INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 17 (2006) R175–R195 doi:10.1088/0957-0233/17/12/R01
REVIEW ARTICLE
Energy harvesting vibration sources for
microsystems applications
S P Beeby, M J Tudor and N M White
School of Electronics and Computer Science, University of Southampton,
Southampton SO17 1BJ, UK
Received 3 March 2005, in final form 19 July 2006
Published 26 October 2006
Online at stacks.iop.org/MST/17/R175
Abstract
This paper reviews the state-of-the art in vibration energy harvesting for
wireless, self-powered microsystems. Vibration-powered generators are
typically, although not exclusively, inertial spring and mass systems. The
characteristic equations for inertial-based generators are presented, along
with the specific damping equations that relate to the three main
transduction mechanisms employed to extract energy from the system.
These transduction mechanisms are: piezoelectric, electromagnetic and
electrostatic. Piezoelectric generators employ active materials that generate
a charge when mechanically stressed. A comprehensive review of existing
piezoelectric generators is presented, including impact coupled, resonant
and human-based devices. Electromagnetic generators employ
electromagnetic induction arising from the relative motion between a
magnetic flux gradient and a conductor. Electromagnetic generators
presented in the literature are reviewed including large scale discrete devices
and wafer-scale integrated versions. Electrostatic generators utilize the
relative movement between electrically isolated charged capacitor plates to
generate energy. The work done against the electrostatic force between the
plates provides the harvested energy. Electrostatic-based generators are
reviewed under the classifications of in-plane overlap varying, in-plane gap
closing and out-of-plane gap closing; the Coulomb force parametric
generator and electret-based generators are also covered. The coupling
factor of each transduction mechanism is discussed and all the devices
presented in the literature are summarized in tables classified by transduction
type; conclusions are drawn as to the suitability of the various techniques.
Keywords: energy harvesting review, vibration power, self-powered systems,
power scavenging
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Wireless systems are becoming ubiquitous; examples include
wireless networking based upon the IEEE 802.11 standard and
the wireless connectivity of portable devices and computer
peripherals using the Bluetooth standard. The use of
wireless devices offers several advantages over existing,
wired methodologies. Factors include flexibility, ease of
implementation and the ability to facilitate the placement
of sensors in previously inaccessible locations. The ability
to retrofit systems without having to consider issues such
as cabling, offers a significant advantage in applications for
areas such as condition-based monitoring (CBM) [1], where
embedded wireless microsensors can provide continuous
monitoring of machine and structural health without the
expense and inconvenience of including wiring looms. The
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wires (and associated connectors) are often a source of failure
in such systems and present a considerable cost issue.
At present, many wireless sensor nodes are battery-
powered and operate on an extremely economical energy
budget since continuous battery replacement is not an option
for networks with thousands of physically embedded nodes
[2]. Some specific examples of wireless sensor networks
include the WiseNET platform developed by the Swiss Centre
for Electronics and Microtechnology (CSEM) [3] and those
discussed by Warneke et al [4] and Callahan [5]. The low-
power characteristics of wireless sensor network components
and the design of the system architecture are crucial to the
longevity of the sensor nodes. The most power hungry
aspect is the wireless communication. Examples of low-
power wireless sensor protocols include the IEEE 802.15.4 [6]
specification, Zigbee [7] and the ad hoc network architecture
demonstrated by the PicoRadio system developed at Berkeley
[8]. Intelligence can also be incorporated at the sensor
node to perform signal processing on the raw sensor data,
execute communications protocols and manage the node’s
power consumption [9].
These low-power wireless sensor nodes provide a real
incentive for investigating alternative types of power source to
traditional batteries. Solutions such as micro fuel cells [10]
and micro turbine generators [11], both involve the use of
chemical energy and require refuelling when their supplies are
exhausted. Such systems are capable of high levels of energy
and power density and show good potential for the recharging
of, or even replacing, mobile phone or laptop batteries [12].
Renewable power can be obtained by generating electrical
energy from light, thermal and kinetic energy present within
the sensor’s environment. These sources can be used as
either a direct replacement or to augment the battery, thereby
increasing the lifetime and capability of the network [13–16]
and mitigate the environmental impact caused by issues
surrounding the disposal of batteries. In this context, solar
power is probably the most well known. Solar cells offer
excellent power density in direct sunlight but are limited in
dim ambient light conditions and are clearly unsuitable in
embedded applications where no light may be present, or
where the cells can be obscured by contamination. Thermal
energy can be conveniently transduced into electrical energy
by the Seebeck effect. Early thermoelectric microgenerators
produced only a few nW [17] but more recently this approach
has been combined with micro-combustion chambers to
improve output power to ∼1 µW/thermocouple [18, 19].
