Stresa, Italy, 26-28 April 2006
?TIMA Editions/DTIP 2006 -page- ISBN: 2-916187-03-0
VIBRATIONAL ENERGY SCAVENGING WITH SI TECHNOLOGY
ELECTROMAGNETIC INERTIAL MICROGENERATORS
C. Serre
1
, A. P?rez-Rodr?guez
1
, N. Fondevilla
1
, J.R. Morante
1
, J. Montserrat
2
, and J. Esteve
2
.
1
EME/CEMIC/CERMAE ? Dept. Electr?nica, Univ. Barcelona, Mart? Franqu?s 1, 08028 Barcelona, Spain.
2
Centre Nacional de Microelectr?nica CNM-CSIC, Campus UAB, 08193 Bellaterra, Spain
ABSTRACT
In this work, we present the design and optimization of an
electromagnetic inertial microgenerator for energy
scavenging applications, compatible with Si technology.
It consists of a fixed micromachined coil and a movable
magnet (inertial mass) mounted on a resonant structure
(Kapton? membrane). The modeling of the device, based
on a velocity damped resonator, includes the losses
related to the coil series resistance and has allowed the
analysis of the design and loading conditions required to
optimize both the generated power and output voltage.
The characterization of a first (not optimized) prototype
has allowed the validation of the model, which is then
used as a roadmap for a number of optimizations for the
final device design. For this design, the model developed
shows the possibility to achieve power levels up to
hundreds of ?W?s, with voltage levels compatible with
the requirements of standard rectifying circuits.
1. INTRODUCTION
The autonomy requirements of modern microsystems for
wearable, ubiquitous and self-powered applications have
raised an increasing demand for the development of power
supplies suitable for their integration with next generation
of micro and nanosensors. On the other hand, owing to the
miniaturization of the devices, the power consumption
have considerably decreased, allowing to consider
powering alternatives based on harvesting ?residual?
ambient energy. Among other sources, mechanical
vibrations inherent in our environment -- from the
movement of our bodies to the hum of a computer -- can
account for a permanent power density. This residual
ambient energy can be harnessed to generate electrical
power. For such applications, an interesting option is the
use of inertial microgenerators for energy scavenging from
the vibrations in the environment [1, 2]. These devices
constitute perpetual energy sources without the need for
refilling, thus being well suited for abandoned sensors,
wireless systems or microsystems which must be
completely embedded within the structure, with no outside
physical connections.
This work describes the design and optimization of an
electromagnetic inertial microgenerator for energy
scavenging applications, compatible with Si technology.
The design is based on a velocity damped resonator,
which is suitable for harvesting of mechanical energy
from vibrations induced by operating machines and
engines. These vibrations are characterized by a well
defined frequency and low displacement amplitudes [3].
Adjusting the resonant frequency of the system to that of
the vibrations allows to amplify these low amplitude
displacements. Moreover, for these applications, the use
of an electromagnetic device has the potential advantages
of a high level of compatibility with Si Microsystem
technology, as well as the possibility of relatively high
electromechanical coupling with simple designs. The
device proposed in this work has a simplified structure
formed by a fixed coil and a movable magnet (inertial
mass) mounted on a resonant structure (Kapton
?
membrane). The modeling and optimization, based on the
calculation of the em damping coefficient [1], and
performed by Finite elements analysis (ANSYS) are
presented. The mechanical and electrical characterization
of a preliminary prototype is compared to those expected
with a next prototype including some of the proposed
optimizations. The results obtained point out the
compatibility of this simple device structure with the
generation of power values up to hundreds of ?W?s, with
voltage levels compatible with the requirements of
standard rectifying circuits.
2. DEVICE MODELLING
The modeling of the device is based on a velocity damped
resonator, as represented in figure 1. This system is formed
by an inertial mass m linked to the frame with an elastic
constant k. The movement is damped by two forces related
to the electromechanical transductor (F
g
= D
g
?) and to a
parasitic damping (F
p
= D
p
?) due to air resistance and
hysteresis loss effects in the mechanical resonator.
C. Serre, A. P?rez-Rodr?guez, N. Fondevilla, J.R. Morante, J. Montserrat, and J. Esteve.
Vibrational energy scavenging with Si technology electromagnetic inertial microgenerators.
