IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 58, . 7, JULY 2011 1460
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2011 IEEE
Relationship Between Acceleration and
the Scattering Matrix in a SAW-MEMS
Accelerometer
Jaime Octavio Guerra-Pulido and Pablo Roberto Pérez-Alcázar
Abstract—Phase velocity of a surface acoustic wave (SAW)
varies when the electric field associated with the wave inter-
acts with a conductive material located above the propagation
plane. In this paper, we propose a general method to approxi-
mate the scattering matrix when the conductive structure has
a specific geometry. This structure has reflective properties
of SAW. As an example, we considered a previously reported
SAW-MEMS microaccelerometer which mainly consists of a
slotted beam. By applying this method, we obtained the rela-
tionship between acceleration and the reflection and transmis-
sion coefficients. The dynamic of the slotted beam was studied
using the finite element method (FEM). It was observed that
relatively small variations in the size of the microstructure
could cause significant changes in the reflection and transmis-
sion coefficients. We also show that the slotted beam acts as
an acoustic wave bandpass filter, and its response is similar to
that of reflective gratings, but with linear phase.
I. I
S
the 1960s, several SAW devices have been studied
for their interesting properties. For example, the wave
phase velocity of a SAW is about 10
5
times smaller than
electromagnetic wave phase velocity, which allows the
fabrication of smaller devices than those operating with
electromagnetic waves of the same frequency. Moreover,
SAWs have some advantages over BAWs: the propagation
properties of the SAW, such as velocity, can be modified
if the conditions around the propagation path change [1].
On the other hand, it has also been shown how SAW de-
vices could be used to measure various physical variables
such as pressure, acceleration, electric potential, and the
presence of chemical gases [2].
There are two operation modes for such SAW sensors.
The first mode is a feedback configuration and the second
mode is a wireless configuration. The main advantage of
the latter is that the sensors are passive, thus they do
not need a power source present onsite. Some researchers,
such as Li et al. [3], Reindl et al. [4], Jose et al. [5], and Fu
et al. [6], have sought ways to develop devices with proper-
ties that expand the possible applications and enhance the
versatility of SAW sensor technology.
To increase the versatility of SAW sensors, and consid-
ering the tremendous growth of micro electromechanical
systems (MEMS), several researchers integrated these two
technologies [7]–[9]. The combination of these technolo-
gies may provide some advantages over commonly used
technologies [9].
Whereas Li et al. [3], Reindl et al. [4], and Jose et al.
[5] took advantage of the change in characteristics of
piezoelectric materials, caused by changes in the vari-
ables of interest (pressure or temperature) or variations
in the mechanical conditions at the boundary; Varadan
et al. [9] used one conductive microstructure, which was
composed of a slotted beam, located on the piezoelectric
surface as an inertial mass, modifying the phase velocity
of the propagating wave. This microstructure is designed
to achieve the reflection of the acoustic wave to the inter-
digital transducer (IDT). The reflections of the acoustic
signal are produced by the acoustic impedance changes
when the wave propagates through the device. The acous-
tic impedance varies because of phase velocity changes
along the propagation media. In this case, the variations
in the wave phase velocity are due to the interaction be-
tween the electric field associated with the acoustic wave
and the microstructure. This device is a clear example
of the combination of the two technologies. Throughout
this work, we propose a model to obtain the scattering
matrix and to determine the mechanisms by which SAWs
propagate when they interact with a reflective structure.
This model considers the position of the microstructure
in space and then calculates the SAW phase velocities in
each acoustic region. These acoustic regions are defined by
the slotted beam, which shall be explained in detail later.
Once the velocities have been determined, it is possible to
calculate the reflection and transmission coefficients and,
therefore, the scattering matrix. Using electrical circuit
theory, it is possible to transform the scattering matrix
into a transmission matrix [10], [11]. Once a matrix model
of the IDTs is known, we can use the transmission matrix
to determine the electrical response of this device. A com-
mon matrix model used to simulate the IDT response is
the P matrix and the coupling of modes (COM) theory
[12]. Much research has been done on acoustic wave sen-
sors and MEMS, and many sensors have been proposed
for each of these technologies, but the way that a micro-
mechanical structure acts as a SAW reflector has not been
studied in great detail.
In summary, the goal of this work is to elucidate the
relationship between acceleration and reflection and trans-
Manuscript received May 25, 2010; accepted April 21, 2011. This work
was supported by grants of DGAPA-UNAM (IN17510-3). J. O. Guerra-
Pulido is grateful for the economic support of CEP-UNAM.
The authors are with UNAM (National Autonomous University of
Mexico), Faculty of Engineering, Electronics Department, Ciudad Uni-
versitaria, D. F. México, México (e-mail: pperezalcazar@fi-b.unam.mx).
Digital Object Identifier 10.1109/TUFFC.2011.1965