The subject of this review paper is kinetic energy
generators, which convert energy in the form of mechanical
movement present in the application environment into
electrical energy. Kinetic energy is typically present in
the form of vibrations, random displacements or forces
and is typically converted into electrical energy using
electromagnetic, piezoelectric or electrostatic mechanisms.
Suitable vibrations can be found in numerous applications
including common household goods (fridges, washing
machines, microwave ovens etc), industrial plant equipment,
moving structures such as automobiles and aeroplanes and
structures such as buildings and bridges [20]. Human-
based applications are characterized by low frequency high
amplitude displacements [21, 22]. The amount of energy
generated by this approach depends fundamentally upon the
quantity and form of the kinetic energy available in the
application environment and the efficiency of the generator
and the power conversion electronics. The following sections
will discuss the fundamentals of kinetic energy harvesting and
the different transduction mechanisms that may be employed.
These mechanisms will then be illustrated by a comprehensive
review of generators developed to date.
2. General theory of kinetic energy harvesting
2.1. Transduction mechanisms
Kinetic energy harvesting requires a transduction mechanism
to generate electrical energy from motion and the generator
will require a mechanical system that couples environmental
displacements to the transduction mechanism. The design of
the mechanical system should maximize the coupling between
the kinetic energy source and the transduction mechanism
and will depend entirely upon the characteristics of the
environmental motion. Vibration energy is best suited to
inertial generators with the mechanical component attached
to an inertial frame which acts as the fixed reference.
The inertial frame transmits the vibrations to a suspended
inertial mass producing a relative displacement between them.
Such a system will possess a resonant frequency which
can be designed to match the characteristic frequency of
the application environment. This approach magnifies the
environmental vibration amplitude by the quality factor of the
resonant system and this is discussed further in the following
section.
The transduction mechanism itself can generate electricity
by exploiting the mechanical strain or relative displacement
occurring within the system. The strain effect utilizes
the deformation within the mechanical system and typically
employs active materials (e.g., piezoelectric). In the case
of relative displacement, either the velocity or position
can be coupled to a transduction mechanism. Velocity is
typically associated with electromagnetic transduction whist
relative position is associated with electrostatic transduction.
Each transduction mechanism exhibits different damping
characteristics and this should be taken into consideration
while modelling the generators. The mechanical system can be
increased in complexity, for example, by including a hydraulic
system to magnify amplitudes or forces, or couple linear
displacements into rotary generators.
2.2. Power output from a resonant generator
The analysis presented in section 2.2.1 presents the maximum
power available in a resonant system. This is based upon
a conventional second-order spring and mass system with a
linear damper and is most closely suited to the electromagnetic
case, since the damping mechanism is proportional to velocity.
The general analysis, however, still provides a valuable insight
into resonant generators and highlights some important aspects
that are applicable to all transduction mechanisms. The
damping factors of each transduction mechanism are discussed
in more detail in section 2.2.2.
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m
k
c
T
z(t)
y(t)
Figure 1. Model of a linear, inertial generator.
2.2.1. General resonant generator theory. Inertial-based
generators are essentially second-order, spring-mass systems.
Figure 1 shows a general example of such a system based
on a seismic mass, m, on a spring of stiffness, k. Energy
losses within the system (comprising parasitic losses, c
p
,and
electrical energy extracted by the transduction mechanism,
c
e
) are represented by the damping coefficient, c
T
.These
components are located within the inertial frame which is
being excited by an external sinusoidal vibration of the form
y(t) = Y sin(ωt). This external vibration moves out of phase
with the mass when the structure is vibrated at resonance
resulting in a net displacement, z(t), between the mass and
the frame. Assuming that the mass of the vibration source
is significantly greater than that of the seismic mass and
therefore not affected by its presence, and also that the external
excitation is harmonic, then the differential equation of motion
is described as
m
¨
z(t) + c
˙
z(t) + kz(t) =−m
¨
y(t). (1)
Since energy is extracted from relative movement between
the mass and the inertial frame, the following equations apply.
