Page 401 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

APPLICATIONS 381

As technology matures, the market for low-cost angular sensors will extend into high
volume of micromachined sensors for complete automotive pitch and roll control, which
is the final step toward realisation of integrated chassis control (Eddy and Soarks 1998).
This includes sensing the steering, suspension, power train and breaking systems for real-
time vehicle control. All these systems require an application-specific low-cost sensor
and actuator. Future air bag systems will be equipped with a low-g accelerometer and a
gyroscope. Low-cost and low-g accelerometers are already in use, whereas gyroscopes that
are compatible with the automotive industries' requirements, are not yet on the market.
The construction of the gyroscope is based on integration of a SAW resonator (Bell
and Li 1976; Staples 1974) and a SAW sensor (White 1985; Ballantine et al 1997)
that operates primarily in the Rayleigh mode. The Rayleigh wave is a SAW that has its
energy concentrated within one wavelength of the substrate surface (Achenbach 1973).
The displacement of particles near the surface, due to the Rayleigh wave, has out-of-
surface motion that traces an elliptical path (Slobodnik 1976). The Rayleigh wave can
be generated at the surface of a piezoelectric material by applying a voltage to an IDT
patterned on the substrate (White and Voltmer 1965). Lao (1980) derived theoretically the
dependence of SAW velocity on the rotation rate of the wave-propagating medium and
it is established that, for an isotropic medium, the rotation rate is a function of Poisson's
ratio. Kurosowa et al. (1998) proposed a SAW gyroscope sensor based on an equivalent
circuit simulation. He concluded that the angular velocity could not be detected because
of the mismatch of resonant frequencies. Whereas Varadan et al. (2000a,b) presented the
design, proof of concept through fabrication, and performance evaluation of a SAW gyro-
scope using a two-port resonator and a sensor. In this section, we present the equivalent
circuit model analysis and experimental evaluation of a SAW gyroscope (Varadan et al.
2000b). The SAW resonator is designed and optimised using the coupled-mode theory.
The gyroscope is optimised using a cross-field circuit model for numerical simulation.
This gyroscope has the added capability that it can be used as a wireless gyroscope that
can be easily integrated onto a SAW accelerometer (Subramanian et al. 1997).

13.4.5.1 Principle of SAW-based gyroscope

Any mechanical gyroscope must have a stable reference vibrating motion (V) of a mass
(m) such that when subjected to a rotation, the angular rotation (£2) perpendicular to the
reference motion would cause Coriolis forces at the frequency of the reference motion.
The strength of the Coriolis force F is a measure of the rotation rate and is given by

F = 2mV X& (13.62)

It is well known that in a standing Rayleigh surface wave, the particle vibration will
be perpendicular to the surface. This particle vibration can be cleverly utilised for the
creation of a reference vibratory motion for the gyroscope.
The concept of utilising a SAW for gyroscopic motion is illustrated in Figure 13.19.
It consists of IDTs, reflectors, and a metallic dot array within the cavity, which are
fabricated through microfabrication techniques on the surface of a piezoelectric substrate.
The resonator IDTs create a SAW that propagates back and forth between the reflectors
and forms a standing wave pattern within the cavity because of the collective reflection