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.Comment: Submitted on behalf of EDA Publishing Association
  (http://irevues.inist.fr/handle/2042/16838

Basrour, S.

Boussetta, Hela

Marzencki, M.

English

arXiv

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-Revues

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 Félix 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 σin 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 
-3
-2
-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.  
 
-70 
-60 
-50 
-40 
-30 
-20 
-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 (800µm by 800µm) with a SOI 
wafer (525 µm 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. 
-2
-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 Rhônes 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, Göteborg, 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. 


Top-Down Behavioral Modeling Methodology of a Piezoelectric Microgenerator For Integrated Power Harvesting Systems

Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838)International audienceIn 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

Top-Down Behavioral Modeling Methodology of a Piezoelectric Microgenerator For Integrated Power Harvesting Systems

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