Page 123 - An Introduction to Microelectromechanical Systems Engineering

102 MEM Structures and Systems in Industrial and Automotive Applications

electrode for the two capacitors. The inertial mass consists of the comb fingers and
the central backbone element to which these suspended fingers are attached. Under
no externally applied acceleration, the two capacitances are identical. The output sig-
nal, proportional to the difference in capacitance, is null. An applied acceleration dis-
places the suspended structure, resulting in an imbalance in the capacitive half bridge.
The differential structure is such that one capacitance increases, and the other
decreases. The overall capacitance is small, typically on the order of 100 fF (1 fF =
10 −15 F). For the ADXL105 (programmable at either ±1G or ±5G), the change in
capacitance in response to 1G is minute, about 100 aF (1 aF = 10 −18 F). This is equiva-
lent to only 625 electrons at an applied bias of one volt and thus must be measured
using on-chip integrated electronics to greatly reduce the impact of parasitic capaci-
tance and noise sources, which would be present with off-chip wiring. The basic
read-out circuitry consists of a small-amplitude, two-phase oscillator driving both
ends of the capacitive half bridge in opposite phases at a frequency of 1 MHz. A
capacitance imbalance gives rise to a voltage in the middle node. The signal is then
demodulated and amplified. The 1-MHz excitation frequency is sufficiently higher
than the mechanical resonant frequency that it produces no actuation force on the
plates of the capacitors, provided its dc (average) value is null. The maximum accel-
eration rating for the ADXL family varies from ±1G (ADXL 105) up to ±100G
(ADXL 190). The dynamic range is limited to about 60 dB over the operational
bandwidth (typically, 1 to 6 kHz). The small change in capacitance and the relatively
small mass combine to give a noise floor that is relatively large when compared to
similarly rated bulk micromachined or piezoelectric accelerometers. For the
ADXL105, the mass is approximately 0.3 µg, and the corresponding noise floor,
dominated by Brownian mechanical noise, is 225 µG Hz. By contrast, the mass for
a bulk-micromachined sensor can easily exceed 100 µg.
Applying a large-amplitude voltage at low frequency—below the natural fre-
quency of the sensor—between the two plates of a capacitor gives rise to an electro-
static force that tends to pull the two plates together. This effect enables the
application of feedback to the inertial mass: Every time the acceleration pulls the set
of suspended fingers away from one of the anchored sets, a voltage significantly
larger in amplitude than the sense voltage, but lower in frequency, is applied to the
same set of plates, pulling them together and effectively counterbalancing the
action of the external acceleration. This feedback voltage is appropriately propor-
tioned to the measured capacitive imbalance in order to maintain the suspended
fingers in their initial position, in a pseudostationary state. This electrostatic actua-
tion, also called force balancing, is a form of closed-loop feedback. It minimizes
displacement and greatly improves output linearity (because the center element
never quite moves by more than a few nanometers). The sense and actuation plates
may be the same, provided the two frequency signals (sense and actuation) do not
interfere with each other.
A significant advantage to surface micromachining is the ease of integrating two
single-axis accelerometers on the same die to form a dual-axis accelerometer, so-
called two-axes. In a very simple configuration, the two accelerometers are orthogo-
nal to each other. However, the ADXL200 series of dual-axis sensors employs a
more sophisticated suspension spring mechanism, where a single inertial mass is
shared by both accelerometers.