Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)
LOW VOLTAGE ENERGY HARVESTING FOR MEMS APPLICATIONS
1
Daniel Guyomar1, Lauric Garbuio1 and Mickaël Lallart1
Université de Lyon, INSA-Lyon, LGEF EA 682, F-69621, Villeurbanne, France
Abstract: Harvesting energy from near environment has become a challenge that is nevertheless more and
more possible due to advances in microelectronics and energy conversion. Thanks to their high integrability
and high power density, piezoelectric materials are good candidates for microscale energy harvesters. The
piezoelectric conversion can besides be improved by the use of non-linear treatment of the output voltage.
However, low voltage output of MEMs harvesters is a particular issue when dealing with energy scavenging.
This paper proposes a new approach that dramatically minimizes the effect of voltage gaps of discrete c
components, therefore allowing harvesting energy even under slight solicitations and/or high frequencies.
Key words: energy harvesting, piezoelectric, nonlinear
of the piezovoltage that consists of intermittently
connecting the piezoelement on an electrical network
made of a transformer. Thanks to the transformer ratio,
the voltage drops of discrete components are
significantly reduced. It will be theoretically and
experimentally shown that such an approach permits a
great gain in terms of output power for systems
submitted to low solicitations.
1. INTRODUCTION
Progresses in ultralow-power electronics as well as
in energy conversion have made the conception of
truly autonomous wireless systems no longer
chimerical ([1], [2], [3]). Such a trend is also
encouraged by an increasing demand from industrial
companies in terms of autonomous sensor networks.
Therefore, the future of sensing is about to experience
a technological breakdown, especially for integrated
systems such as micro- and nano-scale sensors.
In order to operate, these systems harvest energy
from their immediate environment. Several sources
can be considered: solar, thermal, magnetism.
Mechanical energy through vibrations is one of the
most commonly available sources ([4], [5]). In this
field, piezoelectric elements are good candidates for
scavenging vibrational energy. These materials offer
high power densities as well as high integration
abilities. Besides, the piezoelectric conversion can be
greatly enhanced using a non-linear treatment of their
output voltage, allowing a typical gain of nine
compared to the classical approach in terms of output
power ([6], [7], [8]).
However, when dealing with integrated material,
the output voltage is generally low (a few hundred of
millivolts), which leads to problems for harvesting
energy, due to voltage gaps of discrete components
such diode bridge rectifiers. Moreover, the resonance
frequency of such systems is often quite high (a few
kilohertz). Therefore, the vibration levels are low and
little energy is harvested per cycle, but as the number
of cycles is high, the associated power is significant.
This paper proposes a new approach for energy
scavenging when the vibration level and associated
voltage are low. This technique, called SSHI-MR (for
Synchronized Switch Harvesting on Inductor with
Magnetic Rectifier), is based on a non-linear treatment
2. PRINCIPLES
In this section is exposed the underlying physical
effects that intervene when harvesting energy. The
most simply technique consists in directly connecting
the piezoelectric element to a diode bridge rectifier
connected to a smoothing capacitor as shown in Fig.
1.a. When the absolute value of the piezovoltage is less
than the rectified voltage VDC plus two times the diode
voltage gaps 2VD, then the rectifier bridge is blocked,
and the piezoelement (that has a clamped capacitance
C0) is left in open circuit. When the piezovoltage is
higher, there is an energy flow from the piezoelement
to the smoothing capacitor CS and the load RL.
When using the series SSHI technique (Fig. 1.b),
the piezoelement is left in open circuit most of the
time, and therefore the voltage varies accordingly to
the displacement. When the voltage reaches either a
maximal or a minimal value, the digital switch S1 or S2
is closed, and an energy flow appears from the
piezoelement to the storage capacitor. The energy
transfer process is then stopped half a period of the
LC0 circuit later. Such a process leads to an inversion
of the piezoelectric voltage accordingly to the voltage
reference (VDC+2VD). However, due to internal losses
in the switching circuit, this inversion is not perfect
and characterized by the inversion factor γ.
In the case of the SSHI-MR, the inductive element
is replace by a transformer (Fig. 1.c), but the
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Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)
operations are similar to those of the SSHI. The only
difference is that, due to the transformer, the inversion
is done according to the voltage reference
(VDC+2VD)/m, where m is the transformer ratio (this
expression shows that the effect of the voltage gaps.
The associated waveforms for each technique are
given in Fig. 2.
