9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
Top-Down Behavioral Modeling Methodology Of A
Piezoelectric Microgenerator For Integrated Power
Harvesting Systems
Hela Boussetta (hela.boussetta@imag.fr), Skandar Basrour, Marcin Marzencki
Micro and Nano Systems Group - TIMA, 46 avenue F?lix Viallet, 38000 Grenoble, FRANCE
Abstract-In this study, we developed a top/down methodology
for behavioral and structural modeling of multi-domain
microsystems. Then, we validated this methodology through a
study case: a piezoelectric microgenerator. We also proved the
effectiveness of VHDL-AMS language not only for modeling in
behavioral and structural levels but also in writing physical
models that can predict the experimental results. Finally, we
validated these models by presenting and discussing
simulations results.
I. INTRODUCTION AND MOTIVATION
The importance of wireless sensor networks is highlighted
by the increasing number of applications, including disaster
relief applications, intelligent building, facility management,
environment control, machine monitoring and preventive
maintenance.... Realizing such wireless sensor networks is a
crucial step toward a deeply penetrating ambient intelligent
concept. The power supply is a crucial system component
since once the energy supply is exhausted; the node fails
(Ref. [2]). To ensure truly long-lasting nodes, limited energy
storage is unacceptable. Rather, Self Powered Micro
Systems (SPMS) with their extended autonomy represent a
promising answer. The challenge while designing such
systems is to deal with the diversity of subsystems
containing complex MEMS and different physical domains
(mechanical and electrical). Since it is not possible to
comprehend such complex systems in their entirety, we need
to find methods of dealing with this complexity. In this
work, we adopted a top/down methodology for behavioral
and structural modeling of multi-domain microsystems.
Then, we verified the efficiency of such a methodology by
modeling and simulating an integrated power harvesting
circuit.
II. MODELING MULTI-DOMAINS SYSTEMS
Several definitions of a model can be found in the
literature. One possible definition is the following: ?A model
represents that information which is relevant and abstracts
away irrelevant detail? (Ref. [3]). A direct consequence of
this definition is that a system can be represented by several
models depending on aspects the designer focus on. Usually,
three aspects of modeling are considered: function, structure
and geometry. The most abstract model considered in this
work is the functional level where the system is described by
is function but information about the implementation of this
function is not considered. The structural model describes a
system as a composition of subsystems connected together.
Details about the geometrical and physical parameters of the
system are only considered in the physical layer.
The chosen modeling language in this work is VHDL-
AMS. Actually, this language offers facilities for describing
structure and function of systems in physical domains.
III. PIEZOELECTRIC MICROGENERATOR MODELING
The purpose of this section is to establish a generic
library of piezoelectric microgenerators in different
abstraction levels. Depending on the wanted compromise
time/precision, the user can make its choice.
A. A functional transducer model
The simplest and probably the most abstract model of a
transducer is an equivalent electrical circuit composed of an
ideal sinusoidal current source, in parallel with a capacitor
Cp. This model represents electrical characteristics of the
microgenerator. The current amplitude ip depends of the
amount of mechanical vibrations but still relatively
insensitive to external charge. However, it is not suitable to
our study case since the coupling effect is considerable.
B. A structural piezoelectric microgenerator model
.
Fig. 1. Structural bimorph piezoelectric microgenerator model
The structural model described in Fig. 11. is developed by
Ref. [4]. As shown in the left side of Fig. 11., the structure is
a two layer bender mounted as a cantilever beam. The
equivalent inductance represents the generator inertia. The
mechanical stiffness is represented by the equivalent
capacitance CK and ?in represents the stress resulting of
input vibrations. The transformation ratio n represents the
coupling effect, Cb is the piezoelectricity capacitance and
v(t) is the output voltage. The VHDL-AMS model is simple,
doesn?t require a lot of time to be written since it?s obtained
9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
by a simple connection of basic components (current source,
inductor, resistance, capacitor and transformer). However,
physical aspects of the system are not considered.
The same model can be described by analytical equations
obtained from constitutive piezoelectric and circuit
equations. The comparison between these two models is
done in section IV.
