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.
Highlights
Embedding a micromachined sensing element in a closed loop, force feedback system is a technique commonly used to realise high performance MEMS sensors due to the many advantages attainable in terms of better linearity, increased dynamic range and bandwidth, and reduced parameter sensitivity to fabrication tolerances
Several research groups have designed and implemented electro-mechanical ΣΔM (EMΣΔM) in which the sensing element is cascaded with an electronic filter comprising several integrators; this has been successfully applied to MEMS accelerometers [5,6,7,8], and to control the sense mode of MEMS gyroscopes [9,10,11,12] resulting in far superior noise shaping abilities
In this work we present a novel design methodology for EMΣΔM based on genetic algorithms (GA)
Summary
Embedding a micromachined sensing element in a closed loop, force feedback system is a technique commonly used to realise high performance MEMS (micro-electro-mechanical systems) sensors due to the many advantages attainable in terms of better linearity, increased dynamic range and bandwidth, and reduced parameter sensitivity to fabrication tolerances. Genetic algorithms are based on the mechanics of natural selection and genetics combining the fittest individuals in the population in order to search for the best solution [18]. Initial population consisting of a number of individuals (parameter sets) has been randomly chosen, based on the fitness function the fittest individuals are selected and combined to produce a new offspring. Since the result of the optimisation is a large number of optimal solutions the design procedure subsequently carries out a robustness analysis based on statistical simulations to ensure stability of the design in the presence of fabrication tolerances, which can be substantial for micromachined sensing elements. This paper is organised as follows: Section 2 describes the developed GA process in general; Section 3 gives an example for the design of a 5th order EMΣΔM MEMS accelerometer; Section 4 gives a second example of a band-pass EMΣΔM for a MEMS gyroscope; in Section 5 the design approach is discussed and in Section 6 conclusions are drawn
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