The standard steady-state solution for the mass displacement
is given by
z(t) =
ω
2
k
m
− ω
2
2
+
c
T
ω
m
2
Y sin(ωt −φ), (2)
where φ is the phase angle given by
φ = tan
−1
c
T
ω
(k − ω
2
m)
. (3)
Maximum energy can be extracted when the excitation
frequency matches the natural frequency of the system, ω
n
,
given by
ω
n
=
k/m. (4)
The power dissipated within the damper (i.e. extracted by the
transduction mechanism and parasitic damping mechanisms)
is given by [23]
P
d
=
mζ
T
Y
2
ω
ω
n
3
ω
3
1 −
ω
ω
n
2
2
+
2ζ
T
ω
ω
n
2
, (5)
where ζ
T
is the total damping ratio (ζ
T
= c
T
/2mω
n
).
Maximum power occurs when the device is operated at ω
n
and in this case P
d
is given by the following equations:
P
d
=
mY
2
ω
3
n
4ζ
T
(6)
P
d
=
mA
2
4ω
n
ζ
T
. (7)
Equation (7) uses the excitation acceleration levels, A,inthe
expression for P
d
which is simply derived from A = ω
2
n
Y .
Since these are steady-state solutions, power does not tend
to infinity as the damping ratio tends to zero. The maximum
power that can extracted by the transduction mechanism can be
calculated by including the parasitic and transducer damping
ratios as
P
e
=
mζ
e
A
2
4ω
n
(ζ
p
+ ζ
e
)
2
, (8)
P
e
is maximized when ζ
p
= ζ
e
. Some parasitic damping
is unavoidable and it may be useful to be able to vary
damping levels. For example, it may indeed be useful
in maintaining z(t) within permissible limits. However,
conclusions should not be drawn without considering the
frequency and magnitude of the excitation vibrations and
the maximum mass displacement z(t) possible. Provided
sufficient acceleration is present, increased damping effects
will result in a broader bandwidth response and a generator
that is less sensitive to frequency. Excessive device amplitude
can also lead to nonlinear behaviour and introduce difficulties
in keeping the generator operating at resonance. It is clear that
both the frequency of the generator and the level of damping
should be designed to match a particular application in order
to maximize the power output. Furthermore, the mass of the
mechanical structure should be maximized within the given
size constraints in order to maximize the electrical power
output. It should also be noted that the energy delivered to the
electrical domain will not necessarily all be usefully harvested
(e.g., coil losses).
Since the power output is inversely proportional
to the natural frequency of the generator for a given
acceleration, it is generally preferable to operate at the
lowest available fundamental frequency. This is compounded
by practical observations that acceleration levels associated
with environmental vibrations tend to reduce with increasing
frequency. Application vibration spectra should be carefully
studied before designing the generator in order to correctly
identify the frequency of operation given the design constraints
on generator size and maximum permissible z(t).
2.2.2. Transduction damping coefficients. The damping
coefficient arising from electromagnetic transduction c
e
can
be estimated from [24]
c
e
=
(NlB)
2
R
load
+ R
coil
+jωL
coil
, (9)
where N is the number of turns in the generator coil,lis the side
length of the coil (assumed square), and B is the flux density
to which it is subjected and R
load
, R
coil
and L
coil
are the load
resistance, coil resistance and coil inductance, respectively.
Equation (9) is an approximation and only ideal for the case
where the coil moves from a high field region B, to a zero
field region. A more precise value for the electromagnetic
damping should be determined from finite-element analysis.
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m
K
c
T
z(t)
y(t)
Figure 2. Model of an electrostatic resonant generator.
Equation (9)showsthatR
load
can be used to adjust c
e
to match
c
p
and therefore maximize power, although this must be done
with the coil parameters in mind. It can be shown that the
optimum R
load
can be found from equation (10) and maximum
average power delivered to the load can be found from
equation (11)[25]:
R
load
= R
coil
+
(NlB)
2
c
p
, (10)
P
eloadmax
=
mA
2
16ζ
p
ω
n
1 −
R
coil
R
load
. (11)
An expression for the piezoelectric damping coefficient is [26]
c
e
=
2mω
2
n
k
2
2
ω
2
n
+ (1/(R
load
C
load
)
2
)
, (12)
where k is the piezoelectric material electromechanical
coupling factor and C
load
is the load capacitance. Again R
load
can be used to optimize ζ
e
and the optimum value can be found
from equation (13) and as stated previously, maximum power
occurs when ζ
e
equals ζ
p
.
R
opt
=
1
ω
n
C
2ζ
p
4ζ
2
p
+ k
4
. (13)
Electrostatic transduction is characterized by a constant force
damping effect, denoted as Coulomb damping and the basic
system is shown in figure 2 [27].