C. Physical piezoelectric microgenerator model
? Piezoelectric microgenerator 1D model
The target of this simple model is to validate our approach
for transduction modeling. The whole system is subjected to
mechanical vibrations y(t).
Fig. 2. Piezoelectric transducer model
The system is represented in Fig. 2. where:
? w(t) is the displacement of the seismic mass M.
? The stiffness K is calculated from the material
stiffness c33 and device dimensions.
Considering that this coupled electromechanical structure
can be modeled as a damped harmonic oscillator, the
analytical model is directly deduced from the Newton?s
second law of motion and the constitutive piezoelectricity
equations.
The deduced differential equations are then correctly
incorporated into a VHDL-AMS architecture.
This model was kept intentionally simple to focus on the
functionality of the piezoelectric transduction. It is simple
enough to have fast simulations as will be proven in section
5. This model is perfect for a first validation but it is neither
accurate nor predictive.
? Piezoelectric microgenerator 3D model
The micropower generator is based on the structure
illustrated in Fig. 3. It is based on a cantilever beam of
length Lp, width Bp and the thickness HP on which a thin
piezoelectric layer is deposited. A big seismic mass of length
LM, width BM and thickness HM is attached at the end of
the beam. This seismic mass is used to decrease the
resonance frequency and increase the harvested energy. An
applied acceleration induces the displacement of the mass
and the deformation of the beam. Therefore, the beam apply
constraints on the piezoelectric layer whose generate electric
charges. Thanks to the proposed dimensions of this mass, we
can tune the resonant frequency of the generator.
Fig. 3. Schematic of the structure modeled for the physical model
Several important considerations are taken into account
especially the important size of the mass compared to the
one of the beam, the rigidity of the mass and its rotational
inertia. It is also important to consider that the acceleration is
applied to the mass and not to the end of the beam. The
impact of the electrical and mechanical properties of
materials was introduced in the expression of the effective
parameters deduced from boundary conditions. Additional
information about the description of the model can be found
in reference Ref. [1].
IV. SIMULATIONS RESULTS
A. Comparison between analytical and structural model
results
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-1
0
1
2
3
0 50m 100m 150m 200m
U
[V
]
TIME [S]
Fig. 4. comparison between structural and analytical model of bimorph
piezoelectric model
Fig. 4. shows a comparison between analytical and
structural models. The two curves are similar. The difference
between the two models become from the abstraction done
in the analytical model. In fact, the analytical model takes
into account only the steady state while structural model
consider both transient and steady state.
B. Impact of physical properties study
First, we have studied the impact of the piezoelectric
properties of the material used on the model by keeping the
same dimensions of both devices and just changing the
piezoelectric material layer. The used piezoelectric
Analytical model
Structural model
9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
materials can be either Aluminium Nitrite (AlN) or Lead
Zirconium Titanate (PZT) thin layers.
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-10
0
500.0 1.0k 1.5k 2.0k 2.5k
V [
d
B
]
FREQ [Hz]
Fig. 5. Comparison between the piezoelectric microgenerator model based
on PZT material and the one based on AlN material keeping the same mass
dimensions
To do so, we just had to substitute the generic parameters
responsible of physical properties of the used material (PZT)
in the entity declaration of the previous of the VHDL-AMS
model by AlN ones. The used stimulus is 1g acceleration.
As shown in For the AlN material, we have noted lower
amplitude and higher resonant frequency. This result was
expected because of the poor coupling coefficient of AlN
material compared to PZT one.
However, microfabrication process in case of AlN by
sputtering techniques is easier than for PZT ones. The
deposition of AlN is relatively simple, compatible with
CMOS process and does not require post process
polarization. For that reasons, we decided to investigate
structures based on this material.
We have changed the dimensions of the structure and
analyzed the output voltage produced. We used twice the
dimensions for the mass (800?m by 800?m) with a SOI
wafer (525 ?m thick). For acceleration stimuli of 1g
amplitude, we obtained the output voltage versus time
reported in Fig. 6. We can successfully harvest 1.8V across
the electrodes in open circuit.