?TIMA Editions/DTIP 2006 -page- ISBN: 2-916187-03-0
Under an harmonic excitation y(t) = Y
o
cos (?t), the
amplitude Z
o
of the response is given by the module of the
transfer function as follows:
222
2
)2()1(
cc
c
o
o
Y
Z
???
?
+?
= (1)
where ? represents the total damping coefficient ? = ?
p
+
?
g
, ?
g
= D
g
/(2 m ?
n
) and ?
p
= D
p
/(2 m ?
n
) are the
normalized electromagnetic and parasitic damping factors,
respectively, and ?
c
is the angular frequency normalized to
the system natural frequency ?
n
.
A schematic representation of the proposed design is
shown in figure 2. Assuming a resistive load, the device
behaves as an inertial resonator if the inductive component
of the coil impedance is much lower than the resistance in
the circuit. In this case, the power generated at resonant
conditions is given by:
()
2
32
4
pg
nog
res
mY
P
??
??
+
= (2)
In this design, the normalized electromagnetic damping
factor ?
g
can be expressed as follows:
2
)(2
1
?
?
?
?
?
?
+
=
dz
d
RRm
nLC
g
?
?
? (3)
where R
c
and R
L
are the coil series and load resistances,
respectively. (d?/dz) is the magnetic flux rate through the
coil due to the magnet displacement. This model also takes
into account the existence of a parasitic damping ?
p
, related
to air resistance and hysteresis loss effects in the
mechanical resonator.
From (2), it can be derived that one condition leading to
a maximum value of P
res
is ?
g
= ?
p
. However, this doesn?t
takes into account the power dissipated in the coil series
resistance, which determines that only a fraction P
L
of the
power given by (2) is available at the load resistance. By
deriving this power in relation to R
L
, it is possible to
determine the optimum value of R
L
which maximizes P
L
:
C
pn
Lopt
R
dz
d
m
R +
?
?
?
?
?
?
=
2
2
1 ?
??
(4)
which gives the following expression for the maximum
power dissipated at the resistive load:
pc
c
p
no
Lopt
mY
P
??
?
?
?
+
=
16
32
(5)
where ?
c
corresponds to the electromagnetic damping
obtained with R
L
=0. This function increases
monotonously with ?
c
which, in turn, is inversely
proportional to R
C
. According to this, the maximum
power, obtained when R
c
?0, is P
Lmax
= [(Y
o
2
?
n
3
m)/(16
?
p
)]. Then, the optimum design in terms of the generated
power corresponds to a minimum value of both R
C
and
?
p
. On the other hand, the generated voltage is given by
the time derivative of the magnetic flux. At resonant
conditions, the voltage amplitude at the load is given by:
?
?
?
?
?
?
++
=
dz
dY
RR
R
V
pg
no
LC
L
o
?
??
?
)(2)(
(6)
In this case, the voltage increases with the value of R
L
,
and tends asymptotically to V
om?x
:
?
?
?
?
?
?
=
dz
dY
V
p
no
o
?
?
?
2
max
(7)
This implies that, in relation to R
L
, the conditions leading
to a maximum voltage (R
L
??) are different from those
corresponding to the maximum output power (R
L
= R
Lopt
).
Figure 1. Schematic representation of a velocity
damped resonator.
D
g
kD
p
m
y(t)
z(t)
Membrane
r
nucl
z
h
r
mag
Planar coil
Figure 2. Schematics cross section of the device
C. Serre, A. P?rez-Rodr?guez, N. Fondevilla, J.R. Morante, J. Montserrat, and J. Esteve.
Vibrational energy scavenging with Si technology electromagnetic inertial microgenerators.
?TIMA Editions/DTIP 2006 -page- ISBN: 2-916187-03-0
3. FIRST PROTOTYPE FABRICATION AND
CHARACTERIZATION
A first prototype has been designed and fabricated, using
a coil with an area of about 1 cm
2
. The design of the
device has been based on the FE analysis (ANSYS) of the
flux rate (d?/dz)
max
as a function of the different device
parameters This has been performed assuming coils
formed by 30 ?m wide, 1.5 ?m thick Al metal tracks,
with a separation between tracks of 20 ?m, and for both
circular and square shaped configurations. The results
indicate that i) (d?/dz) increases with the magnet size, and
the optimum case is obtained when the magnet fills the
whole nucleus area and ii) that there is a maximum value
of the flux rate when the upper surface of the magnet is
located in the plane of the coil. This analysis also shows
that the optimum flux rate value for this first prototype
was obtained with square shaped coils, made of 29 turns.