The energy dissipated within the damper, and therefore
the power, is given by the force–distance product shown
in equation (14)whereω
c
= ω/ω
n
and U = (sin(π/ω
c
)/
[1 + cos(π/ω
c
)]):
P =
4y
0
Fωω
2
c
2π
1
1 − ω
2
c
−
F
mY
0
ω
2
ω
c
U
2
1/2
. (14)
The optimum damping force is given by
F
opt
=
y
0
ω
2
m
√
2
ω
c
1 − ω
2
c
U
. (15)
The application of these equations to practical applications is
quite involved and beyond the scope of this review. The paper
by Mitcheson et al [27] should be studied if further detail is
required.
6
5
4
(X)
1
(Z)
3
(Y)
2
Direction o
f
polarisation
Figure 3. Notation of axes.
3. Piezoelectric generators
3.1. Introduction
Piezoelectric ceramics have been used for many years to
convert mechanical energy into electrical energy. The
following sections describe the range of piezoelectric
generators described in the literature to date. For the purposes
of this review, piezoelectric generators have been classified
by methods of operation and applications and include both
macro scale (>cm) and micro scale (µm to mm) devices. It
begins with a brief description of piezoelectric theory in order
to appreciate the different types of generator and the relevant
piezoelectric material properties.
3.2. Piezoelectricity
The piezoelectric effect was discovered by J and P Curie in
1880. They found that if certain crystals were subjected to
mechanical strain, they became electrically polarized and
the degree of polarization was proportional to the applied
strain. Conversely, these materials deform when exposed
to an electric field. Piezoelectric materials are widely
available in many forms including single crystal (e.g. quartz),
piezoceramic (e.g. lead zirconate titanate or PZT), thin film
(e.g. sputtered zinc oxide), screen printable thick-films based
upon piezoceramic powders [28, 29] and polymeric materials
such as polyvinylidenefluoride (PVDF) [30].
Piezoelectric materials typically exhibit anisotropic
characteristics, thus, the properties of the material differ
depending upon the direction of forces and orientation of
the polarization and electrodes. The anisotropic piezoelectric
properties of the ceramic are defined by a system of symbols
and notation [31]. This is related to the orientation of
the ceramic and the direction of measurements and applied
stresses/forces. The basis for this is shown in figure 3.
The level of piezoelectric activity of a material is defined
by a series of constants used in conjunction with the axes
notation. The piezoelectric strain constant, d, can be defined
as
d =
strain developed
applied field
m/V, (16)
d =
short circuit charge density
applied stress
C/N. (17)
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Piezoelectric generators that rely on a compressive strain
applied perpendicular to the electrodes exploit the d
33
coefficient of the material whilst those that apply a transverse
strain parallel to the electrodes utilize the d
31
coefficient.
The power output achieved in the compressive mode can be
improved by increasing the piezoelectric element’s thickness
or by using multi-layer stacks. Compressive loading, however,
is not a practical coupling mechanism for vibration energy
harvesting in the majority of applications. Typically, in the
case of piezoelectric films or piezoelectric elements bonded
onto substrates, the elements are coupled in the transverse
direction. Such an arrangement provides mechanical
amplification of the applied stresses.
Another important constant affecting the generation of
electrical power is the electro-mechanical coupling coefficient,
k. This describes the efficiency with which the energy is
converted by the material between electrical and mechanical
forms in a given direction. This is defined in equation (18)
where W
i
e
is the electrical energy stored in the i axis and W
j
m
is the mechanical input energy in the j axis.
k
2
ij
=
W
e
i
W
m
j
. (18)
Furthermore, k
p
is defined as the planar coupling factor, which
is typically used for radial modes of thin discs, and k
t
is defined
as the thickness mode coupling factor for a plate or disk.
The efficiency of energy conversion, η, for a piezoelectric
element clamped to a substrate and cyclically compressed at
its resonant frequency [32] is given in equation (19)where
Q is the quality factor of the generator. This relationship
suggests that the efficiency is improved by increasing k and
Q, which provides a useful guideline when choosing materials
and designing generators.
η =
k
2
2(1−k
2
)
1
Q
+
k
2
2(1−k
2
)
. (19)
Goldfarb et al [33] have investigated the efficiency of a
piezoelectric stack operated in compression. It was found that
the efficiency was maximized at frequencies several orders of
magnitude below the resonant frequency (e.g. around 5 Hz).
This is due to the capacitance of the piezoelectric stack, which
is in parallel with the load. Efficiency was also found to
increase with increasing force and load resistance but these
factors are less significant than frequency.