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-1.5
-1
-0.5
0
0.5
1
1.5
2
0.2 0.2005 0.201 0.2015 0.202 0.2025 0.203
U[V
]
]
TIME[s]
Fig. 6. Output voltage at resonance at micropower generator (with ALN
as piezoelectric layer and modified dimensions of the mass) versus time
V. DISCUSSION
The various models of the piezoelectric microgenerator
developed in this paper demonstrate clearly that the choice
of the degree of abstraction is closely related to the wanted
performance: behavior virtual IP for a functional verification
early in the design process which is very useful for
simulation of complex and big designs or a predictive model
comparable to experimental results.
Since all models are generic interfaces lists, several
analysis possibilities can be performed just by changing
geometric and physical parameters. This kind of tests is very
important in the design process since it offers to the designer
the opportunity to optimize his model early in the design
process. In section C, we studied the impact of geometric
properties of the device. We demonstrate by changing the
dimensions of the structure and the piezoelectric material,
we can harvest a great voltage with easier micro fabrication
process. The user still has the possibility to experiment other
materials and other geometric dimensions in order to
optimize his design without dealing with complicated details
of the model. Finally, we had performed global simulations
using the MEMS model connected to an electrical circuit
based on ultra low threshold voltage diodes used to boost
and rectify the weak amplitudes AC signals delivered by
such generators (voltages often inferior to 200 mV) (Ref.
[5]).
VI. CONCLUSION AND FUTURE WORK
The reusable aspect of our models offers to designers the
possibility to select and use their suitable configurations
without having to understand the details of blocks just by
changing some parameters. Indeed, the piezoelectric
generator model remains valid for other materials and the
voltage multiplier circuit is extensible to other technologies.
We also proved the effectiveness of VHDL-AMS for
modeling behavioral, structural and physical level that can
predict the experimental results. Thus, because the models
respect energy conservation laws, we had performed global
simulations using the MEMS model connected to an
electrical circuit used to manage power delivered by the
microgenerator. Further work must be done to take into
account the damping effect not considered in this work; only
viscous damping was considered.
ACKNOWLEDGMENT
The ? Region Rh?nes Alpes? and the University Agency
for Francophony (AUF) are gratefully acknowledged for
their financial support.
REFERENCES
[1] M. Marzencki, S. Basrour Enhanced Models For Power Output
Prediction from Resonant Piezoelectric Micro Power Generators,
Eurosensors XX, G?teborg, Sweden, September 17-20, 2006 ISBN
1-54244-0842-3/07.
[2] H. Karl, A.Willig, Protocols and Architectures for Wireless Sensor
Networks, John Wiley & Sons, ISBN 0-470-09510-5.
[3] P. J. Ashenden, The System Designer's Guide To Vhdlams, 2003,
Elvesier, ISBN 1-55860-749-8.
[4] S. Roundy, P. S. Wright, Energy Scavenging for Wireless Sensor
Networks with Special Focus in Vibrations, Kluwer Academic
Publishers, 2004, I-4020-7663-0
PZT material
AlN material
9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
[5] H. Boussetta, M. Marzencki, Y. Ammar and S.Basrour, Multilevel
Modeling Of Integrated Power Harvesting System Using Vhdl-Ams
And Spice, BMAS2007 IEEE conf, ISBN 978-1-4244-1567-0.
BIBLIOGRAPHY
Hela BOUSSETTA was born in 1980
in Tunis, Tunisia. She is an
electronical engineer and received a
master degree in NTSID (New
Technologies Of Computer Systems
Dedicated Technologies) in 2004 from
the ENIS (Tunisia). The master
internship was done at
STMicroelectronics-Tunis. During her
internship, Ms Boussetta participates
in developing STBus Transaction Level Models (TLM) using
SystemC2.0. Currently, Ms Boussetta is being PhD student at
TIMA Laboratory-Grenoble, where her researches focus on
multi-domain modeling using VHDL-AMS and SPICE.