This determines an 8x8 mm
2
coil nucleus. A structure
formed by a square shaped membrane with an inertial
mass corresponding to the magnet has been implemented,
using Kapton? membrane with a thickness of 127 ?m.
This polymer has a Young modulus significantly lower
than that of Si related materials (E = 2.5 GPa), which is
better suited for the design of structures with resonant
frequencies in the range from few Hz?s to few kHz?s.
This has been fixed on a PCB square frame and the
NdFeB permanent magnet has been glued on the centre of
the membrane. To avoid potential collisions of the
magnet with the edges of the coil nucleus, a magnet with
a size a bit smaller than that of the nucleus has been used
(7x7 mm
2
). The characterization has been performed with
the following experimental setup: excitation is provided
by a piezoelectric actuator (15 ?m displacement at 100
V), with a resonant frequency at 69kHz (i.e. far from our
range of interest). The mechanical response of the
structure is measured with a Microtak 7000 displacement
sensor system coupled to a MT-250-200 laser head (MTI
Instruments Inc.), allowing a vertical resolution of
0.127?m with a 20kHz bandwidth. The laser head is
mounted on a XYZ translation stage, and clamped to a
damped mounting post to avoid noise from interaction
with the excitation. The excitation signal, the analogue
output of the Microtak 7000, and the electrical response
of the device are monitored by an oscilloscope for easier
analysis.
The mechanical characterization of this structure
with an 11x11 mm
2
membrane shows a resonant
frequency (figure 3) in agreement with that simulated by
ANSYS (about 920 Hz). The fitting of the experimentally
measured resonant peak according to (1) has allowed to
estimate the parasitic damping coefficient in this
resonator to a value of ?
p
= 0,011.
The electrical characterization of the microgenerator
with a 7x7x4 mm
3
magnet and a 13x13 mm
2
membrane
(resonant frequency of 360 Hz, Y
0
= 3.4 ?m) is shown in
figure 4. A peak power of about 45 nW was obtained. By
increasing the excitation conditions up to Y
o
= 6.8 ?m, an
experimental increase in the generated power up to 0.2
?W has been obtained (higher excitation amplitudes led
to non linear resonant behavior). One reason of such low
power values is that in this first prototype, the 1.5 ?m
thick Al metal tracks determine a high value of the coil
series resistance, R
C
? 910 ?, which drastically limits the
performance of the device.
In figure 5 and 6, the obtained data are plotted as a
function of the load resistance. These data correspond to
the output power and voltage amplitude measured at
resonant conditions using the same excitation amplitude
as in the previous figure. The figures also show the fitting
of the experimental data using the theoretical equations
800 850 900 950 1000
0
5
10
15
20
25
30
d (
?
m)
f (Hz)
d (?m)
user2 simulation
0
0,01
0,02
0,03
0,04
0,05
0,8 1 1,2
wc
P
L
(m
ic
ro
W
)
Figure 3. Mechanical characterization of the structure
formed by a 7x7x2 mm
3
magnet fixed onto an 11x11
mm
2
Kapton membrane (thickness 127 ?m).
Figure 4. Output power P
L
vs normalized angular
frequency ?
c
,
measured with a load resistance R
L
=
1300 ? and an excitation amplitude Y
o
=3.4 ?m.
C. Serre, A. P?rez-Rodr?guez, N. Fondevilla, J.R. Morante, J. Montserrat, and J. Esteve.
Vibrational energy scavenging with Si technology electromagnetic inertial microgenerators.
?TIMA Editions/DTIP 2006 -page- ISBN: 2-916187-03-0
described in Section 2. As shown in these figures, there is
a good agreement between the experimental data and the
theoretical model developed for these devices. The fitting
of these data gives in this case a value of the parasitic
damping ?
p
= 0.03, taking into account the magnetic flux
rate value of (d?/dz) = 0.124 Wb/m calculated by ANSYS
for this structure. This parasitic damping is higher than
that obtained from the measurements shown in figure 3,
where a magnet significantly smaller was used.
These results corroborate the validity of the model
developed for the electromagnetic generator. The data
also show the ability of this first (not optimized)
prototype to generate powers in the range between nW?s
and ?W?s.