Other relevant piezoelectric constants include the
permittivity of the material, ε, which is defined as the dielectric
displacement per unit electric field and compliance, s,whichis
the strain produced per unit of stress. Lastly, the piezoelectric
voltage constant, g, is defined as the electric field generated
per unit of mechanical stress, or the strain developed for an
applied charge density. These constants are anisotropic and
are further defined using the system of subscripts described
above. For a more complete description of the constants the
reader is referred to the IEEE standards [34].
The piezoelectric properties vary with age, stress and
temperature. The change in the properties of the piezoceramic
with time is known as the ageing rate and is dependant
on the construction methods and the material type. The
changes in the material tend to be logarithmic with time, thus
the material properties stabilize with age, and manufacturers
Table 1. Coefficients of common piezoelectric materials [35, 36].
Property PZT-5H PZT-5A BaTiO
3
PVDF
d
33
(10
−12
CN
−1
) 593 374 149 −33
d
31
(10
−12
CN
−1
) −274 −171 78 23
g
33
(10
−3
VmN
−1
) 19.7 24.8 14.1 330
g
31
(10
−3
VmN
−1
) −9.1 −11.4 5 216
k
33
0.75 0.71 0.48 0.15
k
31
0.39 0.31 0.21 0.12
Relative permittivity (ε
/ε
o
) 3400 1700 1700 12
usually specify the constants of the device after a specified
period of time. The ageing process is accelerated by
the amount of stress applied to the ceramic and this
should be considered in cyclically loaded energy harvesting
applications. Soft piezoceramic compositions, such as PZT-
5H, are more susceptible to stress induced changes than
the harder compositions such as PZT-5A. Temperature is
also a limiting factor with piezoceramics due to the Curie
point. Above this limit the piezoelectric material will lose
its piezoelectric properties effectively becoming de-polarized.
The application of stress can also lower this Curie temperature.
The piezoelectric constants for common materials, soft
and hard lead zirconate titanate piezoceramics (PZT-5H
and PZT-5A), barium titanate (BaTiO
3
) and polyvinylidene
fluoride (PVDF), are given in table 1.
3.3. Impact coupled devices
The earliest example of a piezoelectric kinetic energy
harvesting system extracted energy from impacts. Initial work
explored the feasibility of this approach by dropping a 5.5 g
steel ball bearing from 20 mm onto a piezoelectric transducer
[37]. The piezoelectric transducer consisted of a 19 mm
diameter, 0.25 mm thick piezoelectric ceramic bonded to a
bronze disc 0.25 mm thick with a diameter of 27 mm. This
work determined that the optimum efficiency of the impact
excitation approach is 9.4% into a resistive load of 10 k
with most of the energy being returned to the ball bearing
which bounces off the transducer after the initial impact.
If an inelastic collision occurred, simulations predicted an
efficiency of 50% assuming a ‘moderate’ system Q-factor and
typical electromechanical coupling and dielectric loss factors
based upon PZT. Later research further explored the feasibility
of storing the charge on a capacitor or battery [38]. The output
of the generator was connected in turn to 0.1, 1 and 10 µF
capacitors via a bridge rectifier. The ability of the generator to
charge the capacitors depended upon the value of the capacitor
and its initial voltage. Optimum efficiency was found to occur
with a capacitor value of 1 µF for multiple impacts, but larger
capacitors can obviously store more energy. The generator
was also attached to nickel cadmium, nickel metal hydride and
lithium ion batteries with a range of capacities. The charging
characteristics were found to be unaffected by the battery type
or capacity and were very similar to that of a 10 µF capacitor.
The time taken for this approach to recharge the batteries was
not determined.
Recent work by Cavalier et al has explored the coupling of
mechanical impact to a piezoelectric (PZT) plate via a nickel
package [39]. The impact occurs on the outside of the nickel
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![Figure 7. Tapered thick-film PZT generator (not to scale) after Glynne-Jones et al [55].](/figures/figure-7-tapered-thick-film-pzt-generator-not-to-scale-after-vccw1pbl.webp)
![Figure 14. Cross-section of the electromagnetic generator proposed by Williams et al [23, 82].](/figures/figure-14-cross-section-of-the-electromagnetic-generator-179xmxe5.webp)
![Figure 4. PVDF shoe insole (after Kymiss et al [44]).](/figures/figure-4-pvdf-shoe-insole-after-kymiss-et-al-44-soflsw7z.webp)
![Figure 5. Schematic of the piezoelectric dimorph (after Shenck et al [45]).](/figures/figure-5-schematic-of-the-piezoelectric-dimorph-after-shenck-2vludo9v.webp)