.e. the mass of the generator is << than the mass of the system).

f = 10Hz (5)u = 0.01m (6)a = (2 · π · f)2 · d = 39.47m/s2 ≈ 4G (7)F = m · a = 1kg ∗ 39.47m/s2 = 39.47N (8)W = F · s = F · d = 39.47N · 0.01m = 0.3947Nm = 0.3947J (9)

(10)

The MFC M8527P2 is defined to have a piezoelectric constant of d31 = −170pC/N . TheMFC behaves purely capacitive below 300kHz (as seen in impedance analysis in XXX).Thus the charge generated can be described by the capacitor relation between work andcharge:

Q = d31 ·W (11)Q = 170pC/N · 39.47N = 6.71nC (12)

(13)

Stiffness change/damping of structure can be found by comparing the short- and open-circuit resonance frequencies of the piezo [28].

77

Appendix

Figure B.1: Vibrational acceleration [g] vs frequency [Hz] [35]

78

C. Strain

C Strain

In the MFC datasheet a value for charge generated per strain is defined.The MFC can be seen as a thin beam and the strain can be defined as an equationdependent on the bending radius shaped by the bended MFC beam, ”arc”-shape, and thedistance from the MFC material to the neutral axis of the arc. See fig. C.1 where theneutral axis is the broken line.

Figure C.1: Definition of the neutral axis, ie. the broken line, X

The neutral axis needs to be located outside the piezoelectric material in order to havea uniform strain the MFC. If the neutral axis is inside the material, then on one sidethere will be a compression (inner arc) and on the other side (outer arc) there will be astrain. Though if the MFC is mounted on a material with same or larger stiffness andequal or thicker thickness, the neutral axis will bemoved outside the material and nowwhen bending the whole material will be either compressed or strained, and thus gettinga uniform energy generation.Different material Young modules can be seen in table C.1. Youngs modulus, Y , alsocalled elasticity, is the ratio of stress, T (force,F per unit area, A0 ) to strain,S (changein length,∆L , per unit length, L ):

Y =T

S=

F/A0

∆L/L0

(14)

The energy generated by the piezoelectric element depends on the strain applied. Thestrain, S , is a function of the distance to the neutral axis, dn.axis , and the bending radiusrbend:

S =1

rbend· dn.axis (15)

The strain is usually defined in a value of ppm - parts per million. That means when theMFC is defined to have a maximum tensile strain of 4500 ppm before cracking it meansthatCalculation example.The strain is to be the maximum 4500 ppm (from MFC datasheet REF!) then the bendingradius can be a maximum of the following if the MFC is mounted in a 7 mill material. Indatasheet it says that 0.3mm is approx 12 mil. The 7mil is prob. the distance to neutralaxis and must be around 0.15mm. From eq. 15:

79

Appendix

Table C.1: Different material Young modules [8]

Material Youngs Module [GPa]

Rubber 0.01Plexiglass 0.4Teflon 0.5Polypropylene 1.5-2Epoxy 2Oak wood 11Piezo ceramic PZT Y33 49Piezo ceramic PZT Y11 63Aluminium 69Glass 50-90Copper 117Silicon 130-185Steel 200

rbend−max =dn.axisS

=0.15mm4500ppm

(16)

rbend−max = 3.3cm (17)

Bending Radius.To calculate the bending radius one can use the formula derived from the pythagoreantheorem, where , ch is the chord length, sa is the sagita length (see fig. C.2).

rbend =ch2

8 · sa+sa

2(18)

Figure C.2: Arc with marked sagita and cord in bending beam. Sagita is the vertical lineorthogonal on the horizontal line. tegn ny tegning?

80

D. LCR Measurement Setup

D LCR Measurement Setup

PSM1735 N4L Numetric is a phase sensitive multimeter used with its impedance analysisinterface.