4. OPTIMIZATIONS
Optimizations to this design can be made in three main
ways: decrease of the parasitic damping, geometric
optimizations in order to maximize the magnetic flux rate
d?/dz, and electric optimizations aiming at maximizing
the electromagnetic coupling represented by the
electromagnetic damping ?
g
.
According to equation (5) and (7), decreasing the
parasitic damping in the structure allows to improve both
the generated power and the output voltage. In this sense,
our estimated values of ?
p
for the Kapton membranes are
significantly higher than that previously reported in the
literature for devices with a similar design structure (?
p
=
0.0037, [1, 4]). To minimize the parasitic damping effects,
several options are being implemented, which include the
fabrication of the membrane by deposition of a polymeric
film (such as SU-8 or PMMA) onto a micromachined
structure, and the replacement of the polyimide films by Si
based membranes (which have very low mechanical
hysteresis losses). A further reduction of the parasitic
damping could be achieved by performing the
encapsulation of the devices under vacuum conditions.
However, the optimization of the device in terms of
parasitic damping has also to take into account that
decreasing the total damping in the system also leads to a
decrease in the range of Y
o
values compatible with the
device design. This is determined by the existence of a
higher limit Z
L
for the displacement of the inertial mass in
the device, imposed by the potential collision of the mass
with fixed parts in the system. For a given value of Y
o
, this
imposes the need to have a value of total damping (?
g
+ ?
p
)
? [Y
o
/(2Z
L
)]. To quote this value, we have made a
conservative estimation of Z
L,
by limiting the highest
vertical position of the magnet base to the position of the
plane of the coil. This gives Z
L
= z + h/2 (see figure 1),
which leads to a lower limit value for the total damping of
? = 0.00125 for Y
o
? 5 ?m.
The analysis of the flux rate as a function of the coil
tracks parameters reveals the possibility to obtain a
further increase of the value of the magnetic flux rate by
decreasing both the width and separation, and increasing
the number of turns. With a value of 6 ?m (minimum
value compatible with high aspect ratio tracks, as
0,5
0,6
0,7
0,8
0,9
0 50 100 150 200
number of turns
(d
?/
dz
)
ma
x
(Wb
/
m
)
Figure 7. Maximum flux rate for coils with 6 ?m metal
track width and separation between metal tracks vs
number of turns
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
0,04
0,045
100 1000 10000 100000 1000000
RL (ohms)
PL
(
m
icr
o
W)
exp
model
Figure 5. Output power P
L
vs load resistance R
L
,
measured at resonant conditions.
0
5
10
15
20
25
100 1000 10000 100000 1000000
RL (ohms)
Vo (m
V)
exp
model
Figure 6. Output voltage V
o
vs load resistance R
L
,
measured at resonant conditions.
C. Serre, A. P?rez-Rodr?guez, N. Fondevilla, J.R. Morante, J. Montserrat, and J. Esteve.
Vibrational energy scavenging with Si technology electromagnetic inertial microgenerators.
?TIMA Editions/DTIP 2006 -page- ISBN: 2-916187-03-0
explained later) for both width and separation of the
tracks, a maximum flux rate is obtained for 120 turns
(figure 7). However, this tends to increase the coil series
resistance R
c
, which can compromise the potential
increase of the generated power related to the
optimization of the flux rate.
Finally, as shown in equation (3), optimizing ?
g
requires reducing the value of R
C
. This can be achieved
by using a thicker metal for the coil tracks. For this, the
selective growth of thick Cu tracks by electrochemical
deposition [5] is proposed, in combination with a
previous high aspect ratio lithography process. For 50 ?m
thick tracks, the series resistance of a device with the
same design as our first prototype should drop down to a
value of R
C
= 8.4 ?. This would lead to an increase of
two orders of magnitude in the generated power assuming
the same conditions as in the previous case, obtaining a
value of P
L
? 100 ?W.
