Please cite this article in press as: Y. Dong, et al., Microgyroscope control system using a high-order band-pass continuous-time sigma-delta modulator, Sens. Actuators A: Phys. (2007), doi:10.1016/j.sna.2007.10.057 ARTICLE IN PRESS +Model SNA-6084; No. of Pages 7 Available online at www.sciencedirect.com Sensors and Actuators A xxx (2007) xxx–xxx Microgyroscope control system using a high-order band-pass continuous-time sigma-delta modulator Y. Dong a,∗ , M. Kraft a , N. Hedenstierna b,1 , W. Redman-White a a School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK b Infineon Technologies SensoNor AS, Horten, Norway Received 29 June 2007; received in revised form 3 October 2007; accepted 16 October 2007 Abstract The paper presents a novel 6th order continuous-time, force-feedback band-pass sigma-delta modulator control system for the detection mode of micromachined vibratory gyroscopes. Compared with the architecture using a low-pass sigma-delta modulator, this band-pass solution uses a much lower sampling frequency for the sigma-delta modulator and thus reduces the requirement for frequency response of the detection interface and control electronics. In this work, the sigma-delta modulator operates at only four times of mechanical resonant frequency, which allowed its implementation in a continuous-time circuit using discrete electronic components on a PCB; this has the advantage of simple prototyping and can improve the signal anti-aliasing characteristics. © 2007 Elsevier B.V. All rights reserved. Keywords: Band-pass; Closed loop control; Gyroscope; MEMS; Sigma-delta 1. Introduction The principle of operation of a vibratory gyroscope is based on the Coriolis force [1,2]. There are two orthogonal vibration modes: excitation and detection mode, with two correspond- ing control loops for each mode. In the excitation mode, the proof mass is electrostatically driven to oscillate with a constant amplitude and frequency in a fixed direction. This oscillation is usually controlled by a closed loop control system, for exam- ple, a phase-lock-loop (PLL) and automatic gain control (AGC) [3–6]. However, this loop is not the topic of this work and will not be discussed in detail here. If the sensor is rotated about its axis of sensitivity, a Coriolis force is induced on the proof mass in the orthogonal direction to the excited vibration, and the displace- ment of the proof mass can be detected by a capacitive readout circuit. This mode is usually referred to as the detection mode. To increase the bandwidth, reduce nonlinearity and improve the immunity to fabrication tolerances, it is of considerable advan- ∗ Corresponding author at: University of Southampton, School of Electronics and Computer Science, Building 86, Room 2003, Southampton SO17 1BJ, UK. Tel.: +44 23 8059 3278. E-mail addresses: yd@ecs.soton.ac.uk (Y. Dong), nils.hedenstierna@sensonor.no (N. Hedenstierna). 1 Tel.: +47 33 03 51 72. tage to include the detection mode in a force feedback control loop. The controllers for the detection loop are mainly based on either a modified analogue proportional-integral-derivative (PID) algorithm [7] or digital signal processing such as adaptive algorithms [8,9]. Analogue control is a mature technique and its implementation is simple but it may suffer from instability problems due to loop delay. If a gyroscope controller is imple- mented in the digital domain, not only a powerful digital signal processor (DSP) is necessary, but also a high speed and high per- formance analog-to-digital converter (ADC). Recently, a control strategy based on a sigma-delta modulation (M) has proven to be advantageous [3,4,10]. However, to date the control loop makes use of a low-pass M, which requires a high sampling frequency due to the relatively high mechanical resonant fre- quency and results in demanding requirements for the interface circuits. If a second-order  control loop is realized with the sensing element acting as a mechanical double integrator (or resonator), the loop is known to suffer from a dead-zone prob- lem [10] and noise interaction [11]; consequently the signal to noise ratio (SNR) of a second-order  loop has an upper limit and cannot be improved only by increasing the oversampling frequency. A gyroscope is usually designed to have a high mechanical quality factor in both detection and excitation modes to increase the sensitivity of the output response and can thus be regarded as 0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.10.057