D.1 PSMcomm Settings

—————-Mode: LCR

Acquisition Settings: mode: normal speed: medium phase reference: ch1 filter: normalfilter dynamics: auto reset low frequency: off datalog: disabled bandwidth: autoSweep Settings: sweep start: 1.00000Hz sweep end: 1.00000MHz steps: 32 sweep:single graph scaling: autoTrim Settings: ac trim data: off ac level: 1.00000 V tolerance: 10 Alarm Settings:parallel port: disabled monitor data: zoom 1 analogue scale: 180 analogue zero: 0 alarmtype: disabledAuxiliary Settings: fixture: impedance analyser interface lcr head shunt: normalOutput Settings: amplitude: 2.00000Vpk frequency: 1.00000kHz offset: 0V waveform:sinewave amplitude step: 1.10000 times frequency step: 2.00000 times output: onChannel 1 Settings: input 1: voltage input connection: main minimum range: 10mVautoranging: full autorange coupling: ac+dc scale factor: 1.00000Channel 2 Settings: input 2: external shunt connection: main minimum range: 10mVautoranging: full autorange coupling: ac+dc scale factor: 1.00000 external shunt: 50OhmSystem Settings: phase convention: -180 deg to +180 deg low blanking: on graph: lineskeyboard beep: on autozero: auto length units: m shunt: default step message: enabledprogram 1-6 direct load: disabledMode Settings: operating mode: LCR meter parameter: auto conditions: manualgraph: tan delta / QF sweep: series

81

Appendix

E Electromechanical Coupling Factor

It is shown in [2] the energy gained from using SSHI in comparison with a standard fullbridge is dependent on the piezo elements electromechanical coupling factor squared timesthe mechanical coupling factor, k2QM . The lower the k value, the more gained fromSSHI. The electromechanical coupling factor can be described as in eq. 19, where KD isthe open circuit stiffness of the piezo, the force factor α and piezo capacitance, Cp. TheMFC material is not stiff in comparison to other piezo materials so this means that thecoupling can be higher than regular PZT and other piezo materials.

k2 =α2

KDCp(19)

The mechanical quality factor, QM , depends on the physical structure and elasticity, thepiezo material elasticity and the type of medium connecting them (eg. type of glue). Itis beyond the scope of this project to evaluate this factor, but it is noted that the SSHItopology output power is independent from this, where the SECE topology output powerdecreases at larger coupling factors at seen in fig. E.1.

Figure E.1: Comparison of SSHI and SECE output power dependence on electromechanicalcoupling factor and mechanical quality factor. From [15]

82

F. MFC Measurements

F MFC Measurements

Figure F.1: Measurement setup for characterizing the MFC piezoelectric material. DCmotor is seen on the right mounted on a stand. This rotates a rod in connection with theMFC which is mounted on a thin plastic plate. The rotations causes the plastic sheet andthe MFC to bend.

F.1 Capacitive load

Fig. F.2 shows the energy harvested from the MFC connected to a full bridge and a lowleakage capacitor. The harvested energy is dependent on the size of the capacitance. Thetest is conducted with the WindSpear which consists of the MFC glued to a plexiglass rod.This is applied a single impulse and resonates around 2 Hz, i.e the rod is applied a stressand thereafter released. This creates a resonating decaying motion. The same motion ismade for different capacitor sizes.

0 5 10 15 20 258

8.5

9

9.5

10

10.5

11

11.5

12Energy harvested from spear vs storage capacitance

Capacitance [uF]

Ener

gy [m

J]

Energy from flicking spear

Figure F.2: Energy produced by MFC vs capacitive load

83

Appendix

G Technical Low Power Laboratory Challenges

G.1 Measuring Voltages

When measuring the voltages produced by the piezo it is also important to keep the probeimpedance in mind. If it is a 1MΩ probe, it will dampen the measured signal as it willdraw 1/V . In order to prevent this an OPA129 operational amplifier with an input biascurrent draw of 1fA was used, configured as a voltage follower. The PCB design in usefor this voltage follower is from [21]. This circuit made sure the measured signal was notdampened.

G.2 Measuring Low Current

Measuring current in the order of 1− 10µA is not possible with a regular oscilloscope anda current probe. The noise in the oscilloscope is larger than the measurement.

A method is to wind a copper wire 100 times round the current probe to get 100 timesamplification of the magnetic field measured by the current probe. One do though has tokeep the inductance of the wire in mind at higher frequencies, but at 2Hz frequency theinductance will be negligible. An oscilloscope capable of filtering the high frequency noisein the signal is needed.

84

H. Components

H Components

H.1 MOSFETs

H.2 Opamps

Opamps with low power consumption on the market are stated in table H.1.

Table H.1: Low power operational amplifiers from different commercial manufacturers

Manufacturer Partnumber Supply range [V] IDD [uA]

Linear Technology LTC6003 1.6-16 1Analog Devices AD850 1.8-5.5 1Texas Instruments TLC25L2B 1.4-16 20Advanced Linear Devices ALD2706 2-10 20Fairchild FAN4852 2.5-5 800National Semiconductor LPV521 1.6-5.5 0.4

H.3 Comparators

A similar table with specifications of low power comparators are seen in table H.2. Theseare push-pull comparators.

