Mixed
Signal Model - Micro Accelerometer
with Digital Feedback Control
Click
here to execute the VisualSim model
and view analysis results
Introduction
Micro accelerometers are MEMS devices
that use beams, gaps, and electrostatics
to measure acceleration. Beams and
anchors, separating by gaps, form
parallel plate capacitors. When the
device is accelerated in the sensing
direction, the displacement of the
beams causes the change of the gap
sizes, which further causes the change
of the capacitance. By measuring the
change of capacitance (e.g. using
the Wheatstone capacitor bridge),
the acceleration can be obtained accurately.
A schematic diagram is shown below:
Feedback
can be applied to the beams by charging
the capacitors. Using feedback can reduce
the sensitivity to process variations,
eliminate mechanical resonances, and
increase sensor bandwidth, selectivity
and dynamic range. The feedback effectively
reduces the mechanical excursion of
the beams.
Sigma-delta
modulation[1], also called the pulse
density modulation or the bang-bang
control, is a digital feedback technique.
It gets the A/D conversion functionality
for free, since the same mechanism that
is used to generate the feedback control
can be used to measure the capacitance.
The central part of the digital feedback
is an one bit quantizer.
Implementation:
We implemented the system as Mark Alan
Lemkin designed in [2]. As shown in
the figure below, a second order CT
subsystem is used to model the beam.
The voltage on the beam-gap capacitor
is sampled every T seconds (much faster
than the required output of the digital
signal), then filtered by a lead compensator
(an FIR filter), and fed to an one-bit
quantizer. The outputs of the quantizer
are converted to force and fed back
to the beams. The outputs are also counted
and averaged every NT seconds to produce
the digital output. In our example,
the external acceleration is a sine
wave.
Simulation
To run the simulation, click Go in the
above applet.
Results
If the model runs correctly, the result
should look like:
Continuous time part:
Discrete
time part:
References
[1] James C. Candy, "A Use of Limit
Cycle Oscillations to Obtain Robust
Analog-to-Digital Converters",
IEEE Trans. on Communications, Vol.
COM-22, No. 3, March 1974, pp298-305
[2] Mark A. Lemkin, "Micro Accelerometer
Design with Digital Feedback Control",
doctoral dissertation, University of
California, Berkeley, Fall 1997 Copyright
2004 © Mirabilis Design Inc. and
University of California Berkeley. All
Rights Reserved.
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