University of Southern California Dissertations and Theses

Electromagnetic energy harvesting from vibrations

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Electromagnetic energy harvesting from vibrations

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ELECTROMAGNETIC ENERGY HARVESTING FROM VIBRATIONS

by
Qian Zhang

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

December 2014

Copyright 2014 Qian Zhang

ii
Acknowledgements

Firstly, I would like to express my deepest gratitude to my advisor, Dr. Eun
Sok Kim, for his constant support, guidance and encouragement far beyond research.
I am very fortunate to have such a nice advisor, who supported me not only by
teaching science and technology, but also academically and emotionally during
tough times in the past years. Without Dr. Kim’s leadership and insightful
instructions, it would have been impossible to carry out this work.
I am also grateful to Dr. Mahta Moghaddam and Dr. Mark Thompson as my
dissertation committee for their valuable advice on my research work.
I am indebted to all the members in the USCMEMS group for their
camaraderie and support. My deepest gratitude goes to Dr. Shih-jui Chen, Dr.
Anderson Lin, Dr. Youngki Choe, Dr. Lingtao Wang and Dr. Lukas Baumgartel,
who trained me for lots of equipment when I first joined this group and gave me
tremendous helps. Much gratitude goes to my fellow, Arash Vafanejad, for his
friendship, assistance regarding technical questions, and collaboration in mass-
sensing project and equipment maintenance. Special thanks to Dr. Hongyu Yu for his
indispensable advice and support. I also want to thank my colleagues, Yufeng Wang,
Lurui Zhao and Anton Shkel for many useful discussions.
Finally, I would like to give my sincere thanks to my parents for their sacrifice
and endless love. Without their support, I would never reach where I am now.

iii
Table of Contents
Acknowledgements ...................................................................................................... ii
List of Tables............................................................................................................... vi
List of Figures ............................................................................................................ vii
Abstract ...................................................................................................................xviii
Chapter 1
Introduction .................................................................................................................. 1
1.1 Fully-integrated MEMS Electromagnetic Energy Harvesters ............. 3
1.2 Wafer-scale Electromagnetic Energy Harvesters................................. 4
1.3 Macroscale Electromagnetic Energy Harvesters ................................. 6
1.4 Rotational Electromagnetic Energy Harvesters ................................... 7
1.5 Energy Harvesting From Low-frequency Vibrations .......................... 8
1.6 Overview of the Chapters................................................................... 10
Chapter 1 References ..................................................................................... 12

Chapter 2
Theoretical Model and Analysis of Vibration-driven Power Generator .................... 17
2.1 Model of Vibration-driven Power Generator ..................................... 17
2.2 Energy-Conversion Efficiency ........................................................... 24
2.3 An Array of Electromagnetic Energy Harvester with Permanent
Magnets .............................................................................................. 26
2.3.1 Electromagnetic energy harvesters fabricated and assembled
on silicon wafers ........................................................................ 26
2.3.2 An array of electromagnetic power generators .......................... 30
2.4 Summary ............................................................................................ 36
Chapter 2 References ..................................................................................... 37

iv
Chapter 3
Microelectromagnetic Power Generator and Its Stack with Integrated Magnets ...... 38
3.1 Microelectromagnetic Power Generator with Integrated Magnets .... 39
3.1.1 Design ........................................................................................ 39
3.1.2 Fabrication.................................................................................. 42
3.1.3 Results and discussion ............................................................... 45
3.2 Micromachined Energy-Harvester Stack with Integrated Magnets ... 49
3.2.1 Design ........................................................................................ 49
3.2.2 Fabrication.................................................................................. 55
3.2.3 Results and discussion ............................................................... 59
3.3 Summary ............................................................................................ 67
Chapter 3 References ..................................................................................... 69

Chapter 4
Energy Harvesting with High Electromagnetic Conversion Efficiency through
Magnet and Coil Arrays ............................................................................................. 71
4.1 Design ................................................................................................ 71
4.2 Microfabricated Electromagnetic Energy Harvesters ........................ 79
4.2.1 Magnet array as proof mass ....................................................... 79
4.2.2 Coil array as proof mass ............................................................. 85
4.3 Miniature Electromagnetic Energy Harvesters .................................. 90
4.3.1 Fabrication.................................................................................. 91
4.3.2 Measurements of miniature electromagnetic energy harvesters
.................................................................................................... 92
4.3.3 Energy-conversion efficiency .................................................. 102
4.4 Microfabrication of Coils ................................................................. 103
4.4.1 Electroplated coils with silicon mold ....................................... 103
4.4.2 Microfabricated coils with multiple layers .............................. 106
4.5 Energy Harvesting from 2-DOF Vibrations ..................................... 109
4.6 Summary .......................................................................................... 114
Chpater 4 References ................................................................................... 116

v
Chapter 5
Power Generation from Human Body Motion through Magnet and Coil Arrays with
Magnetic Spring ....................................................................................................... 120
5.1 Modeling and Design ....................................................................... 121
5.2 Microfabricated Coils on Flexible Substrate.................................... 132
5.3 Miniature Energy Harvesters ........................................................... 139
5.4 Summary .......................................................................................... 148
Chpater 5 References ................................................................................... 150

Chapter 6
Conclusion and Future Directions ............................................................................ 151
6.1 Microfabrication Processes for Electromagnetic Energy Harvesters .....
.......................................................................................................... 151
6.2 Miniature Electromagnetic Energy Harvesters ................................ 152
6.3 Energy Harvesting from Low-frequency Vibrations ....................... 153

Bibliography ............................................................................................................. 155

vi
List of Tables
Table 2.1 Parameters of the electromagnetic power generator on silicon
wafers .................................................................................................... 29
Table 2.2 Parameters of the array of electromagnetic power generators .............. 33
Table 3.1 Parameters of the electromagnetic power generator ............................. 45
Table 3.2 Values used in the simulations .............................................................. 54
Table 3.3 Parameters of a power-generator unit in the stack ................................ 59
Table 3.4 Summary of the reviewed electromagnetic power generators .............. 67
Table 4.1 Parameters used in the simulations ....................................................... 75
Table 4.2 Parameters of the microelectromagnetic energy harvester ................... 81
Table 4.3 Parameters of the microelectromagnetic energy harvester with
gap control ............................................................................................. 88
Table 4.4 Parameters of the fabricated miniature energy harvester ...................... 92
Table 4.5 Summary of the reviewed electromagnetic power generators ............ 100
Table 4.6 Summary of the reviewed piezoelectric [16-22], electrostatic
[23-27], electret [28-30] and magnetostrictive [31-32] power
generators ............................................................................................ 102
Table 5.1 Parameters used in the calculation of the relative motion for
non-linear magnetic suspension system .............................................. 127
Table 5.2 Parameters used in the simulations ..................................................... 128
Table 5.3 Parameters of the energy harvester with microfabricated
flexible coils ........................................................................................ 134
Table 5.4 Parameters of the miniature energy harvester I with magnetic
spring ................................................................................................... 141
Table 5.5 Parameters of the miniature energy harvester II with magnetic
spring ................................................................................................... 141

vii
List of Figures
Figure 2.1 Model of vibration-driven power generator .......................................... 18
Figure 2.2 Calculated magnitude and phase of the relative displacement
amplitude Z
0
versus vibration frequency  as a function of
damping ratio  ..................................................................................... 19
Figure 2.3 Calculated magnitude and phase of the electromotive force
(EMF) at a given acceleration versus vibration frequency  as
a function of damping ratio  ................................................................ 21
Figure 2.4 Schematic showing the components in the energy harvester. ............... 28
Figure 2.5 Fabrication and assembly process of the electromagnetic
energy harvester .................................................................................... 28
Figure 2.6 (a) Top-view photo of a 3” silicon wafer with trenches for
housing the magnet and the coil. (b) Bottom-view photo of the
silicon wafer after the diaphragm is released ........................................ 28
Figure 2.7 (a) 200-turn coil wound around an acrylic spool. (b) The
permanent magnet glued on the diaphragm. (c) Top-view
photo after the magnet and the coil are assembled ............................... 29
Figure 2.8 Measured EMF versus vibration frequency at various input
accelerations .......................................................................................... 30
Figure 2.9 Power output at the resonant frequency as a function of the
input acceleration .................................................................................. 30
Figure 2.10 The fabrication and assembly process of the array of
electromagnetic power generators......................................................... 31
Figure 2.11 The components of the array of electromagnetic power
generators. (a) Seven permanents magnets mounted on a 3”
acrylic plate. (b) The 127 μm thick silicone sheet glued on
another patterned 3” acrylic plate. (c) Seven coils glued on the
silicone sheet. (d) Four acrylic blocks placed on the coils plate ........... 32
Figure 2.12 (a) Top-view and (b) perspective view photos of the assembled
array of electromagnetic power generators ........................................... 32

viii
Figure 2.13 Measured peak voltage versus vibration frequency at different
input accelerations for each electromagnetic power generator ............. 34
Figure 2.14 Measured peak voltage and power output across a load resistor
with different resistances, at the input acceleration of 1 g .................... 35
Figure 2.15 The maximum power output versus input acceleration when
seven electromagnetic power generators are connected in
series ...................................................................................................... 35
Figure 3.1 Top-view schematic of the electromagnetic power generator
with integrated magnets ........................................................................ 40
Figure 3.2 Top-view and cross-sectional view of the magnet-proof-mass
and coils. Also shown are the magnetic field lines and
vibration direction ................................................................................. 40
Figure 3.3 Top-view 2D simulation results of the magnetic field lines in
the electromagnetic power generator .................................................... 41
Figure 3.4 Brief microfabrication process of the microelectromagnetic
power generator ..................................................................................... 43
Figure 3.5 Top-view photos of the coils and micromagnets of the
fabricated electromagnetic power generator ......................................... 44
Figure 3.6 Bottom-view photos of the fabricated electromagnetic power
generator ................................................................................................ 45
Figure 3.7 Experimental test set-up to characterize the fabricated
electromagnetic power generator .......................................................... 46
Figure 3.8 Measured EMF versus vibration frequency at the vibration
amplitudes of 5 μm and 10 μm .............................................................. 47
Figure 3.9 Measured EMF versus vibration amplitude at the vibration
frequency of 200 Hz .............................................................................. 47
Figure 3.10 Measured output voltage and power across a load resistor with
different resistances, at a vibration frequency and amplitude of
350 Hz and 10 μm, respectively ............................................................ 48
Figure 3.11 Schematic of the microelectromagnetic power-generator stack
with integrated magnets ........................................................................ 50

ix
Figure 3.12 (a) Cross-section schematic of a stacked power generator. (b)
Magnetic poles and magnetic field lines. (c) Counter-clockwise
induced current caused by downward movement of the two
magnets. (d) Clockwise induced current caused by upward
movement of the two magnets .............................................................. 51
Figure 3.13 Simulation results of (a) the magnetic flux densities versus
distance and (b) the gradients of magnetic flux (|dΦ/dz|) along
z-direction for one magnet and two magnets with same
magnetic poles facing each other .......................................................... 54
Figure 3.14 Brief microfabrication process of the microelectromagnetic
power-generator stack. (a) Etch silicon from backside by KOH.
(b) Electroplate the first-layer coil. (c) Deposit and pattern
parylene isolation layer. (d) Electroplate the second-layer coil.
(e) Etch parylene and silicon nitride by RIE, and silicon by
DRIE. (f) Fill the silicon cavity with magnetic powders and
deposit parylene. (g) Release parylene diaphragm by XeF
2

etching of silicon followed by RIE etching of silicon nitride. (h)
Stack two wafers ................................................................................... 57
Figure 3.15 SEM photos of the fabricated energy harvester showing (a) the
proof mass, cavity, and coils and (b) the details of the dual-
layer coils .............................................................................................. 58
Figure 3.16 (a) Top-view and (b) bottom-view photos of an array of four
units. (c) Top-view and (d) perspective-view photos of a stack
formed of two wafers containing Array I and Array II ......................... 58
Figure 3.17 Measured EMF (peak value) versus vibration frequency at
different accelerations for a single unit (SU) ........................................ 61
Figure 3.18 Measured and simulated EMF (peak value) versus vibration
amplitude at different resonant frequencies for a single unit
(SU) ....................................................................................................... 61
Figure 3.19 Measured EMF (peak value) versus vibration frequency at
different accelerations for a four-unit Array I with Array II
(AIS) ...................................................................................................... 63

x
Figure 3.20 Measured EMF (peak value) versus vibration amplitude at the
vibration frequency of 400 Hz for a single unit (SU), a four-
unit Array I without Array II (AI) and a four-unit Array I with
Array II (AIS) ........................................................................................ 64
Figure 3.21 Voltage waves of a single unit (SU) and a four-unit Array I
with Array II (AIS) at vibration frequency of 400 Hz and
vibration amplitude of 10 μm ................................................................ 64
Figure 3.22 Measured output voltage (rms value) and power across a load
resistor with different resistances for a four-unit Array I
without Array II (AI) and a four-unit Array I with Array II
(AIS), at a vibration frequency and amplitude of 400 Hz and
10 μm, respectively ............................................................................... 65
Figure 4.1 (a) Cross-sectional view of the magnetic field lines produced
by one magnet. (b) Magnetic flux density (
z
B ) and its gradient
( /
z
dB dz ) from one magnet ................................................................ 73
Figure 4.2 (a) Cross-sectional view of the magnetic field lines of two-
magnet array. (b) Magnetic flux density (
z
B ) and its gradient
( /
z
dB dy ) at a height of 50, 250 and 500 μm over two-magnet
array....................................................................................................... 74
Figure 4.3 Calculation of magnetic flux through a multi-turn coil ........................ 76
Figure 4.4 Magnetic flux (
z
 ) and its z-gradient ( /
z
d dz  ) versus the
distance between the coil and the magnet for a single magnet ............. 77
Figure 4.5 Magnetic flux (
z
 ) and its y-gradient ( /
z
d dy  ) versus the
coil center position when the coil is placed at a height of 50,
250 and 500 μm over the magnet array ................................................. 77
Figure 4.6 Magnetic flux (
z
 ) and its y-gradient ( /
z
d dy  ) versus the
coil center position when the coils with different outmost
diameters are placed at a height of 250 μm over the magnet
array....................................................................................................... 78
Figure 4.7 Schematic of the energy harvester with alternating north- and
south-orientation magnet array ............................................................. 78

xi
Figure 4.8 Brief fabrication process of the microelectromagnetic energy
harvester with magnet and coil arrays ................................................... 80
Figure 4.9 Top-view and bottom-view photos of the fabricated
microelectromagnetic energy harvester occupying 0.09 cc and
weighing 0.5 gram ................................................................................. 81
Figure 4.10 Measured EMF (peak-to-peak value) versus vibration
frequency at different accelerations for the microfabricated
electromagnetic energy harvester occupying 0.09 cc and
weighing 0.5 gram ................................................................................. 83
Figure 4.11 Measured EMF of 30 mV
peak-to-peak
at 290 Hz in response to a
vibration amplitude of 11 μm for the microfabricated
electromagnetic energy harvester occupying 0.09 cc and
weighing 0.5 gram ................................................................................. 83
Figure 4.12 Measured output voltage (peak-to-peak value) and power
across a load resistor with different resistances at the
acceleration of 3.75 g for the microfabricated electromagnetic
energy harvester occupying 0.09 cc and weighing 0.5 gram ................ 84
Figure 4.13 Measured power output (into 10.8 Ω load) versus input
acceleration for the microfabricated electromagnetic energy
harvester occupying 0.09 cc and weighing 0.5 gram ............................ 84
Figure 4.14 (a) Schematic of the coil array integrated to the frame with a
trench and a space. (b) Cross-sectional view of the
microelectromagnetic energy harvester with magnet array and
gap control ............................................................................................. 85
Figure 4.15 Brief fabrication process of the microelectromagnetic energy
harvester with magnet and gap control ................................................. 86
Figure 4.16 Photos of the fabricated microelectromagnetic energy harvester
with gap control..................................................................................... 87
Figure 4.17 Measured EMF versus vibration frequency at different
accelerations for the microfabricated electromagnetic energy
harvester with coil arrays as proof mass ............................................... 88

xii
Figure 4.18 Measured output voltage and power of the microfabricated
energy harvester versus load resistance at the acceleration of
3.75 g, showing a maximum power delivery when the load
resistance matches the harvester’s resistance ........................................ 89
Figure 4.19 Measured power output (into 13.8 Ω load) versus input
acceleration for the microfabricated energy harvester with coil
arrays as proof mass .............................................................................. 90
Figure 4.20 Perspective-view and top-view photos of the miniature energy
harvester occupying 26 cc and weighing 90 gram ................................ 92
Figure 4.21 Measured EMF versus vibration frequency at different
accelerations for the miniature electromagnetic energy
harvester with coil arrays as proof mass ............................................... 93
Figure 4.22 Measured EMF of 22 V at 82 Hz in response to a vibration
amplitude of 414 μm for the miniature electromagnetic energy
harvester with coil arrays as proof mass ............................................... 93
Figure 4.23 Measured power output (into 96 Ω load) versus input
acceleration for the miniature electromagnetic energy harvester
with coil arrays as proof mass ............................................................... 94
Figure 4.24 Photo of an incandescent light bulb being lit up by the
miniature energy harvester with coil array as proof mass
occupying 26 cc and weighing 90 gram that also produced the
measured data shown in Fig. 4.23, when the energy harvester
is subject to vibration amplitude of 414 µ m at 82 Hz ........................... 94
Figure 4.25 Measured EMF (peak-peak value) versus vibration frequency
at different accelerations for the miniature energy harvester
with magnet array as proof mass occupying 26 cc and
weighing 90 gram .................................................................................. 96
Figure 4.26 Measured EMF of 28.8 V
peak-to-peak
at 65 Hz in response to a
vibration amplitude of 660 μm for the miniature energy
harvester with magnet array as proof mass occupying 26 cc
and weighing 90 gram ........................................................................... 96
Figure 4.27 Measured power output (into 96 Ω load) versus input
acceleration for the miniature energy harvester with magnet
array as proof mass occupying 26 cc and weighing 90 gram ............... 97

xiii
Figure 4.28 Photos of an incandescent light bulb being lit up by the energy
harvester at input accelerations of (a) 5.6 g (corresponding to
330 µ m vibration amplitude), (b) 7.5 g (440 µ m vibration
amplitude), (c) 9.5 g (560 µ m vibration amplitude) and (d)
11.2 g (660 µ m vibration amplitude) for the miniature energy
harvester with magnet array as proof mass occupying 26 cc
and weighing 90 gram ........................................................................... 98
Figure 4.29 (a) Power output per harvester volume and FOM versus input
acceleration for various published electromagnetic energy
harvesters. (b) Power output per harvester volume and FOM
versus vibration frequency for various published
electromagnetic energy harvesters ........................................................ 99
Figure 4.30 (a) Power output per harvester volume and FOM versus input
acceleration for various published vibration-driven energy
harvesters. (b) Power output per harvester volume and FOM
versus vibration frequency for various published vibration-
driven energy harvesters ..................................................................... 101
Figure 4.31 Brief microfabrication process of electroplated Cu with Si
mold .................................................................................................... 104
Figure 4.32 (a) Silicon wafer patterned by DRIE as a mold. (b) and (c)
Perspective-view and top-view photos of 300 μm thick
electroplated coils on silicon wafer. (d) and (e) Detailed
microscopic photos of the coils ........................................................... 104
Figure 4.33 Measured EMF versus vibration frequency at different
accelerations for the fabricated microelectromagnetic power
generator with 300 μm thick electroplated coils ................................. 105
Figure 4.34 Comparison of measured output voltages and powers across
matched loads versus input acceleration for electroplated coils
with Si mold and photoresist mold ..................................................... 105
Figure 4.35 Schematic of multi-layer coils (an example of 6 coils in serial
connection) interconnected through copper filling vias ...................... 106
Figure 4.36 Brief microfabrication steps for 3D stacked multi-layer coils
with a large number of turns ............................................................... 107

xiv
Figure 4.37 (a) and (b) Top-view and bottom-view photos of silicon wafer
with electroplated coils on both sides of the wafer,
interconnected by vias through the silicon. (c) Perspective-
view photo of a three-wafer stack having multi-layers of 1080-
turn coils. (d) Magnet array suspended by laser-machined
plastic springs ...................................................................................... 107
Figure 4.38 Measured EMF versus vibration frequency at different
accelerations for the fabricated microelectromagnetic power
generator with 3D stacked multi-layer coils ....................................... 108
Figure 4.39 Measured output voltage and power across a load resistor with
different resistances at the acceleration of 1.7 g and 2.9 g for
the fabricated microelectromagnetic power generator with 3D
stacked multi-layer coils ..................................................................... 108
Figure 4.40 Measured power output (into 190 Ω load) versus input
acceleration for the microelectromagnetic energy harvester
with 3D stacked multi-layer coils ....................................................... 109
Figure 4.41 Schematic of the electromagnetic power generator harvesting
from 2-DOF vibration. Coil
X
is for harvesting from X-
direction vibration, while Coil
Y
is for harvesting from Y-
direction vibration ............................................................................... 110
Figure 4.42 Schematics to illustrate (a) energy harvesting from Y-direction
vibration and (b) energy harvesting from α-direction vibration ......... 111
Figure 4.43 Calculated normalized EMF and power output versus vibration
direction ( α-direction) ......................................................................... 112
Figure 4.44 Photos of the fabricated 2-DOF electromagnetic energy
harvester .............................................................................................. 113
Figure 4.45 Measured performance of the electromagnetic energy harvester
from X-direction vibration: (a) measured EMF versus vibration
frequency as a function of input acceleration and (b) measured
EMF and power output (into 9 Ω load) versus input
acceleration ......................................................................................... 113

xv
Figure 4.46 Measured performance of the electromagnetic energy harvester
from Y-direction vibration: (a) measured EMF versus vibration
frequency as a function of input acceleration and (b) measured
EMF and power output (into 9 Ω load) versus input
acceleration ......................................................................................... 114
Figure 4.47 Measured performance of the electromagnetic energy harvester
from 45
o
-direction vibration: (a) measured EMF versus
vibration frequency as a function of input acceleration and (b)
measured EMF and power output (into 18 Ω load) versus input
acceleration ......................................................................................... 114
Figure 5.1 Schematic of the energy harvester with flexible coils (rolled
and aligned to a magnet array for maximum magnetic flux
change) and a magnetic spring ............................................................ 122
Figure 5.2 The simulated magnetic force (a) and spring constant (b)
versus displacement as a function of magnetic field intensities
(Q
T
Q
B
) for a proof mass of 40 gram. The simulated magnetic
force (c) and spring constant (d) versus displacement as a
function of proof mass for Q
T
Q
B
=400A
2
m
2
........................................ 123
Figure 5.3 Calculated relative displacement between two magnets in the
magnetic spring with 10 Hz resonant frequency under a fixed
vibration amplitude of 0.1 m at (a) 2, 3 and 4 Hz, (b) 8, 10, 12
Hz, and (c) 20, 30, and 40 Hz ............................................................. 126
Figure 5.4 (a) Calculated magnetic field distribution of the array of two
alternating north- and south-orientation magnets passing
through a coil. The simulated output voltage in time as a
function of the displacement amplitude from 0.1 to 12.7 mm (b)
and from 19.1 to 38.1 mm (c) for two magnets. (d) Magnetic
field distribution of the array of four alternating north- and
south-orientation magnets passing through a coil. The
simulated output voltage in time as a function of the
displacement amplitude from 0.1 to 12.7 mm (e) and from 19.1
to 38.1 mm (f) for four magnets. (g) The rms values of the
simulated EMFs versus the displacement amplitude .......................... 132

xvi
Figure 5.5 Brief microfabrication process of the flexible coils: (a) Spin
photoresist and deposit parylene. (b) Deposit and pattern Ti/Cu
for connection between the coils. (c) Deposit and pattern
parylene isolation layer. (d) Electroplate copper coils. (e) Dice
the wafer to expose photoresist. (f) Lift-off to release the coils.
(g) Roll the coils on a teflon cylinder.................................................. 133
Figure 5.6 (a) Photos of the coils on a released parylene film. (b) Side-
view and (c) top-view photos of the energy harvester with
microfabricated flexible coils and magnetic spring. (d) Magnet
array suspended by the magnetic spring in the teflon cylinder ........... 134
Figure 5.7 Measured EMF of the energy harvester with microfabricated
flexible coils: (a) EMF versus vibration frequency as a
function of accelerations and (b) EMF and power output (into
21 Ω load) versus input acceleration at the resonant frequency ......... 136
Figure 5.8 Photos of plastic springs: (a) four-branch spring and (b) two-
branch spring ....................................................................................... 137
Figure 5.9 Simulated displacement under a fixed load of (a) four-branch
spring and (b) two-branch spring ........................................................ 137
Figure 5.10 Photos of the magnets suspended by (a) four-branch spring, (b)
two-branch spring and (c) the energy harvester with cylinder
magnet array surrounded by microfabricated flexible coils ................ 137
Figure 5.11 Measured output voltages and powers of the energy harvester
with two-branch spring: (a) output voltage vs. frequency and (b)
power vs. input acceleration. At the resonant frequency (52
Hz), 3.5 g acceleration (~320 μm vibration amplitude)
produces 30 μW power into 17.1 Ω load ............................................ 138
Figure 5.12 Measured output voltages and powers of the energy harvester
with two-branch spring: (a) output voltage vs. frequency and (b)
power vs. input acceleration. At the resonant frequency (17
Hz), 0.24 g acceleration (~206 μm vibration amplitude)
produces 0.3 μW power into 17.1 Ω load ........................................... 138
Figure 5.13 Schematic of the miniature energy harvester (with magnet and
coil arrays) suspended by magnetic spring ......................................... 140

