Behavioral Modelling of Vibrating Piezoelectric Micro-Gyro Sensor and Detection Electronics S. Megherbi1, R. Levy1, F. Parrain1, H. Mathias1, 0. Le Traon2, D. Janiaud2, J. P. Gilles1 'Institut d'Electronique Fondamentale, UMR 8622, Univ. of Paris-Sud, 91405 Orsay cedex. France 2ONERA-DMPH, 29 av. de la division Leclerc, 92322, Chatillon, France Email: souhil.megherbigief.u-psud.fr Abstract This paper describes the development of a model of vibrating piezoelectric micro-gyro sensor using analog hardware description. Our procedure implies several steps with emphasis in model complexity reduction and identification of critical parameters. The proposed macro-model permits multi-physic simulations including mechanical, piezo-electric and electrical analytic descriptions and allows a top-down development approach. As a tool for coding our descriptions, we use analog hardware description language (Verilog-A). For achieving the behavioural computation results, CADENCE simulation environment was used. The critical parameters of the gyro are then studied: the output noise, the output bias and scale factor stability over temperature. 1. Description of the Vibrating Integrated Gyrometer (VIG) Vibrating micro-gyrometers bodies are machined on silicon or piezoelectric material wafers. The physical phenomenon used for vibrating gyros is the Coriolis force induced by rotation. The VIG used in our study has been developed and integrated by ONERA [2], it's principle is based on a tuning fork which allows two orthogonal modes of vibration; the drive mode along the x-axis which is excited at resonance, and the Coriolis force induced by a rotation along the z-axis that induces a y-axis vibration, the detection mode, whose amplitude is proportional to the angular rate velocity Q (fig. 1 and fig. 2). Classically, modelling of such sensors has been focused on the device level, typically using FEM solvers. But, the maturity of the technology needs more and more simulation to achieve precise description. It is our purpose to present a behavioral modelling methodology for our micro-gyro sensor in order to study the limiting effects as thermal instability and parasitic noise upon geometrical and physical parameters. Flexion v IZ v Figure 2 : the whole piezo-electric VIG's structure with its electrodes (ONERA-DMPH). A first model based on the mechanical description is presented on fig.3. It describes the mass and stiffness model of the sensor and its associated equations (eq. 1,2). In this description, the drive and detection modes are respectively the mechanical displacements along x and y axis. For the drive mode; Fx is the excitation force, Vx the excitation voltage, x the mechanical displacement and m the mass of the mass and stiffness model of the gyrometer. Fx Ez Torsion 4Q kx Px x Figure 3: first level mechanical modelling of the VIG Fx = mx+m x 5+mct)2x x {]Q x (eq. 1) coy MY + m ~y +MICOYy + 2mQfi 0 (eq. 2) Figure 1: The VIG's tuning fork A // y