Page 187 - MEMS Mechanical Sensors

176 Inertial Sensors

k
ω =
n
m
and the sensitivity (for an open sensor) by

m
S =
k

As an accelerometer can typically be used at a frequency below its resonant fre-
quency, an important design trade-off becomes apparent here since sensitivity and
resonant frequency increase and decrease with m/k, respectively. This trade-off can
be partly overcome by including the sensing element in a closed loop, force-feedback
control system, as will be described later.

For the dynamic performance of an accelerometer, the damping factor is crucial.
For maximum bandwidth the sensing element should be critically damped; it can
be shown that for b =2mω this is the case. It should be noted here that in
n
micromachined accelerometers the damping originates from the movement of the
proof mass in a viscous medium. Depending on the mechanical design, however, the
damping coefficient cannot be assumed to be constant; rather, it increases with the
deflection of the proof mass and also with the frequency of movement of the proof
mass—this phenomenon is called squeeze film damping. This is a complex fluid
dynamic problem and goes beyond of the scope of this book. For further reading on
this topic, the interested reader is referred to the literature [3–6].
A common factor for all micromachined accelerometers is that the displacement
of the proof mass has to be measured by a position-measuring interface circuit, and
it is then converted into an electrical signal. Many types of sensing mechanisms have
been reported, such as capacitive, piezoresistive, piezoelectric, optical, and tunneling
current. Each of these has distinct advantages and drawbacks (as described in
Chapter 5). The first three sensing mechanisms are the most commonly used. The
characteristic and performance of any accelerometer is greatly influenced by the
position measurement interface, and the main requirements are low noise, high line-
arity, good dynamic response, and low power consumption. Ideally, the interface
circuit should be represented by an ideal gain block, relating the displacement of the
proof mass to an electrical signal.

8.2.1.2 Open Loop Accelerometer

If the electrical output signal of the position measurement interface circuit is directly
used as the output signal of the accelerometer, this is called an open loop acceler-
ometer, as conceptually shown in Figure 8.2.
Most commercial micromachined accelerometers are open loop in that they are
the most simple devices possible and are thus low cost. The dynamics of the
mechanical sensing element are mainly to determine the characteristics of the sensor.
This can be problematic as the mass and spring constant are usually subject to con-
siderable manufacturing tolerances (depending on the fabrication process, this could
be up to ±20%). Furthermore, second order effects for larger proof mass deflection