xvii
Figure 5.14 (a) Photo of the miniature electromagnetic energy harvester I
with magnetic spring occupying 26 cc and weighing 98 gram.
(b) Photos of the miniature energy harvester II with magnetic
spring occupying 120 cc and weighing 180 gram. (c) Photo of
a light-emitting diode being lit up by hand shaking the energy
harvester .............................................................................................. 140
Figure 5.15 Measured EMF of the miniature energy harvester I (26 cc, 98
gram): (a) EMF versus vibration frequency as a function of
acceleration, (b) EMF and power output (into 108 Ω load)
versus input acceleration at 6 Hz, and (c) EMF and power
output (into 108 Ω load) versus input acceleration at 2 Hz ................ 143
Figure 5.16 Measurements of the miniature electromagnetic energy
harvester I (26 cc, 96 gram): (a) The energy harvester mounted
in a backpack of a human, (b) output voltage at a walking
speed of 0.45 m/s, (c) output voltage at a walking speed of
1.12 m/s, (d) output voltage at a walking speed of 2.68 m/s,
and (e) power output (into 108 Ω load) versus the walking
speed .................................................................................................... 145
Figure 5.17 (a) Measured EMF versus vibration frequency at two different
accelerations. (b) Measured EMF and power output (into 96 Ω
load) versus input acceleration at the resonant frequency .................. 146
Figure 5.18 (a) Measured output voltage at a walking speed of 1.12 m/s. (b)
Measured output voltage at a walking speed of 3.58 m/s. (c)
Measured power output (into 96 Ω load) versus the walking
speed .................................................................................................... 147

xviii
Abstract
This thesis presents microfabricated and miniature electromagnetic transducers
for vibration-energy harvesting, including theoretical analysis of a mass-spring
system and energy-conversion efficiency, fully-integrated microelectromechanical
systems (MEMS) electromagnetic power generator and its stack, a new energy-
conversion technique to convert mechanical vibration into electrical energy, and a
magnetic suspension system for harvesting energy from human body motion.
A microelectromagnetic power generator is fabricated by MEMS technologies
and characterized at different vibration frequencies, amplitudes and load resistances.
This compact generator occupies a volume of 15 × 13 × 0.4 mm
3
, as no external
permanent magnets are needed. Experimental results show that with a 20-turn spiral
coil, the device can generate an induced electromotive force (EMF) of 0.27 mV at a
vibration frequency and amplitude of 350 Hz and 10 μm, respectively. In addition,
this thesis presents a stacked microfaricated power generator that vertically
integrates multiple magnets on silicon wafers in a batch process to enhance
electromagnetic induction multiple times. The power output is increased by
increasing the magnetic flux change for each power-generator unit in the stack, in
addition to the increase due to increased number of unit. A stack consisting of two
arrays of four power-generator units is fabricated and characterized. Experimental
results show an improvement by about a factor of four on the power output from the
same coils when two power-generator arrays are stacked vertically. Specifically, an

xix
array of four microfabricated power generators occupying a volume of 51 × 11 × 0.4
mm
3
in the stack produces an induced EMF of 1.02 mV with 0.55 nW power output
when it is vibrated at 400 Hz with vibration amplitude of 10 μm.
For a new energy-conversion technique to convert mechanical vibration into
electrical energy, an array of alternating north- and south-orientation magnets is used
to enhance magnetic flux change by more than an order of magnitude. Based on this
technique, various versions of the electromagnetic energy harvester are designed and
fabricated. A fabricated harvester occupying 51 × 51 × 10 mm
3
(=26 cc) and
weighing 90 gram generates an EMF of V
p-p
=28.8 V with 263 mW power output
(into 96 Ω load) when it is vibrated at 65 Hz with vibration amplitude of 660 μm.
The power level is high enough to light an incandescent light bulb. Also, its
microfabricated version occupying 20 × 5 × 0.9 mm
3
(=0.09 cc) and weighing 0.5
gram generates an EMF of V
p-p
=30 mV with 2.6 μW power output (into 10.8 Ω load)
when it is vibrated at 290 Hz with vibration amplitude of 11 μm. Also, two
microfabrication approaches are described for 3D multi-layer coils with hundreds
microns thickness and thousands turns, which have been integrated in
microelectromagnetic energy harvesters.
For the magnetic suspension system, an analytical model of vibration-driven
energy harvester with magnetic spring through magnet and coil arrays is developed
to explore the power generation with various magnet ranges and vibration amplitudes.
Microfabricated flexible coils (rolled and aligned to a magnet array for maximum

xx
magnetic flux change) with plastic and magnetic springs are fabricated to completely
utilize the three-dimensional space. The miniature energy harvester I (occupying 26
cc and weighing 98 gram) and II (occupying 120 cc and weighing 180 gram) with
ten permanent magnets and sixteen 200-turn wire-wound coils show the resonant
frequencies of 6 Hz and 4 Hz, respectively. When the energy harvester I is placed in
a backpack of a human walking at various speeds, the power output is increased as
the walking speed is increased from 0.45 m/s (slow walking) to 2.68 m/s (slow
running), and reaches 14.8 mW at 2.68 m/s. For the energy harvester II, the power
output increases as the walking speed increases from 0.45 m/s (slow walking) to 3.58
m/s (slow running), and reaches 32 mW at 3.58 m/s.

1
Chapter 1
Introduction

During recent decades, renewable energy sources have drawn increasing
attention mainly due to ever increasing energy consumption for the world with
limited energy sources. Renewable energy sources are also reliable, last long, and
emit no pollution. One of the most exciting applications of renewable energy sources
is in powering electronic devices and systems including sensors and actuators along
with wireless communication, to rid of batteries. The primary disadvantages of
batteries are limited supply of energy that requires routine replacement, harmful
contents to the environment, and large volume and weight. There exists a significant
need for power sources that do not need a routine maintenance or replacement, as the
electronic devices and systems are embedded in a living body or placed in a harsh
environment where such routine maintenance or replacement is prohibitively too
costly. Energy harvesting from environmental sources, like motion, light, thermal
gradients and radiation, has been investigated as a clean and economic alternative
power source. Among the various environmental energy sources, vibration energy is
most promising due to its wide availability and potentially high power density.
As vibration energy is ubiquitous, harvesting vibration energy to generate
electrical power is well suited to power the low-power electronic devices, wireless
sensors and their networks. There are three main transduction mechanisms employed

2
to extract energy from vibrating environment: electrostatic, piezoelectric and
electromagnetic. Each mechanism has its pros and cons. Electrostatic energy
harvester generates an electrical voltage or charge through varying capacitance.
Although its fabrication process can be compatible with conventional integrated
circuit (IC) technologies, the capacitor needs to be initially charged with an
implanted charge or an external DC voltage source that limits its practical
application [1-2]. Piezoelectric materials can also be used for harvesting energy, as
they are capable of generating a relatively high voltage output due to mechanical
strain caused by external motion. However, piezoelectric energy harvesters have
high impedance, which mandates the load impedance to be high [3-4].
Electromagnetic energy conversion, on the other hand, is advantageous due to its
capability to drive a low impedance load and generate a high output current. But with
decreasing device size, electromagnetic energy harvesters have had a limited success
of generating a larger power level since the induced EMF rapidly reduces [5-10].
Although the energy harvesters have been optimized and fabricated with strong
bulky magnets and wound multi-turn coils, the typical output voltage is still less than
1 V [7-9]. Even with stacked multilayer magnets to enhance the magnetic field [10],
the power output of less than one milli-Watt has been reported. Especially, for
microfabricated electromagnetic energy harvesters, it is difficult to integrate a strong
magnet and a low resistance coil in a planar microfabrication process. Converting
kinetic energy (present in vibrating environment) into electrical energy with
electromagnetic transduction has already been used in macroscale power-generation

3
in hydroelectric and fossil-fuel power plants as well as in wind turbines. However,
microscale or miniature power generators are not widespread, mainly because the
induced electromotive force (EMF) decreases rapidly as the device size scales down.
1.1 Fully-integrated MEMS Electromagnetic Energy Harvesters
Various microfabrication processes such as sputter-deposition, electroplating,
packing magnetic powders, etc. have been developed for integrating permanent
magnets with micromachined silicon structure, but the quality of such processed
magnets has not been good [11-13]. For example, 10 µ m thick Nd-Fe-B/Ta was
sputter-deposited as micromagnets in a microfabricated electromagnetic energy
harvester [14], which showed a relatively low power density of 1.2 nW/cm
3
. Another
integrated microelectromagnetic energy harvester with electroplated CoNiMnP
magnets produced a maximum output voltage of 7.5 μV at the frequency of 64 Hz
[15]. It is generally difficult to deposit a thick magnet with sputter-deposition or
electroplating due to the slow deposition rate and the residual stress which increases
with increasing thickness, and may cause cracking. Magnetic powders of wax-
bonded Nd-Fe-B micromagnets have been embedded in a silicon wafer, and have
been shown to have good magnetic properties [16]. Using this method, a fully batch-
fabricated MEMS energy harvester generated 13.2 μV
rms
(predicted maximum power
of 23 pW) at resonant frequency of 530 Hz from excitation acceleration of 1g [17].
However, it is difficult to remove the residual powders cleanly by manually wiping
the wafer surface with a flat edge for this magnet fabrication process. Similarly, Nd-

4
Fe-B powders dispersed in epoxy resin have been magnetized as micromagnets and
used in a microelectromagnetic vibration energy harvester, which occupied the
volume of 20 mm
3
and generated a maximum peak-to-peak voltage of 20.9 μV at the
resonant frequency of 365 Hz and input acceleration of 1 g [18]. To avoid
voluminous external permanent magnets, various deposition techniques have been
used for micromagnets in microelectromagnetic energy harvesters, but only a low
power level of pW – nW has been delivered.
1.2 Wafer-scale Electromagnetic Energy Harvesters
Relative voluminous magnets are usually used to produce a magnetic field in
the devices because of difficulty of manufacturing micron sized magnets. Even with
permanent magnets, wafer-scale microelectromagnetic energy harvesters have been
shown to generate less than a few microwatts [19-21]. A microscale electromagnetic
energy harvester presented by Williams et al. [22] had a SmCo permanent magnet
attached to a polyimide membrane and a planar Au coil on the backside of the device,
and generated 0.3 μW from vibration amplitude of 0.5 μm at 4.4 kHz. A
microelectromagnetic energy harvester made of a permanent magnet (6 × 6 × 6 mm
3
)
on an array of coil-containing parylene cantilevers [23] was shown to generate a
maximum voltage and power of 0.67 mV and 56 pW, respectively, from 1 µ m
vibrational amplitude at 3.4 kHz. As most of commonly available environmental
vibrations are very low (less than tens of Hz), a frequency up-conversion technique
has been explored with a 50 mm long styrene cantilever, on top of which a 3-turn

5
copper coil and Nd-Fe-B magnet of 20 × 20 × 5 mm
3
reside [24]. For a 1 Hz input
vibration, the device up-converted the frequency to 25 Hz, and generated 4 nW. Also,
the frequency up-conversion technique was used, with a magnet (3.8 × 3.8 × 1.5
mm
3
) glued to a parylene diaphragm, and was shown to generate 0.57 mV voltage
and 0.25 nW power from 1.1 mm vibrational amplitude at 95 Hz [25]. When a coil
was patterned on a cantilever (25 × 10 × 1 mm
3
) surface and a permanent magnet (30
× 10 × 6 mm
3
) was close to the cantilever’s free end, 0.4 nW was delivered into 128
Ω load from vibration amplitude of 0.64 μm at 700 Hz [26]. To reduce coil resistance,
electroplating of copper was used on a silicon substrate, which was then integrated
with bulk Nd-Fe-B magnets glued on Perspex chips [27]. The harvester produced a
maximum power of 23 nW into a load resistance of 52.7 Ω from 2.6 nm vibrational
amplitude at 9.84 kHz. Yet, a different approach of letting a proof mass to vibrate in-
plane directions (rather than a more common approach of out-of-plane vibration) has
been reported with a conventionally-wound, enameled copper coil on a
micromachined silicon-cantilever paddle that vibrates between two Nd-Fe-B
magnets [28]. It generated 122 nW into 100 Ω load from vibration amplitude of 1.1
nm at 9.5 kHz. In all the cases cited here, permanent magnets are used, and manually
assembled into an energy harvester. However, the external permanent magnets
occupy a relatively large volume, and also present a cost-increasing alignment issue.

6
1.3 Macroscale Electromagnetic Energy Harvesters
Much higher power levels have been demonstrated with relatively large scale
electromagnetic energy harvesters. Through optimizing the arrangement of magnets
to maximize the spatial variation of magnetic flux, another electromagnetic energy
harvester (9.3 cc) was reported to generate 290 µW into 76 Ω load out of 3.6 g (85
µ m vibration amplitude) at 102 Hz [29]. With Nd-Fe-B magnets (4 mm in diameter
and in height) suspended by a piezoelectric bimorph, the resonant frequency of the
electromagnetic energy harvester was electrically tuned through a static electric field
applied to the piezoelectric bimorph, and more than 50 µW was delivered into 200 Ω
load, out of 2.8 µ m vibrational amplitude, over the tunable frequency range between
265 and 325 Hz [30]. With two fixed magnets (volume of 0.84 cc) assembled on a
cantilever structure that was made with traditional machining, 180 μW was obtained
from a free-end beam displacement of 0.85 mm at its resonant frequency of 322 Hz
[31]. Instead of letting magnet(s) to move in response to applied vibration, coil(s)
can be made to vibrate, while fixing the magnet(s). A coil-moving electromagnetic
generator was reported to generate output power of 400 µ W from 2 cm vibrational
amplitude at 2 Hz [32]. Now, the following summarizes various attempts to improve
several aspects of electromagnetic energy harvesters. To make energy harvester
planar, a copper foil was used to make planar coils to be integrated with planar
spring, and an electromagnetic energy harvester was reported to deliver 10.7 µ W into
100 Ω load out of 24.4 µm vibration amplitude at 371 Hz, the fundamental resonant
frequency of the harvester [33]. To lower the resonant frequency, a laser-

7
micromachined Cu spiral spring was used to support a Nd-Fe-B permanent magnet,
and an energy harvester with 1 cc volume generated 830 μW from 200 μm vibration
amplitude at 110 Hz [34]. To increase electromagnetic coupling, Halbach array was
used to obtain 150 μW, with a 55 × 55 × 4 mm
3
harvester, from 0.5 g acceleration at
45 Hz [35]. To reduce the manufacturing cost, printed circuit board and Poly(methyl
methacrylate) (PMMA) were used to produce a 7-gram harvester that generated 315
μW (into 1.2 kΩ load) out of 1 g acceleration at 78 Hz [36]. A smaller energy
harvester occupying 240 mm
3
volume was built on a cantilever beam with two Nd-
Fe-B magnets (on the beam’s free end) that provided a constant magnetic field, and
produced 0.53 mW from 25 μm vibration amplitude at 320 Hz [37]. Though these
macroscale harvesters have shown orders of magnitude higher power than the
microfabricated energy harvesters, they are still short of the most desirable power
level of Watt and beyond.
1.4 Rotational Electromagnetic Energy Harvesters
Energy associated with gas or liquid flow can be converted to electrical power
effectively through a rotational power generator. When millimeter sized permanent
magnets were manually inserted into a laser machined SU8 rotor, it delivered 1.1
mW from a rotation speed of 30,000 rotations per minute (rpm) due to about 35
L/min gas flow [38]. Another in-plane, rotary electromagnetic generator (with a four-
layer stacked Cu winding and eight arc-shaped Nd-Fe-B magnets) has been reported
to produce a maximum power of 0.412 mW when an external spindle drives the rotor

8
at 2.2 krpm [39]. A planar turbo-generator (8 mm in diameter) consisting of a
permanent-magnet-disc rotor and a silicon stator with electroplated three-phase
multi-turn coils delivered a power output of 14.6 mW and 5 W at the rotor speed of
5.8 and 400 krpm, respectively [40]. A miniaturized permanent-magnet generator
with 2-pole and multi-turn (2 mm in diameter) generated a maximum open-circuit
voltage of 51 mV
rms
and power output of 3.6 mW at 392 krpm [41]. A three-phase,
axial-flux, synchronous permanent-magnet generator with SmCo magnets rotor (9.5
mm in diameter) delivered 1.1 mW to 25 Ω load at a rotational speed of 120 krpm
[42]. To reduce friction and provide robust support, ball bearings were integrated
into a turbo generator, and 5.6 μW power was obtained at a rotational speed of 23
krpm, with 6% turbine efficiency [43]. To achieve high power output, rotational
generators need a high rotational speed, which requires a unique energy source that
is not common in environment vibrations.
1.5 Energy Harvesting From Low-frequency Vibrations
All vibration-driven energy harvesters based on these mechanisms can be
analyzed as a mass-spring system within a frame, and produce a maximum power at
its resonant frequency. Previous energy harvesters, whose resonant frequency is tens
or hundreds of hertz, are ineffective in harvesting vibration energy at less than 10 Hz
[20, 26]. Thus, it is highly desirable to make the harvester’s resonant frequency less
than 10 Hz, where many commonly available vibrations such as human body motion,
bridge vibration, ocean wave, etc. are occurring. For scavenging traffic-induced

9
bridge vibrations, an electromagnetic energy harvester occupying 68 cc was shown
to generate an average power of 2.3 µ W (into 1.5 kΩ load) from 0.54 m/s
2

acceleration at 2 Hz (about 3.4 mm vibration amplitude) [44]. Another
electromagnetic power generator with stacked multilayer magnets occupying 18 cc
generated an average power of 120 µ W (into 680 Ω load) from a root-mean-square
(rms) acceleration of 0.25 m/s
2
at 4.1 Hz [10]. To increase the power output at low
vibration frequency, the energy harvesters were developed to convert low-frequency
vibrations to a higher frequency by employing the frequency up-conversion
technique [25, 45]. However, the resonant frequencies for these devices were still
around 100 Hz, and much of the vibration energy was lost in the conversion process.
The kinetic energy from human body can be converted to electrical energy for
powering portable devices. For example, a suspended-load backpack consisting of a
pinion gear and a set of springs fixed on a pack frame was developed to show a 7.37
W power when a person carries the 38 kg heavy mass during normal walking [46].
When a sliding electromagnetic generator with permanent magnets (10 mm in
diameter, 5 mm in thickness) moving inside wire-wound coils was designed to fit in
the heel of a shoe, the harvester with two 7-gram magnets generated 8.5 mW at 5 Hz
[47]. A non-resonant energy harvester was built using a magnet ball in two
symmetric hemispheres, which are wrapped with copper wire to scavenge energy
from ordinary human motion. The prototype occupying 70 cc and weighing 68 gram
delivered a maximum power of 234 μW when mounted on the ankle during jogging
[48]. The eccentric rotor in self-winding watch industry was also introduced to non-

10
resonant generator technologies for harvesting energy from human movements [49].
A 1.5 cc prototype was fabricated with conventional winding coils and two Nd-Fe-B
magnets as an eccentric rotor, and was shown to generate power of 3 mW from 75
μm vibration amplitude at 80 Hz with initial angular rate larger than 200 rad/s [50].
When stacked microfabricated planar coils and multiple permanent magnets with an
eccentric brass mass were assembled and tested on human body, an average power of
472 μW was obtained from the 2 cc device placed on the ankle while walking at 1.79
m/s [51]. Although magnetic springs with two fixed magnets and one moving
magnet housed in a teflon tube were reported to show resonant frequencies in 7-10
Hz [52], the energy-conversion efficiency was not high for harvesting energy from a
human body walking or running. Another harvester having a volume of 13 cc was
reported to produce 0.95 mW and 2.46 mW during walking and slow running
conditions, respectively [53].
1.6 Overview of the Chapters
In Chapter 1, reviews of the current methods used for fully-integrated MEMS,
wafer-scale, macroscale, rotational electromagnetic energy harvesters, and energy
harvesting from low-frequency vibrations along with the motivation of the thesis
work are described as a brief introduction to the thesis.
Chapter 2 describes the basic principle, model and energy-conversion
efficiency of electromagnetic vibration-energy harvesting. An array of
electromagnetic energy harvester with permanent magnets is also presented.

11
Chapter 3 describes the design, fabrication and characterization of a
microelectromagnetic power generator and its stack with integrated magnets.
Chapter 4 describes a new energy-conversion technique to convert mechanical
vibration into electrical energy with unprecedented power level and incredible
mechanical-to-electrical energy-conversion efficiency.
Chapter 5 describes a magnetic suspension system, combined to
electromagnetic power generators with magnet and coil arrays, to harvest energy
from vibrations at several Hz. The hand-held electromagnetic energy harvesters
which can be used to harvest tens of mW power level from human body motion are
also presented.
Finally, Chapter 6 presents conclusions and future research directions.

12
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16
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[49] K. Sasaki, Y. Osaki, J. Okazaki, H. Hosaka and K. Itao, “Vibration-based
automatic power-generation system,” Microsyst. Technol., vol. 11, pp. 965–969,
Aug. 2005.
[50] D. Spreemann, Y. Manoli, B. Folkmer and D. Mintenbeck, “Non-resonant
vibration conversion,” J. Micromech. Microeng., vol. 16, S169-S173, 2006.
[51] E. Romero, M. R. Neuman and R. O. Warrington, “Rotational energy harvester
for body motion,” IEEE International Micro Electro Mechanical Systems
Conference, Cancun, Mexico, January 23 – 27, 2011, pp. 1325-1328.
[52] A. R. M. Foisal, C. Hong and G. S. Chung, “Multi-frequency electromagnetic
energy harvester using a magnetic spring cantilever,” Sensors and Actuators A,
vol. 182, pp. 106-113, 2012.
[53] C. R. Saha, T. O'Donnell, N. Wang and P. McCloskey, “Electromagnetic
generator for harvesting energy from human motion,” Sensors and Actuators A,
vol. 147, pp. 248-253, 2008.

17
Chapter 2
Theoretical Model and Analysis of Vibration-driven
Power Generator

This chapter describes the basic principle, model and energy-conversion
efficiency of electromagnetic energy harvesters. A vibration-driven power generator
is analyzed as a mass-spring system and the conversion efficiency as the output
electrical power over the input mechanical power is calculated. An array of
electromagnetic energy harvester with permanent magnets is also presented.
2.1 Model of Vibration-driven Power Generator
A vibration-driven power generator consists of a mass-spring system with
proof mass m suspended by a spring k and moving within a frame, as shown in Fig.
2.1. A damper d incorporates any electrical, parasitic mechanical and aerodynamic
damping. The absolute motions of the proof mass and the frame are x(t) and y(t),
respectively, while the relative displacement between the proof mass and the frame is
z(t)(= x(t) - y(t)). The equation of motion for the system is given by:
( )'' ( )' ( ) 0 mx t dz t kz t    (2-1)

18
y(t)
x(t)
z(t)
V
out
Coil
Magnet
Spring
Damper
Mass

Fig. 2.1 Model of vibration-driven power generator.
For sinusoidal, steady-state vibration y(t) = Y
0
cos t = Re{Y
0
e
j t
}, z(t) =
Z
0
cos( t+ ) = Re{Ze
j t
}, and we get kZ dZ j mZ Y m       
2
0
2
from Eq. 2-1.
Consequently,
 
 
2
2
0 0
2 2
/
1 / 2 /
n
nn
Y mY
Z
m j d k
j
 

    

  


(2-2)
where
0
Y is the frame’s vibration amplitude or the input vibration amplitude;
( / )
n
km   is the resonant frequency;  is the vibration frequency; and
( / 2 )
n
dk   is the damping ratio. The magnitude (
0
Z ) and the phase (  ) of the
relative motion are obtained from Eq. 2-2 as follows.
2
00
2
22
12
n
nn
ZY










   
 
   

   

(2-3)

19
1
2
2
tan
1 ( )
n
n









(2-4)
The relationship between
0
Z and
0
Y is dependent on the frequency  and damping
ratio 

as shown in Fig. 2.2. Near the resonant frequency
n
 ,
0
Z

increases as the
damping ratio  decreases, while
0
Z is close to
0
Y at a frequency significantly
higher than
n
 , as Eq. 2-3 simplifies to

(2-5)

10
1
10
2
10
3
-40
-30
-20
-10
0
10
20
Magnitude (dB)
Bode Diagram
Frequency (rad/sec)
ζ=0.05
ζ=0.15
ζ=0.25
ζ=0.35
ζ=0.45
ζ=0.55
0.1 ω
n
ω
n
10 ω
n
10
1
10
0
10
-1
Z
0
/ Y
0
Decreased ζ

10
1
10
2
10
3
180
225
270
315
360
Phase (deg)
Bode Diagram
Frequency (rad/sec)
0.1 ω
n
ω
n
10 ω
n
0
-90
Phase (degree)
ζ=0.05
ζ=0.15
ζ=0.25
ζ=0.35
ζ=0.45
ζ=0.55

Fig. 2.2 Calculated magnitude and phase of the relative displacement amplitude Z
0

versus vibration frequency  as a function of damping ratio .
0
2
Y

0
Y
()
n
 
()
n
 
0
Z 

20
According to Faraday’s law, the electromotive force (EMF)  is proportional to
the time-rate change of magnetic flux Φ through a coil, and is
0
sin( )
d d dz d
Zt
dt dz dt dz
   
  
      (2-6)
Then substitution of Eq. 2-3 into Eq. 2-6
3
2
0
2
22
sin( )
12
n
nn
d
Yt
dz











   
 
   

   

 (2-7)
Thus, the zero-to-peak magnitude of EMF is expressed as
3
2
0
2
22
0
0
2
2
22
12

12
n
nn
n
p
n
eak
n
d
Y
dz
d
A
dz














   
 
   

   




   
 
   

   



(2-8)
where
2
00
AY  

is the acceleration amplitude. (Note that at a fixed acceleration,
vibration amplitude Y
0
is inversely proportional to the square of the vibration
frequency ). Thus, the EMF depends on the vibration frequency, peaking at the
resonant frequency with its magnitude dependent on the damping ratio 

as shown
in Fig. 2.3. At a fixed acceleration, the magnitude and phase of EMF change rapidly

21
around the resonant frequency, especially for low damping ratio. At the resonant
frequency, the EMF simplifies to
00
0
22
n
peak
n
YA dd
dz dz


  


 (2-9)
10
1
10
2
10
3
-60
-50
-40
-30
-20
Magnitude (dB)
Bode Diagram
Frequency (rad/sec)
ζ=0.05
ζ=0.15
ζ=0.25
ζ=0.35
ζ=0.45
ζ=0.55
0.1 ω
n
ω
n
10 ω
n
10
1
10
0
ω
n
ε
0-peak
/ │d Φ/dz │A
0
Decreased ζ

10
1
10
2
10
3
-90
-45
0
45
90
Phase (deg)
Bode Diagram
Frequency (rad/sec)
0.1 ω
n
ω
n
10 ω
n
90
0
Phase (degree)
ζ=0.05
ζ=0.15
ζ=0.25
ζ=0.35
ζ=0.45
ζ=0.55

Fig. 2.3 Calculated magnitude and phase of the electromotive force (EMF) at a given
acceleration versus vibration frequency  as a function of damping ratio .
The average power dissipated through a damper (d) is expressed by [1]
0
0
3
23
0
2
22
2 ( )'
12
Z
zZ n
nn
d z t dz
mY
P
T












   
 
   

   


(2-10)
Since the damper (d) is consisted of the electrical damping (d
e
) and mechanical
damping (d
m
), we have

22
em
d d d  (2-11)
where ( 2 )
e n e
dm  is due to electrical resistive elements, while ( 2 )
m n m
dm  is
due to mechanical damping. Thus, the generated electrical power is
3
23
0
2
22
12
e
n
e
nn
mY
P











   
 
   

   

(2-12)
At the resonant frequency, Eq. 2-12 simplifies to
23
0
2
4
en
e
mY
P


 (2-13)
If a load resistor is connected to the energy harvester, the electrical circuit can
be described by [2]
' ( )
C C L
Kz i R j L R     (2-14)
where K is electromechanical coupling coefficient; i is the current; R
C
and L
C
are the
resistance and inductance of the coil; R
L
is the load resistance. The force F
e

generated by the electromechanical coupling is
'
ee
F Ki d z  (2-15)
And substitution of Eq. 2-14 into Eq. 2-15 leads to
2
'
e
C C L
Kz
F
R j L R 


(2-16)
Hence, the electrical damping coefficient is

23
2
e
C C L
K
d
R j L R 


(2-17)
Since the inductive impedance is much less than the resistive impedance at lower
frequencies, the electrical damping ratio is
2
2 ( )
e
n C L
K
m R R




(2-18)
At the resonant frequency, the power output into the load resistor is calculated
2 2 2 4
2
0
22
1
2 2 [ ( ) ]
n LL
L L e
C L m L C
m K Y RR
P i R P
R R d R R K

  
  
(2-19)
Thus, the power output delivered to the load is maximized when
2
LC
m
K
RR
d
 (2-20)
And the maximum power output delivered to the matched load is given by
2 2 4
0
2
8 ( 1)
n
L
mC
m
mY
P
dR
d
K



(2-21)
For mesoscale and microscale electromagnetic energy harvesters with planar
coils, the second term K
2
/d
m
in Eq. 2-20 is usually negligible [3], but may not be so,
in case of large electromechanical coupling coefficient (K) and small mechanical
damping (d
m
).

