Quadrature error cancellation for micro-machined vibratory gyroscope embedded in high order electromechanical Sigma Delta modulator

Abstract

Vibratory micro-machined gyroscopes utilize Coriolis force to detect the rotation rate. Recently it has been proved that embedding the gyroscope in an electromechanical ΣΔ modulator (EMSDM), results in increased linearity, rate detection range, and immunity to fabrication variations. In addition, this architecture can be deployed as a ΣΔ modulator (SDM) analogue to digital converter (ADC), providing a digital bit stream that can be used directly by any digital signal processing system (e.g. micro-processors). Furthermore, recent research has proved that higher order EMSDMs proved to deliver better performance in terms of signal to noise ratio while retaining linearity, dynamic range, fabrication tolerance and bandwidth advantages. Furthermore, in the view of ADC performance, higher order SDMs achieve higher resolution performance which is a desired feature for an ADC. Considering all these advantages, there have been attempts to deploy this approach in designing micro-machined gyroscopes interface in form of low-pass and band-pass EMSDM in order to achieve detection of high angular rate motions and angular motions with faster variation (which requires higher band width). However, the fabrication process of vibratory micro machined gyroscopes just like any other micro fabrication process is prone to flaws and inaccuracies. One of these flaws in the case of vibratory gyroscopes is the root cause of a mechanical coupling that occurs between the excitation direction and detection direction. This coupling results in appearance of an error signal in the detection direction which is known as quadrature error. Existence of this mechanical error results in reduction of performance in this type of gyroscopes and most importantly it limits the dynamic range of the sensor. In this work, a novel interface is proposed that eliminates the quadrature error while retaining the advantages of EMSDM for micro-machined gyroscopes system. The approach is a combination of quadrature amplitude modulation technique which is quite mature in communication systems, time division modulation in digital systems and the fundamental theory of EMSDM. A system level model of the novel architecture has been developed by using Matlab and Simulink. The system level simulation of the novel interface indicates that attenuation of -80dB can be achieved for the quadrature error signal. Furthermore, circuit level simulation model has been developed using Orcad/Pspice, in order to verify the consistency of the system level simulation. Finally a prototype PCB has been built characterized to evaluate the practical system performance. The measurement results on the hardware implementation show that the quadrature error power spectral density is attenuated by -70dB. In another words, the quadrature error is attenuated by about 3 orders of magnitude in the hardware implementation prototype.

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