國立臺灣大學工學院工程科學暨海洋工程學系 博士論文
Department of Engineering Science and Ocean Engineering College of Engineering
National Taiwan University Doctoral Dissertation
適用於微型與一般型
超低耗能與寬頻壓電能量擷取器系統之設計
Designs of MEMS and Bulk-Sized Piezoelectric Energy Harvesting Systems
for Ultra Low Power and Bandwidth Extension
施雅蘐 Ya Shan Shih
指導教授: 吳文中 博士、Dejan Vasic 博士 Advisors: Wen-Jong Wu, Ph.D and Dejan Vasic, Ph. D
中華民國 107 年 1 月
January 2018
致謝
最想感謝的是讓我自由自在做選擇的爸媽，謝謝你們一直都信任我做的任 何事情。不管我在學業中間做了多奇怪的副業也是讓我自由發展，I love you。還有小舅舅一家人，大姨一家人，在我求學的時候給了我台北的家~ 尤其 是小姨，是我的生活好夥伴監護人，教會我很多事情。室友詩雯也一直很體 諒，我總是不在家，謝謝你們讓我們一起住的家一直都這樣溫暖。還有老是被 我靠盃的老朋友丹，你是我的垃圾話救星。
還有研究生活中最重要的吳大，沒有你我也不會唸博士班~ 謝謝你在我有 任何困難的時候也給予我各種支持，你是最帥氣的阿宅! 而且還很瘦! 師母也 是把我當孩子一樣多元成家(笑)，貓貓狗狗的交給我吧! 也謝謝 Lance 給我繼 續待在公司的機會，協助我在博士班最後的時間在生活上不至於匱乏。學校裡 還有從碩士班就一直照顧我的已經畢業的學長姐們，感謝順區學長為我在碩士 班的時候打下研究的底子、心目中第一名的小白學姊、怡潔、還有同一天生日 的芠羽、後來到法國認識才發現沒有那麼機歪，而且還很罩的歪歪哥都非常的 照顧我。一起在歐洲的時候，美麗的嫂嫂桂玲跟歪歪哥把我養得白白胖胖 der。
欣潔和嘉恩也總是很貼心不厭其煩的幫助忘性有如神的我。然後謝謝學弟們雖 然我沒有常常去學校也沒有排擠我。公司的同事也都很罩，總是義氣相挺，能 夠有機會認識大家真的很有趣。
還要謝謝我的改論文朋友們，芊君、鈞憶，老是麻煩你們幫我改英文，誰 教你們英文這麼好我忍不住阿~
然後是我的校外奇幻旅程認識的朋友、老師們，讓我在學校、工作的壓力
獲得了調劑，給了我很多的協助，也讓我有了豐富的生活。我的金湯匙小毛 哥、看起來很聰明其實少根筋的艾大，被你們疼愛著真的是很幸福的事情。呂 秋猴蘭能夠聚在一起，是很美好的緣分。秀莉姊默默的關照。寶叔給我了一個 很棒的做人典範，還有很穩重的協助。也謝謝絲雨老師在我很貧瘠的時候還給 我一份工作，有了看見另外一個世界的機會。
還有無敵重要的幼幼姐姐，接受一直該該叫的我，給我很多勇氣跟力量，
讓我也學會表達自己。
由於覺得自己太得人疼了，就算是念到博士，還是一直被照顧著。要謝的人真 的太多，就只好先這樣了。
雅蘐 2018 年 1 月
中文摘要
隨著科技的進步，物聯網(IoT)成為莫可阻遏的趨勢，能量擷取技術也因此成 為其核心技術之一。為了使生活中的物品具有感受周遭環境的能力，吾人必須將 物品之感測器安裝於其上，以使所有的物品皆具有「感受力」。這樣的感測裝置 必須是微型、無線，以便能不著痕跡地安裝在我們的生活物品中。為了維持這些 裝置的永續作動，避免頻繁的電源更換(如電池)，自供電系統的重要性不言而喻。
除了日常生活之外，在健康照護系統、公用建設的健康監測、軍事用途...等，
也都有自供電系統的需求。
能量擷取系統提供自供電系統一個從外部環境擷取資源的途徑。能提供能量擷 取的環境能量，例如太陽能、溫度差、與各種機械能。其中震動能量擷取被廣為 研究，因為震動幾乎是無所不在的。作為機械能擷取的其中一部份，三種常見的 方法有: 電磁式、靜電式、壓電式能量擷取。其中又以壓電式能量擷取的能源效 率最高。因此，此論文主要探討壓電能源擷取的介面電路與壓電能量擷取裝置之 機構設計。
本研究針對壓電懸臂樑能量擷取系統中最常見的能量損耗與頻寬問題，提出了 兩種有效的新方式，利用機構與電路的設計，成功的降低同步開關的能量耗損以 及增加使用頻段，並探討常用的電子式開關操作在微能源輸入的損耗。並且針對 此裝置設計合適的擷取系統：透過懸臂樑陣列、電路研究與機構設計，提升系統 效能與頻寬。最後並利用自製的微型壓電懸臂樑配合機電混和開關，以確認所提 出的電路在微型能量範圍的可行性。
為建構一個完整的擷能系統，文中主要提出的新方式如下: 一、透過陣列的編排 與機構設計，利用磁石的磁性將陣列串聯，達到物理串連，並產生類似多維度機 構的效果。 二、利用磁簧開關組成的機械電子混合開關代替同步開關電路中常 用的智慧電子式開關(smart switch)，以減少電路損耗並能降低閥值損耗。此外，
機電混和開關也被成功的應用於輸出電能較一般懸臂樑(cm scale)低的小型懸 臂樑(mm scale)。本文中提到的兩種方法能併用，或是分開使用，針對應用情境 達到各自的成效。研究中，除了機構設計的模擬與討論，模擬與實驗結果都顯示 出此架構增加了能量擷取的效能。另一方面，為克服機械開關的喋喋(chatter) 問題，我們提出三種解決方式，並更深入探討同步開關電路中物理開關位置的設 計，以利效能的最佳化。
關鍵字: 能量擷取系統、壓電懸臂樑、懸臂樑陣列、寬頻、非接觸式機械同步開 關、低耗能
ABSTRACT
The future trend of Internet of Things (IoT) is bringing energy harvesting in to the core technique due to its requirement of self-power supplying. To realize the IoT, “the ability to sense the world” is the basic requirement of every “thing” in the Internet. That is, each and every object would have its own sensing systems. To achieve this, sensors are installed in the objects. With the aim to retain the user habits, the goal is to keep the
“things” in form just as they were. To achieve, additional sensing systems are to be designed small and wireless- they are best to be self-powering. Imagine, if each and every single object in your life has a sensor and all of them requires your attention every few months in different times to recharge the batteries, does that seem like a bright future? Smart house is only one of the reason for self-powered IoT system, not mentioning health care, infrastructure monitoring, and military usages… etc.