24
2.2 Energy-Conversion Efficiency
The instantaneous mechanical power that a vibrating surface has, before an
energy harvester is loaded, is
( ) ( )" ( )'
i i i
p t My t y t  (2-22)
where M and y
i
(t) are the mass of the vibrating surface and the vibration
displacement of the vibrating body itself without an energy harvester, respectively.
Since the kinetic momentum is My
i
(t)′ before an energy harvester is loaded and
because the harvester adds the mass of the proof mass m and other auxiliary mass m
h

to M, we have My
i
(t)′ = (M + m + m
h
)y(t)′ from conservation of kinetic momentum,
and we obtain, in terms of Y
0
(the vibration amplitude with the harvester having m +
m
h
mass),
2
32
0
()
( ) cos sin
h
i
M m m
p t Y t t
M
  

 (2-23)
And the maximum instantaneous mechanical power (that a vibrating surface has
before an energy harvester is loaded), in terms of Y
0
(the vibration amplitude after the
harvester is loaded), is
2 3 2
32 0
0
( ) ( )
( ) (1 )
22
h h h
i
M m m Y M m m m m
p t Y
MM


    
   (2-24)
With p
e,max
defined to be the maximum instantaneous electrical power, the overall
energy-conversion efficiency is obtained by
,max
,max
- ( )
e
i
p
Energy Conversion Efficiency ECE
p
 (2-25)

25
In electromagnetic energy conversion, we obtain the maximum electrical power from
Eq. 2-9 at the resonant frequency 
n
of an energy harvester as
2
22
0
,max 2
16
n
e
Y d
p
R dz



 (2-26)
where R is the load resistance that is matched to the energy harvester’s source
resistance. Thus, the maximum theoretical energy-conversion efficiency of an
electromagnetic energy harvester is
2
22
1
( ) 8
hn
Md
ECE
M m m R dz 



(2-27)
For a given mass of an energy harvester (m+m
h
), the ECE is maximized when M =
m+m
h
, and the maximum ECE is equal to
2
max 2
1
32
n
d
ECE
M R dz 

 (2-28)
Another mentioned the harvester effectiveness as the output electrical power
over the maximum possible output. The maximum possible output is expressed as [4]
3
0
1
2
ml
P Y Z m   (2-29)
where Z
l
is the maximum amplitude of relative displacement between the proof mass
and the frame. Thus, the harvester effectiveness is
3
0
Output Electrical Power
1
2
H
l
E
Y Z m 
 (2-30)

26
2.3 An Array of Electromagnetic Energy Harvester with Permanent Magnets
This section presents a fabrication and assembly process for a mass production
method of electromagnetic energy harvesters at wafer level with different materials
as suspension system. With a parylene diaphragm as the suspension system
fabricated by MEMS process on a silicon wafer, a highly efficient electromagnetic
energy harvester generates microwatt level of power at low input acceleration (and
micron level of vibration amplitude). With a 200-turn coil, the power generator
generates power outputs of 5.63 μW and 0.21 μW, at input accelerations of 0.5 g and
0.08 g (corresponding to vibration amplitudes of 3.65 µ m and 0.44 µ m), respectively.
Based on the same structure, with a silicone membrane as the suspension system, an
array of electromagnetic power generators are assembled by permanent magnets and
coils on two 3’’ acrylic plates. Experimental results show that each power generator
provides a stable and comparable performance at a wide range of input acceleration,
and 605 μw total power output can be generated at an input acceleration of 2 g when
seven power generators are connected in series.
2.3.1 Electromagnetic energy harvesters fabricated and assembled on silicon
wafers
Electromagnetic power generators with permanent magnets have been explored
for harvesting vibrational energy from the environment. In one implementation,
permanent magnets are held by a spring suspension system made by a traditional
machining. The mechanical spring suspension system requires a large volume and

27
cost-increasing alignment, and is difficult to be manufactured in a batch process.
This section describes a parylene diaphragm fabricated by MEMS process on a
silicon wafer as the suspension system, which is assembled with a permanent magnet
and coil to make mass production possible. The measured power level of the power
generator shows great potential application at low input acceleration or extremely
low vibration amplitude.
Figure 2.4 shows the components in the electromagnetic energy harvester. The
permanent magnet and coil are assembled on the silicon wafer through the aligning
trenches. The parylene diaphragm holds the magnet, as the magnet responds to
external vibration. Following the fabrication and assembly process illustrated in Fig.
2.5, we etch silicon about 100 μm from the front side with silicon deep reactive ion
etching (DRIE) to form the trenches for aligning and housing the magnet and coil.
Then after depositing 10 μm thick parylene on the front side, we release the
diaphragm by DRIE etching of the silicon from the backside. (Photos of the silicon
wafer processed thus far are shown in Fig. 2.6.) Ten parylene diaphragm suspension
systems are designed and fabricated on a silicon wafer at the same time. Copper wire
is wound around an acrylic spool to form a 200-turn coil by a coil winder. The
magnet and coil are glued in the trenches on the silicon to form an electromagnetic
power generator, as shown in Fig. 2.7. The whole volume of the power generator is
almost the same as the coil volume because the magnet is suspended by the parylene
diaphragm and inserted into the hollow spool that holds the coil. The detailed device
parameters are listed in Table 2.1.

28

Fig. 2.4 Schematic showing the components in the energy harvester.
(b) DRIE etching
(c) Deposit parylene as diaphragm
(d) DRIE releasing Si
(a) Oxidation
Magnet
(e) Assembly of magnet and coil
Coil
Si SiO
2
Parylene

Fig. 2.5 Fabrication and assembly process of the electromagnetic energy harvester.

Fig. 2.6 (a) Top-view photo of a 3” silicon wafer with trenches for housing the
magnet and the coil. (b) Bottom-view photo of the silicon wafer after the diaphragm
is released.
Coil
Permanent magnet
Parylene diaphragm
Silicon wafer
Assembly
(a) (b)
Aligning magnet Aligning coil Parylene diaphragm

29

Fig. 2.7 (a) 200-turn coil wound around an acrylic spool. (b) The permanent magnet
glued on the diaphragm. (c) Top-view photo after the magnet and the coil are
assembled.

The fabricated electromagnetic power generator is characterized by a vibration
shaker system. Figure 2.8 shows the induced EMF as a function of vibration
frequency at various input accelerations. At the resonant frequencies, the maximum
EMFs of 12.0 mV and 2.3 mV are measured at input accelerations of 0.5 g and 0.08
g, respectively. The power output at a resonant frequency as a function of the
vibration acceleration is shown in Fig. 2.9. The power outputs (into 3.2 Ω load) are
increased from 0.21 to 5.63 μW with the input acceleration increasing from 0.08 to
0.5 g. The 0.5 g of acceleration at 185 Hz corresponds to about 3.65 μm vibrational
amplitude, and the electromagnetic power generator can harvest some very small
vibrations that exist in walls, bridges, etc. This power level of the power generator is
comparable with those manufactured by traditional machining, according to
published literature [5].
Table 2.1 Parameters of the electromagnetic power generator on silicon wafers
Cylinder magnet size (mm) D=4.8 H=9.6
Magnet mass (gram) 1.2
Acrylic spool size (mm) ID=8 OD=18 H=18 (4.6cc)
Coil turns 200
Coil resistance (Ω) 3.2

(a) (b) (c)

30
120 160 200 240 280 320
0
3
6
9
12
EMF (mV)
Frequency (Hz)
0.08g
0.18g
0.32g
0.5g

Fig. 2.8 Measured EMF versus vibration frequency at various input accelerations.
0.0 0.2 0.4 0.6
0
2
4
6
Power ( W)
Acceleration (g)
Power vs. Acceleration

Fig. 2.9 Power output at the resonant frequency as a function of the input
acceleration.
2.3.2 An array of electromagnetic power generators
The array of electromagnetic power generators are composed of permanent
magnets and coils, separately placed on two 3’’ acrylic plates (magnets plate and
coils plate). The assembly process and components of the array of electromagnetic
power generators are shown in Fig. 2.10 and Fig. 2.11, respectively. The permanent
185Hz, 3.65μm

31
magnets are mounted on a 3” acrylic plate (Fig. 2.11a). Copper wire is wound around
an acrylic spool to form a 400-turn coil by a coil winder. Then a 127 μm thick
silicone sheet is glued on another patterned 3” acrylic plate as the diaphragm which
holds the coils (Fig. 2.11b and Fig. 2.11c). The acrylic supporting blocks, which are
1mm higher than the coils, are placed on the coils plate (Fig. 2.11d). After that, the
magnets are inserted into the hollow spools that hold the coils when the two acrylic
plates are assembled together to complete the array of electromagnetic power
generators (Fig. 2.12a). There is a 1mm gap between the coils and the magnets plate
due to the supporting blocks so that the coils are suspended by the silicone
diaphragm as shown in Fig. 2.12b. The detailed parameters of the fabricated array of
electromagnetic power generators are listed in Table 2.2.
Coil
Magnet
Silicone sheet
Acrilyc plate
(a) Mount magnets on the acrylic plate
(b) Glue silicone sheet on the acrylic plate as the
diaphragm, and glue coils on the diaphragm
Supporting block
(c) Place supporting blocks on the acrylic plate
(d) Assemble two acrylic plates to complete
the array of electromagnetic power generators

Fig. 2.10 The fabrication and assembly process of the array of electromagnetic
power generators.

32

Fig. 2.11 The components of the array of electromagnetic power generators. (a)
Seven permanent magnets mounted on a 3” acrylic plate. (b) The 127 μm thick
silicone sheet glued on another patterned 3” acrylic plate. (c) Seven coils glued on
the silicone sheet. (d) Four acrylic blocks placed on the coils plate.

Fig. 2.12 (a) Top-view and (b) perspective view photos of the assembled array of
electromagnetic power generators.
(c) (d)
400-turn coil
Supporting block
(a)
(b)
Permanent magnet Silicone diaphragm
(a)
(b)
Gap=1mm

33

Figure 2.13 shows the peak voltage as a function of vibration frequency at
various input accelerations for each electromagnetic power generator. The silicone
diaphragm makes the resonant frequency of each power generator less than 100 Hz
due to its low Young’s modulus. The similar performance of seven single power
generators indicates that the fabrication and assembly process is stable at wafer level
for mass production.
60 80 100 120
0
4
8
12
16
20
V
0-peak
(mV)
Frequency (Hz)
0.05g
0.1g
0.2g
0.3g
60 80 100 120
0
4
8
12
16
20
V
0-peak
(mV)
Frequency (Hz)
0.05g
0.1g
0.2g
0.3g

60 80 100 120
0
4
8
12
16
20
V
0-peak
(mV)
Frequency (Hz)
0.05g
0.1g
0.2g
0.3g
60 80 100 120
0
4
8
12
16
V
0-peak
(mV)
Frequency (Hz)
0.05g
0.1g
0.2g
0.3g

Table 2.2 Parameters of the array of electromagnetic power generators
Cylinder magnet (mm) D=4.8 H=9.6
Silicon diaphragm (mm) D=20 H=127μm
Acrylic spool (mm) ID=8 OD=18 H=18
Coil turns 400
Coil resistance (Ω) 6.8
Supporting block (mm) 8 × 8 × 16

(a) (b)
(c)
(d)

34
60 80 100 120
0
4
8
12
16
20
V
0-peak
(mV)
Frequency (Hz)
0.05g
0.1g
0.2g
0.3g
60 80 100 120
0
4
8
12
16
20
V
0-peak
(mV)
Frequency (Hz)
0.05g
0.1g
0.2g
0.3g

60 80 100 120
0
4
8
12
16
20
V
0-peak
(mV)
Frequency (Hz)
0.05g
0.1g
0.2g
0.3g

Fig. 2.13 Measured peak voltage versus vibration frequency at different input
accelerations for each electromagnetic power generator.
To increase the power output, seven electromagnetic power generators are
connected in series and measured at various input accelerations. The peak voltages
are measured across various load resistors, and the power outputs are calculated from
the measured voltages when the resistors are connected to the array of power
generators, at the input acceleration of 1 g (Fig. 2.14). When the load resistance is
equal to the coil resistance, the power generator delivers a maximum power. The
maximum power output is increased from 0.05 g to 2 g of input accelerations and
605 μw total power can be generated at the input acceleration of 2 g (vibration
frequency of 80 Hz), as shown in Fig. 2.15. Since the array of electromagnetic power
(e)
(f)
(g)

35
generator can provide high power output and work at a wide range of input
acceleration due to the high tensile strength of silicone diaphragm, it can be suitable
for most microscale devices and applied to various vibrational conditions.
0
50
100
150
200
0 1 2 3 4
50
100
150
200
250
300
V
0-peak
(mV)
Current (mA)
Peak voltage vs. Current
Power vs. Current
Power ( W)

Fig. 2.14 Measured peak voltage and power output across a load resistor with
different resistances, at the input acceleration of 1 g.
0.0 0.4 0.8 1.2 1.6 2.0
0
100
200
300
400
500
600
700
Power ( W)
Acceleration (g)
Power vs. Acceleration

Fig. 2.15 The maximum power output versus input acceleration when seven
electromagnetic power generators are connected in series.

80Hz, 78μm

36
2.4 Summary
In this chapter the fundamentals of vibration-driven power generator have been
discussed. The principle concept and energy-conversion efficiency of
electromagnetic energy harvesters have been explored. An array of electromagnetic
power generator has been developed by a batch process for mass production and
improving power output. Notable advantages are as follows:
1) Assembly process is an inexpensive and reproducible approach to mass
production.
2) Silicone sheet with high tensile strength and low Young’s modulus, as the
diaphragm to hold proof-mass, makes the device suitable for wide range of
application (wide range of input acceleration) with low resonant frequency.
3) The array of electromagnetic power generator at wafer level provides high power
output when all generators are connected in series.

37
Chapter 2 References
[1] P. D. Mitcheson, T. C. Green, E. M. Yeatman and A. S. Holmes, “Architectures
for vibration-driven micropower generators,” J. Microelectromech. Syst., vol.
13, no. 3, pp. 429-440, June 2004.
[2] N. G. Stephen, “On energy harvesting from ambient vibration,” J. Sound
Vibration, vol. 293, pp. 409-425, 2006.
[3] F. Khan, F. Sassani and B. Stoeber, “Copper foil-type vibration-based
electromagnetic energy harvester,” J. Micromech. Microeng., vol. 20, 125006
(11pp), 2010.
[4] P. D. Mitcheson, E. M. Yeatman, G. K. Rao, A. S. Holmes and T. C. Green,
“Energy harvesting from human and machine motion for wireless electronic
devices,” Proceedings of the IEEE, vol. 196, no. 9, pp. 1457-1486, September
2008.
[5] W. C. Chye, et al., “Electromagnetic Micro Power Generator – A
Comprehensive Survey,” IEEE Symposium on Industrial Electronics and
Applications, Penang, Malaysia, October 3-5, 2010, pp. 376-382.

38
Chapter 3
Microelectromagnetic Power Generator and Its Stack
with Integrated Magnets

This chapter describes a microelectromagnetic power generator and its stack
with integrated magnets that can be fabricated on silicon wafers in a batch process.
A microelectromagnetic power generator is fabricated by MEMS technologies
and characterized at different vibration frequencies, amplitudes and load resistances.
This compact generator occupies a volume of 15 × 13 × 0.4 mm
3
, as no external
permanent magnets are needed. Experimental results show that with a 20-turn spiral
coil, the device can generate an induced electromotive force (EMF) of 0.27 mV at a
vibration frequency and amplitude of 350 Hz and 10 μm, respectively.
In addition, this chapter presents a stacked microfaricated power generator that
vertically integrates multiple magnets on silicon wafers in a batch process to enhance
electromagnetic induction multiple times. The power output is increased by
increasing the magnetic flux change for each power-generator unit in the stack, in
addition to the increase due to increased number of unit. A stack consisting of two
arrays of four power-generator units is fabricated and characterized. Wax-bonded
Nd-Fe-B powders are embedded in the silicon wafer and magnetized as an integrated
micromagnet, which serves as a proof mass suspended by a parylene diaphragm.
Dual-layer coils are isolated by a parylene layer, connected by a via hole and

39
fabricated with electroplating copper on the same wafer. Experimental results show
an improvement by about a factor of four on the power output from the same coils
when two power-generator arrays are stacked vertically. Specifically, an array of
four microfabricated power generators occupying a volume of 51 × 11 × 0.4 mm
3
in
the stack produces an induced EMF of 1.02 mV with 0.55 nW power output when it
is vibrated at 400 Hz with vibration amplitude of 10 μm.
3.1 Microelectromagnetic Power Generator with Integrated Magnets
This section describes a compact microelectromagnetic power generator with
integrated magnets fabricated with a planar MEMS technology. A lift-off process is
employed to leave the magnetic powders only in the trenches to act as micromagnets.
The power generator is compact with dual-layer coils and magnets fabricated on the
same wafer in a batch process, and has great potential to meet the demand of
miniaturizing power supply and integrating it in microsystems.
3.1.1 Design
According to Faraday’s law, change in magnetic flux through an electric circuit
induces an electromotive force (EMF). In our design, the flux variation is realized by
moving coil in a constant magnetic field. Figure 3.1 illustrates the schematic of the
microelectromagnetic energy harvester with integrated magnets. The parylene
diaphragm holds the multi-turn coils and a micromagnet, which serves as a proof
mass and also provides the magnetic field along with two other micromagnets
embedded in the silicon wafer. Assuming the magnetic flux density between the

40
magnets to be constant along the in-plane direction, we see that a diaphragm
deflection in response to external vibrations causes the magnetic flux to vary through
the coils, and produces an induced EMF at the terminals of the coils, as shown in Fig.
3.2.
Second layer coil
First layer coil
Magnets
Pad Via
Parylene membrane
Vibration
Si Substrate

Fig. 3.1 Top-view schematic of the electromagnetic power generator with integrated
magnets.
B
B
Top view
Cross-sectional view
z
Vibration
L

Fig. 3.2 Top-view and cross-sectional view of the magnet-proof-mass and coils. Also
shown are the magnetic field lines and vibration direction.

41
The magnetic field produced by three micromagnets in the electromagnetic
power generator is simulated by COMSOL, and the 2D magnetic field lines are
shown in Fig. 3.3. An in-plane magnetization of μ
0
M = 0.22 T (along X-direction) is
used for the magnets in the simulation [1]. The simulation shows an almost constant
magnetic field between the magnets with the magnetic flux density of about 0.06 T
on the coils. This magnetic field is strengthened by using the magnet as the proof
mass and can be further enhanced by increasing the size of the magnet.
Magnets
10mm
11mm
Coils position
Y
X

Fig. 3.3 Top-view 2D simulation results of the magnetic field lines in the
electromagnetic power generator.
According to Faraday’s law, the EMF  is proportional to the time-rate change
of magnetic flux Φ through a coil, and is
1 1 1
()
()
n n n
i i i i
ii
i i i
d B S dB dS d
N N S B
dt dt dt dt

  
 
        
  
(3-1)
where N is the number of coil turn; B is the magnetic flux density; S is the coil area
vertical to the direction of magnetic flux density. Here we assume that the magnetic
flux density between the magnets to be constant for a coil composed of N identical

42
turns (with same coil area S
a
). For this energy harvester with coil between the
magnets, the magnetic flux density is time invariant. Thus, Eq. 3-1 simplifies to
a
dS
NB
dt
  (3-2)
For harmonically varying vibration input, z(t) = Z
0
cos( t+ ) being defined to be the
relative displacement between the magnet-proof-mass and the coils, the zero-to-peak
magnitude of EMF becomes
00
()
a
peak
dS d Lz
NB NB NBLZ
dt dt


   (3-3)
where L is the coil length; Z
0
is the relative displacement amplitude between magnet-
proof-mass and coils.
3.1.2 Fabrication
The fabrication process of the microelectromagnetic power generator is
illustrated in Fig. 3.4 and described in detail as follows. First, a silicon wafer is
etched from the backside by potassium hydroxide (KOH) wet etching to form low
pressure chemical vapor deposition (LPCVD) silicon-nitride microdiaphragms for
front-to-backside alignment [2], followed by a second KOH etching 300 μm deep
trenches on the two sides of a silicon wafer to form the generator structure. Then a 4
μm thick parylene D is deposited on the front side, followed by deposition and
patterning of Cr/Al (20 nm/200 nm) for the first layer coil. A 1 μm thick parylene D
is then deposited for isolation between dual-layer coils, and patterned to open via
holes. The second layer coil is formed by another Cr/Al deposition, followed by

43
another 1 μm thick parylene D. Then Nd-Fe-B powders and wax powders are packed
into the trenches, after photoresist coating and patterning. The residual powders are
removed by a lift-off process. After the filling of the powders into the trenches, the
wafer is placed in a magnetizer (magnetic field of 3 T) to magnetize the
micromagnets in-plane direction. After depositing a 4 μm thick parylene D to protect
the micromagnets and patterning to expose the coil pads, the diaphragm is released
by xenon difluoride (XeF
2
) etching the silicon in trenches on the back side.
(a) KOH etching
(b) Deposit parylene, Cr and Al,
then pattern the 1
st
metal layer
(d) Deposit Al and pattern the 2
nd
metal layer,
then deposit parylene
(c) Deposit parylene and Cr to form the vias
SiN
Parylene
The 1
st
metal layer
Vias
The 2
nd
metal layer
(e) Pattern photoresist and fill the powders
(g) Deposit and pattern parylene
(h) Release Si and SiN
(f) Lift-off to remove the residual powders
Photoresist Magnetic powders & wax
Pads

Fig. 3.4 Brief microfabrication process of the microelectromagnetic power generator.
The micromagnets and coils are fabricated in a batch process on the same
wafer. The Nd-Fe-B magnetic powders, supplied by Magnequench (MQP-S-11-9),

44
are mixed with the wax powders, supplied by Logitech Ltd. (0CON-196). The
loading fraction of the wax is 10 wt%, and the wax is melt at 160
o
C and air-cooled
to bond the magnetic powers as the micromagnets. To improve the poor adhesion
between parylene and Al, the parylene surface is roughened by O
2
plasma before the
deposition of metal layers and the Cr is deposited as an adhesion layer.
Photos of the dual-layer coils and integrated micromagnets are shown in Fig.
3.5. The wax-bonded Nd-Fe-B powders are only left in the 300 μm deep trenches by
the lift-off process. Figure 3.6 shows the bottom-view of the electromagnetic power
generator, which clearly shows the middle micromagnet serving as the proof mass.
In the bottom-view photo, the dual-layer coils on the parylene diaphragm show up
when the silicon in trenches on the backside is completely released. The detailed
parameters of the fabricated electromagnetic power generator are listed in Table 3.1.