Table H.2: Low power comparators from different commercial manufacturers

Manufacturer Partnumber Supply range [V] IDD [uA]

Analog Devices ADCMP370 2.25-5.5 4Fairchild FAN156 1.6-5.5 6Texas Instruments TLC352 1.4-18 65National Semiconductor LPV7215 1.8-5.5 0.58National Semiconductor LPM7215 2-8 0.7

85

Appendix

I Prototype

In fig. I.2 the P-SSHI circuit schematic is seen and in fig. I.2 the S-SSHI circuit schematicis seen. The only difference between them is the placement of the rectifying bridge withthe output. A photo of the P-SSHI prototype is seen in fig. I.3.

Figure I.1: Parallel Synchronized Switch Harvesting on Inductor Prototype Schematic

86

I. Prototype

Figure I.2: Series Synchronized Switch Harvesting on Inductor Prototype Schematic

87

Appendix

The prototype is mounted on a copper plate which forms the ground plane. The resistancesin the peak detection control circuit are implemented with potentiometers in order to beable to tune the differentiation and comparation as the peak detection did not perform asdesired. The load is connected in upper left corner after an rectifying bridge along with a10µF electrolytic capacitor.

Figure I.3: Implemented P-SSHI prototype

88

J. Half-wave Rectifier Supply

J Half-wave Rectifier Supply

Half wave rectifier with smoothing capacitor on each supply pin of opamp and comparator.For calculating the required capacitor size in the half wave rectifier, CHWR, one can lookat the average charge removed from CHWR during one period which will correspond tothe average load current drawn from the opamp and comparator, Is. This removed chargelowers the capacitor voltage with a ripple of Vr. Thus:

Qs = IsT (20)Qs = VrC (21)IsT = VrC (22)

→ C =IsT

Vr(23)

With a current draw off Is = 1µA, a period of T = 0.5s and a chosen max ripple ofVr = 0.5V the capacitance should be: C = 1µA0.5s

0.5V = 1µF

The rise/fall time of the MOSFETs is dependent on the output current of the comparator.The output current of the comparator is limited by the supply to the comparator.

The comparator used in the prototype, LMV7215, uses 700nA but the supply should beable to supply the switch current aswell.

The gate charge current is 2.2mA in 10µs. Ref to MOSFET section . Size supply capaci-tance so it will not drop the voltage from the intermediate gate current draw.

The start current draw is I = 2mA (max) in t = 10µs. This will cause a capacitor voltagedrop of (C = 1uF ):

Vc = V0e−tRC (24)

R =V0

I=

2V2mA

= 1kΩ (25)

VcV0

= e−tRC (26)

= e−10µs/1kΩ1µF = 0.99 (27)

Thus a 1uF should be able to supply the gate current. But meanwhile it should supply500 nA constantly.

89

Appendix

K Inductor

The inductor used in the prototype has a impedance-phase characteristic measured in fig.K.1. It is noted that 180mH inductor has a high DC resistance of 500Ω.

100

101

102

103

104

105

101

102

103

104

105

Impe

danc

e [Ω

]

Frequency [Hz]

Impedance

100

101

102

103

104

105

0

20

40

60

80

100Phase

Pha

se [

° ]

Frequency [Hz]

Figure K.1: Impedance-phase measurement of the inductor in use in the prototype of180mH. Measured on a phase sensitive multimeter described in app. D. The bump in thegreen graph corresponds to 50Hz and is due to equipment noise. Could be removed withlarger test signals.

K.1 Self Wound Inductor

Instead of using an off-the-shelf inductor, a design guide for a self wound inductor is heredescribed.

90

K. Inductor

K.2 Build Inductor

The inductor to be build has 980µH inductance and 700mΩ DC resistance. This is con-structed on an RM4 core with AWG29 wire (0.26mm) and 91 turns on the winding. Theair can be made with a small piece of yellow post-it paper.

K.3 Calculations

Core Material and Turns

The inductor should not be saturated by the current in it. With a ferrite core one canuse Bsat = 300mT as a limit. Then the product of the number of turns N and the crosssectional area of the core, Ae can be calculated and then used to estimate number of turnsfor a chosen core material.

Bsat ≥I · LN ·Ac

(28)

N ·Ac ≥I · LBsat

(29)

N ·Ac ≥0.7A · 1mH

300mT(30)

N ·Ac ≥ 0.0023 (31)

An RM8 ferrite core has Ae = 64mm2 = 0.64cm2

This leads to N = 0.0023Ae

= 0.00230.64·10−4 = 35.9turns. So the winding on a RM8 core needs 36

turns to give 1mH inductance.