Energy harvesting provides a way to realize the self-powered system, it enables the device itself to obtain its own energy from their environment. For instance, solar energy, thermal gradient, mechanical forces, are some commonly seen methods to obtain energy from the environment. Among the mechanical energy harvesting techniques, three major methods are used commonly: electromagnetic, electrostatic, and piezoelectric.
In this work, a simple model of the original electrical smart switch is proposed. By using the miniature device to drive the smart switch, the efficiency when low power is provided was examined. To construct an energy harvesting system in a more complete aspect, two newly proposed methods are as below: First, the hybrid-electrical- mechanical switches were utilized to replace the commonly seen electrical smart switches, to reduce its energy consumption such as threshold loss. Moreover, the hybrid
switch system was also successfully introduced to micro-piezoelectric energy harvesting systems (in scale of mm), which usually has lower energy outputs comparing to bulk sized systems in scales of cm. Secondly, we designed a new mechanical structure for the cantilever array by connecting the beams using magnetic repelling force. In this way, the beams within the array were connected physically, forming a nonlinear multi-degree of freedom (MDOF) -like result. The two methods mentioned above can be applied separately or together, considering the application circumstance.
Simulation and experiment was performed, proving the improve of output voltage peaks of the structure. On the other hand, to resolve the inherited chattering of the reed switch, we propose three methods and also further discuss about the effect of the closing time delay of the synchronized switch to optimize the output.
Keywords: Energy harvesting system, piezoelectric cantilever beam, beam arrays, bandwidth expansion, non-contact mechanical synchronized switch, low power.
CONTENTS
致謝 ... i
中文摘要 ... iii
ABSTRACT ... v
CONTENTS ... vii
LIST OF FIGURES ... xi
LIST OF TABLES ... xvi
TABLE OF ABBRIEVATIONS ... xvii
Chapter 1. Introduction ... 1
1.2 The Energy Harvesters ... 6
1.2.1 Radioactive Harvesters ... 8
1.2.2 Kinetic Energy Harvesters ... 11
1.2.3 Modeling of Cantilever-Based Energy Harvester ... 16
1.3 Harvesting with a Broader Bandwidth ... 18
1.3.1 Beam arrays ... 19
1.3.2 Stoppers ... 20
1.3.3 Bistable Structures ... 22
1.3.4. MDOF structures ... 25
1.3.5 Up Conversion ... 29
1.3.6 Active Resonance tuning ... 30
1.4 The Interfacing Circuits ... 32
1.4.1 Theoretical Modeling of the Interfacing Circuits ... 36
1.4.2 Autonomous Switches for Self-Powered Systems ... 40
1.4.3 Multiple Beam Circuitry ... 45
1.5 Dissertation Organization ... 46
Chapter 2. Electric Circuit Losses: Modeling of a Smart Switch Driven in Low Voltage ... 48
2.1 Power Provided with Micro PEH Device ... 48
2.2 The Circuit Loss ... 51
2.2.1 The Rectifying Loss ... 51
2.2.2 The Smart Switch Loss ... 54
2.3 The Loss Experiment ... 62
2.3.1 Driven with voltage too low ... 62
2.3.2 Driven with voltage in between ... 64
2.3.3 Driven with enough voltage ... 65
2.4 Discussion ... 67
Chapter 3. Hybrid Switch on SSH Methods ... 70
3.1 Design Concepts ... 70
3.1.1 Reed switch introduction ... 70
3.1.2 Reed switch replacement on SSH techniques ... 72
3.1.3 Resolving the chatter: snubbers (de-bouncers) ... 75
3.2 Energy Loss Due to Switching Phase Difference ... 79
3.3 Experiment and Results ... 82
3.3.1 Experiment Setup ... 83
3.3.2 Chatter Loss and the de-bouncers ... 88
3.3.3 Loss due to switch delay ... 95
3.3.4 Working Mechanisms of De-bouncers ... 96
3.3.5 Low voltage driven S-SSHI ... 98
3.4 Discussion ... 99
3.4.1 Chatter Loss on P-SSHI and S-SSHI ... 99
3.4.2 Comparisons of the proposed switching methods ... 100
3.4.3 Designing the hybrid switched SSH system ... 102
3.4.4 Comparison to the original smart switch considering the phase difference ... 104
Chapter 4. Magnetically Connected Array ... 106
4.1 Design concepts ... 106
4.2 Theoretical Assumption and Simulation ... 107
4.2.1 Interaction between 2 Beams ... 109
4.2.2 Interaction between 3 Beams ... 113
4.3 Experiment ... 124
4.3.1 Experiment Setup ... 124
4.3.2 Experiment results for symmetric alignment of 3 beams ... 125
4.3.3 Experiment results for asymmetric alignment ... 130
5.4 Discussion ... 140
Chapter 5. Conclusion and Future work ... 142
5.1 Hybrid Switches ... 142
5.2 Magnetically Connected Arrays ... 142
5.3 Summary (Impact) ... 143
5.4 Future Work ... 144
5.4.1 The hybrid switches on miniaturized systems ... 144
5.4.2 Magnetically connected beam arrays ... 146
REFERENCES ... 149
LIST OF FIGURES
Figure 1-1The world fossil fuel production curve forecast [1] ... 1
Figure 1-2 The IoT concepts ... 3
Figure 1-3 The energy harvesting market forecast ... 4
Figure 1-4 Energy harvesting devices in different scale in size corresponding to power output [7] [8] [9, 10] ... 8
Figure 1-5 Solar harvesters in different scales ... 9
Figure 1-6 Thermal Energy Harvester ... 10
Figure 1-7 A radio frequency energy harvester, acquiring energy 6.5 km from the TV tower ... 11
Figure 1-8 General spring mass damper model for transducers ... 12
Figure 1-9 Magneto-electrical energy harvester ... 13
Figure 1-10 Three configurations of the electrostatic energy harvesting ... 14
Figure 1-11 A piezoelectric cantilever based energy harvester ... 15
Figure 1-12 Working modes of the piezoelectric beam ... 15
Figure 1-13 Equivalent circuit model of a single beam considering only the first resonance ... 18
Figure 1-14 A typical voltage output respond to chirping frequency. ... 19
Figure 1-15 Cantilever array to create broad band [25] ... 19
Figure 1-16 Model for stopper in forms of cantilever adopted from [26] ... 20
Figure 1-17 Results comparisons of different stopper distances on both sides ... 21
Figure 1-18 Bistable energy harvesting concepts ... 23
Figure 1-19 Output result of buckled-spring-mass systems ... 24
Figure 1-20 Stacked MDOF Modeling ... 25
Figure 1-21. Mother-Sibling Model of MDOF PEH redrawn from[23] ... 26
Figure 1-22 2DOF Structure design and results [44] ... 28
Figure 1-23 Stress simulation of a 2DOF beam [45] ... 28
Figure 1-24 Spiral MEMS 2DOF device [46]. ... 29
Figure 1-25 Up conversion design using electromagnetic energy harvesting [31] ... 30
Figure 1-26 Tuning by preloading on axial direction ... 31
Figure 1-27. Magnetic resonance tuner ... 31
Figure 1-28 Different SSH circuits, adopted from [21] ... 34
Figure 1-29 Normalized harvested powers under constant vibration magnitude. [21] 35 Figure 1-30 SEH circuit and the power feedback ... 37
Figure 1-31 SSHI topologies with tagged voltage and current flow ... 38
Figure 1-32. Reduced power feed-back using SSH techniques (P-SSHI). ... 39
Figure 1-33 Electrical autonomous switches ... 43
Figure 1-34 Mechanical switch designs ... 44
Figure 1-35 Circuit connection for cantilever arrays [83] ... 45
Figure 1-36 Connecting two beams using OSECE [84] ... 46
Figure 2-1 Schematic diagrams of the piezoelectric MEMS generator. [10] ... 49
Figure 2-2 Schematic diagram of bimorph poling and connection ... 50
Figure 2-3 Power and voltage outputs of Micro PEH excited with varying acceleration levels ... 51
Figure 2-4 Diode Analysis using Keithley 2420 source meter ... 53
Figure 2-5 Rectify loss experiment of IC DB155 ... 53
Figure 2-6 Diagrams showing different states of a SSH switching ... 57
Figure 2-7 Inversion investigations ... 58