Fig. 3.5 Top-view photos of the coils and micromagnets of the fabricated
electromagnetic power generator.

45

Fig. 3.6 Bottom-view photos of the fabricated electromagnetic power generator.

3.1.3 Results and discussion
The performance of the fabricated microelectromagnetic power generator is
characterized with a vibration shaker system, which includes a function generator,
power amplifier, shaker table, pre-amplifier, laser Doppler displacement meter
(LDDM) and oscilloscope, as shown in Fig. 3.7. The shaker table provides vibration,
while the function generator controls the vibration frequency and amplitude. The
Table 3.1 Parameters of the electromagnetic power generator
Total size (mm) 15 × 13 × 0.4
Coil width (μm) 25
Coil thickness (μm) 0.2
Number of coil turns 20
Number of coils 2
Coil resistance (Ω) 4770
Magnet size (middle) 10 mm × 1 mm × 0.3 mm
Magnet size (sides) 10 mm × 3 mm × 0.3 mm

46
vibration amplitude is measured with the LDDM, while the EMF from the power
generator is amplified with the pre-amplifier before being observed at the
oscilloscope.

Fig. 3.7 Experimental test set-up to characterize the fabricated electromagnetic
power generator.
The measured EMF of the power generator as a function of the vibration
frequency at a fixed vibration amplitude is shown in Fig. 3.8. As the vibration
frequency is increased from 200 to 350 Hz, the EMF increases from 0.03 to 0.14 mV
at the vibration amplitude of 5 μm with reproducibility of 18.0%, and from 0.04 to
0.27 mV at the vibration amplitude of 10 μm with reproducibility of 14.6%. The
fabricated generator produces a peak voltage of 0.27 mV at a vibration frequency
and amplitude of 350 Hz and 10 μm, respectively.
Figure 3.9 shows the EMF of the power generator as a function of the vibration
amplitude at a fixed vibration frequency. The EMF increases from 0.02 to 0.09 mV

47
as the vibration amplitude is increased from 3 to 20 μm with the reproducibility of
17.7% at a vibration frequency of 200 Hz. Thus, the experimental results show that
the measured EMF has a linear relationship with the vibration frequency and
amplitude.
0 2 4 6 8 10
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Voltage (mV)
Time (ms)
0.27mV
350Hz
200 250 300 350 400
0.0
0.1
0.2
0.3
EMF (mV)
Vibration frequency (Hz)
EMF vs. Vibration frequency at d=5 m
EMF vs. Vibration frequency at d=10 m

Fig. 3.8 Measured EMF versus vibration frequency at the vibration amplitudes of 5
μm and 10 μm.
3 6 9 12 15 18 21
0.02
0.04
0.06
0.08
0.10
EMF (mV)
Vibration amplitude ( m)
EMF vs. vibration amplitude at f=200Hz

Fig. 3.9 Measured EMF versus vibration amplitude at the vibration frequency of 200
Hz.

48
Figure 3.10 shows the measured output voltage and power across a load
resistor with different resistances, at a vibration frequency and amplitude of 350 Hz
and 10 μm, respectively. The output voltages are measured across various load
resistors, and the powers are calculated from the measured voltages when the
resistors are connected to the fabricated power generator. A relatively low power of
2 pW is delivered to a load resistance of 3.90 kΩ, because the thin and long coil
layer of the power generator has a large resistance of 4.77 kΩ, which can be reduced
by 10 – 100 times with a thicker, wider and shorter coil made of a lower resistive
metal.
0.0
0.5
1.0
1.5
2.0
0 20 40 60 80
0.0
0.1
0.2
0.3
Output voltage (mV)
Current (nA)
Output voltage vs. Current
Power vs. Current
Power (pW)

Fig. 3.10 Measured output voltage and power across a load resistor with different
resistances, at a vibration frequency and amplitude of 350 Hz and 10 μm,
respectively.

49
3.2 Micromachined Energy-Harvester Stack with Integrated Magnets
This section describes a microelectromagnetic power-generator stack, in which
the magnetic flux variation is realized with two moving magnets, whose fluxes are
linked to a fixed coil. Thus, the induced EMF in the coil is increased. A theoretical
model of vibration-driven energy harvesters is analyzed to compare the change of
magnetic flux for one magnet and two magnets, and simulated to evaluate the output
of the energy harvester. A planar fabrication process of a fully-integrated
microelectromagnetic energy-harvester stack with wax-bonded Nd-Fe-B
micromagnets and electroplating dual-layer coils is presented. The EMFs produced
from the non-stacked and stacked coils are measured and compared, and nW power
level is generated from an array of four coils connected serially in the
microelectromagnetic energy-harvester stack.
3.2.1 Design
Figure 3.11 illustrates the schematic of the microelectromagnetic energy-
harvester stack. For each magnet-coil power generator, a parylene diaphragm holds a
micromagnet, which serves also as a proof mass in addition to providing magnetic
field. A diaphragm deflection in response to external vibration causes the magnetic
flux to vary through the dual-layer coils, which are fixed on the silicon substrate and
produce an induced EMF. The magnet-coil power generators are connected serially
in an array. Then a multiple number of such arrays are glued on top of each other to
complete a stack. When the arrays of magnet-coil power generators are stacked

50
vertically to form a stacked energy harvester, each coil is fixed between two magnets
of the adjacent arrays, as shown in Fig. 3.12a. The magnetic poles of the two
magnets are aligned toward the coil such that the currents induced by the magnets
may have the same direction, as shown in Fig. 3.12b, and may be superposed for
increasing of the power level. According to Lenz’s law, a current in counter-
clockwise direction is induced by the downward movement of the two magnets,
while a clockwise current is caused by the upward movement of the two magnets, as
shown in Figs. 3.12c and 3.12d, respectively.

Fig. 3.11 Schematic of the microelectromagnetic power-generator stack with
integrated magnets.

51

Fig. 3.12 (a) Cross-section schematic of a stacked power generator. (b) Magnetic
poles and magnetic field lines. (c) Counter-clockwise induced current caused by
downward movement of the two magnets. (d) Clockwise induced current caused by
upward movement of the two magnets.
Here we assume that for a coil composed of N identical turns, the change in
magnetic flux through each turn is the same. For this energy-harvester stack with
each coil fixed on the silicon substrate, the coil area is time invariant. Thus, for
harmonically varying vibration input, Eq. 3-1 becomes
0
1 1 1
sin( )
n n n
i i i
i i i
i i i
dB dB dB dz
N S N S N S Z t
dt dz dt dz
   
  
        
  
(3-4)
Then substitution of Eq. 2-3 into Eq. 3-4 leads to
3
2
0
2
2
1
2
sin( )
12
n
n
n
i
i
i
n
Y
dB
N
d
t S
z










   
 
   

   

  


(3-5)
Thus, the peak value of the EMF is

52
0
1
3
2
0
2
22
1
2
0
2
22
12

12
n
i
peak i
i
n
i
i
n
nn
n
nn
i
Y
A
dB
NS
dz
dB
NS
dz















   
 
   

   



   
 



   

   




(3-6)
At the resonant frequency, the EMF simplifies to
0
1
0
2
n
in
peak i
i
dB
NS
dz
Y







(3-7)
For the magnet-coil power generator, the magnetic flux change is caused by a
distance change from a magnet. The magnetic flux density around a single magnet is
expressed by [3]
11 1 2 1 2
2 2 2 2 2 2
1 2 1 2
[tan tan ]
2 4 2( ) 4( )
r
z
hh
B a a a a
B
d a a d a d a a a d



     
(3-8)
where B
r
is residual magnetic flux density; a
h
is magnet thickness in magnetization
direction; a
1
is magnet length; a
2
is magnet width; and d is distance from magnet.
The magnetic field produced by one magnet (5 × 5 × 0.3 mm
3
wax-bonded Nd-Fe-B
micromagnet with a constant magnetization of 0.22 T [1]) is simulated by COMSOL,
and the magnetic flux densities as a function of distance for one magnet and two
magnets are shown in Fig. 3.13a. The plots show the magnetic flux densities only on
the centerline along the magnetization direction. The two magnets are arranged such
that the magnetic fields between the two oppose each other, and the magnetic flux

53
density (B
z
) along z-direction varies rapidly. Also, we assume that the multi-turn coil
(with the coil area varying from 7.5 × 7.5 to 10.5 × 10.5 mm
2
) is treated as a coil
with N identical turns, each with the same area (9 × 9 mm
2
). The magnetic flux (Φ) is
a numerical integral of magnetic flux density across the entire coil area. The
gradients of magnetic flux (dΦ/dz) along the z-direction are calculated and compared
for one magnet and two magnets, as shown in Fig. 3.13b. The gradient of magnetic
flux does not vary much over a relatively small distance of tens of microns, and we
use a constant value for dΦ/dz in Eq. 3-6 to calculate the EMF at a specific frequency
and vibration amplitude. For example, for one magnet, we use |dΦ/dz|=1.14 × 10
-3

Wb/m, the value at 100 μm away from the magnet, in case of a harvester formed
with a coil placed at 100 μm away from the magnet. The values used in the
simulations are listed in Table 3.2. Thus, at a fixed vibration frequency, the EMF has
a linear relationship with the vibration amplitude, as can be seen in Eq.3-6. The
simulations show that the change of magnetic flux for the two magnets is higher than
that of one magnet. Thus, the power output from the energy-harvester stack is
increased since the magnetic flux variation through each coil in the stack is increased,
in addition to the increase associated with increased number of power-generator unit.

54

Fig. 3.13 Simulation results of (a) the magnetic flux densities versus distance and (b)
the gradients of magnetic flux (|dΦ/dz|) along z-direction for one magnet and two
magnets with same magnetic poles facing each other.

Table 3.2 Values used in the simulations
Magnet size (mm
3
) 5 × 5 × 0.3
Coil area (mm
2
) 9 × 9
Coil turn 20
Distance between magnet and coil (μm) 100
Residual magnetic flux density (T) 0.22
Permeability constant (H/m) 4π × 10
-7

Vibration frequency  (rad/s) 400 Hz × 2π
|dΦ/dz| at 100 μm from one magnet (Wb/m) 1.14 × 10
-3

Damping ratio  0.0625
Vibration amplitude Y
o
(μm) 3~10

55
3.2.2 Fabrication
The coils and micromagnets are fabricated on the same wafer as shown in Fig.
3.14. First, a silicon wafer is etched from the backside by potassium hydroxide
(KOH) wet etching to form low pressure chemical vapor deposition (LPCVD)
silicon-nitride microdiaphragms for front-to-backside alignment [2], followed by a
second KOH etching to form 300 µ m deep trenches. A Ti/Cu (10 nm/200 nm) is
deposited by E-beam evaporator as a seed layer, and then the photoresist AZ4620 is
spin-coated and patterned to obtain a mold for the copper coil. After 4 μm thick
copper is electroplated on the front side, the photoresist is removed in acetone, and
the seed layer is etched away to form the first-layer coil. Then a 1 µ m thick parylene
is deposited for isolation between dual-layer coils, and patterned to open via holes.
The electroplating process is repeated to form the second-layer coil, which is covered
by another 1 μm thick parylene patterned to expose the coil pads. The silicon nitride
and parylene are patterned by reactive ion etching (RIE), and 300 μm silicon is
etched by silicon deep RIE (DRIE) from the front side to form the cavities, as shown
in Fig. 3.15a. Then Nd-Fe-B powders and wax powders are packed into the trenches
on the backside, after photoresist coating and patterning. The residual powders are
removed by a lift-off process. After the filling of the powders into the trenches, the
wafer is placed in a magnetizer (magnetic field of 3 T) to magnetize the
micromagnets in-plane direction. Finally, after 10 μm thick parylene is deposited on
the backside, the diaphragm is released by xenon difluoride (XeF
2
) etching of the
silicon (followed by RIE etching of silicon nitride) in the cavities on the front side.

56
The wafers of energy harvesters are stacked to form a stack of arrayed energy
harvesters.
In each power-generator unit, the first-layer coil and second-layer coil are
connected through a via hole and fixed on the silicon substrate as shown in Fig.
3.15b. Figure 3.16 shows a fabricated array of four units and a stack consisting of
two such arrays (Array I and Array II), occupying a volume of 51 × 11 × 0.8 mm
3

(=0.45 cc) and weighing 1.2 gram (each array occupies a volume of 51 × 11 × 0.4
mm
3
). Adjacent power-generator units are connected through a connection pad so
that the four units in an array are connected in series as shown in Fig. 3.16a. Wax-
bonded Nd-Fe-B micromagnets are integrated with two layers of 4 μm thick copper
coil in a batch process on the same wafer. The Nd-Fe-B magnetic powders, supplied
by Magnequench (MQP-S-11-9), are mixed with the wax powders, supplied by
Logitech Ltd. (0CON-196). The loading fraction of the wax is 10 wt%, and the wax
is melt at 160
o
C and air-cooled to bond the magnetic powders as the micromagnets.
The wax-bonded Nd-Fe-B powders are only left in the 300 μm deep trenches on the
3 inch wafer by the lift-off process, and the distance between micromagnets and
dual-layer coils is around 100 μm, which can be easily controlled by the KOH wet
etching. The volume of each micromagnet is 5 × 5 × 0.3 mm
3
and the areas of the
multi-turn square coils vary from 7.5 × 7.5 to 10.5 × 10.5 mm
2
. The detailed
parameters of the microelectromagnetic energy-harvester stack are listed in Table 3.3.

57
Parylene
The 2
nd
metal layer
Si
x
N
y
Via holes
Pad
Magnetic powders & wax
The 1
st
metal layer
Silicon Nitride Silicon Ti Cu
Parylene Magnetic powders & wax
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)

Fig. 3.14 Brief microfabrication process of the microelectromagnetic power-
generator stack. (a) Etch silicon from backside by KOH. (b) Electroplate the first-
layer coil. (c) Deposit and pattern parylene isolation layer. (d) Electroplate the
second-layer coil. (e) Etch parylene and silicon nitride by RIE, and silicon by DRIE.
(f) Fill the silicon cavity with magnetic powders and deposit parylene. (g) Release
parylene diaphragm by XeF
2
etching of silicon followed by RIE etching of silicon
nitride. (h) Stack two wafers.

58

Fig. 3.15 SEM photos of the fabricated energy harvester showing (a) the proof mass,
cavity, and coils and (b) the details of the dual-layer coils.

Fig. 3.16 (a) Top-view and (b) bottom-view photos of an array of four units. (c) Top-
view and (d) perspective-view photos of a stack formed of two wafers containing
Array I and Array II.

59

3.2.3 Results and discussion
When Array I and Array II are stacked vertically as shown in Figs. 3.16c and
3.16d, each coil in Array I is fixed between two magnets from Array I and Array II.
The measurements are carried out to evaluate the enhanced electromagnetic
induction on Array I before and after stacking arrays. A single unit (SU) in Array I, a
four-unit Array I without Array II (AI), and a four-unit Array I with Array II (AIS)
are characterized with the vibration shaker system (Fig. 3.7).
The measured EMFs of SU as a function of vibration frequency at various
input accelerations are shown in Fig. 3.17. At a fixed acceleration, the EMFs depend
on the vibration frequency, peaking at the resonant frequency. From the acceleration
of 3.6 g at the resonant frequency of 400 Hz, a peak value of 0.15 mV
zero-to-peak
is
measured. The decreasing resonant frequency with increasing acceleration is
possibly due to the fact that larger displacement due to a larger input acceleration
causes the coil to experience larger amount of variation in |dΦ/dz|, which lowers the
EMF, resulting in a lower frequency where the EMF peaks, lower than the actual
Table 3.3 Parameters of a power-generator unit in the stack
Active area (mm
2
) 7 × 7
Total volume (mm
3
) 12.8 × 10.8 × 0.4 (0.055 cc)
Weight (g) 0.15
Magnet size (mm
3
) 5 × 5 × 0.3
Coil turn 20
Coil width (μm) 60
Coil thickness (μm) 4
Coil resistance (Ω) 55

60
mechanical resonant frequency. The non-linear effect of the spring system under
large strain may be another reason, since decrease in Young’s modulus decreases the
spring constant and resonant frequency, as was found to be the case in a lead
zirconate titanate (PZT) cantilever [4]. All these and/or other mechanisms may result
in the decreasing resonant frequency. The measured plot of EMF versus vibration
frequency for an input acceleration of 3.6 g at the resonant frequency of 400 Hz
shows a 3-dB bandwidth (   ) of 50 Hz, and a quality factor (Q) is estimated to be 8
from /
n
Q   . Thus, the damping ratio is / 2 1/ 2 0.0625
n
d k Q     . The
measured EMFs of SU as a function of the vibration amplitude at a fixed vibration
frequency is shown in Fig. 3.18. As the vibration amplitude is increased from 3 to 10
μm, the measured EMFs increase from 0.03 to 0.08 mV, from 0.04 to 0.13 mV, from
0.05 to 0.17 mV, and from 0.07 to 0.22 mV at the vibration frequency of 250, 300,
350 and 400 Hz, respectively. These four measured plots of the EMF versus the
vibration amplitude show that the EMF has a linear relationship with the vibration
amplitude at a fixed vibration frequency, as expected from Eq. 3-6, and the SU
generates the highest output at the resonant frequency of 400 Hz, which shows an
agreement with the analytical results as the vibration amplitude increases from 3 to
10 μm.

61
200 300 400 500 600
0.05
0.10
0.15
V
0-p
(mV)
Frequency (Hz)
1.2g
2.4g
3.6g
Bandwidth=50Hz
0.15mV@400Hz

Fig. 3.17 Measured EMF (peak value) versus vibration frequency at different
accelerations for a single unit (SU).
2.5 5.0 7.5 10.0
0.0
0.1
0.2
0.3
V
0-P
(mV)
Vibration amplitude ( m)
Measured EMF vs. Vibraiton amplitude at 250 Hz
Measured EMF vs. Vibraiton amplitude at 300 Hz
Measured EMF vs. Vibraiton amplitude at 350 Hz
Measured EMF vs. Vibraiton amplitude at 400 Hz
Simulated EMF vs. Vibraiton amplitude at 400 Hz

Fig. 3.18 Measured and simulated EMF (peak value) versus vibration amplitude at
different resonant frequencies for a single unit (SU).
The measured EMFs of AIS as a function of vibration frequency at various
input accelerations are shown in Fig. 3.19 when four coils in Array I are connected in
series. From the acceleration of 3.6 g at the resonant frequency of 410 Hz, a peak
value of 0.67 mV
zero-to-peak
is measured. Fig. 3.20 shows the EMFs of the power
generators as a function of the vibration amplitude at a fixed vibration frequency. As

62
the vibration amplitude is increased from 3 to 10 μm at a vibration frequency of 400
Hz, the EMF of SU, AI and AIS increase from 0.07 to 0.22 mV with the
reproducibility of 9.3%, from 0.14 to 0.57 mV with the reproducibility of 1.6%, and
from 0.23 to 1.02 mV with the reproducibility of 5.7%, respectively. Among the
various power generators based on Array I in Fig. 3.20, AIS produces a peak voltage
of 1.02 mV, almost double of what AI generates, at vibration frequency of 400 Hz
and vibration amplitude of 10μm, due to the superposition of magnetic flux change.
The measured plots of EMF versus vibration frequency for an input acceleration of
3.6 g for SU and AIS in Fig. 3.17 and Fig. 3.19, respectively, show that the 3-dB
bandwidth (   ) is twice larger for AIS than SU (110 vs. 50 Hz) while the resonant
frequency remains about the same. In addition, AIS produces EMF which is not eight
times larger than SU although AIS consists of a total of four power-generator units
that are connected in series with enhanced electromagnetic induction. The reduced Q
and less-than-optimal output voltage are caused by the multiple resonant frequencies
of multiple power-generator units in Array I. As the input vibration frequency
departs from the resonant frequency, the magnitude of EMF decreases and the phase
of EMF changes rapidly, especially for low damping ratio as shown in Fig. 2.3. Both
the magnitude and phase of EMF from each power-generator unit determine the
overall output power when all units are connected in series. Due to the fact that all
the four power-generator units do not have an exact same resonant frequency, all the
units do not generate the maximum EMFs together at a specific vibration frequency.
In addition, the phases of the EMFs from the units are different, and make the

63
magnitude of the total output be less than the simple sum of the four magnitudes.
The voltage waveforms from SU and AIS recorded in the same time period at
vibration frequency of 400 Hz and vibration amplitude of 10 μm are shown in Fig.
3.21. The two signals show a time difference ( t  ) of 0.2 ms, which leads to a phase
angle difference (   ) of 29
o
as
n
t     . The phase difference among the
voltages from the four units also degrades the overall output power when the four
units are connected in series. The variation of the resonant frequency for each power-
generator unit is mainly caused by the relatively poor control over the fabrication
step of filling wax-bonded Nd-Fe-B powders. Varying amount of the powders in
each trench affects the proof mass and thus the resonant frequency. In addition, the
repulsive force between two magnets from neighboring arrays induces tensile stress
on the parylene diaphragm, and increases the resonant frequency of the stacked
energy harvester [5].
300 400 500
0.2
0.4
0.6
V
0-p
(mV)
Frequency (Hz)
1.2g
2.4g
3.6g
0.67mV@410Hz
Bandwidth=110Hz

Fig. 3.19 Measured EMF (peak value) versus vibration frequency at different
accelerations for a four-unit Array I with Array II (AIS).

64

Fig. 3.20 Measured EMF (peak value) versus vibration amplitude at the vibration
frequency of 400 Hz for a single unit (SU), a four-unit Array I without Array II (AI)
and a four-unit Array I with Array II (AIS).
400 Hz
Δt = 0.2 ms
0 2 4 6 8
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
Voltage (mV)
Time (ms)
SU
AIS

Fig. 3.21 Voltage waves of a single unit (SU) and a four-unit Array I with Array II
(AIS) at vibration frequency of 400 Hz and vibration amplitude of 10 μm.
Figure 3.22 shows the measured output voltage and power across a load
resistor with different resistances for AI and AIS, at a vibration frequency and
amplitude of 400 Hz and 10 μm, respectively. The load resistor is directly connected
to the fabricated energy harvester, and the voltage across the load resistor is
amplified by a pre-amplifier and the amplified waveform is observed at the

65
oscilloscope. Thus, the unamplified voltage across the load resistor produced by the
energy harvester is the amplified voltage divided by the gain of the pre-amplifier. As
we vary the resistance of the load resistor, the waveforms of the output voltages are
recorded for each resistance value. With the root-mean-square (rms) values of the
voltages that are obtained from the waveforms, the power outputs delivered to the
loads of various resistances are calculated. In case of our microelectromagnetic
energy harvester, the electromechanical coupling coefficient (K) is very small (as
|dΦ/dz| is 1.14 × 10
-3
Wb/m at 100 μm away from the magnet in the simulation), and
the K
2
/d
m
is negligible compared to the coil resistance (220 Ω). In Fig. 3.22, the load
resistance is varied from 39 Ω to 33 kΩ, and we see that the maximum power of 0.55
nW is delivered to 220 Ω load. Thus, when the load resistance is 220 Ω, AIS delivers
a maximum power of 0.55 nW, almost four times larger than 0.14 nW delivered by
AI.
0.0
0.2
0.4
0.6
0.8
0 1 2 3 4
0.0
0.3
0.6
0.9
1.2
V
rms
(mV)
I
rms
( A)
Output Voltage vs. Current for AIS
Power vs. Current for AIS
Output Voltage vs. Current for AI
Power vs. Current for AI
Power (nW)

Fig. 3.22 Measured output voltage (rms value) and power across a load resistor with
different resistances for a four-unit Array I without Array II (AI) and a four-unit
Array I with Array II (AIS), at a vibration frequency and amplitude of 400 Hz and 10
μm, respectively.

66
The stacked stand-alone array of four units in this work is compared with other
energy harvesters reported in literature as shown in Table 3.4. Typically, the power
densities (nW/cm
3
) of macroscale energy harvesters are much higher than those of
fully-integrated MEMS ones, since weak magnetic field provided by microfabricated
magnets and high resistive coils limit the performance of energy harvesters
fabricated using MEMS technologies. However, it is highly desirable to employ
fully-integrated MEMS energy harvesters for mass production at low cost and
combination with CMOS circuits and microsystems. Although microfabrication of
high-quality magnets is still challenging for integration in microdevices, our
approach of power-generator stack with integrated magnets and dual-layer coils
fabricated on the same wafer in a batch process is very promising for increasing the
power output of a fully-integrated MEMS energy harvester to the level of powering
low-power microsystems. The stacked stand-alone array with four dual-layer coils in
series generates a power of 0.55 nW, which can be further improved by
electroplating thicker copper to reduce the coil resistance, increasing the number of
power-generator unit in the array and the number of stacked array.

