Mixed Signal Model -
Micro Accelerometer with Digital Feedback Control
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