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