67

3.3 Summary
A microelectromagnetic power generator with integrated magnets is presented
in this work. The wax-bonded Nd-Fe-B powders are embedded in the silicon wafer
as the micromagnets, and the residual powders are removed with a lift-off process.
The compact generator, occupying a volume of 15 × 13 × 0.4 mm
3
, is fabricated by
the MEMS technologies on the wafer in a batch process. The experimental results
show that the prototype with a 20-turn spiral coil generates an induced EMF of 0.27
mV at a vibration frequency and amplitude of 350 Hz and 10 μm, respectively. The
relatively low power delivered to a load can be improved by further increasing the
magnetic flux density and reducing the coil resistance.
Table 3.4 Summary of the reviewed electromagnetic power generators
Power
generators
(Fabrication
method)
Vibration
Frequency
(Hz)
Vibration
amplitude
(μm)
Acceleration
(g=9.8m/s
2
)
Volume
(cm
3
)
Open-
circuit
Voltage
(mV)
Power
output
(nW)
Power
density
(nW/cm
3
)
[6] (MEMS coil
and spring)
4400 0.5 39 g - - 300 -
[7] (Fully
Assembly)
110 200 9.7 g 1
4400
(p-p)
830000 8.3 × 10
5

[8] (Fully
Assembly)
322 25 10.4 g 0.24 - 530000 2.2 × 10
6

[9] (MEMS
spring)
9500 0.0011 0.4 g 0.1 - 122 1220
[10]
(Fully MEMS)
94.9 24 0.9 g - - 0.76 -
[11]
(Fully MEMS)
115 200 10.6 g 0.1
1
(0-p)
0.12 1.2
[12]
(Fully MEMS)
64 - - 0.025
0.0075
(0-p)
- -
[13]
(Fully MEMS)
530 0.88 1 g 0.0143
0.0132
(rms)
0.023 1.6
[14]
(Fully MEMS)
365 1.87 1 g 0.02
0.0209
(p-p)
- -
This work
(Fully MEMS)
400 10 6.4 g 0.22
1.02
(0-p)
0.55 2.5

68
Also, a stacked micromachined power generator has been designed, fabricated,
and characterized. Integrating wax-bonded Nd-Fe-B micromagnets on a wafer level
allows us to form multiple energy harvesters in lateral and vertical dimensions, i.e.,
three-dimensional stacking of harvester arrays that is afforded by the planar, batch
fabrication process. The power output of each power-generator unit in the stack is
increased by enhancing the electromagnetic induction through vertical integration of
magnets, which is verified by the simulations of the magnetic flux changes for one
magnet and two magnets. The induced EMFs are theoretically calculated with a
model of vibration-driven power generators and compared to experimental results. A
non-stacked, stand-alone array of four power generators generates V
zero-to-peak
=0.57
mV and 0.14 nW power output (into 220 Ω load) when it is vibrated at 400 Hz in
response to a vibration amplitude of 10 μm, which improves to 1.02 mV with 0.55
nW power output when two of such arrays are stacked.

69
Chapter 3 References
[1] S. S. Je, N. G. Wang, H. C. Brown, D. P. Arnold and J. Chae, “An
electromagnetically actuated microspeaker with fully-integrated wax-bonded
Nd-Fe-B micromagnets for hearing aid applications,” Transducers’09, IEEE
International Conference on Solid-State Sensors and Actuators, Denver, CO,
June 21-25, 2009, pp. 885-888.
[2] E. S. Kim, R. S. Muller and R. S. Hijab, “Front-to-backside alignment using
resist-patterned etch control and one etching step,” J. Microelectromech. Syst.,
vol. 1, no. 2, pp. 95-99, Jun. 1992.
[3] J. Svoboda, Magnetic Techniques for the Treatment of Materials. Dordrecht,
The Netherlands: Kluwer, 2004, pp. 260–263.
[4] D. N. Shen, J. H. Park, J. Ajitsaria, S. Y. Choe, H. C. Wikle III and D. J. Kim,
“The design, fabrication and evaluation of a MEMS PZT cantilever with an
integrated Si proof mass for vibration energy harvesting,” J. Micromech.
Microeng., vol. 18, 055017 (7pp), 2008.
[5] C. Q. Gui, R. Legtenberg, H. A. C. Tilmans, J. H. J. Fluitman and M.
Elwenspoek, “Nonlinearity and hysteresis of resonant strain gauges,” IEEE
International Micro Electro Mechanical Systems Conference, Amsterdam,
Netherlands, Jan. 29-Feb. 2, 1995, pp. 157–162.
[6] C. B. Williams, C. Shearwood, M. A. Harradine, P. H. Mellor, T. S. Birch and
R. B. Yates, “Development of an electromagnetic micro-generator,” IEE Proc.
Circuits Devices Syst., vol. 148, no. 6, pp. 337–342, Dec. 2001.
[7] N. N. H. Ching, H. Y. Wong, W. J. Li, P. H. W. Leong, and Z. Wen, “A laser-
micromachined multi-modal resonating power transducer for wireless sensing
systems,” Sensors and Actuators A, vol. 97, pp. 685–690, Apr. 2002.
[8] M. El-hami, P. Glynne-Jones, N. M. White, M. Hill, S. Beeby, E. James, A. D.
Brown, and J. N. Ross, “Design and fabrication of a new vibration-based
electromechanical power generator,” Sensors and Actuators A, vol. 92, no. 1–3,
pp. 335–342, Aug. 2001.
[9] E. Koukharenko, S. P. Beeby, M. J. Tudor, N. M.White, T. O’Donnell, C. Saha,
S. Kulkarni, and S. Roy, “Microelectromechanical systems vibration powered
electromagnetic generator for wireless sensor applications,” Microsyst. Technol.,
vol. 12, no. 10–11, Sep. 2006.

70
[10] S. Miki, T. Fujita, T. Kotoge, Y. Jiang, M. Uehara, K. Kanda, K. Higuchi and K.
Maenaka, “Electromagnetic energy harvester by using buried NdFeB,” IEEE
International Micro Electro Mechanical Systems Conference, Paris, France,
January 29- February 2, 2012, pp. 1221 – 1224.
[11] Y. Jiang, S. Masaoka, T. Fujita, M. Uehara, T. Toyonaga, K. Fujii, K. Higuchi
and K. Maenaka, “Fabrication of a vibration-drivenelectromagnetic energy
harvester with integrated NdFeB/Ta multilayered micro-magnets” J. Micromech.
Microeng. 21 (2011) 095014 (6pp).
[12] Q. Yuan, X. M. Sun, D. M. Fang and H. X. Zhang, “Design and
Microfabrication of Integrated Magnetic MEMS Energy Harvester For Low
Frequency Application,” Transducers '11, IEEE International Conference on
Solid-State Sensors and Actuators, Beijing, China, June 5 - 9, 2011, pp. 1855-
1858.
[13] N. Wang and D. P. Arnold, “Fully batch-fabricated MEMS magnetic vibration
energy harvesters,” Proc. PowerMEMS 2009, Washington, DC, USA, pp 348-
351.
[14] K. Tao, G. Ding, P. Wang, Z. Yang and Y. Wang, “Fully integrated micro
electromagnetic vibration energy harvesters with micro-patterning of bonded
magnets,” IEEE International Micro Electro Mechanical Systems Conference,
Paris, France, January 29- February 2, 2012, pp. 1237 – 1240.

71
Chapter 4
Energy Harvesting with High Electromagnetic
Conversion Efficiency through Magnet and Coil Arrays

This chapter describes a new idea to increase the energy-conversion efficiency
of electromagnetic transduction by orders of magnitude for vibration-driven power
generator. A rapidly changing magnetic field is produced through an array of
alternating north- and south-orientation magnets. Magnetic flux change for the
magnet array is simulated, optimized and compared to that for a single magnet.
Based on the new idea, microfabricated and miniature electromagnetic energy
harvesters with magnet and coil arrays are designed, fabricated and demonstrated to
harvest vibration energy with unprecedented conversion efficiency.
4.1 Design
According to Faraday’s law, the magnitude of electromotive force (EMF) is
obtained in Eq. 2-8 and expressed as
 
2
0 0 0
2
2
2
/
1 / 2
n
peak
n
n
d d dz d d
ZA
dt dz dt dz dz



  


   
   






(4-1)
At the resonant frequency, the EMF simplifies to
00
0
2
n
peak
Y mA dd
dz dz d





 (4-2)

72
For energy harvesters, maximum power outputs are delivered into matched loads of
which the resistances are equal to the coil resistances. For a sinusoidal voltage wave,
the power output is expressed as
2 2
22
0
0
2
()
88
peak
L
mA d
P
R dz Rd



 (4-3)
where R is the load resistance that is matched to the energy harvester’s source
resistance. It indicates that the power output (P
L
) is proportional to the square of
magnetic flux gradient ( / d dz  ), proof mass (m) and acceleration amplitude (A
0
).
Consequently, magnets with larger volume (which typically provide stronger
magnetic field), more coil turns, larger coil area, or larger coil cross-sectional area
result in a higher power output, but increase the volume and weight. Thus, for
electromagnetic energy harvesters, maximizing the spatial magnetic flux gradient
( / d dz  ) is essential in increasing the power output as the magnets or coils move
in response to the environmental vibration. For conventional electromagnetic energy
harvester, the magnetic field is provided by a single magnet, and the magnetic flux
change is caused by a distance change from the magnet. We have simulated the
magnetic field produced by one magnet with COMSOL, and the magnetic field lines
are shown in Fig. 4.1a. Figure 4.1b shows the calculated magnetic flux density (B
z
)
and its z-gradient ( /
z
dB dz ).

73

Fig. 4.1 (a) Cross-sectional view of the magnetic field lines produced by one magnet.
(b) Magnetic flux density (
z
B ) and its gradient ( /
z
dB dz ) from one magnet.
In order to provide a rapidly changing field, we design a new electromagnetic
transduction based on an array of magnets with alternating north- and south-
orientation arranged on a planar surface. Figures 4.2a and 4.2b show that the change
of magnetic flux density in the direction parallel to the planar surface ( /
z
dB dy )
peaks at the boundary between two magnets, for different heights (d) over the
magnet surface. The simulations show that the change of magnetic flux density
( /
z
dB dy ) for the magnet array depends on the distance from the magnet surface,
and can be more than hundred times higher than that of one magnet ( /
z
dB dz ). Thus,
(a)
(b)

74
the key innovation is the usages of a magnet array (along with a coil array) and the
in-plane (not out-of-plane) field gradient. In the simulations and experiments, Nd-Fe-
B permanent magnets (Grade N52) which are the strongest commercial magnets we
found at the time are used to provide the magnetic field. The parameters used in the
simulations are listed in Table 4.1.

Fig. 4.2 (a) Cross-sectional view of the magnetic field lines of two-magnet array. (b)
Magnetic flux density (
z
B ) and its gradient ( /
z
dB dy ) at a height of 50, 250 and
500 μm over two-magnet array.
(b)
(a)

75

The magnetic flux (  ) through a multi-turn coil (Fig. 4.3) is obtained with
11
()
i
nn
ii
ii
S
B dS

    


(4-4)
where n is the number of coil turns;
i


is magnetic flux through the i
th
coil; B is
magnetic flux density; and S
i
is the area of the i
th
coil. The magnetic flux is a
numerical integral of magnetic flux density across the entire coil area. Figure 4.4
shows the simulated magnetic flux (
z
 ) and its z-gradient ( /
z
d dz  ) versus the
distance between the coil and the magnet for a single magnet. Similarly calculated
magnetic flux (
z
 ) and its y-gradient ( /
z
d dy  ) for an array of magnets when a
coil is placed at a different position over the magnets are shown in Fig. 4.5. The
/
z
d dy  for an array of magnets peaks when the coil center is located at the
boundary between the magnets; increases as the distance (d) from the magnet surface
Table 4.1 Parameters used in the simulations
Magnet length (mm) 12.7
Magnet thickness (mm) 3.2
Residual magnetic flux density (T) 1.32
Relative permeability (in vacuum environment) 1
Coil turn
1
100
Coil number 1
Lateral space between coils (μm) 60
Outmost diameter of the coil
1
(mm) 12.7
Distance between the coil and magnet surface
2
(μm) 250
1
For simulations when the coil is placed at different heights over the magnet array in
Fig. 4.5.
2
For simulations when the coils with different outmost diameters are placed over the
magnet array in Fig. 4.6.

76
is decreased; and is much higher than that for a conventional one magnet. Figure 4.6
shows the magnetic flux (
z
 ) and its y-gradient ( /
z
d dy  ) for the coil for various
diameters of the outmost coil (of the multi-turn coil), showing that the magnetic flux
change increases as the coil size increases. Thus, when an array of coils is placed
over a magnet array, the optimal outmost diameter of the coils is equal to the side
length of a magnet (if square magnets are used to form the array). Based on the
simulations, we designed and fabricated various versions of the electromagnetic
energy harvester illustrated in Fig. 4.7 with the magnets arranged on a planar surface
such that north and south poles alternate. Coils are placed over the boundaries
between the magnets, as the magnet array is suspended by a spring system providing
a low spring constant in the direction parallel to the planar surface.

Fig. 4.3 Calculation of magnetic flux through a multi-turn coil.

77

Fig. 4.4 Magnetic flux (
z
 ) and its z-gradient ( /
z
d dz  ) versus the distance
between the coil and the magnet for a single magnet.

Fig. 4.5 Magnetic flux (
z
 ) and its y-gradient ( /
z
d dy  ) versus the coil center
position when the coil is placed at a height of 50, 250 and 500 μm over the magnet
array.

78

Fig. 4.6 Magnetic flux (
z
 ) and its y-gradient ( /
z
d dy  ) versus the coil center
position when the coils with different outmost diameters are placed at a height of 250
μm over the magnet array.

Fig. 4.7 Schematic of the energy harvester with alternating north- and south-
orientation magnet array.

79
4.2 Microfabricated Electromagnetic Energy Harvesters
This section describes the fabrication, measurements and comparison of
microelectromagnetic power generators with magnet and coil arrays. An array of
permanent magnets is used to provide the rapidly changing magnetic field.
Electroplated coil array and silicon cantilever as the spring system are fabricated on
the same silicon wafer.
4.2.1 Magnet array as proof mass
A microfabrication process has been used to fabricate a microelectromagnetic
energy harvester with a magnet array as shown in Fig. 4.8. First, a silicon wafer is
etched from the backside by potassium hydroxide (KOH) wet etching to form low
pressure chemical vapor deposition (LPCVD) silicon-nitride microdiaphragms for
front-to-backside alignment [1], followed by a second KOH etching to form 300 μm
deep trenches. A Ti/Cu (10 nm/100 nm) is deposited by E-beam evaporator as a seed
layer, and then photoresist AZ4620 is spin-coated and patterned to obtain a mold for
the copper coil. After 22 μm thick copper is electroplated on the front side, the
photoresist is removed in acetone, and the seed layer is etched away. Then the silicon
is etched through from the front side by silicon deep reactive ion etching (DRIE) to
form a 200 μm wide two-fold cantilever spring. Finally, an array of magnets is glued
to the cantilever spring in the trench on the silicon backside. Photos of the fabricated
microelectromagnetic energy harvester with four magnets and three coils, occupying
0.09 cc and weighing 0.5 gram, are shown in Fig. 4.9. The magnets physically touch

80
the silicon membrane, without being bonded or glued to it. Consequently, the narrow
gap between the magnet array and coil array is the silicon-membrane thickness,
which is controlled easily by the KOH wet etching. In this case, a 300 μm deep
trench on a 400 μm thick silicon wafer is etched by KOH wet etching to leave 100
μm thick silicon membrane, so that the gap between the magnets and coils may be
100 μm. The coil array on the front side of the wafer is located exactly over the
boundaries between the adjacent magnets on the backside, due to the
microdiaphragm-based front-to-backside alignment technique. The detailed
parameters of the fabricated microelectromagnetic energy harvester are listed in
Table 4.2.

Fig. 4.8 Brief fabrication process of the microelectromagnetic energy harvester with
magnet and coil arrays.

81

Fig. 4.9 Top-view and bottom-view photos of the fabricated microelectromagnetic
energy harvester occupying 0.09 cc and weighing 0.5 gram.

The fabricated electromagnetic energy harvester is characterized with a
vibration shaker system, which includes a function generator, power amplifier,
shaker table, pre-amplifier, laser Doppler displacement meter (LDDM) and
oscilloscope.
For the microfabricated electromagnetic energy harvester with four magnets
and three coils, the measured EMFs as a function of vibration frequency at various
input accelerations are shown in Fig. 4.10 when three coils are connected in series.
Table 4.2 Parameters of the microelectromagnetic energy harvester
Total volume (mm
3
) 20 × 5 × 0.9 (0.09 cc)
Weight (g) 0.5
Magnet size (mm
3
) 4.8 × 4.8 × 0.8
Coil turn 20
Coil resistance (Ω) 3.6
Coil number 3
Gap between magnet array and coil array (μm) 100

82
At a fixed acceleration, the EMFs depend on the vibration frequency, peaking at the
resonant frequency. From the acceleration of 3.75 g at the resonant frequency of 290
Hz, a peak value of 30 mV
peak-to-peak
is measured as shown in Fig. 4.11. Figure 4.12
shows the measured output voltage and power across a load resistor with different
resistances, at the acceleration of 3.75 g. The load resistor is directly connected to the
fabricated energy harvester, and the voltage across the load resistor is amplified by a
pre-amplifier and the amplified waveform is observed at the oscilloscope. Thus, the
unamplified voltage across the load resistor produced by the energy harvester is the
amplified voltage divided by the gain of the pre-amplifier. As we vary the resistance
of the load resistor, the waveforms of the output voltages are recorded for each
resistance value. With the root-mean-square (rms) values of the voltages that are
obtained from the waveforms, the power outputs delivered to the loads of various
resistances are calculated. A maximum power of 2.6 μW is delivered to a 10.8 Ω
load from the 3.75 g acceleration at vibration frequency of 290 Hz. The power output
(into 10.8 Ω load) at a resonant frequency of the microelectromagnetic energy
harvester as a function of the vibration acceleration is shown in Fig. 4.13. As the
acceleration is increased from 0.75 to 3.75 g, the maximum power output increases
from 0.2 to 2.6 μW. The 3.75 g of acceleration at 290 Hz corresponds to about 11 μm
vibration amplitude, and the microelectromagnetic energy harvester can harvest
some very small vibrations that exist in walls, bridges, etc. However, in practical
applications, the harvested power level may differ from the one measured with a
mono-frequency sinusoidal vibration source, even for a same vibration amplitude,

83
since the frequency spectrum of a practical vibration source is typically broadband
(unlike the one produced by the mechanical shaker used in the current experiments
that produces a mono-frequency sinusoidal vibration) and because a vibration-driven
energy harvester produces the maximum power at its resonant frequency.
240 260 280 300 320 340
0
10
20
30
V
P-P
(mV)
Frequency (Hz)
0.75g
1.5g
2.25g
3g
3.75g

Fig. 4.10 Measured EMF (peak-to-peak value) versus vibration frequency at
different accelerations for the microfabricated electromagnetic energy harvester
occupying 0.09 cc and weighing 0.5 gram.
290 Hz
30 mV
0.000 0.005 0.010
-10
0
10
Voltage (mV)
Time (s)

Fig. 4.11 Measured EMF of 30 mV
peak-to-peak
at 290 Hz in response to a vibration
amplitude of 11 μm for the microfabricated electromagnetic energy harvester
occupying 0.09 cc and weighing 0.5 gram.

84

0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.2 0.4 0.6 0.8 1.0
0
10
20
30
V
p-p
(mV)
Current (mA)
V
p-p
vs. Current
Power vs. Current
Power ( W)

Fig. 4.12 Measured output voltage (peak-to-peak value) and power across a load
resistor with different resistances at the acceleration of 3.75 g for the microfabricated
electromagnetic energy harvester occupying 0.09 cc and weighing 0.5 gram.
1 2 3 4
0
1
2
3
Power ( W)
Acceleration (g)
Power vs. Acceleration

Fig. 4.13 Measured power output (into 10.8 Ω load) versus input acceleration for the
microfabricated electromagnetic energy harvester occupying 0.09 cc and weighing
0.5 gram.

290Hz, 11μm

85
4.2.2 Coil array as proof mass
As shown in Fig 4.5, simulation results show that the magnetic flux change in
the direction parallel to the planar surface (
z
d
dy

) peaks at the boundary between the
magnets, and increases as the distance (d) from the magnet surface is decreased. As
the gap between magnet array and coil array needs to be as close as possible, we
controlled the gap accurately through an etch step formed on silicon by etching.
The schematic of the microelectromagnetic energy harvester with magnet and
coil arrays is shown in Figs. 4.14. An array of coils is suspended by a spring system
fixed to a frame with a trench and a space. An array of magnets is integrated into the
trench, while the distance between the magnet and coil arrays is kept narrow and
accurate by the space-creating etch step.
Trench
Space
Coil array
Frame
Spring
Gap between magnet
and coil array
Coil array
Magnet array
Vibration

Fig. 4.14 (a) Schematic of the coil array integrated to the frame with a trench and a
space. (b) Cross-sectional view of the microelectromagnetic energy harvester with
magnet array and gap control.

86
A microfabrication process has been used to fabricate the electromagnetic
energy harvester with magnet array and step control in a process illustrated in Fig.
4.15. First, 200 μm deep trenches are etched on the backside of the wafer by KOH
etching, and the silicon deep reactive ion etching (DRIE) is used to form the trench
for integrating magnets and a 30 μm space. After 25 μm thick Cu is electroplated as
the coils on the front side, the photoresist is removed in acetone, and the seed layer is
etched away. Then the silicon is etched through from the front side by silicon DRIE
to form the 400 μm wide two-fold cantilever spring. Finally, an array of magnets is
glued to the trench on the front side, and a 5 μm gap between magnet and coil array
is formed.
(a) KOH etching
SiN
(b) DRIE etching
(c) Electroplating copper
(d) Si released by DRIE
(e) Assembling magnets
Copper

Fig. 4.15 Brief fabrication process of the microelectromagnetic energy harvester
with magnet and gap control.

87
The fabricated microelectromagnetic energy harvester with magnet and coil
arrays is shown in Fig. 4.16. Since the magnet array does not need to be suspended
by silicon cantilever, thicker and heavier permanent magnets (6.4 × 6.4 × 3.2 mm
3
)
are used and inserted into the trench to provide a stronger magnetic field. The total
weight almost comes from the magnets since the mass of silicon wafer (whole area
of 13 × 29 mm
2
) is far less than that of magnets. The detailed parameters of the
fabricated microelectromagnetic energy harvester are listed in Table 4.3. The coil
array is placed precisely over the boundaries between the magnets, where a magnetic
field distribution has a steep field gradient, and produces EMF with a very high
electromechanical coupling efficiency, as the coils vibrate in the direction parallel to
the planar surface.
13mm
29mm

Fig. 4.16 Photos of the fabricated microelectromagnetic energy harvester with gap
control.

88

The fabricated electromagnetic energy harvester with gap control is
characterized with a vibration shaker system when the three coils are connected in
series. The EMFs as a function of vibration frequency at various input accelerations
show a peak value of 42 mV
p-p
at a resonant frequency of 410 Hz for a vibration
amplitude of 17 μm (corresponding to 11.25 g acceleration) as shown in Fig. 4.17.
The higher resonant frequency is mainly caused by the light coils-proof-mass
compared to the energy harvester with magnet array as proof mass in the chapter
4.2.1.
360 390 420 450 480
0
10
20
30
40
V
p-p
(mV)
Frequency (Hz)
2.25g
3g
3.75g
7.5g
11.25g

Fig. 4.17 Measured EMF versus vibration frequency at different accelerations for the
microfabricated electromagnetic energy harvester with coil arrays as proof mass.
Table 4.3 Parameters of the microelectromagnetic energy harvester with gap control
Magnet size (mm
3
) 6.4 × 6.4 × 3.2
Weight (g) 5
Coil turn 30
Coil resistance (Ω) 4.6
Coil number 3
Coil thickness (μm) 25
Gap between magnet array and coil array (μm) 5

89
Figure 4.18 shows the measured output voltage and power across a load
resistor with different resistances, at the acceleration of 3.75 g. The output voltages
are measured across various load resistors, and the powers are calculated from the
measured voltages when the resistors are connected to the fabricated energy
harvester. A maximum power of 0.34 μW is delivered to a 13.8 Ω load from the 3.75
g acceleration at vibration frequency of 410 Hz. This maximum power output is
much lower than that of 2.6 μW generated by the device with magnet array as proof
mass, although the stronger permanent magnets are used and the gap between the
magnet array and coil array is reduced from 100 μm to 5 μm. At the resonant
frequency, the maximum power output is obtained in Eq. 4-3. Thus, the power is
proportional to the square of the proof mass and lighter coil-proof-mass degrades the
power output much.
0.0
0.1
0.2
0.3
0.4
0.0 0.2 0.4 0.6
0
3
6
9
12
V
p-p
(mV)
Current (mA)
V
p-p
vs. Current
Power vs. Current
Power ( W)

Fig. 4.18 Measured output voltage and power of the microfabricated energy
harvester versus load resistance at the acceleration of 3.75 g, showing a maximum
power delivery when the load resistance matches the harvester’s resistance.

90
The power output (into 13.8 Ω load) at a resonant frequency of the
microelectromagnetic energy harvester as a function of the vibration acceleration is
shown in Fig. 4.19. As the acceleration is increased from 2.25 g to 11.25 g, the
maximum power output increases from 0.1 μW to 4 μW. The energy harvester with
coil-proof-mass can work at much higher acceleration (11.25 g) than that with
magnet-proof-mass.
2 4 6 8 10 12
0
1
2
3
4
Power ( W)
Acceleration (g)
Power vs. Acceleration

Fig. 4.19 Measured power output (into 13.8 Ω load) versus input acceleration for the
microfabricated energy harvester with coil arrays as proof mass.
4.3 Miniature Electromagnetic Energy Harvesters
This section describes fabrication and measurements of miniature power
generators scaled up to 16 magnets and 12 coils based on the same conversion
principle. The performance is compared with various energy harvesters reported in
literature.