Figure 2-8 The voltage distribution on the smart switch ... 60
Figure 2-9 Circuit modeling of charging state during SSHI switch ... 61
Figure 2-10 Bode plot simulation of the model on Matlab ... 62
Figure 2-11 Experimental results of power outputs with voltage inputs less than requirements ... 63
Figure 2-12 Power output results of transient voltage driven cases using d31#2 , from Table 5 ... 64
Figure 2-13 Experimental results of parallel SSHI with power sources enough to drive SSHI. ... 66
Figure 2-14 Comparison between the harvested power of self-powered SSHI and SEH ... 69
Figure 3-1 The glass sealed reed switch ... 71
Figure 3-2 Reed chattering experiment ... 73
Figure 3-3 Applying reed switch on LF-P-SSHI ... 74
Figure 3-4 Conventional snubbers used in microprocessor controls ... 75
Figure 3-5 Unidirectional reed switch de-bounced on resistor (RDR) ... 77
Figure 3-6 Unidirectional reed de-bounced on inductor (RDI) ... 77
Figure 3-7 Schematic diagram of SCR ... 78
Figure 3-8 Unidirectional SCR de-bouncer ... 79
Figure 3-9 The cause of switching time difference ... 80
Figure 3-10 Flow chart of experiment concept ... 82
Figure 3-11 Experimental setup ... 84
Figure 3-12 Reed switch applied on LF-P-SSHI without de-bouncing ... 89
Figure 3-13 Energy loss due to switch chattering driven on 0.07 g, beam 1 ... 90
Figure 3-14 Current flow of filter snubbed LF-P-SSHI on switching ... 91
Figure 3-15 Power output experiments for filtered de-bouncers ... 92
Figure 3-16 Piezo voltage output when high impedance is loaded at the RDI S-SSHI ... 93
Figure 3-17 Current flow of SCR snubbed LF-P-SSHI on switching, 0.03g beam 1 .. 93
Figure 3-18 Output of SCR de-bounced comparing to other circuits ... 94
Figure 3-19 SCR malfunctioning waveform with overdriven voltage. ... 94
Figure 3-20 Phase difference relations to P-SSHI and S-SSHI gains. ... 96
Figure 3-21 Voltage and current tracking of LF-P-SSHI using RDI ... 97
Figure 3-22 Voltage and current tracking of LF-P-SSHI using SCR ... 98
Figure 3-23 A low voltage driven experiment using RDI ... 99
Figure 4-1 Design concept of the magnetically connected beams ... 107
Figure 4-2 Magnetic interaction between two beams ... 110
Figure 4-3 Implementation of the MCK model for simulation ... 111
Figure 4-4 Simulation of the magnetic spring coefficient between beam 1 and 2, k12 ... 112
Figure 4-5 Simulation results of the 2 beam interaction ... 113
Figure 4-6 Interactions between three beams ... 114
Figure 4-7 PSIM Simulation diagram for 3 beams ... 115
Figure 4-8 Simulation results for the symmetric 3-Beam alignment ... 116
Figure 4-9 Simulation result of the Dirac response ... 118
Figure 4-10 Simulation results for asymmetrically aligned 3 beam array ... 120
Figure 4-11 A new configuration for 3-beam alignments ... 121
Figure 4-12 Simulation results for the modified beam 1 ... 122
Figure 4-13 Bird view of frequency – distance –voltage for one fixed distance ... 123
Figure 4-14 Cross section of D12=D13=0.035 m; ... 124
Figure 4-15 Experiment setup for magnetic connected beam array ... 124
Figure 4-16 . Experimental results symmetric 3 beam alignment ... 126
Figure 4-17 Experiment results of identical distances between beams. D12=D13=10mm. ... 132
Figure 4-18 Experiment results of identical distances between beams. D12=D13=15mm. ... 133
Figure 4-19 Experiment results of identical distances between beams. D12=11mm, D13=17mm... 135
Figure 4-20 Experiment results of identical distances between beams. D12=11mm, D13=17mm... 137
Figure 4-21 Experiment results of identical distances between beams. D12=13mm, D13=9mm... 138
Figure 4-22 Experiment results of identical distances between beams. D12=131mm, D13=9mm... 139
Figure 5-1 Experiment setup of the Micro PEH with reed switch SSH ... 145
Figure 5-2 Experiment results of SCR P-SSHI using micro piezoelectric energy harvester ... 146
Figure 5-3 Circuit simulation for summing up the harvested power ... 148
LIST OF TABLES
Table 1 Recreated from [5, 6] ... 4
Table 2 Energy storage density comparison of kinetic energy harvesting [6] ... 5
Table 3. Approximate scale definition of the energy harvesting systems ... 7
Table 4 Corresponding parameters between the mechanical and electrical modeling for MCK based PEHs ... 17
Table 5. Lump parameters derived through a network analyzer for the d31 and bimorph devices used in this section ... 50
Table 6. Experimental results with voltage inputs less than requirements in comparison to estimated cases, Voc = 2.75 peak ... 63
Table 7. Beam Parameters ... 85
Table 8. Component list used in the reed switch based SSH experiment ... 88
Table 9. Performance of proposed methods under varying operating circumstances 101 Table 10. Geometric parameters of the applied beams. ... 108
Table 11. Parameters of the beams applied in experiment and simulation. ... 108
Table 12. Parameters of Magnets used in the experiment and simulation. ... 109
Table 13. Beam Parameters for asymmetric 3-beam experiment ... 127
TABLE OF ABBRIEVATIONS
IoT Internet of Things
MDOF Multi-Degree of Freedom
TE Thermal Electric
SEH Standard Energy Harvesting
SSH Synchronized Switch Harvesting
PEH Piezoelectric Energy Harvester
MEMS Micro-electro-mechanical-systems
SSD Synchronized Switch for Damping
SSHI Synchronized Switch Harvesting on Inductance SECE Synchronous Electric Charge Extraction
SSDCI
Synchronized Switching and Discharging to a storage Capacitor through an Inductor
DSSH Double Synchronized Switch Harvesting
LF-P-SSHI Load Free Parallel SSHI
P-SSHI Parallel SSHI
S-SSHI Series SSHI
PI Pull-in
DO Drop-out
SCR Silicon Controlled Rectifier
RDR Reed De-bounced on Resistor
RDI Reed De-bounced on Inductor
SP-SSHI Self-Powered SSHI
Chapter 1. Introduction
The energy crisis and the demand of smart objects have attracted the scholar’s attention to energy harvesting. Among the methods, piezoelectric materials have a relatively high energy density, comparing to other forms of mechanical energy harvesting materials. However, there are some limitations to break still, which would be furthermore mentioned in the next sessions. In this chapter, motivation, bottleneck and the project aim would be pointed out, followed by the research method, the result contribution, and lastly the dissertation organization
Figure 1-1The world fossil fuel production curve forecast [1]
1.1 Motivation and Aims
Internet of Things (IoT), a future concept that is now approaching to reality. In the near future, most objects in daily life come to be “smart”- they are connected to the internet as their brains, with their own sensors to “feel” the world. Looking to the future, Cisco IBSG predicts there will be 25 billion devices connected to the internet on the upcoming 2020 [2] (Figure 1-2(c)). In the near future,
infrastructures like bridges, roads can be self-monitoring. At home, not only the electronics, anything you can name: garage, table, bed curtain… may bear wireless sensors, to make life easier (Figure 1-2). It would bring inconvenience, however, if each of the sensing nodes not connecting to electrical power requires battery replacement. On the other hand, to supply all the additional sensor, the electrical power is a certain requirement. However, the energy crisis is also a happening event. The major source of electrical power – crude oil has reached its peak of discovery and also other fossil fuels that come with it are facing the same crisis (Figure 1-1). Renewable and clean energy sources are developed, and energy harvesting is among which.
