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An
accelerometer
is a device that measures acceleration, or the rate of change of
velocity with respect to time. Accelerometers come in various forms and
sizes, but cutting edge micromachining technology advancements in recent
years have allowed them to be built in microchip form. Today, there are
a multitude of semiconductor companies that manufacture accelerometer
IC's that not only measure linear acceleration, but other parameters as
well such as angular speed, vibrations, shock, and even tilt positions.
One of the
pioneers in fabricating accelerometers in integrated circuit form is
Analog Devices, which produces the ADXL50 accelerometer. The ADXL50
provides an output voltage that varies
proportionally with the amount of
acceleration experienced along its sensitive axis. It has an input range
of -50g to +50g, with a sensitivity of approximately 1 V per 50 g.
Thus, a 50-g acceleration would either decrease or increase the output
at 0 g by 1V, depending on the direction of the acceleration. Since the
ADXL50 is calibrated to output 1.8V when there is no acceleration, the
output would either 0.8 V or 2.8 V at 50 g, again depending on the
acceleration's direction.
The ADXL50 is
an example of a capacitive accelerometer, i.e., it measures capacitances
in order to measure the acceleration. This accelerometer applies two
basic principles of physics in its operation. The first one is Hooke's
Law, which states that a spring, when stretched, will exert a restoring
force F that's proportional to its increase in length x,
i.e., F = kx. The second one is Newton's Second Law, which states that
the force F exerted by a body is equal to its mass m
multiplied by its acceleration a, i.e., F = mA.
Combining
these two equations, A = kx/m, which means that a body with mass m will
stretch a spring (whose elongation property is characterized by k) by a
distance of x if its acceleration is A. The ADXL50 has a mass-spring
system consisting of a bar of silicon (which is the mass) that is held
by four tethers (one at each corner), as shown in Figure 1. The four
tethers, the feet of which are anchored, compose the spring system. When
the mass is subjected to an acceleration, it moves with respect to the
anchored feet of the tethers, causing the tethers to 'stretch' like a
spring. The greater the acceleration experienced, the larger is the
displacement. This system therefore translates the acceleration into a
displacement, allowing the acceleration to be measured by measuring the
displacement.
Figure 1.
A Differential Capacitive Accelerometer Mass-Spring
System at
rest (left) and when subjected to acceleration (right)
The
displacement of the bar is measured in terms of the difference between
two capacitances formed by the accelerometer's structure in Figure 1.
The two fixed capacitor plates form a capacitor each with the inner
capacitor plate that's attached to the moving mass, i.e., they both
share a common capacitor plate (the one that moves with the mass). The
value of the capacitance of each capacitor changes with the movement of
the inner capacitor. Since the change in capacitance of one capacitor
is opposite to that of the other capacitor, even the direction of the
acceleration can be determined from the changes.
The amounts
and rates of change of these two capacitances are then translated by
on-chip signal conditioning circuits into an output voltage that
indicates the strength and direction of the acceleration. The on-chip
signal conditioning circuitry may consist of
amplifiers, filters, oscillators, demodulators, and even self-test
circuitry.
Note
that velocity is simply the integral of acceleration, and displacement
is simply the integral of velocity. As such, information about the
velocity and displacement of the body may also be known by performing
the necessary integration steps on the acceleration information obtained
from the accelerometer.
Performance
parameters for accelerometers include: 1) the Zero g Offset, or the
voltage output at 0 g; 2) the Sensitivity, or the output voltage per g;
3) the Noise, which determines the minimum resolution of the sensor; 4)
the Temperature Range; 5) the Bias Drift with Temperature, or how the 0
g output changes with temperature; 6) the Sensitivity Drift with
Temperature, or how the 0 g output changes with temperature; 7) the
Bandwidth; and 8) the Power Consumption.
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