410Hz, 17μm

91
4.3.1 Fabrication
The miniature energy harvester has been fabricated with magnet and coil
arrays using two plastic cantilevers as the spring system. We use a coil winder to
wind copper wire (0.127 mm in diameter) around a laser-machined acrylic spool to
form a 200-turn coil. Twelve such coils are mounted on a plastic plate, which is
connected to a 250 μm-thick plastic beam at the top as well as at the bottom. The thin
beams are then connected to a 16-magnet array such that the beams suspend the
magnet array with an air gap (about 250 μm wide) between the magnet array and the
coil array. Photos of the fabricated miniature energy harvester with 16 magnets and
12 coils, occupying 26 cc and weighing 90 gram, are shown in Fig. 4.20. The two
suspension beams at the top and bottom, rather than just at one place, are used to
make the vibration direction of the proof mass (i.e., the magnet array in this design)
more parallel to the coil plate so that the energy lost due to the hitting of magnets and
coils is reduced. The thin plastic beam also provides a low spring constant as well as
a sturdy support for a relatively heavy magnet array, and facilitates a low resonant
frequency, making the energy harvesters work at a wide frequency range of input
acceleration. The detailed parameters of miniature energy harvester are listed in
Table 4.4.

92
51 mm
51 mm
Plastic cantilever
10 mm

Fig. 4.20 Perspective-view and top-view photos of the miniature energy harvester
occupying 26 cc and weighing 90 gram.

4.3.2 Measurements of miniature electromagnetic energy harvesters
Based on the same conversion principle, a miniature energy harvester scaled up
to 16 magnets and 12 coils occupying 26 cc and weighing 90 gram, has been
fabricated and characterized. The pre-amplifier is not needed in this case, since the
output voltage from the miniature energy harvester is very large. Firstly, the magnet
array is fixed on the shaker and the coil array is suspended by the plastic spring as
Table 4.4 Parameters of the fabricated miniature energy harvester
Total volume (mm
3
) 51 × 51 × 10 (26 cc)
Weight (g) 90
Magnet size (mm
3
) 12.7 × 12.7 × 3.2
Coil turn 200
Coil resistance (Ω) 8
Coil number 12
Gap between magnet array and coil array (μm) 250
Acrylic spool size (mm)
Outside diameter=12.7
Inner diameter=3.5
Height=1.5
Plastic cantilever size (mm
3
) 18 × 10 × 0.25

93
proof mass. When the 12 coils are connected in series, the EMFs as a function of
vibration frequency at various input accelerations show a peak value of 7.2 V
p-p
at a
resonant frequency of 70 Hz for a vibration amplitude of 142 μm (corresponding to
2.8 g acceleration) as shown in Fig. 4.21. It generates an EMF of V
p-p
= 22 V at a
resonant frequency of 82 Hz when the vibration amplitude is 414 μm, as shown in
Fig. 4.22.
40 60 80 100
2
4
6
8
V
p-p
(mV)
Frequency (Hz)
2.1g
2.8g

Fig. 4.21 Measured EMF versus vibration frequency at different accelerations for the
miniature electromagnetic energy harvester with coil arrays as proof mass.
0.00 0.01 0.02 0.03 0.04 0.05
-15
-10
-5
0
5
10
15
Voltage (V)
Time (s)
82 Hz
22V

Fig. 4.22 Measured EMF of 22 V at 82 Hz in response to a vibration amplitude of
414 μm for the miniature electromagnetic energy harvester with coil arrays as proof
mass.

94
The power output (into 96 Ω load) at a resonant frequency of the energy
harvester as a function of the vibration acceleration is shown in Fig. 4.23. As the
acceleration is increased from 2.1 g to 11.2 g, the miniature energy harvester delivers
power output to a 96 Ω load from 9.1 mW to 158 mW. When we connect the energy
harvester to an incandescent light bulb (0.12 W 0.06 A 2 V) directly, the power level
is enough to light the bulb. With increasing input acceleration, the light intensity
from the bulb increases, and reaches close to the bulb’s full capacity as shown in
4.24. As far as we know, this is the first demonstration of an incandescent light bulb
(not light emitting diode) being lit up by an energy harvester.
3 6 9 12
0
40
80
120
160
Power (mW)
Acceleration (g)
Power vs. Acceleration

Fig. 4.23 Measured power output (into 96 Ω load) versus input acceleration for the
miniature electromagnetic energy harvester with coil arrays as proof mass.

Fig. 4.24 Photo of an incandescent light bulb being lit up by the miniature energy
harvester with coil array as proof mass occupying 26 cc and weighing 90 gram that
also produced the measured data shown in Fig. 4.23, when the energy harvester is
subject to vibration amplitude of 414 µ m at 82 Hz.
82Hz, 414μm

95
As discussed before, in order to increase the power output, the coil array is
fixed on the shaker and the heavier magnet array is suspended by the plastic spring
as proof mass. The same miniature energy harvester with 16 magnets and 12 coils
occupying 26 cc and weighing 90 gram has been characterized. The measured EMFs
as a function of vibration frequency at various input accelerations are shown in Fig.
4.25 when twelve coils are connected in series. At a fixed acceleration, the EMFs
depend on the vibration frequency, peaking at the resonant frequency. Among the
various versions of the fabricated energy harvesters, the miniature energy harvester
with 16 magnets and 12 coils has shown to have the best performance, generating an
EMF of 28.8 V
peak-to-peak
at 65 Hz when the vibration amplitude is 660 μm, as shown
in Fig. 4.26. The measured plot of EMF versus vibration frequency for an input
acceleration of 0.21 g at the resonant frequency of 65 Hz (Fig. 4.25) shows a 3-dB
bandwidth (   ) of 20 Hz, and a quality factor ( Q ) can be estimated to be 3.25, as
/
n
Q   . Thus, the damping ratio is / 2 1/ 2 0.15
n
d k Q     . At the
acceleration of 2.1 g, the quality factor ( Q ) is reduced to 1.44 with the 3-dB
bandwidth (   ) of 45 Hz, and the corresponding damping ratio is 1/ 2 0.35 Q  .
As the input acceleration increases, the damping ratio increases, indicating the
decreasing energy-conversion efficiency.

96
40 60 80 100
0.4
0.6
0.8
1.0
1.2
V
p-p
(V)
Frequency (Hz)
0.21g
0.3g
6.12 V @ 65 Hz
40 60 80 100
0
2
4
6
8
10
12
V
p-p
(V)
Frequency (Hz)
0.21g
0.3g
2.1g
2.8g
3.6g
0.68 V @ 65 Hz
Bandwidth=20Hz Bandwidth=45Hz

Fig. 4.25 Measured EMF (peak-peak value) versus vibration frequency at different
accelerations for the miniature energy harvester with magnet array as proof mass
occupying 26 cc and weighing 90 gram.
0.00 0.02 0.04
-10
0
10
20
Voltage (V)
Time (s)
65 Hz
28.8 V

Fig. 4.26 Measured EMF of 28.8 V
peak-to-peak
at 65 Hz in response to a vibration
amplitude of 660 μm for the miniature energy harvester with magnet array as proof
mass occupying 26 cc and weighing 90 gram.
The power output (into 96 Ω load) at a resonant frequency of the energy
harvester as a function of the vibration acceleration is shown in Fig. 4.27. As the
acceleration is increased from 2.1 to 11.2 g, the miniature energy harvester delivers
power output to 96 Ω load from 11.7 to 263 mW. As far as we know, this is a record

97
power level, by far, for this kind of volume and weight. When we connect the energy
harvester to a “0.12 W 0.06 A 2 V” incandescent light bulb directly, the harvested
power level is so high that it can light the bulb to a level close to burning out its
filament. Figures 4.28a-4.28d show the light bulb being lit up by the energy
harvester as the input acceleration at 65 Hz is increased from 5.6 g to 7.5 g, 9.5 g and
then 11.2 g (corresponding to 660 μm vibration amplitude). With increasing
acceleration (or vibration amplitude), the light intensity from the bulb increases, and
a very bright light is emitted (Fig. 4.28d), as the power harvested at a higher
acceleration exceeds the bulb’s full capacity. As far as we know, this is the first
demonstration of an incandescent light bulb (not light emitting diode) being lit up by
an energy harvester.
3 6 9 12
0
60
120
180
240
300
Power (mW)
Acceleration (g)
Power vs. Acceleration
65 Hz, 660 μm

Fig. 4.27 Measured power output (into 96 Ω load) versus input acceleration for the
miniature energy harvester with magnet array as proof mass occupying 26 cc and
weighing 90 gram.

98
(a) (b)
(c) (d)

Fig. 4.28 Photos of an incandescent light bulb being lit up by the energy harvester at
input accelerations of (a) 5.6 g (corresponding to 330 µ m vibration amplitude), (b)
7.5 g (440 µ m vibration amplitude), (c) 9.5 g (560 µ m vibration amplitude) and (d)
11.2 g (660 µ m vibration amplitude) for the miniature energy harvester with magnet
array as proof mass occupying 26 cc and weighing 90 gram.
We compare the newly developed energy harvester with various energy
harvesters reported in literature [2-15], in terms of power output per harvester
volume (mW/cm
3
) and Figure of Merit (FOM) defined to be the mW/cm
3
normalized
with respect to the square of acceleration (mW/cm
3
/g
2
), and show them in Figs.
4.29a and 4.29b for various input accelerations and vibration frequencies,
respectively. The FOM typically drops as the input acceleration increases, as shown
in Fig. 4.29b, indicating that it is difficult to generate high power with high
efficiency, since the increasing acceleration causes larger damping. As can be seen in
Figs. 4.29a and 4.29b, our energy harvester produced the highest power output (263
mW) and highest power density (10.12 mW/cm
3
), by orders of magnitude, and

99
showed the best FOM (0.081 mW/cm
3
/g
2
), among the energy harvesters reported in
literature. The energy harvester based on the new ideas is orders of magnitude better
than any reported energy harvester, as can be seen in Table 4.5.
1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
0.1 1 10 100
1E-4
1E-3
0.01
0.1
1
10
Power density (mW/cm
3
)
Acceleration (g)
Power density
FOM
FOM (mW/cm
3
/g
2
)
[3]
[15]
[11]
[7]
[9]
[15]
[11]
[3]
[9]
[7]
[2]
[12]
[13]
[4]
[4]
[2]
[13]
[12]
[14]
[6]
[6]
[14]
[5]
[5]
[10]
[10] [8]
[8]
This work

1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
1 10 100 1000
1E-4
1E-3
0.01
0.1
1
10
Power density (mW/cm
3
)
Frequency (Hz)
Power density
FOM
FOM (mW/cm
3
/g
2
)
This work
[3]
[3]
[15]
[7]
[15]
[7]
[13]
[9]
[13]
[2]
[4]
[9]
[4]
[6]
[6]
[2]
[14]
[11]
[14]
[12]
[12]
[5]
[5]
[11]
[10]
[10] [8]
[8]

Fig. 4.29 (a) Power output per harvester volume and FOM versus input acceleration
for various published electromagnetic energy harvesters. (b) Power output per
harvester volume and FOM versus vibration frequency for various electromagnetic
published energy harvesters.
(a)
(b)

100

Figures 4.30a and 4.30b show the power density and FOM of other types of
vibration-driven energy harvesters, including piezoelectric [16-22], electrostatic [23-
27], electret [28-30] and magnetostrictive types [31-32], for various input
accelerations and vibration frequencies, respectively. The important parameters for
these energy harvesters are listed in Table 4.6. Piezoelectric method produces
relatively high power density and FOM at high vibration frequency with highly
piezoelectric material (such as lead zirconate titanate). But since the piezoelectric
materials need to be strained to generate electricity, the vibration amplitude and
lifetime are limited. Electrostatic energy harvesters that require an external
polarization voltage or an implanted charge show the lowest power density and FOM,
even though their sizes are typically small. In addition, mechanical constraints for
the moving electrodes need to be carefully designed to control the small vibration
displacement. Magnetostrictive materials (which deform when placed in a magnetic
Table 4.5 Summary of the reviewed electromagnetic power generators
Power
output
(mW)
Resonant
frequency
(Hz)
Vibration
amplitude
(μm)
Acceleration
(g=9.81m/s
2
)
Volume
(cm
3
)
Power
density
(mW/cm
3
)
FOM
(mW/cm
3
/g
2
)
Reference
0.001 94 50 1 0.025 0.04 0.04 [2]
0.057 2 4000 0.055 68 8.4e-4 0.277 [3]
0.29 102 85 3.6 9.3 0.031 0.0024 [4]
0.83 110 200 9.7 1 0.83 0.009 [5]
2.09 8.5 172 0.5 40.18 0.052 0.208 [6]
0.0004 5000 1 100 1.4 2.9e-4 2.86e-8 [7]
0.0004 75 9 0.2 2.703 1.5e-4 0.0037 [8]
0.0032 938 14 50 9.504 3.4e-4 1.35e-7 [9]
0.00015 580 0.14 0.19 0.0271 0.0055 0.153 [10]
0.02356 371 24.4 13.5 1 0.02356 1.3e-4 [11]
0.05 340 5 2.3 1.35 0.037 0.007 [12]
0.00061 55 125 1.52 0.13 0.0047 0.002 [13]
0.0615 111 61 3 2.25 0.027 0.003 [14]
1.18 9 500 0.16 7.39 0.16 6.24 [15]
263 65 660 11.2 26 10.12 0.081 Ours

101
field, or inversely induce a change of magnetic field upon deformation) can be used
independently [31] or in piezoelectric-magnetostrictive composites [32] for energy
harvesting. This method still needs to overcome the challenges of limited film
thickness and non-linear effects. Although piezoelectric-magnetostrictive composites
show a higher power density, relative motion between an external magnet and the
composites has not been realized on a vibrating surface.
This work
1E-4
1E-3
0.01
0.1
1
10
0 4 8 12
1E-4
1E-3
0.01
0.1
1
10
Power density (mW/cm
3
)
Acceleration (g)
FOM (mW/cm
3
/g
2
)
[22]
[22]
[19]
[32]
[16]
[20]
[20]
[21]
[21]
[29]
[29]
[27] [27]
[23]
[23]
[30]
[30]
[28]
[28]
[16]
[26]
[24]
[24] [25]
[25]
[26]
[19]
[32]
[31]
[31]
[18]
[18]
[17]
[17]
1E-4
1E-3
0.01
0.1
1
10
0 4 8 12
1E-4
1E-3
0.01
0.1
1
10
Power density (Piezoelectric)
Power density (Electrostatic)
Power density (Electret)
Power density (Magnetostrictive)
Power density (This work)
FOM (Piezoelectric)
FOM (Electrostatic)
FOM (Electret)
FOM (Magnetostrictive)
FOM (This work)

This work
1E-4
1E-3
0.01
0.1
1
10
0 300 600
1E-4
1E-3
0.01
0.1
1
10
Power density (mW/cm
3
)
Frequency (Hz)
FOM (mW/cm
3
/g
2
)
[19]
[18]
[18]
[26]
[19]
[22]
[22]
[25]
[25]
[17]
[17]
[26]
[24]
[30]
[23]
[23]
[27] [27]
[28]
[29]
[29]
[28]
[16]
[30]
[24]
[32]
[16]
[32]
[31]
[31]
[20]
[20]
[21]
[21]
1E-4
1E-3
0.01
0.1
1
10
0 300 600
1E-4
1E-3
0.01
0.1
1
10
Power density (Piezoelectric)
Power density (Electrostatic)
Power density (Electret)
Power density (Magnetostrictive)
Power density (This work)
FOM (Piezoelectric)
FOM (Electrostatic)
FOM (Electret)
FOM (Magnetostrictive)
FOM (This work)

Fig. 4.30 (a) Power output per harvester volume and FOM versus input acceleration
for various published vibration-driven energy harvesters. (b) Power output per
harvester volume and FOM versus vibration frequency for various published
vibration-driven energy harvesters.
(a)
(b)

102

4.3.3 Energy-conversion efficiency
The maximum ECE for the miniature energy harvester weighing 90 gram at
the resonant frequency of 65 Hz under 11.2 g acceleration can be calculated from Eq.
2-25 as
2
,max
max 3 2 3 3 3 2
0
28.8
( ) / 96
4
10%
2 2 90 10 (2 65) (0.66 10 )
e
P
ECE
MY

  
     
(4-6)
As can be seen in Fig. 7a, the damping ratio increases as the input acceleration
is increased. At the acceleration of 2.1 g, the maximum ECE increases to 13%, 1.3
times higher than that at the acceleration of 11.2 g. The maximum ECE for the
microfabricated energy harvester can be estimated by the same way.
Table 4.6 Summary of the reviewed piezoelectric [16-22], electrostatic [23-27],
electret [28-30] and magnetostrictive [31-32] power generators
Power
output
(mW)
Resonant
frequency
(Hz)
Vibration
amplitude
(μm)
Acceleration
(g=9.81m/s
2
)
Volume
(cm
3
)
Power
density
(mW/cm
3
)
FOM
(mW/cm
3
/g
2
)
Reference
0.375 120 4.4 0.26g 1 0.375 5.55 [16]
0.18 50 10 0.1g 9 0.02 2 [17]
0.0163 100 184 7.4g 0.2 0.0815 0.0015 [18]
0.205 154 15.7 1.5g 0.15 1.37 0.61 [19]
0.00215 461 2.3 2g 6.6e-4 3.27 0.82 [20]
0.06 572 1.5 2g 0.1 0.6 0.15 [21]
0.014 235 4.5 1g 0.05 0.28 0.28 [22]
0.036 6 9000 1.3g 15 0.00242 0.00143 [23]
1.052 50 90 0.9g 18 0.058 0.072 [24]
0.0022 150 11 1g 0.042 0.052 0.052 [25]
0.0013 110 5.1 0.25g 0.038 0.034 0.547 [26]
1.5e-4 96 27 1g 1.86 8.1e-5 8.1e-5 [27]
0.006 10 1000 0.4g 0.4 0.015 0.09375 [28]
0.0025 10 4000 1.6g 0.044 0.057 0.022 [29]
0.0015 28 158 0.5g 0.3 0.005 0.02 [30]
0.576 58 73.9 1g 0.95 0.606 0.606 [31]
1.2 30 138 0.5g 1 1.2 4.8 [32]

103
4.4 Microfabrication of Coils
Microfabricated electromagnetic energy harvesters have a difficulty of
incorporating a low resistance coil with multiple turns. Tens microns thick
electroplated copper with photoresist mold is usually used as the coils in a planar
fabrication process. However, the number of turns is limited in the 2D space, and
also photoresist mold is not suitable for hundreds microns thick metal and presents
difficulties in its formation and removal. This section presents two microfabrication
approaches for 3D multi-layer coils with hundreds microns thickness and thousands
turns, which have been integrated in microelectromagnetic energy harvesters.
4.4.1 Electroplated coils with silicon mold
Following the microfabrication process illustrated in Fig. 4.31, we etch a
silicon wafer with DRIE to form a mold (Fig. 4.32a), and bond it to another wafer
with photoresist, followed by electroplating of 300 μm thick copper over Ti/Cu seed
layer. Then after 200 nm thick Al is deposited by evaporator on the other side of the
wafer to protect the wafer, the silicon mold is etched away by TMAH, and the seed
layer is removed (Figs. 4.32b-4.32e).

104

Fig. 4.31 Brief microfabrication process of electroplated Cu with Si mold.
(a)
(b)
(c)
(d)
(e)
1mm
200μm
200μm

Fig. 4.32 (a) Silicon wafer patterned by DRIE as a mold. (b) and (c) Perspective-
view and top-view photos of 300 μm thick electroplated coils on silicon wafer. (d)
and (e) Detailed microscopic photos of the coils.
A vibration-energy harvester composed of four 7-turn 300 μm-thick coils (0.7
Ω) fabricated with Si mold is characterized and compared with a harvester with four
15-turn 25 μm-thick coils (15.5 Ω) fabricated with photoresist mold. The EMF peaks

105
to 17.9 mV
p-p
at 250 Hz for vibration amplitude of 6 μm (Fig. 4.33). Although the
EMF is lower due to the less number of turns, the maximum power of 14.3 μW is
delivered, almost 7 times higher power than 2.1 μW from the coils fabricated with
photoresist mold (Fig. 4.34).

Fig. 4.33 Measured EMF versus vibration frequency at different accelerations for the
fabricated microelectromagnetic power generator with 300 μm thick electroplated
coils.
0.0 0.5 1.0 1.5
0
5
10
15
Electroplating Cu with Si mold
Electroplating Cu with PR mold
Electroplating Cu with Si mold
Electroplating Cu with PR mold
Power ( m)
Acceleration (g)
0.0 0.5 1.0 1.5
0
10
20
30
V
p-p
(mV)
Acceleration (g)

Fig. 4.34 Comparison of measured output voltages and powers across matched loads
versus input acceleration for electroplated coils with Si mold and photoresist mold.
200 220 240 260 280 300
0
5
10
15
20
V
p-p
(mV)
Frequency (Hz)
0.38g
0.75g
1.05g
1.5g

106
4.4.2 Microfabricated coils with multiple layers
To fabricate 3D stacked multi-layer coils, we use through-silicon vias with
copper filling to interconnect the coils on both sides of the wafer (Figs. 4.35 and
4.36). After via holes are etched by KOH etching on a wafer deposited with Si
x
N
y

layer (Fig. 4.36a), Ti/Cu (10 nm/200 nm) is deposited, and Si
x
N
y
and Ti in the via
holes are etched away. Then after spin-coating photoresist on the front side, we
electroplate copper on the backside to fill the via holes, remove the photoresist, and
electroplate 25 μm thick copper with photoresist mold for coil on the front side (Fig.
4.37a) and then on the backside, with the coils on the two sides being interconnected
by the copper filling vias (Fig. 4.37b). A 1 μm thick parylene layer is deposited as
isolation layer and patterned to expose the pads. Such fabricated wafers are stacked,
and the pads from adjacent wafers are connected by silver paste (Fig. 4.37c).
Top-layer coils
Interconnection via
Bottom-layer coils

Fig. 4.35 Schematic of multi-layer coils (an example of 6 coils in serial connection)
interconnected through copper filling vias.

107

Fig. 4.36 Brief microfabrication steps for 3D stacked multi-layer coils with a large
number of turns.
(a)
(b) (d)
20mm
13mm
200μm
200μm
20mm
13mm
26mm
13mm
(c)

Fig. 4.37 (a) and (b) Top-view and bottom-view photos of silicon wafer with
electroplated coils on both sides of the wafer, interconnected by vias through the
silicon. (c) Perspective-view photo of a three-wafer stack having multi-layers of
1080-turn coils. (d) Magnet array suspended by laser-machined plastic springs.
The energy harvester with the stacked multi-layer coils shows a resonant
frequency of 75 Hz (Fig. 4.38), and the output voltages measured across various load
resistors (Fig. 4.39) show that the maximum power of 1.04 mW is delivered to a 190
Ω load from 5 g acceleration (Fig.4.40).

108
50 60 70 80 90 100 110
0
100
200
300
400
V
p-p
(mV)
Frequency (Hz)
0.2g
0.3g
0.4g
0.6g
0.8g

Fig. 4.38 Measured EMF versus vibration frequency at different accelerations for the
fabricated microelectromagnetic power generator with 3D stacked multi-layer coils.
0
100
200
300
400
0 2 4 6 8
0.0
0.5
1.0
1.5
V
p-p
(V)
I
p-p
(mA)
V
p-p
vs. I
p-p
at 1.7g
Power vs. I
p-p
at 1.7g
V
p-p
vs. I
p-p
at 2.9g
Power vs. I
p-p
at 2.9g
Power ( W)

Fig. 4.39 Measured output voltage and power across a load resistor with different
resistances at the acceleration of 1.7 g and 2.9 g for the fabricated
microelectromagnetic power generator with 3D stacked multi-layer coils.

109
0 1 2 3 4 5
0.0
0.4
0.8
1.2
Power (mW)
Acceleration (g)
Power vs. Acceleration

Fig. 4.40 Measured power output (into 190 Ω load) versus input acceleration for the
microelectromagnetic energy harvester with 3D stacked multi-layer coils.
4.5 Energy Harvesting from 2-DOF Vibrations
Conventional power generators harvest energy from just one direction, along
which the distance between magnet and coil is changed in response to the
environmental vibration. A high mechanical-to-electrical energy-conversion
efficiency is produced by an array of magnets with alternating north- and south-
orientation as the coils vibrate in the direction parallel to the planar surface. This
approach provides also a method to harvest energy from multiple directions. Figure
4.41 illustrates the schematic of the 2-DOF (degree of freedom) electromagnetic
energy harvester with magnet and coil arrays. As long as the vibration direction is
parallel to the magnet surface, the magnetic flux is changed in the coils. Four coils
(two coils called “Coil
X
” for harvesting from X-direction vibration and two coils
called “Coil
Y
” for harvesting from Y-direction vibration) are designed over the
boundaries between the adjacent magnets.
75Hz, 220μm

110
S
N
S
N
Coil
X
Coil
Y
Y
X

Fig. 4.41 Schematic of the electromagnetic power generator harvesting from 2-DOF
vibration. Coil
X
is for harvesting from X-direction vibration, while Coil
Y
is for
harvesting from Y-direction vibration.
For the Y-direction (or the X-direction) vibration (Fig. 4.42a), an induced
electromotive force (EMF) from Coil
Y
(or Coil
X
) is
3
2
0
2
22
12
n
n
Y
n
d
Y
dz








   
 
   

   



(4-7)
where ω is vibration frequency; ω
n
is resonant frequency; Y
0
is vibration amplitude;
N is coil turns; S is coil area; and  is damping ratio. The EMF (
Y
 ) is proportional
to Y
0
, and the power output (P
Y
) is proportional to Y
0
2
. When the energy harvester
vibrates along α-direction (i.e., at α degree with respect to X-direction), the magnetic
flux is changed through each coil, as illustrated in Fig. 4.42b. Considering the
vibration amplitudes along X and Y-direction, the EMF with the four coils in series
is

111
2
0 2
(sin cos ) (sin cos )
12
n
Y
nn
dB
e j Y NS e
dz
j



    






   




(4-8)
In terms of the power output (P
Y
) of the two coils from Y-direction vibration, the
power output of the four coils from α-direction vibration is
2
(sin cos ) / 2 (0 90 )
oo
Y
PP

       (4-9)
Thus, the energy harvester can provide power output when it vibrates along any in-
plane directions. The EMF and power output (normalized to that from vibration
along Y or X-direction) as a function of vibration direction (α degree) show a peak
value at α=45
o
(Fig. 4.43), as expected. Assuming the same resonant frequency, the
EMF and power output from 45
o
-direction vibration are 2
Y 
 

and P
α
=P
Y
,
respectively.
Y
0
Y
X
α
α
Y
0
cosα
Y
0
sinα
Y
0
Y
X
Vibration
(a) (b)

Fig. 4.42 Schematics to illustrate (a) energy harvesting from Y-direction vibration
and (b) energy harvesting from α-direction vibration.