To supply the sensing nodes with clean and renewable energy, energy harvesting systems arose from the researches, and became a popular field of study. As the development of the ultra-low power electronic strives, the power requirement of the wireless sensing nodes has dropped to the scale of milli-watts and microwatts. The lowering of the power requirement creates the possibility to self- power by energy harvesting the ambient environment. The strong need of the market, is predicted to grow from the market value of $1,276 million to $6,225 by 2024, as forecasted by Inkwood Research during 2017. (Figure 1-3).
Energy harvesting, is to transform energy from another form to electricity, e.g. from solar power, heat gradient, or other mechanical forms. Mechanical forms such as vibration can be found everywhere in our daily life, any equipment with rotating motors may vibrate when the center is not placed ideally. Infrastructures such as bridges vibrate as vehicles passes by. Natural sources such as wind or human motion, are also popular field for vibrational energy harvesting. Moreover, vibrational sources provide a feasible power density comparing to other commonly seen source Table 1.
(a) (b)
(c)
Figure 1-2 The IoT concepts
(a) Smart home concept [3] in IoT (b) Typical wireless sensing node system driven by an energy harvester (c) CISCO’s projection to the number of devices connected to the IoT
As mentioned in Table 2, piezoelectric energy harvesting has a relatively high energy density compared to electrostatic and electromagnetic means. Thus, we have chosen the piezoelectric energy harvesting method, as it could harvest mechanical energy such as vibration or deformation of its hosting device.
Figure 1-3 The energy harvesting market forecast
The value of 2016 was $1276 million, and is forecasted to grow to $6225 million by 2024. Provided by Inkwood Research. [4]
Table 1 Recreated from [5, 6]
Energy Source
Power Density
W/cm2
Draw Backs
Requires Rectifier?
Solar
15000
Outside Input range is wide due to light source. X 100 Inside
Vibrational 375
Limited operating frequencies, varying vibrational frequencies
O
Temperature 40 Gradients are usually not large enough X
RF
Range too Wide
Coupling and Rectification O
Table 2 Energy storage density comparison of kinetic energy harvesting [6]
Type
Practical Maximum (millijoules/cm3)
Aggressive Maximum (millijoules/cm3)
Piezoelectric 35.4 335
Electrostatic 4 44
Electromagnetic 24.8 400
Cantilever beam, as an old topic in vibrational energy harvesting, is easy to fabricate and analyze.
It is frequently used as a mother structure of the vibrational energy harvesting device. For example, by attaching a piezoelectric patch on its root, a simple vibration harvester is born. However, cantilever beams inherit an efficiency issue of operating frequency. As we know, mechanical structures have resonance frequencies, which would transform the input power to the greatest level of deformation.
When the operating frequency is near the resonance, the device then works with its optimal efficiency.
Therefore, expanding the working bandwidth has been long studied. Using multiple beams with close resonances is a commonly used technique. One of the target in this work, is to expand the working bandwidth using a new form of beam arrays mechanically coupled with repulsive magnetic forces.
To harvest the generated electrical power, an interfacing circuit for energy collection is required.
Synchronized switch harvesting (SSH) is a popular solution to increase the harvested power. The main idea is to switch on and off the switches on certain time to alter the current flow, so that the electrical characteristic is changed to a better efficiency. Other than the circuit topology, the switch design is also essential. Electrical smart switches were designed to determine the switching instance, due to the passive component used, certain amount of energy loss is inevitable.
Despite the well-designed functions proposed by previous works for the SSH, the complexity of the circuit also brings new issues due to the vast components, threshold voltage, frequency selectivity and inherited filters which are undesired. These tradeoffs may pay-off when supplant power is generated, such as in bulk sized piezoelectric harvesters (PEH). But when the generated power is limited, to make the best use of the power is then important. In this work, we aim to design a circuit with simplicity, ultimately compatible with Micro-electro-mechanical system (MEMS) devices, which are limited in power generation.
In this research, we aimed on the two previously mentioned issues, by designing two new methods to improve them. A type of mechanical-electrical hybrid switch was designed based on reed switches, to reduce the energy loss of the circuitry. The operating bandwidth was improved by magnetic connection, which gives the structure a MDOF like output, but with evenly spread stresses.
Comparing to electrical connections, this method can achieve a broader bandwidth without considering the parallel or shunt connection effects. A suitable circuit was referenced, where the connection between the beams are separated by inductors, and the interference during connection is reduced.
1.2 The Energy Harvesters
To meet different applications and working conditions, energy harvesters come in different size (Figure 1-4), from macro to nano, there are also vast applications. Table 3 shows some practical applications that goes with different scales of energy harvesting devices (in size, assuming the power/size ratio is positive). The applications that suits within multiple are colored with the same hue.
From above mentioned, one can understand that, all of the devices can be included in IoT.
The power-grid can be provided by macro scale harvesters such as wind turbines, solar panels,
or piezoelectric alignments under the road. The harvested energy from macro sized devices can be used to provide street lights, and also monitor structural health of the infrastructures. For a scale lower, at the bulk size, wearable devices for consumer’s industries or health monitoring like smart watches can be supplied. Then, to the micro scale, system on chips and some biomedical implants lies within the size. As for the nano-scale, some nano-sensors such as for military gas sensing can be applied.
