Genetic Algorithm for the Design of Electro-Mechanical Sigma Delta Modulator MEMS Sensors

Abstract

This paper describes a novel design methodology using non-linear models for complex closed loop electro-mechanical sigma-delta modulators (EMΣΔM) that is based on genetic algorithms and statistical variation analysis. The proposed methodology is capable of quickly and efficiently designing high performance, high order, closed loop, near-optimal systems that are robust to sensor fabrication tolerances and electronic component variation. The use of full non-linear system models allows significant higher order non-ideal effects to be taken into account, improving accuracy and confidence in the results. To demonstrate the effectiveness of the approach, two design examples are presented including a 5th order low-pass EMΣΔM for a MEMS accelerometer, and a 6th order band-pass EMΣΔM for the sense mode of a MEMS gyroscope. Each example was designed using the system in less than one day, with very little manual intervention. The strength of the approach is verified by SNR performances of 109.2 dB and 92.4 dB for the low-pass and band-pass system respectively, coupled with excellent immunities to fabrication tolerances and parameter mismatch.

Design optimization of RF-MEMS switch considering thermally induced residual stress and process uncertainties

“…Traditionally, an optimized geometrical MEMS configuration is achieved by developing analytical design models, FEM modeling, genetic algorithms, artificial neural networks and topology optimization [13][14][15][16][17][18]. For the robust design optimization, Shalaby et al have proposed strength Pareto evolutionary algorithm for RF MEMS cantilever switches [19].…”

Comparisons of Feed-Forward and Multiple-Feedback Sigma-Delta Modulators for MEMS Accelerometers

“…Traditionally, an EMSDM accelerometer system consists of the MEMS capacitive sensing element and the electrical interface circuit [9]. The sensing element, which is modeled as a mass-damping-spring system with a second order transfer function, converts acceleration into the displacement of the proof mass, which is reflected by the change of differential capacitances.…”

Fully differential electro-mechanical phase locked loop sensor circuit

“…This causes distortion of the signal, which can be seen in the simulations as a harmonic A selection of simulation results is presented which illustrate the performance and properties of the EMPLL. All simulations were conducted using models in Matlab and the system parameters were optimized using the Cheetah GA system [5]. In order to provide a comparison to existing methods, a 5th order Σ∆ based modulator system was analysed as a representative Table 1 lists the sensor parameter used for the simulation of both the EMΣ∆ and the EMPLL, Table 2 lists the system values used for the simulation of the EMΣ∆ and Table 3 …”

“…Even if the parameters are designed to be more robust to variation, as suggested in [5], this involves a complex and time consuming optimization process. This research therefore provides insight into the possibility of using a Phase Locked Loop (PLL) sensing circuit rather than Σ∆ based modulator, to establish whether there would be any potential advantages which would alleviate the sensitivity and difficulty in obtaining effective and robust design parameters.…”

“…In spite of these efforts, it has become necessary to provide advanced optimization tools [5] to establish the correct Σ∆ design parameters to ensure stability.…”