112
0.4
0.6
0.8
1.0
1.2
1.4
0 15 30 45 60 75 90
0.4
0.6
0.8
1.0
1.2
1.4
Normalized EMF
Angle  (degree)
Normalized EMF
Normalized Power
Normalized Power

Fig. 4.43 Calculated normalized EMF and power output versus vibration direction
(α-direction).
The electromagnetic energy harvester with magnet and coil arrays is fabricated
with four silicone cantilevers as the spring on a plastic pedestal as shown in Fig. 4.44.
Copper wire is wound around a plastic spool by a coil winder, and forms a 200-turn
coil. An array of the coils, suspended by four silicone cantilevers, is placed over the
boundaries between the magnets. The fabricated electromagnetic energy harvester
with magnet and coil arrays is characterized with a vibration shaker system when the
coils are connected in series. For the vibrations along X and Y-direction, the EMFs
as a function of vibration frequency are shown in Fig. 4.45, and the maximum EMFs
and powers (into 9 Ω load) as a function of input acceleration are shown in Fig. 4.46.
From 3.1 g acceleration, the energy harvester provides EMFs of V
P-P
=380 mV and
384 mV with 501 μW and 512 μW power outputs (out of either Coil
X
or Coil
Y
) at
resonant frequencies of 150 Hz and 120 Hz, along X-direction and Y-direction,
respectively. For the vibration along 45
o
-direction, the device (out of the combined

113
Coil
X
and Coil
Y
) provides an EMF of V
P-P
= 532 mV with 491 μW power output (into
18 Ω load) at resonant frequency of 130 Hz, as shown in Fig. 4.47.
Silicone cantilever
Magnet array Coil array

Fig. 4.44 Photos of the fabricated 2-DOF electromagnetic energy harvester.
120 140 160 180 200 220
0
40
80
120
160
200
V
P-P
(mV)
Frequency (Hz)
0.31g
0.62g
0.93g
1.24g
1.55g
0
200
400
600
0 1 2 3
0
100
200
300
400
500
V
P-P
(mV)
Acceleration (g)
V
P-P
vs. Acceleration
Power vs. Acceleration
Power ( W)
(a) (b)

Fig. 4.45 Measured performance of the electromagnetic energy harvester from X-
direction vibration: (a) measured EMF versus vibration frequency as a function of
input acceleration and (b) measured EMF and power output (into 9 Ω load) versus
input acceleration.

114
120 140 160 180 200 220
0
40
80
120
160
200
V
P-P
(mV)
Frequency (Hz)
0.31g
0.62g
0.93g
1.24g
1.55g
0
200
400
600
0 1 2 3
0
100
200
300
400
500
V
P-P
(mV)
Acceleration (g)
V
P-P
vs. Acceleration
Power vs. Acceleration
Power ( W)
(a) (b)

Fig. 4.46 Measured performance of the electromagnetic energy harvester from Y-
direction vibration: (a) measured EMF versus vibration frequency as a function of
input acceleration and (b) measured EMF and power output (into 9 Ω load) versus
input acceleration.
100 120 140 160 180
0
40
80
120
160
200
240
280
V
P-P
(mV)
Frequency (Hz)
0.31g
0.62g
0.93g
1.24g
1.55g
0
200
400
600
0 1 2 3
0
200
400
600
V
P-P
(mV)
Acceleration (g)
V
P-P
vs. Acceleration
Power vs. Acceleration
Power ( W)
(a) (b)

Fig. 4.47 Measured performance of the electromagnetic energy harvester from 45
o
-
direction vibration: (a) measured EMF versus vibration frequency as a function of
input acceleration and (b) measured EMF and power output (into 18 Ω load) versus
input acceleration.
4.6 Summary
This chapter presents a new technique of converting mechanical energy to
electrical energy that can be used to harvest mW – W power level from a vibrating
surface of tens – hundreds microns amplitude. An array of magnets with alternating
north- and south-orientation arranged on a planar surface is utilized in both
microfabricated and miniature electromagnetic energy harvesters to provide a rapidly

115
changing magnetic field. Experimental results show that a microfabricated energy
harvester of 20 × 5 × 0.9 mm
3
(=0.09 cc) weighing 0.5 gram generates an induced
EMF of V
p-p
=30 mV with 2.6 μW power output (into 10.8 Ω load) when it is
vibrated at 290 Hz with vibration amplitude of 11 μm. Its miniature version, that is
scaled up to 51 × 51 × 10 mm
3
(=26 cc) weighing 90 gram, generates an EMF of V
p-
p
=28.8 V with 263 mW power output (into 96 Ω load) when it is vibrated at 65 Hz
with vibration amplitude of 660 μm. The high power level allows us to light an
incandescent light bulb (which requires much larger power than a light emitting
diode) with a single energy harvester for the first time. For the miniature energy
harvester having a total mass of 90 gram and a resonant frequency of 65 Hz under
11.2 g acceleration, the energy-conversion efficiency (ECE) peaks at 10% when the
mass of the vibrating surface is equal to 90 gram. These results from microfabricated
and miniature versions show a great prospect of the new electromagnetic energy-
conversion idea in harvesting vibration energy and also in generating power. The
resonant frequency can be adjusted through design modification of the spring system
to harvest electrical power from various vibrating environments, and scaling up the
number of magnets and coils is an easy way to increase the power.

116
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[25] R. Guilllemet, P. Basset, D. Galayko, F. Cottone, F. Marty and T. Bourouina,
“Wideband MEMS electrostatic vibration energy harvesters based on gap-
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Micro Electro Mechanical Systems Conference, Taipei, Taiwan, January 20–24,
2013, pp. 817 - 820.
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“Non-linear MEMS electrostatic kinetic energy harvester with a tunable
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119
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120
Chapter 5
Power Generation from Human Body Motion through
Magnet and Coil Arrays with Magnetic Spring

This chapter describes a magnetic suspension system, combined to
electromagnetic power generators with magnet and coil arrays, to harvest energy
from vibrations at several Hz.
An analytical model of vibration-driven energy harvester with magnetic spring
through magnet and coil arrays is developed to explore the power generation with
various magnet ranges and vibration amplitudes. An energy harvester with
microfabricated flexible coils (rolled and aligned to a magnet array for maximum
magnetic flux change) and magnetic spring is presented to generate electrical power
from human body motion. Experimental results show that the electromagnetic energy
harvester with six 7-turn microfabricated coils (occupying 3.8 cc and weighing 8.5
gram) generates an induced electromotive force (EMF) of V
rms
=6.7 mV with 0.53
μW power output (into 21 Ω load) from 0.27 g acceleration at 8 Hz (corresponding
to 1.05 mm vibration amplitude).
The miniature energy harvester I with sixteen 200-turn wire-wound coils
(occupying 26 cc and weighing 98 gram) generates an EMF of V
rms
=1.97 V with 9
mW power output (into 108 Ω load) from 0.36 g acceleration at 6 Hz (corresponding
to 2.5 mm vibration amplitude). When the miniature version of the energy harvester

121
is placed in a backpack of a human walking at various speeds, the power output is
increased as the walking speed is increased from 0.45 m/s (slow walking) to 2.68 m/s
(slow running), and reaches 14.8 mW at 2.68 m/s.
When the energy harvester II (occupying 120 cc and weighing 180 gram) is
placed in a backpack of a human walking at various speeds, the power output
increases as the walking speed increases from 0.45 m/s (slow walking) to 3.58 m/s
(slow running), and reaches 32 mW at 3.58 m/s.
5.1 Modeling and Design
Figure 5.1 illustrates an electromagnetic power generator with a magnet array
aligned to a coil array rolled on a teflon cylinder (that houses the power generator)
for maximum magnetic flux change. The magnet array is suspended by a magnetic
spring, which consists of the top (T) movable magnet and the bottom (B) fixed
magnet arranged to face each other with the same pole. The magnet array is levitated
due to the repulsive force in the magnetic spring system, and vibrates in response to
external vibration, making the coil array generate electricity. The repulsive force in
the magnetic spring is [1]
0
2
0
4 ( )
TB
M
QQ
F
rz




(5-1)
where
0


is vacuum permeability; Q (=H
C
A) is magnetic field intensity with H
C
being the coercive force and A being pole surface area; r
0
is the distance between two
magnets at initial position that can be calculated from
0
2
0
4
TB
QQ
mg
r


 (m is proof

122
mass and g is gravitational acceleration); z is relative displacement between two
magnets. The repulsive force (F
M
) and spring constant ()
M
dF
k
dz
 as a function of the
displacement between the two magnets are plotted for a given proof mass (Figs. 5.2a
and 5.2b) and magnetic field intensities of the magnets (Figs. 5.2c and 5.2d). The
spring constant varies with vibration amplitude since the magnetic force has a non-
linear relationship with the displacement, and the resonant frequency
1
()
2
k
f
m 
 at
initial position is calculated. As can be seen in Fig. 5.2, the resonant frequency is
decreased by increasing the magnetic field intensities (Q
T
Q
B
) or decreasing the proof
mass.
Magnetic
spring
Cylinder
Magnet array
Coil array

Fig. 5.1 Schematic of the energy harvester with flexible coils (rolled and aligned to a
magnet array for maximum magnetic flux change) and a magnetic spring.

123
-0.02 0.00 0.02
0.0
0.5
1.0
1.5
Q
M
Q
B
=400A
2
m
2
Q
M
Q
B
=900A
2
m
2
Q
M
Q
B
=1600A
2
m
2
Q
M
Q
B
=2500A
2
m
2
Q
M
Q
B
=3600A
2
m
2
Q
M
Q
B
=4900A
2
m
2
Q
M
Q
B
=6400A
2
m
2
Q
M
Q
B
=8100A
2
m
2
Q
M
Q
B
=10000A
2
m
2
F (N)
Z (m)
-0.02 0.00 0.02
0
200
400
600
k (N/m)
Z (m)
f
0
=7.06Hz
f
0
=5.77Hz
f
0
=5.00Hz
f
0
=4.47Hz
f
0
=4.08Hz
f
0
=3.78Hz
f
0
=3.53Hz
f
0
=3.33Hz
f
0
=3.16Hz

-0.02 -0.01 0.00 0.01 0.02
0
2
4
m=100g
m=88g
m=76g
m=64g
m=52g
m=40g
m=28g
m=16g
m=4g
F (N)
Z (m)
-0.02 -0.01 0.00 0.01 0.02
0
800
1600
2400
k (N/m)
Z (m)
f
0
=8.89Hz
f
0
=8.61Hz
f
0
=8.30Hz
f
0
=7.95Hz
f
0
=7.55Hz
f
0
=7.06Hz
f
0
=6.47Hz
f
0
=5.62Hz
f
0
=3.97Hz

Fig. 5.2 The simulated magnetic force (a) and spring constant (b) versus
displacement as a function of magnetic field intensities (Q
T
Q
B
) for a proof mass of
40 gram. The simulated magnetic force (c) and spring constant (d) versus
displacement as a function of proof mass for Q
T
Q
B
=400A
2
m
2
.
For a vibration-driven power generator, the absolute motions of the proof mass
and the frame are x(t) and y(t), respectively, while the relative displacement between
the proof mass and the frame is z(t) (= x(t) - y(t)). The equation of motion for the
system is given by:
( )'' ( )' ( ) ( )''
M
mz t dz t F mg my t      (5-2)
where d is damping constant. The F
M
in Eq. 5-2 can be approximated with the
following equation for a small vibration near the initial position.
(a)

(b)

(c)

(d)

124
2 0 0 0
2 2 3 4 2 3
0 0 0 0 0 0
1 2 3 1 2
( ) ( )
4 ( ) 4 4
T B T B T B
M
Q Q Q Q Q Q
F z z z
r z r r r r r
  
  
        

(5-3)
For a sinusoidal vibration with frequency , we have y(t) = Y
0
cos t = Re{Y
0
e
j t
} and
z(t) = Z
0
cos( t+ ) = Re{Ze
j t
}, and obtain
2
3
2 0
0
0
2
TB
m Y mZ j d
Q
Z Z
Q
r




    from
Eq. 5-2. Consequently, the complex constant of the relative displacement between
the proof mass and the frame is
 
 
2
22
0 00
2
2
0
2 0
3
0
2
/
1 2 /
2
/ TB
n
nn
Y m Y m Y
Q
Z
j
Q mg
r
m
r
jd m j d
 
    




  

     
(5-4)
where Y
0
is the frame’s vibration amplitude or the input vibration amplitude;
00
2
( 4 )
n
TB
g mg
g
r Q Q





is the resonant frequency;()
2
n
d
m


 is the damping
ratio. According to Faraday’s law, the magnitude of electromotive force (EMF)  is
proportional to the time-rate change of magnetic flux  through a coil, and is
 
2
00
2
2
2
/
1 / 2
n
n
n
d d dz d d
ZA
dt dz dt dz dz



  

   
   







(5-5)
where
2
00
() AY  

is the acceleration amplitude. At the resonant frequency, the EMF
simplifies to
00
2
n
A mA dd
dz dz d



 (5-6)
From the equation for the resonant frequency (
0
2
n
g
r
  ), the initial distance
(r
0
) between the two magnets can be used to estimate the resonant frequency. Also,

125
the resonant frequency is decreased by increasing the magnetic field intensities
(Q
T
Q
B
) or decreasing the proof mass, which increases the initial distance between the
two magnets. Since the initial distance (r
0
) between the two magnets is inversely
proportional to the square of the resonant frequency, there is a trade-off between the
device volume and resonant frequency. However, decreasing the proof mass will
reduce the power output since the EMF has a linear relationship with the proof mass
at a given acceleration, as shown in Eq. 5-6. Thus, increasing the magnetic field
intensities (Q
T
Q
B
) of the magnetic spring is a better way to lower the resonant
frequency.
However, as the vibration amplitude increases, the variation of the spring
constant cannot be neglected for a large relative displacement between the proof
mass and the frame. Since the magnetic force (F
M
) is not linearly proportional to the
relative displacement between the two magnets, the relative motion between the
proof mass and the frame is not sinusoidal even under a sinusoidal vibration, and it is
difficult to express the relationship between the relative displacement amplitude and
the vibration amplitude with an exact solution by solving Eq. 5-2. Thus, a numerical
method is used with MATLAB to describe the relative motion between the proof
mass and the frame for the magnetic spring with 10 Hz resonant frequency at
different vibration frequencies under a fixed vibration amplitude of 0.1 m, as shown
in Fig. 5.3. When the vibration frequency is lower than the resonant frequency, the
relative displacement amplitude is smaller than the vibration amplitude and increases
as the vibration frequency increases (Fig. 5.3a). At a vibration frequency near and

126
higher than the resonant frequency, the relative displacement amplitude is close to
the vibration amplitude (Figs. 5.3b and 5.3c), but the amplitude value is not exactly
same in each vibration period. Even though the motion wave is not sinusoidal, the
non-linear magnetic suspension system shows a similar relationship between the
relative displacement amplitude and the vibration amplitude with the linear system.
The parameters used in the calculation are listed in Table 5.1.
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
Displacement (m)
Time (s)
2Hz
3Hz
4Hz
0.0 0.5 1.0
0.0
0.1
0.2
0.3
Displacement (m)
Time (s)
8Hz
10Hz
12Hz

0.0 0.1 0.2 0.3 0.4 0.5
0.0
0.1
0.2
0.3
Displacement (m)
Time (s)
20Hz
30Hz
40Hz

Fig. 5.3 Calculated relative displacement between two magnets in the magnetic
spring with 10 Hz resonant frequency under a fixed vibration amplitude of 0.1 m at
(a) 2, 3 and 4 Hz, (b) 8, 10, 12 Hz, and (c) 20, 30, and 40 Hz.
(a)

(b)

(c)

127

The magnet array with alternating north- and south-orientation provides a
rapidly changing magnetic field, and a high power level has been generated when the
coil array vibrates near the boundary between the magnets. The relative displacement
between the magnet and coil arrays in response to external vibrations causes the
magnetic flux (  ) to vary through the coils, and the magnetic flux (  ) through a
multiple-turn coil is obtained with
11
()
i
nn
ii
ii
S
B dS

    


(5-7)
where n is number of coil turns;
i
 is magnetic flux through the i
th
coil; B is
magnetic flux density; S
i
is area of the i
th
coil. The magnetic flux (  ) is a numerical
integral of magnetic flux density which is obtained by COMSOL simulation, and the
EMF is calculated by
d
dt


 when the coil vibrates in the direction parallel to the
surface of magnets. Here we assume that a 100-turn coil vibrates sinusoidally with
vibration displacement between the magnets and coils from 0.1 to 38.1 mm at the
height of 250 μm over the magnet array. The values used in the simulations are listed
in Table 5.2.
Table 5.1 Parameters used in the calculation of the relative motion for non-linear
magnetic suspension system
Proof mass (gram) 100
Resonant frequency (Hz) 10
Initial distance between two magnets (mm) 5
Damping ratio 0.16
Vibration amplitude (m) 0.1
Vibration frequency (Hz) 2-40

128

The magnetic flux density (B
z
) along the direction parallel to the planar surface
(y-direction) for an array of two magnets (12.7 × 12.7 × 3.2 mm
3
) with alternating
north- and south-orientation is shown in Fig. 5.4a. Figures 5.4b and 5.4c show the
simulated output-voltage waveforms for various input vibration amplitudes in one
mechanical cycle. The output voltage peaks when the coil passes through the
magnet-to-magnet boundary, and the peak value increases as the displacement
increases, as expected from Eq. 5-5. When the coil moves out of the magnet range
(i.e., the vibration displacement is increased from 19.1 to 38.1 mm), the output
voltage is near zero for a relatively long time during the vibration as shown in Fig.
5.4c. If the vibration displacement increases further, the coil vibrates increasingly
more in the area far away from the boundary of the magnets, and the duration of
near-zero output voltage increases further.
Table 5.2 Parameters used in the simulations
Magnet size (mm
3
) 12.7 × 12.7 × 3.2
Residual magnetic flux density (T) 1.32
Relative permeability (in vacuum environment) 1
Number of turns per coil 100
Number of coils 1
Lateral space between coils (μm) 60
Outmost diameter of the coil (mm) 12.7
Distance between the coil and magnet surface (μm) 250
Relative displacement amplitude (mm) 0.1-38.1
Vibration frequency (Hz) 10

129
The magnetic flux density (B
z
) along the direction parallel to the planar surface
(y-direction) for an array of four magnets (12.7 × 12.7 × 3.2 mm
3
) with alternating
north- and south-orientation is shown in Fig. 5.4d. The simulated output-voltage
waveforms for various input vibration amplitudes in one mechanical cycle are shown
in Figs. 5.4e and 5.4f. The array of magnets provides multiple cycles of magnetic
flux change in each mechanical cycle when the vibration amplitude is large enough
for the coil to pass through the multi-pole magnets. Thus, one mechanical cycle of a
large vibration amplitude produces an electrical output voltage with multiple cycles
with the number of the cycles increasing as the vibration amplitude increases. It is
noted that the peak value in each of the multiple-cycle waveform is different from
one another, since the motional velocity of the coil (with respect to the magnet array)
varies sinusoidally in time.
The root-mean-square (rms) values of the output voltages are calculated from
the measured waveforms in Figs. 5.4b, 5.4c, 5.4e and 5.4f, and are shown to increase
almost linearly as the vibration amplitude increases for the array of four magnets
(Fig. 5.4g). With multiple cycles of magnetic flux change in each mechanical cycle,
the high energy-conversion efficiency through the magnet and coil arrays is
maintained even at a large vibration amplitude. For an array of two magnets, the
waveforms and rms values of the output voltages are almost same as those for a four-
magnet array, when the coil keeps moving in the range of the two magnets (with the
vibration displacement from 0.1 to 12.7 mm). When the coil moves out of the range
of the two magnets (for example, the vibration displacement from 19.1 to 38.1 mm),

130
the voltages increase at a lower rate. Thus, the maximum relative displacement
between the coils and magnets needs to be within the range of the magnets for high
energy-conversion efficiency.

-40 -20 0 20 40
-0.4
-0.2
0.0
0.2
0.4
B
z

(T)
Y position (mm)
B
z
@ d=250 m

0.00 0.05 0.10
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
Voltage (V)
t (s)
Z
0
=0.1mm
Z
0
=0.5mm
Z
0
=1mm
Z
0
=2mm
Z
0
=4mm
Z
0
=8mm
Z
0
=12.7mm

0.00 0.05 0.10
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Voltage (V)
t (s)
Z
0
=19.1mm
Z
0
=25.4mm
Z
0
=31.8mm
Z
0
=38.1mm

Vibration
(Z
0
, 10Hz)

12.7mm
3.2mm

Y
X
Z
(a)

(b)

(c)

131

0.00 0.05 0.10
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
Voltage (V)
t (s)
Z
0
=0.1e-3
Z
0
=0.5e-3
Z
0
=1e-3
Z
0
=2e-3
Z
0
=4e-3
Z
0
=8e-3
Z
0
=12.7e-3
0.00 0.05 0.10
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Voltage (V)
t (s)
Z
0
=19.1mm
Z
0
=25.4mm
Z
0
=31.8mm
Z
0
=38.1mm

12.7mm
Vibration
(Z
0
, 10Hz)

3.2mm

-40 -20 0 20 40
-0.4
-0.2
0.0
0.2
0.4
B
z
(T)
Y position (mm)
B
z
@ d=250 m
Y
X
Z
(d)

(e)

(f)

132
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
V
rms
(V)
Z
0
(mm)
V
rms
vs. Z
0
(two magnets)
V
rms
vs. Z
0
(four magnets)

Fig. 5.4 (a) Calculated magnetic field distribution of the array of two alternating
north- and south-orientation magnets passing through a coil. The simulated output
voltage in time as a function of the displacement amplitude from 0.1 to 12.7 mm (b)
and from 19.1 to 38.1 mm (c) for two magnets. (d) Magnetic field distribution of the
array of four alternating north- and south-orientation magnets passing through a coil.
The simulated output voltage in time as a function of the displacement amplitude
from 0.1 to 12.7 mm (e) and from 19.1 to 38.1 mm (f) for four magnets. (g) The rms
values of the simulated EMFs versus the displacement amplitude.
5.2 Microfabricated Coils on Flexible Substrate
The coil array has been fabricated on a flexible parylene film in a
microfabrication process as shown in Fig. 5.5. First, photoresist AZ4620 is spin-
coated on a silicon wafer as a sacrificial layer, and 8 μm thick parylene is deposited
to cover the whole wafer. After a Ti/Cu (10 nm/200 nm) is deposited by E-beam
evaporator and patterned for connection between the coils, 1 μm thick parylene is
deposited for isolation and patterned to form via holes. Another Ti/Cu (10 nm/200
nm) is deposited as a seed layer, and then photoresist AZ4620 is spin-coated and
patterned to obtain a mold for the copper coil. After 25 μm thick copper is
electroplated on the front side, the photoresist is removed in acetone, and the seed
(g)

133
layer is etched away. The wafer is then partially diced to expose the photoresist
sacrificial layer, and the coils embedded in 9 μm thick parylene are released by a lift-
off process. Six 7-turn coils of 25 μm thick electroplated copper are connected in
series by another copper layer through via holes on the flexible parylene film, and
rolled on the teflon cylinder which is used to house the generator, as shown in Figs.
5.6a and 5.6b. Four diametrically magnetized magnets (6.4 mm in diameter, 3.2 mm
in thickness) are suspended by the magnetic spring in a teflon cylinder (of which the
wall thickness is 1.5mm), and surrounded by the coils aligned to the boundary
between the magnets, as shown in Figs. 5.6c-5.6d. The detailed parameters of the
energy harvester with microfabricated flexible coils are listed in Table 5.3.

Fig. 5.5 Brief microfabrication process of the flexible coils: (a) Spin photoresist and
deposit parylene. (b) Deposit and pattern Ti/Cu for connection between the coils. (c)
Deposit and pattern parylene isolation layer. (d) Electroplate copper coils. (e) Dice
the wafer to expose photoresist. (f) Lift-off to release the coils. (g) Roll the coils on a
teflon cylinder.

134

Fig. 5.6 (a) Photos of the coils on a released parylene film. (b) Side-view and (c) top-
view photos of the energy harvester with microfabricated flexible coils and magnetic
spring. (d) Magnet array suspended by the magnetic spring in the teflon cylinder.