The methods listed in Table 1 can be further classified in to kinetic energy harvesting and radioactive energy harvesting. Solar, RF, and thermal forces are radioactive energy sources, while vibrational is kinetic. For kinetic forces such as vibrational or rotary, it can be further categorized by its harvesting method, such as electrostatic, electromagnetic, and piezoelectric (Table 2).
For ambient energy harvesting, as listed in Table 1, solar energy seems to be the most promising method. However, the application conditions restrict solar energy harvesting system from general use.
That is, some areas on earth do have sunshine all year long, but some don’t. The climate is an unpredictable source. Therefore, other harvesting sources should be also considered. In the following of this section, some energy harvesting techniques from different sources will be introduced.
Table 3. Approximate scale definition of the energy harvesting systems
Size (in meters)
Scale Names Applications
100~103 Macro/Meso Power-grid
structure monitoring
IoT 10-3~100 Meso/Bulk Wearable devices /
Health Monitoring
10-6~10-3 Micro System on chips
Biomed-Implants
~10-9 Nano Military: Dust Project
Figure 1-4 Energy harvesting devices in different scale in size corresponding to power output [7] [8]
[9, 10]
1.2.1 Radioactive Harvesters
Solar energy has been long studied and applied. It is already in use for large scale energy generation. It comes in a great variety of range: from the size of a wrist watch to grid-connected units (Figure 1-5). In different places, the maximum radiation of the sun varies, from Norway to Congo, from indoor to outdoors. The solar cells are usually made from semi-conductor materials, crystalline silicon (89%), amorphous silicon (10%), cadmium telluride (0.5%), copper indium, diselenide and gallium arsenide.
(a) (b)
Figure 1-5 Solar harvesters in different scales
(a) A small scale solar harvester [11] (b) Large scale solar cell connected to the grid [12].
As shown in Figure 1-6, thermal energy harvesters utilize the thermoelectric (TE) conversion to convert thermal energy into electric. A harvesting cell basically consists of a thermocouple, semiconductor of a P-type of an N-type. The two semiconductors are connected electrically is series, and thermally in parallel. As there exists temperature gradient between the hot plate and the cold plate, free carriers flow from the hot plate to the cold, causing a potential difference between the cold plates.
The difference of the potential can then create electric energies to be harvested.
Places with constant thermal differences, such as machines that produces waste heat, human skin and the environment are sources for the devices. However, when human body sense the environment change, the skin will reduce the surface temperature to save the inner heat of the body. This lowers the efficiency of the device. Thus, as long as wearable devices are considered, one has to take account of human self-conditioning.
The theory is, as we live in a life full of radio frequencies, TV stations radiates enormous amount of them. TV, WIFI, radio, cell phones… if we could just setup a set of antenna for current induce, the power can be recycled. A well-known radio frequency energy harvesting technique is the wireless
charging technique for mobile phones. However, for mobile phones, the radio frequencies are produced by the charger, not the natural ambient frequency. It was previously developed for bio- medical uses. For instance, when an implanted cardiac defibrillator is used, the battery gradually dies out. Another surgery to replace the battery is a waste of resources and also a torture to the patient.
(a) (b)
Figure 1-6 Thermal Energy Harvester
(a) Working mechanism of a single cell [13] (b) an actual thermal harvester device[14]
The examples to charge batteries above are both active, where a radio frequency producing device is used, instead of ambient environments. Figure 1-7 shows an academic experiment, where researchers set the harvester 6.5km away from the Tokyo TV tower [15]. The antenna, mounted on the device, is bulky so that the energy capture is enough. No obstacle is between the TV tower and the harvester, and the result, as shown in the right of Figure 1-7 (b). The blue and red curves indicate the power required to charge the super capacitor. The green, in micro-watts is the harvested power from the location.
(a)
(b)
Figure 1-7 A radio frequency energy harvester, acquiring energy 6.5 km from the TV tower (a) Experiment Setup (b) The schematic of work flow (left) and the experiment results (right) [15]
From this result, we can conclude that the radio frequency energy harvesting is a “city” option for IoT. First of all, you have to live close to the TV tower, or anything that strongly emits radio frequency. Then, the antennas set on the device is bulky, at least for now. The efficiency may be greatly reduced indoors. It is however useful, for infrastructure health monitoring in the city, for their antennas can be mounted on the construction itself.
1.2.2 Kinetic Energy Harvesters
Kinetic energy harvesters harvest energy from structural changes such as movements,
displacements or deformations. Vibration and rotary energy harvesting a commonly seen examples.
They can be easily found on human body and also in the environment. Bridges, buildings are examples that vibrates. It is the most intuitive- for instance, conventional power plants use steam from heat created from fuel to drive the rotors. Then, by Faraday laws, current are induced to be stored.
Clean energy harvesting like wind and wave energy harvesting, takes the advantage of air/fluid flows to cause the deformation or rotation of harvesting devices. The two mentioned type can be also in grid-scale.
Figure 1-8 General spring mass damper model for transducers
Other than the magneto-electrical method of Faraday laws, electrostatic and piezoelectric materials are also popular in smaller scale energy harvesting. Vibrational harvesters, as one of the most commonly used structure, usually consists of a host structure, such as a spring or a cantilever beam, that can also be modeled in to a mass-spring-damper model (Figure 1-8). It is however restricted to its resonance frequency. There are several bottlenecks: First, on bulk devices, resonance frequencies can be a few tens to a few Hz. However, the miniaturizing of the device brings the resonance frequency to several hundred or kilo-hertz. The ambient frequencies of our natural world is below 120 Hz. That is, 120 Hz is one of the commonly seen target frequency for energy harvesters,
due to the 60 Hz city power doubled by the rectifier. Secondly, the resonance frequency of the structure, which provides the optimal efficiency, is also restricted. Thus, only a small band of specific frequencies are feasible for optimal power output. To overcome the small operating bandwidth, broadband structures would be discussed later on.
Magneto-electrical method is based on Faraday’s law, as mentioned. The concept is to use a moving magnet, where its flux is linked with a coil, or vice versa. During the movement, changing voltage potential is inducted by the varying magnetic flux m through the coil. Other than vibration, any motion that causes varying flux can induce energy output. It is therefore suitable for wearables since human motion are in low frequency and is not consistent nor periodic, for example the device shown in Figure 1-9(b). With low frequencies and non-consistent movements, the harvested power can be lower than consistent conditions. The proposed wrist band is able to charge a capacitor with 470 μF 25 V up to more than 0.81 V during at most 132 ms from any single excitations.