According to these directives, figure 8 shows the
simulation of an optimized device that includes a coil
made of 50 ?m thick, 6 ?m pitch Cu tracks. For this
design, the signal generated by the device has been
calculated using the excitation conditions corresponding
to the vibrations induced by a small microwave oven, f =
120 Hz and Y
o
= 4.4 ?m. As reported in [3], these are
representative of the low level vibrations typically present
in domestic and office environments, which have
frequencies between 70 and 200 Hz and acceleration
amplitudes between 1 and 10 m/s
2
. In this case, a
maximum power of P
Lopt
= 282 ?W is obtained with R
L
=
R
Lopt
= 600 ?, with an amplitude of the output voltage of
V
o
= 0.58 V. Increasing the load resistance up to R
L
=
1350 ? allows the generation of P
L
= 240 ?W with a
voltage amplitude V
o
= 0.8 V. It is interesting to remark
that these voltage levels are compatible with the
requirements related to the use of standard rectifying
circuits for the generation of a DC signal suitable for
power supply applications.
The comparison of these data with those reported in
the literature for the same excitation conditions points out
the possibility to generate similar power levels with the
electromagnetic device proposed in this paper, obtaining
higher values than with other approaches such as the
electrostatic one. In this last case, Roundy et al [3] have
reported a value of 43 ?W from the simulation of an
optimized design of electrostatic generator. These authors
have also developed a prototype of piezoelectric
generator, which gives a higher power of 70 ?W.
Simulations show that an optimized design would be
capable of generating a power of 250 ?W for the same
vibration source, which is still slightly lower than the
maximum value of P
Lopt
= 280 ?W simulated for our
optimized electromagnetic design. It is interesting to
remark that the devices described in [3] correspond to
designs with a total volume of 0.5 cm
3
, which is of the
same order of magnitude as the volume that can be
estimated for our device (in the range 0.6-0.7 cm
3
).
5. CONCLUSIONS
In this work, we have presented the design and
optimization of an electromagnetic inertial
microgenerator for energy scavenging applications,
compatible with Si technology.
The proposed design consists of a fixed
micromachined coil and a movable magnet (inertial mass)
mounted on a resonant structure (Kapton? membrane).
The modeling of the device is based on a velocity damped
resonator. The inclusion in the model of the losses related
to the coil series resistance has allowed to analyze the
design and loading conditions required to optimize both
the generated power and output voltage, exploring the
capabilities of this simple device structure for the
development of devices suitable for practical applications.
According to this structure, a first prototype (not
optimized) has been designed and fabricated. The
Figure 8. Generated P
L
and V
o
vs R
L
calculated for the
design with the highest flux rate (n = 120, ?
p
= 0.00125,
f = 120 Hz, Y
o
= 4.4 ?m)
0
200
400
600
800
1000
1200
0 2000 4000 6000 8000 10000
RL (ohms)
Vo
(
m
V
)
0
50
100
150
200
250
300
0 2000 4000 6000 8000 10000
RL(ohms)
PL (m
ic
r
o
W)
C. Serre, A. P?rez-Rodr?guez, N. Fondevilla, J.R. Morante, J. Montserrat, and J. Esteve.
Vibrational energy scavenging with Si technology electromagnetic inertial microgenerators.
?TIMA Editions/DTIP 2006 -page- ISBN: 2-916187-03-0
experimental mechanical and electrical characterization
of this prototype has allowed the validation of the model
developed for the inertial electromagnetic micro-
generators, which is then used as a roadmap for a number
of optimizations for the final device design.
These optimizations can be made in three main ways:
decrease of the parasitic damping, geometric
optimizations in order to maximize the magnetic flux rate
d?/dz, and electric optimizations aiming at maximizing
the electromagnetic coupling represented by the
electromagnetic damping ?
g
. In relation to previous works
proposing electromagnetic generators with a similar
structure formed by a fixed coil and a movable magnet [3,
4], the simulation of the devices with the optimum design
using the same excitation conditions as in these works
reveals the possibility to obtain a significant increase of
the flux rate (more than 2 orders of magnitude), thus
allowing to generate much higher power levels.
For the optimum design, these results corroborate the
ability of this devices to generate power up to hundreds of
?W?s, with voltage levels compatible with the
requirements related to the use of standard rectifying
circuits for the generation of a DC signal suitable for
power supply applications. This open interesting
perspectives for the fabrication of power microgenerator
suitable for their integration with advanced
micro/nanosensors in microsystems for autonomous
operation, wireless systems, or microsystem that must be
completely embedded within the structure with no outside
physical connections, allowing to overcome the
limitations of conventional batteries in terms of
miniaturization and devices lifetime.
ACKNOWLEDGEMENTS
The funding of this work by the IST program of the
European Commission under the SENSATION project
(ref. FP6-507231) is acknowledged by the authors from the
University of Barcelona
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