Table 5.3 Parameters of the energy harvester with microfabricated flexible coils
Total volume (cm
3
) π × 0.55
2
× 4 (3.8 cc)
Total weight (gram) 8.5
Magnet array (cm
3
) π × 0.64
2
× 0.32
Teflon tube (cm)
Outside diameter=1.1
Inner diameter=0.8
Height=4
Magnetic spring(cm
3
)
Top: 0.64 × 0.32 × 0.08
Bottom: 0.64 × 0.32 × 0.08
Parylene film (cm
2
) 3.3 × 1.4
Number of turns per coil 7
Coil resistance (Ω) 3.5
Number of coils 6

40mm
11mm

N

S

Teflon cylinder

21mm
Magnet array

Spacer

Top magnet in
magnetic spring

Via

2 0 0 μm

14mm
33mm

(a)

(b)

(c)

(d)

135
For the energy harvester with four disk magnets and six microfabricated
flexible 7-turn coils, the measured EMFs as a function of vibration frequency at
various input accelerations are shown in Fig. 5.7a. At a fixed acceleration, the EMFs
depend on the vibration frequency, peaking at the resonant frequency. From the
acceleration of 0.27 g at the resonant frequency of 8 Hz, a peak value of 6.7 mV
rms
is
measured. The measured plot of EMF versus vibration frequency for an input
acceleration of 0.27 g at the resonant frequency of 8 Hz shows a 3-dB bandwidth
(   ) of 3 Hz, and a quality factor ( Q ) is estimated to be 2.7 from /
n
Q   .
Thus, the damping ratio is / 2 1/ 2 0.19
n
d k Q     . Figure 5.7b shows the
measured EMFs and power outputs as a function of input acceleration at 8 Hz. As
the acceleration is increased from 0.09 to 0.27 g (corresponding to a vibration
amplitude from 0.35 to 1.05 mm), the EMF increases from 4.95 to 6.7 mV
rms
, and the
power output (into 21 Ω load) increases from 0.29 to 0.53 μW. As the acceleration is
increased from 0.36 to 0.63 g (corresponding to a vibration amplitude from 1.4 to
2.45 mm), the EMF increases from 6.84 to 7.13 mV
rms
, and the power output (into 21
Ω load) increases from 0.55 to 0.6 μW. The power output increases at a lower rate
when the vibration amplitude is larger than 1.4 mm. At 0.36 g acceleration, the
relative motion between the magnets and coils (
00
/ 2 3.7 ZY   mm) is larger than
the thickness of the magnet (3.2 mm). Thus, the power output increases at a lower
rate when the magnet array moves out of the coil range, as expected from the
simulations. As the magnetic flux change for an array of magnets peaks when the

136
coil center is located at the boundary between the magnets and increases as the
distance from the magnet surface is decreased, the power output can be improved by
using thinner teflon tube to reduce the distance between the magnet and coil arrays.
In addition, the microfabrication process of electroplated planar coils that are
embedded in parylene film provides an easy method to fabricate flexible coils, which
can easily surround a cylinderical magnet array to completely utilize the 3D space.
6 7 8 9 10 11 12
0
2
4
6
V
rms
(mV)
Frequency (Hz)
0.09g
0.18g
0.27g
6.7mV @ 8 Hz
Bandwidth=3Hz
0.3
0.4
0.5
0.6
0.7
0.0 0.2 0.4 0.6
5
6
7
V
rms
(mV)
Acceleration (g)
V
rms
vs. Acceleration
Power vs. Acceleration
Power ( W)

Fig. 5.7 Measured EMF of the energy harvester with microfabricated flexible coils:
(a) EMF versus vibration frequency as a function of accelerations and (b) EMF and
power output (into 21 Ω load) versus input acceleration at the resonant frequency.
For traditional plastic springs, two designs (four-branch spring and two-branch
spring) are developed and fabricated by laser-machining on a 250 μm thick plastic
sheet as shown in Fig. 5.8a and 5.8b. The simulation results show the resonant
frequencies of 50-58 Hz and 14-16 Hz for four-branch spring and two-branch spring,
respectively, as shown in Fig. 5.9a and 5.9b when the Young’s modulus of plastic
material is 2-2.7 GPa. Four cylinder magnets (6.4mm in diameter and 3.2 mm in
height, diametrically magnetized) are suspended by the springs as proof mass to
provide a rapidly changing magnetic field around the magnets (Fig. 5.10a and 5.10b).
(a)

(b)

137
The six coils in series connection are fabricated on parylene substrate and rolled to
surround the cylinder magnets (Fig. 5.10c).
13mm 13mm
(b) (a)

Fig. 5.8 Photos of plastic springs: (a) four-branch spring and (b) two-branch spring.

Fig. 5.9 Simulated displacement under a fixed load of (a) four-branch spring and (b)
two-branch spring.
(b) (a)
(c)

Fig. 5.10 Photos of the magnets suspended by (a) four-branch spring, (b) two-branch
spring and (c) the energy harvester with cylinder magnet array surrounded by
microfabricated flexible coils.
(a)

(b)

138
The energy harvester with four-branch spring was measured to produce 30μW
power (into 17.1 Ω load) at its resonant frequency (52 Hz) from 3.5 g acceleration
(~320 μm vibration amplitude). On the other hand, the energy harvester with two-
branch spring was measured to produce 0.3 μW power (into 17.1 Ω load) at its
resonant frequency (17 Hz) from 0.24 g acceleration (~206 μm vibration amplitude).
Both of the harvesters had exactly same volume (1.1 cc) and weight (3.4 gram).
40 50 60 70
0
5
10
15
V
p-p
(mV)
Frequency (Hz)
0.25g
0.35g
0.5g
0 1 2 3 4
0
10
20
30
Power ( W)
Acceleration (g)
Power vs. Acceleration

Fig. 5.11 Measured output voltages and powers of the energy harvester with two-
branch spring: (a) output voltage vs. frequency and (b) power vs. input acceleration.
At the resonant frequency (52 Hz), 3.5 g acceleration (~320 μm vibration amplitude)
produces 30 μW power into 17.1 Ω load.
13 14 15 16 17 18 19 20 21
0
5
10
15
V
p-p
(mV)
Frequency (Hz)
0.24g
0.18g
0.12g
0.06g
0.1 0.2 0.3
0.0
0.1
0.2
0.3
Power ( W)
Acceleration (g)
Power vs. Acceleration

Fig. 5.12 Measured output voltages and powers of the energy harvester with two-
branch spring: (a) output voltage vs. frequency and (b) power vs. input acceleration.
At the resonant frequency (17 Hz), 0.24 g acceleration (~206 μm vibration amplitude)
produces 0.3 μW power into 17.1 Ω load.
(a)

(b)

(a)

(b)

139
5.3 Miniature Energy Harvesters
Based on the same principle, a miniature energy harvester I (occupying 1 × 2.6
× 10 cm
3
and weighing 98 gram) and energy harvester II (occupying 2 × 3 × 20 cm
3

and weighing 180 gram) scaled up to ten magnets and sixteen coils have been
fabricated (similar to Fig. 5.13), and shown to generate enough power to light up a
light-emitting diode, when shaken by a hand at a few Hz, as shown in Figs. 5.14a-
5.14c. Sixteen coils wound by a coil winder are arranged over the boundaries
between the magnets of the 2 × 5 magnet array in a laser-machined plastic cylinder
(that houses the harvester). In energy harvester II, graphite sheets, diamagnetic
material which can create a magnetic field in opposition to externally applied
magnetic field, are placed near the movable magnet on the plastic cylinder to provide
repulsive force for reducing the friction. For the energy harvester I, the magnetic
spring with an initial distance of 1 cm between the two magnets is used to suspend
the magnet array in the prototype, and the resonant frequency is estimated to be 7 Hz
from
0
2
n
g
r
  . The energy harvester II is estimated to show a 3.5 Hz resonant
frequency since stronger magnets are used in the magnetic spring with 4 cm initial
distance. The detailed parameters of the energy harvester with microfabricated
flexible coils and the miniature energy harvesters are listed in Table 5.4-5.5.

140
Cylinder
Magnet array
Coil array
Graphite
Magnetic
spring

Fig. 5.13 Schematic of the miniature energy harvester (with magnet and coil arrays)
suspended by magnetic spring.

Fig. 5.14 (a) Photo of the miniature electromagnetic energy harvester I with
magnetic spring occupying 26 cc and weighing 98 gram. (b) Photos of the miniature
energy harvester II with magnetic spring occupying 120 cc and weighing 180 gram.
(c) Photo of a light-emitting diode being lit up by hand shaking the energy harvester.
(b)

(c)

10cm
1cm
2.6cm

Magnet array

Cylinder

Coil array

Spacer

Magnetic
suspension

Graphite

2cm

3cm

20cm
LED

Energy harvester

(a)

141

For the miniature energy harvester I, the measured EMFs as a function of
vibration frequency at various input accelerations are shown in Fig. 5.15a when
sixteen coils are connected in series. At acceleration of 0.1 g (corresponding to 0.69
mm vibration amplitude), the measured resonant frequency is 6 Hz, close to the
theoretical resonant frequency of 7 Hz. The measured plot of EMF versus vibration
frequency shows a 3-dB bandwidth (   ) of 1.2 Hz, and a quality factor ( Q ) is
estimated to be 5 from /
n
Q   . Thus, the damping ratio is
Table 5.5 Parameters of the miniature energy harvester II with magnetic spring
Total volume (cm
3
) 2 × 3

× 20 (120 cc)
Total weight (gram) 180
Magnet array (cm
3
) 1.27 × 1.27 × 3.2
Magnetic spring(cm
3
)
Top: 2.54 × 2.54 × 2.54
Bottom: 2.54 × 2.54 × 5.08
Number of turns per coil 200
Coil resistance (Ω) 6
Number of coils 16

Table 5.4 Parameters of the miniature energy harvester I with magnetic spring
Total volume (cm
3
) 1 × 2.6

× 10 (26 cc)
Total weight (gram) 98
Magnet array (cm
3
) 1.27 × 1.27 × 3.2
Magnetic spring(cm
3
)
Top: 1.9 × 0.95 × 0.32
Bottom: 1.9 × 0.95 × 0.32
Number of turns per coil 200
Coil resistance (Ω) 6.8
Number of coils 16

142
/ 2 1/ 2 0.1
n
d k Q     . The power outputs as a function of input acceleration at 6
Hz are shown in Fig. 5.15b. As the acceleration increases from 0.1 to 0.36 g
(corresponding to a vibration amplitude from 0.69 to 2.48 mm), the power output
(into 108 Ω load) increases from 0.22 to 9 mW. However, the power output does not
increase any further, though the acceleration is increased further, mainly because the
relative motional amplitude (Z
0
) is limited by the initial distance of 1 cm between the
two magnets of the magnetic spring. When the input acceleration is larger than 0.36
g, the relative motion is large enough to cause the hitting of the two magnets of the
magnetic spring. Since the energy lost by the magnets hitting, the power output
cannot increase even though the input acceleration increases. Figure 5.15c shows the
power outputs as a function of input acceleration at 2 Hz. As the acceleration
increases from 0.02 to 0.04 g (corresponding to a vibration amplitude from 1.2 to 2.4
mm), the power output (into 108 Ω load) increases from 5 to 76 μW. At vibration
frequency of 2 Hz, which is lower than the 6 Hz resonant frequency, the relative
motion amplitude (Z
0
) is less than vibration amplitude (Y
0
) as indicated in Figs. 2.2
and 5.3, and the power output keeps increasing with the increased vibration
amplitude without the magnets hitting.

143
Bandwidth=1.2Hz
0.31mV @ 6 Hz
3 4 5 6 7 8 9
0.1
0.2
0.3
V
rms
(V)
Freqnecy (Hz)
0.1g
0
4
8
12
0.1 0.2 0.3 0.4 0.5
0.0
0.8
1.6
2.4
V
rms
(V)
Acceleration (g)
V
rms
vs. Acceleration at 6 Hz
Power vs. Acceleration at 6 Hz
Power (mW)

0
30
60
90
0.02 0.03 0.04
0
50
100
150
200
V
rms
(mV)
Acceleration (g)
Vrms vs. Acceleration at 2 Hz
Power vs. Acceleration at 2 Hz
Power ( W)

Fig. 5.15 Measured EMF of the miniature energy harvester I (26 cc, 98 gram): (a)
EMF versus vibration frequency as a function of acceleration, (b) EMF and power
output (into 108 Ω load) versus input acceleration at 6 Hz, and (c) EMF and power
output (into 108 Ω load) versus input acceleration at 2 Hz.
When the miniature energy harvester I is placed in a backpack of a human
walking at various speeds, the harvester produces mW level of power from a walking
motion (Fig. 5.16a). The measured output voltages at walking speeds of 0.45, 1.12
and 2.68 m/s are shown in Figs. 5.16b, 5.16c and 5.16d, respectively. From the
output-voltage waveforms, we see that the most electrical powers are at 1.33, 1.67
and 2.86 Hz for 0.45, 1.12 and 2.68 m/s walking speed, respectively, similar to
where the most mechanical powers are for those walking paces. As the walking
(a)

(c)

(b)

144
speed increases, the peak value of the output voltage increases, and the frequency
(where most mechanical power resides) also increases. The maximum power outputs
(into 108 Ω load) as a function of walking speed are shown in Fig. 5.16e. The power
output increases as the walking speed increases since both the vibration frequency
and amplitude increase. The power output increases rapidly, as the walking speed
increases beyond 2 m/s (slow running), and reaches 14.8 mW at 2.68 m/s. The speed
higher than 2 m/s corresponds to running, and provides larger vibration amplitude
than walking condition, in addition to increased vibration frequency. This causes the
power level to increase rapidly as the walking speed increases beyond 2 m/s.

Energy Harvester

0 1 2 3
-0.5
0.0
0.5
1.0
Voltage (V)
Time (s)
Waveform of output voltage at 0.45m/s

0 1 2 3
-3
-2
-1
0
1
2
3
Voltage (V)
Time (s)
Waveform of output voltage at 1.12m/s

0 1 2
-10
-5
0
5
10
Voltage (V)
Time (s)
Waveform of output voltage at 2.68m/s

1.33Hz

1.67Hz

2.86Hz
(a)

(b)

(c)

(d)

145
0 1 2 3
0
4
8
12
16
Power (mW)
Speed (m/s)
Power vs. Speed

Fig. 5.16 Measurements of the miniature electromagnetic energy harvester I (26 cc,
96 gram): (a) The energy harvester mounted in a backpack of a human, (b) output
voltage at a walking speed of 0.45 m/s, (c) output voltage at a walking speed of 1.12
m/s, (d) output voltage at a walking speed of 2.68 m/s, and (e) power output (into
108 Ω load) versus the walking speed.
For the miniature energy harvester II, the measured EMFs as a function of
vibration frequency at various input accelerations are shown in Fig. 5.17a. At a fixed
acceleration, the EMFs depend on the vibration frequency, peaking at the resonant
frequency. At acceleration of 0.05 g (corresponding to 0.78 mm vibration amplitude),
the measured resonant frequency is 4 Hz, close to the theoretical resonant frequency
of 3.5 Hz. The measured EMFs and power outputs as a function of input acceleration
at 4 Hz are shown in Fig. 5.17b. As the acceleration increases from 0.03 to 0.11 g
(corresponding to a vibration amplitude from 0.47 to 1.71 mm), the EMF increases
from 0.12 to 0.68 V, and the power output (into 96 Ω load) increases from 0.04 to
1.23 mW.
(e)

146
2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
V
rms
(V)
Frequency (Hz)
0.05g
0.035g
0.0
0.5
1.0
1.5
2.0
0.04 0.08 0.12
0.0
0.2
0.4
0.6
0.8
V
rms
(V)
Acceleration (g)
V
rms
vs. Acceleration
Power vs. Acceleration
Power (mW)

Fig. 5.17 (a) Measured EMF versus vibration frequency at two different
accelerations. (b) Measured EMF and power output (into 96 Ω load) versus input
acceleration at the resonant frequency.
When the energy harvester II is placed in a backpack of a human walking at
various speeds, the harvester produces mW – tens of mW level of power from a
walking motion. The measured output voltages at walking speeds of 1.12 and 3.58
m/s are shown in Figs. 5.18a and 5.18b, respectively. From the output-voltage
waveforms, we see that the most electrical powers are at 1.67 and 3.33 Hz for 1.12
and 3.58 m/s walking speed, respectively, similar to where the most mechanical
powers are for those walking paces. As the walking speed increases, the peak value
of the output voltage increases, and the frequency (where most mechanical power
resides) also increases, getting closer to the harvester’s resonant frequency. The
output voltages (root-mean-square value) are calculated from the measured
waveforms at various walking speeds, and used to obtain the maximum power
outputs delivered into a matched load of which the resistance is equal to the coil
resistance. The maximum power outputs (into 96 Ω load) as a function of walking
speed is shown in Fig. 5.18c. The power output increases as the walking speed
(a)

(b)

147
increases since both the vibration frequency and amplitude increase. The power
output increases rapidly, as the walking speed increases beyond 2.23 m/s (slow
running), and reaches 32 mW at 3.58 m/s.
1 2 3 4 5
-3
-2
-1
0
1
2
3
Voltage (V)
Time (s)
Waveform of output voltage at 1.12 m/s
1 2 3 4 5
-20
-10
0
10
20
Voltage (V)
Time (s)
Waveform of output voltage at 3.58 m/s

0 1 2 3 4
0
10
20
30
Power (mW)
Speed (m/s)
Power vs. Speed

Fig. 5.18 (a) Measured output voltage at a walking speed of 1.12 m/s. (b) Measured
output voltage at a walking speed of 3.58 m/s. (c) Measured power output (into 96 Ω
load) versus the walking speed.
As the walking speed increases, the frequency gets closer to the resonant
frequency (4 Hz) of the harvester II, and the relative motion between the magnet and
coil array increases rapidly. In case of the energy harvester I with 1 cm initial
distance, increasing the walking speed beyond 2.68 m/s does not generate any higher
power due to the hitting of magnets in the magnetic spring. But for the energy
3.33Hz

1.67Hz

(a)

(b)

(c)

148
harvester II, the 4 cm initial distance between the two stronger magnets in the
magnetic spring reduces the resonant frequency, and allows the harvester to work at
a higher waking speed without the magnets hitting each other. The harvester’s
weight and volume are larger, though. No special interface electronic circuit is
needed to drive a resistive load, as the harvesters can drive any resistive loads (e.g.,
incandescent light bulbs, heaters, etc.) without any interface electronics. This is one
unique advantage of electromagnetic energy harvesters over piezoelectric harvesters.
In case of batteries or capacitive loads, a simple rectifier circuit based on a diode is
sufficient for the electromagnetic energy harvester (with sufficiently large EMF, i.e., >
0.7 V) to charge them. We have built a simple rectifier, and used it with one of our
harvesters to charge a battery.
5.4 Summary
The electromagnetic energy harvesters have been designed, fabricated, and
characterized to harvest energy from low-frequency vibrations. A magnetic spring is
analyzed theoretically and employed to suspend a magnet array, which provides a
magnetic field distribution with steep field gradient, for a resonant frequency of
several Hz that is close to the frequency of human’s walking motion. The power
generation through magnet and coil arrays is simulated with different magnet ranges
at low vibration frequencies and large vibration amplitudes. The energy harvester
with microfabricated flexible coils (occupying 3.8 cc and weighing 8.5 gram) shows
a resonant frequency of 8 Hz, and generates power of 0.53 μW delivered into 21 Ω

149
load from 0.27 g acceleration at 8 Hz. An energy harvester that is scaled up to ten
magnets and sixteen non-microfabricated coils (occupying 26 cc and weighing 98
gram) shows a resonant frequency of 6 Hz and generates 9 mW (into 108 Ω load)
from 0.36 g acceleration at 6 Hz. When the miniature energy harvester is placed in
backpack of human walking at various speeds, the frequency of the output voltage
increases as the walking speed increases, and the power output reaches 14.8 mW at a
slow running speed of 2.68 m/s. When another fabricated miniature energy harvester
(occupying 120 cc and weighing 180 gram) with 4 Hz resonant frequency is placed
in a backpack of a human body, it generates 32 mW from a slow-running motion.

150
Chapter 5 References
[1] S. C. Mukhopadhyay, J. Donaldson, G. Sengupta, S. Yamada, C. Chakraborty
and D. Kacprzak, “Fabrication of a repulsive-type magnetic bearing using a
novel arrangement of permanent magnets for vertical-rotor suspension,” IEEE
transactions on magnetics, vol. 39, no. 5, pp. 3220-3222, Sep. 2003.

151
Chapter 6
Conclusion and Future Directions

Various microfabricated and miniature electromagnetic vibration-energy
harvesters have been designed, fabricated and characterized. Microfabrication
processes of permanent magnets and low resistive coils with multi-turn have been
developed for fully-integrated MEMS energy harvester. A new energy-conversion
technique, which uses an array of alternating north- and south-orientation magnets to
enhance magnetic flux change, is provided to convert mechanical vibration into
electrical energy with unprecedented power level. For harvesting energy from low-
frequency vibrations which are commonly present in many environments, the energy
harvester with magnetic spring is presented and applied to generate electrical power
from human body motion.
6.1 Microfabrication Processes for Electromagnetic Energy Harvesters
For the microfabrication techniques of permanent magnets, wax-bonded
magnetic powders have been integrated in the energy harvesters as micromagnets
and a power level of pW – nW has been delivered. The magnetic field provided by
the micromagnets can be further enhanced by increasing the loading fraction of
magnetic powders, packing other types of magnetic powders with higher residual
induction or optimizing the bonding and magnetization process. Electroplating and
sputter-deposition need to be explored as microfabrication methods for integration of

152
magnetic materials. In addition, machining and patterning bulk permanent magnets
by laser cutter or dicing saw provide another way to achieve strong micromagnet.
For the microfabricatd coils, electroplating, photoresist and silicon mold, and
3D multi-layer structure have been developed to deposit 20 - 300 μm think copper
and increase the number of coil turns. The electroplated coils with silicon mold need
to be investigated for integration and forming multi-layer with high yield. The multi-
layer coils can be built on thinner substrate (such as polyimide) rather than silicon
wafer to reduce the device size and the gap between magnet and coil arrays.
6.2 Miniature Electromagnetic Energy Harvesters
A new electromagnetic-transduction idea has been used to increase the
mechanical-to-electrical conversion efficiency. For a given total size and weight, the
magnet size can be optimized. Theoretically, the power output can be calculated and
compared by the magnetic flux change and the coil resistance for different magnet
sizes, and the optimal one can be verified through a series of experiments. The coil
shape can be improved by increasing the length of the edge of the coil that cuts
through the magnetic field. For the same coil area, the output power can be doubled
by switching to a rectangular coil from a square one. Since the magnetic flux change
increases as the distance from the magnet surface is decreased, the gap between
magnet and coil arrays needs to be as close as possible. Hitting of magnets and coils
will cause the energy loss which should be minimized. Lubricant or other
mechanisms maybe help to make the magnet array vibrate vertically.

153
6.3 Energy Harvesting from Low-frequency Vibrations
A magnetic spring has been developed to lower the resonant frequency of the
energy harvesters to several Hz. Since the proof mass cannot be stably suspended by
the magnetic force, teflon balls and graphite sheets can be used to reduce the friction.
Minimizing the friction or building a sturdy and precise suspension is still a
challenge for harvesting energy from low-frequency vibrations. To lower the
resonant frequency, the volume and weight have to be increased, since the stronger
and larger magnets are needed and initial gap of the magnetic spring is increased.
Thus, the magnetic spring needs to be optimized to provide a higher Figure of Merit
(FOM) for generating electrical power from human body motion. To avoid the
hitting of the two magnets of the magnetic spring, a silicone membrane or
mechanical springs can be added on the fixed magnet.
Since optimal performances of the resonant devices occur only over a narrow
frequency band at a relatively high frequency, non-resonant technologies that can
respond to all the frequency components of a vibration at a low frequency range is
highly desired. The idea is to design a mass-spring system with a static proof mass
during the vibration so that the relative displacement is equal to external vibration
amplitude at any frequency. Teflon balls, smooth hinges or bearings can be used to
reduce the friction and make the proof mass static.
For an energy harvester based on linear relative movement between magnets
and coils, the amplitude of the relative movement should be increased to increase the
Electromotive force (EMF). This may increase the volume and add some geometry

154
limitation on the device. Moreover, the energy-conversion efficiency may also be
limited by the movable range of the magnet. A possible way to avoid this limitation
is to transfer linear vibration to rotation. Since the frequency of the rotation can be
high and won’t be limited by the geometry of the device, high EMF (and thus high
power) can be achieved while the volume remains small. A rotation-energy harvester
based on eccentric rotor may be another method for harvesting energy from low-
frequency vibration. There are two states for the energy harvest: swinging and
rotating. The rotating state can give much higher voltage than the swinging.
However, the rotation does not continue, as the rotation is often not in sync with the
applied acceleration, and the direction of rotation is random even if the external
excitation is sinusoidal.

155
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Abstract (if available)

Abstract This thesis presents microfabricated and miniature electromagnetic transducers for vibration-energy harvesting, including theoretical analysis of a mass-spring system and energy-conversion efficiency, fully-integrated microelectromechanical systems (MEMS) electromagnetic power generator and its stack, a new energy-conversion technique to convert mechanical vibration into electrical energy, and a magnetic suspension system for harvesting energy from human body motion.

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Creator Zhang, Qian (author)

Core Title Electromagnetic energy harvesting from vibrations

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 11/11/2014

Defense Date 10/06/2014

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag electromagnetic induction,energy harvesting,OAI-PMH Harvest,vibration-driven power generator

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kim, Eun Sok (committee chair), Moghaddam, Mahta (committee member), Thompson, Mark E. (committee member)

Creator Email qianz@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-516068

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