Figure 1-9 Magneto-electrical energy harvester
wearable device with random movements[16] (Non-spring mass system)
For the IoT wireless sensing nodes, the most appealing advantage of electrostatic energy
harvesters is that its fabrication process is compatible to the MEMS process. It would indicate that it can be made in MEMS size, and also with batch process- ready for massive production. On vibration, the varying capacitance of moving capacitors changes the electric field. The electric potential change then induces charges, and thus the energy can be harvested.in electrostatic energy harvesting. To create the variable capacitance, external voltage bias or pre-charged materials such as electrets are used. As the device vibrates, the relative distance between the two poles changes, inducing the current flow. The vibration can alter the capacitance value by three configurations (Figure 1-10): (a) by changing the gap between the electrodes (b) by changing the overlapping area (c) by changing the overlapping electric field. According to [17], the authors pointed out that, considering the MEMS process, configurations (a) and (b) requires wire leading or bonding on the moving parts, which would lead to the increase of the fragility and thus lowering the feasibility. Therefore, configuration (c), which had both polarities on the same side shows the most promising opportunity with MEMS energy generators. [18, 19]
(a) (b) (c)
Figure 1-10 Three configurations of the electrostatic energy harvesting (a) gap changing (b) overlapping area change (c) counter electrode change
The piezoelectric beam is a widely used conventional vibration energy harvester, as shown in Figure 1-11 (a). It consists of a cantilever beam, with a proof mass to adjust and lower the resonance
frequency. A piezoelectric material patch is bonded to its root, as it is the location with most strain.
Figure 1-11 (a) also shows that when the beam is bending upwards, the beam body has compressive force above its neutral axis. Below the neutral axis, the tense force is present. Therefore, it is also the deformation direction of the piezoelectric patch. With the understanding of the deformation direction of the patch, the poling of electrodes may define the working mode of the piezoelectric patch, d31, and d33. The subscript 31 and 33 describes the two axis directions of stress and electrical field that occurs during the deformation, as shown in Figure 1-12(a) and (b). The devices in this work uses mode D31, for its full utilization of the electric field, and also the fabrication simplicity.
(a) (b)
Figure 1-11 A piezoelectric cantilever based energy harvester (a) Schematic (b) MCK model
(a) (b)
Figure 1-12 Working modes of the piezoelectric beam
(a) The electric field perpendicular to the strain direction in mode d31 (b) The electric field parallel to the strain in mode d33[20]
1.2.3 Modeling of Cantilever-Based Energy Harvester
As a vibrational energy harvesting device, the piezoelectric cantilever beam can be also model into a mass-spring-damper model (MCK) model as shown in Figure 1-11 (b). The model can be then described with eq. (1.2.1) and (1.2.2) [21]. In the equations, 𝑢=𝑢1-𝑢0, representing the beam displacement, F represents the piezoelectric force due to the elasticity and converse piezoelectric action of the piezo patch, for the equivalent damping factor, KE the short circuited stiffness, and M is the equivalent mass. I stands for the output current, V the piezoelectric output voltage of the piezoelectric element, C0 the clamped capacitance and 𝛼 the force factor of the piezoelectric patch (electrical-mechanical turns ratio).
Eq. (1.2.3) depicts the energy distribution between different forms. It is an integrated form of (1.2.1) within the period of working frequencyτ, from the starting time t0. The converted energy will be stored into the piezoelectric element in C0 and also delivered to the circuit through the circuit, which is expressed as eq. (1.2.4). As for eq. (1.2.4), it describes the energy relation by multiplying the voltage to eq. (1.2.2).
( ) E
Mu t F V K uu (1.2.1)
I uC V0 (1.2.2)
2 2 2
1 [( ) ] ( ) [ ] ]
2
o o o
o o
o o
o o o
t t t
t t
t t E t t t
M u C
u dt K u
Fudt
Vudt (1.2.3)0 0
0
0 0 0
2 0
1 [ ]
2
t t
t
t Vudt t VIdt C V t
(1.2.4)The MCK model can be also expressed as equivalent circuits so that one can apply interface circuitry simulations considering the mechanical characteristics [22]. An equivalent model of a
MDOF degree energy harvesting system can be found in Figure 1-21(d). According to [23] and [22], the corresponding parameters between the mechanical and electrical domains is found in Table 4.
Therefore, a single beam with its first resonance frequency considered can be modeled as a simple MCK circuit as shown in Figure 1-13.
Table 4 Corresponding parameters between the mechanical and electrical modeling for MCK based PEHs
Mechanical Parameters ( u0 = system displacement)
Equivalent Electrical Parameters
Relative displacement yn=un-un-1 1, 2,..., n
y y y
Charge q q1, 2,,qn
Relative velocity y y1, 2,...,yn Current i i1, 2,,in
Massm m1, 2,,mn Inductors L L1, 2,,Ln
Damper C nn, 1 C C1, 2,,Cn Resistor R R1, 2,,Rn
Spring Stiffness (Reciprocal)
1 2
1 ,. 1
, .,
1 .
E E En
K K K
Capacitor C C1, 2,,Cn
Inertia force on mass
1u0, 2u0, nu0
m m ,m Ideal Voltage Source v v1, 2,,vn
Electromechanical turns ratio Turns ratio of ideal transformer N
Figure 1-13 Equivalent circuit model of a single beam considering only the first resonance
1.3 Harvesting with a Broader Bandwidth
As mentioned afore, the cantilever structure is hindered by its small working bandwidth near its reonance frequency. Figure 1-14 shows the bandwidth of a piezoelectric cantielver beam output respond to frequency. Qm, or the quality factor, is a reference to define the bandwidth. The higher the quality factor, the higher power output is presented in the resonance, and so is the curve sharper. It would also refer to a small working bandwidth. Meaning that half a hertz away would bring the output back to a very low level. As a tradeoff, increasing the bandwidth, would also lower the peak energy output of the beam.
To apply in different circumstances and to a wider range of operating frequency, it has been long that researchers strived to broaden the operating bandwidth for PEH devices. Stoppers, beam arrays, up conversion, bi-stable structures, and MDOF structures are some of the popular methods. However, one should be reminded that the decrease of the quality factor also lowers the output voltage, to keep the total amount of energy equal. Thus, a target of the broadband design is to increase, or at least not decrease the overall power output.
Figure 1-14 A typical voltage output respond to chirping frequency.
Nonlinear mechanical behaviors are studied to improve the working bandwidth of the oscillating harvesters. Tunable, MDOF, stoppers and bistable techniques are the few popular methods due to the ease of implementation and good performances.
1.3.1 Beam arrays
An intuitive method to create broader bandwidth is to combine multiple beams, each having a different resonant frequency. [24, 25] It is however an issue designing the circuit to handle the energy harvested provided by various beams.
(a) (b)
Figure 1-15 Cantilever array to create broad band [25]
(a) schematic diagram (b) numerical results showing ten beams in series connection
1.3.2 Stoppers
(a) (b)
Figure 1-16 Model for stopper in forms of cantilever adopted from [26]
(Redrawn) (a) MCK model (b) the stiffness k and damping c responding to the distance between the masses dn
Stoppers also enhance bandwidths [27] in forms of rigid or beams. For instance the mechanical switch which also acted as stoppers in [41] was not rigid, and [28] has a rigid case. In [41], two beams with higher frequencies are used, which can be modeled by the MCK model as shown in Figure 1-16.
On the point of contact, the two MCK systems merge, and the k and c values sum up as if it is a step increase.
The research done in [26, 29] showed a promising results using stoppers with cantilever beams.