3. THEORETICAL DEVELOPMENT
This section proposes an analytical formulation of
the expected power output of the piezoelectric
generators. The current I flowing out the active
material is given by ([9]):
I = α u& − C0V&
(1)
with u and V the displacement and voltage
respectively, and α the force factor of the piezoelectric
element.
In the case of standard energy harvesting, the
output power is given by:
(a)
Pstand = f 0 ∫
1/ f0
0
VIdt = 2 f 0αVDC ∫
uM
du
u1
(2)
with f0 the vibration frequency, and uM and u1 the
displacement magnitude and the displacement when
the rectifier bridge starts conducting. The value of u1 is
obtained considering the end of the last conduction
period and the fact that the piezoelectric element is in
open-circuit (I=0), leading to the conditions:
(b)
⎧−
⎪ C0 (VDC + 2VD ) = −α uM + K
⎨
⎪⎩C0 (VDC + 2VD ) = α u1 + K
(c)
Fig. 1: Harvesting circuits: (a) Standard (b) SSHI (c)
SSHI-MR
Actuator voltage
Displacement
V
DC
(3)
With K an integration constant. Therefore
combining Eqs. (2) and (3) leads to the value of the
harvested power in the standard case:
+2V
D
Arbitrary unit
Pstand = 4 f 0VDC ⎡⎣α uM − C0 (VDC + 2VD ) ⎤⎦
(4)
When using the series SSHI, the expression of the
microgenerator output power yields:
Time
PSSHI = f 0 ∫
(a)
1/ f 0
0
Actuator voltage
Displacement
V
Arbitrary unit
M
V
DC
(V
a
DC
VIdt = −2 f 0C0VDC ∫
−Vm
VM
dV
(5)
+2V
D
With VM and Vm the absolute values of the
piezovoltage before and after the harvesting process
respectively. These values are obtained considering the
inversion process, and the open-circuit condition
between two harvesting processes, giving:
or
+2V )/m
D
γa
-V
⎧Vm + (VDC + 2VD ) = γ ⎡⎣VM − (VDC + 2VD ) ⎤⎦
⎪
⎨
α
⎪VM − Vm = 2 uM
C0
⎩
m
Time
(b)
Fig. 2: Voltage waveforms: (a) Standard (b) SSHI
and SSHI-MR
170
(6)
Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)
Therefore the combination of Eqs. (5) and (6)
leads to the value of the harvested power:
PSSHI = 4
1+ γ
f 0VDC ⎡⎣α uM − C0 (VDC + 2VD ) ⎤⎦
1− γ
energy compared to the standard and series SSHI
techniques respectively. As well, the optimal voltage
in the series SSHI and standard techniques is around
0.07 V, while with the SSHI-MR it is equal to 6.5 V,
which better suits typical supply voltage of electronics
components.
(7)
When using a transformer for rectifying, Eqs. (5)
and (6) turn to:
PMR = −2 f 0C0
VDC
m
∫
−Vm
VM
dV
⎧
VDC + 2VD
V + 2VD ⎞
⎛
= γ ⎜ VM − DC
⎟
⎪Vm +
m
m
⎪
⎝
⎠
⎨
⎪V − V = 2 α u
m
M
⎪⎩ M
C0
(8)
(9)
Fig. 3: Experimental structure
Table 1: Parameters of the experimental structure
Parameters
Vibration frequency f0
Force factor α
Diode threshold voltage
VD
Clamped capacitance C0
And therefore the output power is given by:
PMR = 4
1 + γ VDC
f0
1− γ
m
VDC + 2VD ⎞
⎛
⎜ α uM − C0
⎟
m
⎝
⎠
(10)
This expression therefore shows that the effect of
the transformer allows dividing the voltage seen by the
piezoelement by m. Therefore the losses in the diodes
are reduced, and the voltage that optimizes the energy
extraction is increased by a factor m. This last
observation also points out that the SSHI-MR is more
inclined to deliver a significant optimal output voltage.
Inversion factor γ
Transformer ratio m
Value
1kHz
8.3 mN.V-1
0.23 V
312.5 nF
0.33 for the series SSHI
0.52 for the SSHI-MR
22
Harvested Power ( µW)
Theoretical predictions
4. EXPERIMENTAL VALIDATION AND
DISCUSSION
In this Section the previously exposed theoretical
results will be compared to experimental
measurements made on a piezoelectric bimorph as
shown in Fig. 3. This structure is connected to the
electrical circuit according to the technique used
(standard, series SSHI, SSHI-MR). For the nonlinear
techniques, the digital switches are controlled by an
external DSP. The electromechanical parameters of
the structure are given in
Table 1. One can notice that the inversion factor is
better in the case of the SSHI-MR, which is explained
by the fact that this technique allows a greater increase
of the piezovoltage, leading to a decrease of the losses
in the inductor.
