Page 188 - MEMS Mechanical Sensors

8.2 Micromachined Accelerometer 177

Proof mass
displacement Output signal

Position
measurement circuit
Micromachined
sensing element
Figure 8.2 Open loop accelerometer.

introduce nonlinear effects; squeeze film damping was mentioned earlier. Another
effect is that any silicon suspension system will have nonlinear behavior, such as a
spring stiffening effect, for larger deflections, or cross-axes sensitivity. Nevertheless,
for most automotive and other low-cost applications the achievable performance is
still acceptable.

8.2.1.3 Closed Loop Accelerometer
The output signal of the position measurement circuit can be used, together with a
suitable controller, to steer an actuation mechanism that forces the proof mass back
to its rest position. The electrical signal proportional to this feedback force provides
a measure of the input acceleration. This is usually referred to as a closed loop or
force balanced accelerometer. This approach has several advantages:

1. The deflection of the proof mass is reduced considerably; hence, nonlinear
effects from squeeze film damping and the mechanical suspension system are
reduced considerably.
2. The sensitivity is now mainly determined by the control system; hence, the
trade-off between the sensitivity and bandwidth can be overcome.
3. The dynamics of the sensor can be tailored to the application by choosing a
suitable controller (i.e., the bandwidth, dynamic range, and sensitivity can
be increased compared with the open loop case).

The drawback of a closed loop accelerometer is mainly the added complexity in
interface and control electronics.
There is a range of possible actuation mechanisms to keep the proof mass at its
rest position, such as electrostatic, magnetic, and thermal. Electrostatic forces are by
far the most commonly used type since for small gap sizes these forces are relatively
large, allowing typical supply voltages of between 5V and 15V. If capacitive position
sensing is used, the same electrodes can be used for sensing and actuation. Care has
to be taken, however, to ensure that the sense and actuation signal do not interact.
One major problem of electrostatic forces is that they are always attractive and non-
linear because they are proportional to the voltage squared and inversely to the gap
squared. Consequently, it is difficult to produce a linear, negative feedback signal.

Analog Force-Feedback Consider the simple sensing element in Figure 8.3: a proof
mass between two electrodes forms an upper and lower capacitor.