With a stopper on one or both sides, as shown in Figure 1-17 (a), the tip displacement of the beam is limited to the distance of the stoppers. Figure 1-17 (b) shows the result when stopper is applied to cantilever beam when the frequency is scanned upwards. As it is mention in the work, additional stiffness occurs to the system when the beam is exerted to the stoppers. [30] uses a cantilever beam with higher resonance frequency as the top stopper, and rigid case as the lower stopper. The beam
with higher resonance frequency is also equipped with piezoelectric elements, so that the up converted energy can also be harvested. By the term up conversion, means that the structure uses a low or non-resonant device to strike a structure with high resonance frequency, and therefore creates energy output with higher frequency with low frequency driven systems, as shown in Figure 1-17 (c).
(a) (b)
(c)
Figure 1-17 Results comparisons of different stopper distances on both sides
(a) stopper on both side structure, with one side rigid and the other as an up conversion beam [30]
(b) [26] (c) up converted result of [30]
1.3.3 Bistable Structures
Bistable can be implemented by tip magnets [31] [32], bucked structures [33, 34], and other magnetically designed structures[35]. It provides two energy wells, where the beams are stable and is linear like within the trap of the well. According to [36], it provides three different working states depending on the input amplitude. In the first state, where the amplitude input is low, the beam would oscillate within one of the energy well. As the amplitude of the oscillation is increased, the second state is reached. The beam oscillates in a chaotic track, between the two energy wells. When the amplitude is increased, overcoming the wells, a periodic characteristic occurs again. Figure 1-18 shows some schematics of the magnetic driven bi-stable setups.
As another form of realizing bi-stable structure, Figure 1-34 (a) and [34] are non-linear device called Buckled-Spring-Mass system, adopted with stoppers, targeting at the combination of both advantages from the two nonlinear characteristics. The resulting outputs are shown in Figure 1-19.
(a)
(b) (c)
(d)
Figure 1-18 Bistable energy harvesting concepts
(a) Energy well [36] (b) Tip magnet [31] configuration (c) Other magnetic setup [35] (d) Results of under increasing accelerations from 0.1 m/s2 to 10 m/s2 , a-h [35]
(a)
(b)
Figure 1-19 Output result of buckled-spring-mass systems
(a) with a stopper [33] (b) With out stoppers. Theoretical voltage output corresponding chirping frequencies under different acceleration levels with foraward and backward sweep: a. b. 0.075m/s2 ;
c. d.0.5m/s2 ; e. f. 3m/s2 [34]
1.3.4. MDOF structures
(a) (b)
(c)
Figure 1-20 Stacked MDOF Modeling
(a) The dimensionless harvested power and the harvested power density versus the number of DOF of the PVEH (b) General MDOF model used in the work (c)Analytical results comparing to experimental results for 2DOF structures, the left shows the output power for the first beam, and the
right shows the output for the second [37]
Multi-degree of freedom is another method to improve bandwidth[38, 39]. [23], in 2012 proposed a model with a mother structure for the first degree of freedom, with the 2nd and 3rd degree of freedom installed on the mother structure shown in Figure 1-21. In 2015, [37] proposed an analytical proof from 1DOF to 5DOF, with the stacking structure where nth structure mounted on the n-1th body structure (2nd on the 1st , 3rd on the second), shown in Figure 1-20 . In this work, a 2 DOF
experiment is performed to prove the theoretical assumptions. Analytical results showed that the increase of the degree of freedom will also increase the power density of the device. [40-43] showed 2DOF structures and results.
(a) (b)
(c)
(d) (e)
Figure 1-21. Mother-Sibling Model of MDOF PEH redrawn from[23]
(a) 2DOF degree model, piezoelectric harvester on the 1st structure (b) 2DOF degree model, piezoelectric harvester on the 2nd structure (c) Generalized MDOF for PEH, with piezoelectric
element bonded on host structure (d) Equivalent Circuit model of the MDOF degree energy harvesting system (e) Dimensionless optimal power output of 3DOF model from [23]
For 2DOF modeling using the structure [23] has proposed. Eq. (1.3.1) represents the major beam, or beam 1. Coefficients with subscript numbers identify the beam number. Unidentified coefficients y is the displacement difference of the two masses, y= u2-u1. Cn, where the integral n >0, is the damping coefficient of the beam. The MDOF equation and be further expanded, and simulated by circuitry representations as shown in Figure 1-21(d) .
2 2 2 2 2 0
1 2 1 1 2 1 2 0
0
( ) ( ) 0
0
E
E
m y C y K y m x m u
m m u C u K u V m y m m u
u C V V R
(1.3.1)
2 2 2 2 2 0
1 2 1 1 2 1 2 0
0
( ) ( ) 0
0
E
E
L
m y C y K y V m x m u
m m u C u K u m y m m u
u C V V R
(1.3.2)
2DOF devices are most easily fabricated. One of the realized 2DOF structure was proposed by [43, 44]. As shown in Figure 1-22, a cut-off structure was designed to reduce the overall length of the device. The 2DOF structure is originally as the upper right. It can be transformed to the lower right structure. Then beam of m2 is folded in, which is still identical to that of the first. It is then designed with a similar aspect ratio, but with a full width for the root.
An stainless steel based MEMS 2DOF design referencing [44] was fabricated [45]. Simulation was also conducted to understand the stress distributed on the resonance. It was worth noticing that the stress is severe on the edges of the root. This shortens the device lifespan, due to the fatigue fracture which would cause on the most stressed locations.
(a) (b)
Figure 1-22 2DOF Structure design and results [44]
(a) redrawing of the proposed 2DOF structure, (b) two different experimental results with different proof mass ratios.
(a) (b)
Figure 1-23 Stress simulation of a 2DOF beam [45]
(a) on first resonance (b) on second resonance
Another structure of 2DOF is fabricated in MEMS, the structure was designed using spiral springs and two masses [46], shown in Figure 1-24. In the results, we can see that the two resonances are far apart, and the working bandwidth was divided into two bands.
(a) (b)
Figure 1-24 Spiral MEMS 2DOF device [46].
(a) Fabricated device (b) Experimental results
From the researches, one should notice that most 2DOF devices have a host structure, which is used to mount the sub structures. As shown in Figure 1-23, the root of the hosting beam structure endures a high level of stress. From practical consideration, the device should be fragile at the location.
1.3.5 Up Conversion
As the size of the device gets smaller to suit in the small sensors, the operating frequency also gets higher. However, natural vibrating frequencies fall below 120 Hz. To resolve, up conversion was designed to lower the operating frequency. Figure 1-25 (a) shows an typical up-converting design
using electromagnetic energy harvesting [47]. In electromagnetic energy harvesting, the magnetic mass induces the current flow. Figure 1-25 (b) shows that the system is driven in the lower frequency (like the environment), and the mass would trigger a higher output frequency, which is the device resonance.
(a) (b)
Figure 1-25 Up conversion design using electromagnetic energy harvesting [31]
(a) Structure design (b) Trigger signal and up-converted signal
[48] shows a piezoelectric up converter by placing ridges on the lower resonant. When the lower resonant moves, the ridges were then brushed over by the probe attached to the higher resonant.