When the structure is excited such as the
displacement of the central point is 23 µm, the
measured output powers are given in Fig. 4. These
results clearly show the performances of the SSHIMR, that allows harvested 56 and 30 times more
400
300
Standard
Series SSHI
SSHI-MR
15
200
10
5
100
0
0
0.1
0.2
5
Rectified voltage V
0
0
DC
10
(V)
15
Harvested Power ( µW)
Experimental results
400
300
200
100
0
0
15
10
5
0
0
0.1
0.2
5
Rectified voltage V
10
(V)
15
DC
Fig. 4: Experimental results for a 23 µm vibration
magnitude
Fig. 5 depicts the evolution of the maximal output
power for several values of the displacement
magnitude. Once again, the SSHI-MR outperforms the
other techniques, allowing harvesting energy as soon
as the displacement magnitude is 1 µm (which
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Proceedings of PowerMEMS 2008+ microEMS 2008, Sendai, Japan, November 9-12, (2008)
corresponds to an open circuit voltage of 26.6 mV – or
also VD/m), while with the other techniques the opencircuit voltage needs to be at least 2VD (460 mV),
corresponding to a displacement magnitude of 17 µm.
harvesting under low vibration magnitudes has been
proposed. Based on a nonlinear processing of the
output voltage of a piezoelectric element using a
transformer, it is both theoretically and experimentally
shown that the exposed method allows scavenging
energy even under low voltage output, which is the
general case when dealing with MEMS harvesters.
Theoretical predictions
Maximal harvested
power ( µW)
Maximal harvested
power ( µW)
400
20
300
10
200
100
0
0
0
0
400
10
5
20
10
15
Displacement magnitude (µm)
Experimental results
REFERENCES
Standard
Series SSHI
SSHI-MR
20
25
20
25
[1]
Kahn J M, Katz R H, and Pister K S J 1999, Next
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[2] Krikke J 2005 Sunrise for energy harvesting
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[3] Lallart M, Guyomar D, Jayet Y, Petit L,
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press Synchronized Switch Harvesting applied to
Selfpowered Smart Systems: Piezoactive
Microgenerators for Autonomous Wireless
Receiver Sensors and Actuators A : Physical
doi : 10.1016/j.sna.2008.04.006
[4] Sodano H A, Inman D J, Park G 2004 A review
of power harvesting from vibration using
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[5] Priya S 2007 Advances in energy harvesting
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[6] Taylor G W, Burns J R, Kammann S M. Powers,
W B, Welsh T R 2001 The energy harvesting
eel: A small subsurface ocean/river power
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[7] Guyomar D, Badel A, Lefeuvre E, Richard C
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[8] Lefeuvre E, Badel A, Richard C, Petit L and
Guyomar D 2006 A comparison between several
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[9] Badel A, Lagache M, Guyomar D, Lefeuvre E,
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[10] Shen Z J, Lu J, Xu C, Ho Ngwei J, Xun G 2007
On-Chip Bondwire Inductor with Ferrite-Epoxy
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Specialists Conference - PESC 2007, 1599-1604
20
300
10
200
100
0
0
0
0
10
5
20
10
15
Displacement magnitude (µm)
Fig. 5: Experimental maximal output power as a
function of the displacement magnitude
5. IMPLEMENTATION CONSIDERATIONS
The critical component for the implementation of
the non-linear techniques, and particularly the SSHIMR, lies in the inductive element, such as the
transformer. However, Lu et al. has proposed in [10]
an original process for integrating inductors and
transformers using several parallel bondwires
embedded in magnetic ferrite drop. They thus obtained
on-chip inductors of a few hundred of nano-Henry
with a quality factor of 40.
In the case of the previously exposed experimental
set-up, the needed inductance value L and its surface S
can be derived from energetic and magnetic
considerations:
1
⎧1
2
2
⎪ C0V = LI max
2
2
⎨
⎪⎩ Bmax S = LI max
(11)
With Imax and Bmax the maximal current value and
induction field, respectively. Considering a maximal
induction Bmax=0.5 T and a peak current Imax=1A
therefore leads to a needed inductance of L=0.9 µH
that has a surface S=1.8 mm2, which is realistic for
embedded devices.
6. CONCLUSION
In this paper a new technique for energy
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