Airgap

With this number of turns the air gap AL can be found. It has a unit of nHN2 so a 1mH

inductor with 36 turns 1·106nH362 = 771. With this value an estimate of the air gap can be

found in the datasheet of the RM8 core. Here a N41 core with AL = 630 needs an air gapof s = 0.11mm. This value is then used as a starting point for assembling the inductor.

Wire Thickness

The window area on the coil former is AN = 30mm2 which is used to calculate the wirethickness (datasheet of RM8).Wire cross section AW , winding cross section AN , copper fill factor fcu

AW ≤AN ·Ku

NAW ≤

30mm2 · 0.5536turns

AW ≤ 0.46mm2 (32)

The thickest wire possible is then AWG#21 with AW = 0.41mm2.

Wire Resistance

Resistance in AWG#21 is 42mΩ/m.

Average length of turn for RM8 coil former IN = 42mm

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Appendix

Total DC resistance: IN ·N · 42mΩ/m = 42 · 10−3m · 36turns42mΩ/m = 64mΩ

Same calculation of RM4 core gives:

• Coil former

• IN = 8.7mm

• AN = 20.1mm2

Core

• Ae = 13mm2

• AL = 31.9nH

• Material: M33 AL = 40nH

• Space gap s = 0.36mm

Wire

• N = 177

• AW = 0.068mm2

• AWG#29

• IN = 8.7mm

• Rtot(DC) = 0.27Ω

High permeability core means higher inductance per volume but with lower saturationvoltages.

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L. WindSpear Test

L WindSpear Test

The setup for the prototype test is shown in fig. L.1. The WindSpear is in a hangingposition and moved by a small DC motor creating a vibrating spear motion of 1.8 Hz.The motor setup is shown in fig. L.2. The spear is hanging upside down due to ease thetest setup . The lower moving end can oscillate freely unlike if it was mounted vertically,where the gravity would influence and dampen the oscillations. The DC motor makes thefree end move with a displacement estimated to be uspear = 0.7 cm. The resulting MFCdisplacement near the other end of the spear is assumed to be u = 1 mm. The spearlength is 1 m from fixed point to free end.

Figure L.1: WindSpear mounted in hangingconfiguration for the prototype test.

Figure L.2: DC motor is in connection withthe end of the WindSpear via the green stickand makes it vibrate at frequency of 1.8 Hz.

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Appendix

L.1 P-SSHI

The voltage inversion when the NMOS is turned ON is seen in fig. L.3.

−4 −3 −2 −1 0 1 2 3 4 5 6

x 10−4

−6

−4

−2

0

2

4

6

Time [s]

Indu

ctor

Vol

tage

[V]

WindSpear TEST − Inductor inversion voltage NMOS

Figure L.3: P-SSHI inductor inversion voltage when NMOS turns ON

L.2 S-SSHI

In fig. L.4 the inductor inversion voltage when NMOS turns ON is seen when theFDV301N/304P MOSFETs are used. These MOSFETs has an output capacitance ofCoss = 5pF .

−4 −2 0 2 4 6 8

x 10−4

−8

−6

−4

−2

0

2

4

6

Time [s]

Indu

ctor

Vol

tage

[V]

WindSpear TEST − Inductor inversion voltage PMOS

Figure L.4: S-SSHI inductor inversion voltage when PMOS turns ON - FDV301N/304P

Mosfet Comparison

In fig. L.5 it is seen that the resonance after the inversion has ended is twice as big withIRF7307 as with FDV301N/304P.

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M. Envelope Breaker

0 2 4 6

x 10−4

−6

−4

−2

0

2

4

6

Time [s]

Vol

tage

[V]

FDV301N/304P

0 2 4 6

x 10−4

−6

−4

−2

0

2

4

6

Time [s]

Vol

tage

[V]

IRF7307

Figure L.5: Comparison of resonance between inductor and MOSFET output capacitancefor S-SSHI circuit with small signal FET FDV301N/304P and IRF7307.

M Envelope Breaker

The envelope breaker from [41] [27] is seen in fig. M.1. It is a passive peak detectioncircuit capable of operating across two decades. It is stated to consume only 5% of theavailable energy. The main limitation is its required input voltage.

Figure M.1: Electronic breaker for peak detection in SSHI. From [26].

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Low Frequency Low Voltage Vibration Energy...

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