Magnetic methods are also applied [49]. The magnets aligned in front of the beam tip create additional tip displacements over the base displacement.
1.3.6 Active Resonance tuning
By using additional piezoelectric actuators, [50, 51] one is able to alter the moment of inertia or the structural stiffness to reach the goal of tuning. Moving the location [52] or changing the mass of the proof mass can also tune the resonance frequency. However, the methods neither requires additional power sources, or human tuning.
(a) (b) Figure 1-26 Tuning by preloading on axial direction
(a) cantilever [53] (b) fixed beam [54]
(a) (b)
(c)
Figure 1-27. Magnetic resonance tuner
(a) Experiment setup (b) Lump Model of the device (c) Experiment Results. [55]
Tuning the stiffness KE of the structure can also save spaces, it also keeps the calculation and structure simpler. Giving the structure an axial preload can reach this goal [53, 54, 56, 57]. [56, 57]
uses magnets to provide axial forces, while the other two use clamping techniques. An alternative stiffness tuning was realized by using magnetic forces to tune the simple cantilever beam [55] [58]
from the vertical direction. To tune the stiffness, or the spring coefficient in the lump model, one or two magnets can be placed below and/or above the beam, with also a magnet on the tip of the beam.
The distance of the magnets was tuned, resulting in the change of the repulsive or attractive force applied to the tip of the beam.
The force Fmag(d) between cylindrical magnets can be represented as the equation below:
2 2 2
2 2 2 2
0
( ) 1 1 2
( 2 ) ( )
r m
mag
B A l r
F (d)=
l d d l d l
(1.3.3)
To obtain the spring coefficient kmag in Figure 1-27 (b), Hooke’s Law is used with eq. (1.3.3). By differentiating the force equation on the magnet distance d, eq. (1.3.4) can be derived.
2 2 2
2 3 3 3
0
( ) 2 2 4
( ) ( 2 ) ( )
mag
Br Am l r
K d
l d d l d l
(1.3.4)
And therefore, the new system damping coefficient of a single beam K’E would become:
'E mag E
K K K (1.3.5)
1.4 The Interfacing Circuits
To obtain the energy transduced, an interfacing circuit is required. The design of the interfacing circuit determines the performance of the energy harvesting system. Most energy generated in mechanical energy harvesting such as vibration comes in alternative current (AC). To retain the energy in storage devices such as batteries or capacitances, rectification to direct current (DC) is
required. The basic method is to use a diode based full bridge recitfier, and a capacitance in parallel to the load. It is named as standard energy harvesting (SEH) in this dissertation.
However, adding a electrical load would increase the damping of the piezoelectric element.
Lesieutre et al, [59] had discusses the damp increase in the system due to the electrical load. Moreover, due to the large intrinsic capacitance of the piezoelectric element, the impedance matching circuit is important to reach the optimal generated power. Therefore, different types of circuits were designed to balance the drawbacks. [60, 61] showed that with adaptive control and an circuit consisting of an AC-DC rectifore and a DC-DC step down converter, the increased harvested power percentage is around 325%. However, it is not yet feasible for micro-scale self-powered harvesting system – the power consumption of the controllers to drive and calculate the duty cycle may cost more than what’s havested.
One of the most etseemed method is the synchronized switch harvesting (SSH). As mentioned previously, energy harvesting was counter usage of damping control. Originated from synchronized switch damping (SSD) [62], a vibration control method, the switching techniques are originally categorized in to two types according to the circuit topology. The first type has their switches placed before the rectifier: The synchronized switch harvesting on inductance (SSHI) [63] is introduced in 2005. Considering the relative placement of piezoelectric material, two different types of SSHI by the arrangement of the switch-inductor set are defined: When the inductor-switch set is placed in parallel to the piezoelectric element, it is defined as the parallel SSHI, (P-SSHI). Similarly, in series arrangement, the circuit is named as series SSHI (S-SSHI) [64]. Another configuration to improve is the hybrid SSHI, proposed in 2011[65]. Active energy harvesting and improved SSHI [66] (2012) aimed to improve efficiency by integrating the switches into the rectifier. The second group has the switches positioned after the bridge rectifier, such as SECE (Synchronous Electric Charge Extraction,
proposed in 2005 [67]) and SSDCI (Synchronized Switching and Discharging to a storage Capacitor through an Inductor)[68](2009).
Figure 1-28 Different SSH circuits, adopted from [21]
According to [21], SSHI, SSDCI and active energy harvesting provides direct energy transfer to the load. Which would hinder the energy harvesting due to the back coupling. That indicates, with direct energy transfer, one has to consider the impedance matching for optimal load.
To decouple the impedance, SECE and DSSH (Double Synchronized Switch Harvesting) can be used. DSSH places the switches on both sides of the rectifier [69], while decoupling is realized by using the inductor as a de-coupler. When the decoupling occurs, the optimal power is ideally irrelevant to the loading impedance.
Figure 1-29 Normalized harvested powers under constant vibration magnitude. [21]
The above mentioned circuit topologies are shown in Figure 1-28. Later, An advanced version of DSSH, ESSH (Enhanced Synchronized Switch Harvesting) was then proposed during 2010 [70].
The normalized harvested power for comparison is shown in Figure 1-29, where we can visualize the
load decoupling.
Regarding the decoupling effect, SECE and DSSH have successfully decoupled the load with constant power output. SSDCI has good decoupling characteristics with low impedances. Series SSHI has a relatively low optimal load comparing to the other SSHIs. In Figure 1-29, the SSH circuits have their non-ideal circumstances excluded. Therefore, taking account of the switch loss and the damping loss, the actual gain compared to the SEH should be considered lower.
1.4.1 Theoretical Modeling of the Interfacing Circuits 1.4.1.1Standard Rectifier
As the most basic topology, SEH subjects to energy feed backs. Therefore, SEH is not able to provide the maximum power. Figure 1-30 (a) shows the typical AC waveforms of SEH. One can observe that there is a phase difference between the rectifier loaded output piezoelectric voltage V, and the piezo current I Figure 1-30 (b)). Consequently, the product of V and I, or the output power is feedback to the piezoelectric element due to the negative power harvested (colored zone).
The maximal power output of SEH during constant force can be expressed with the equation as follows [71]:
2 2
2 2
0 2
0
/ 2 2
/ 2
L F,standard
L
L
R F
P =
R C C
R C
(1.3.6)
2
2
, 2 2
0 / 2
L
u std M
L
P R u
R C
(1.3.7)
where RL is the optimal load of SEH.
2 0
RL
C
(1.3.8)
Equation (6) can be used to express the relationship with respect to the displacement.
(a)
(b)
Figure 1-30 SEH circuit and the power feedback
(a) Standard Energy Harvesting Circuit (SEH), (b) Energy feedback due to the current-voltage phase difference (below). It is the product of the voltage and current. The piezoelectric voltage (V)
is represented by the red curve. The blue curve indicates the piezoelectric current (I).
