Micromachined vibratory gyroscopes controlled by a high order band-pass sigma delta modulator.

Abstract—This work reports on the design of novel closed-loop control systems for the sense mode of a vibratory-rate gyroscope based on a high-order sigma-delta modulator (SDM). A low-pass and two distinctive bandpass topologies are derived, and their advantages discussed. So far, most closed-loop force-feedback control systems for these sensors were based on low-pass SDM’s. Usually, the sensing element of a vibratory gyroscope is designed with a high quality factor to increase the sensitivity and, hence, can be treated as a mechanical resonator. Furthermore, the output characteristic of vibratory rate gyroscopes is narrowband amplitude- modulated signal. Therefore, a bandpass M is a more appropriate control strategy for a vibratory gyroscope than a low-pass SDM. Using a high-order bandpass SDM, the control system can adopt a much lower sampling frequency compared with a low-pass SDM while achieving a similar noise floor for a given oversampling ratio (OSR). In addition, a control system based on a high-order bandpass SDM is superior as it not only greatly shapes the quantization noise, but also alleviates tonal behavior, as is often seen in low-order SDM control systems, and has good immunities to fabrication tolerances and parameter mismatch. These properties are investigated in this study at system level

High-loop-delay sixth-order bandpass continuous-time sigma-delta modulators

International audienceThis study focuses on the design of high-loop-delay modulators for parallel sigma-delta conversion. Parallel converters, allowing a global low oversampling ratio, consist of several bandpass modulators with adjacent central frequencies. To ensure the global performance, the noise transfer function (NTF) of each modulator must be adjusted regarding its central frequency. In this thematic a new topology of sixth-order modulators based on weighted-feedforward techniques is developed. This topology offers an adequate control of the NTF at each central frequency by simple means. Additive signal paths are moreover proposed to obtain an auto-filtering signal transfer function. An optimisation method is also developed to calculate the optimised coefficients of the modulators at different central frequencies. The main concerns are improving the stability and reducing the sensitivity of the continuous-time circuit to analogue imperfections. This is essential for parallel conversion since, in each channel, the modulator works at a central frequency which differs from the fourth of the sampling frequency. The performance of the optimised modulator is compared with its discrete-time counterpart with good argument

Contribution to the design of continuous -time Sigma - Delta Modulators based on time delay elements

The research carried out in this thesis is focused in the development of a new class of data converters for digital radio. There are two main architectures for communication receivers which perform a digital demodulation. One of them is based on analog demodulation to the base band and digitization of the I/Q components. Another option is to digitize the band pass signal at the output of the IF stage using a bandpass Sigma-Delta modulator. Bandpass Sigma- Delta modulators can be implemented with discrete-time circuits, using switched capacitors or continuous-time circuits. The main innovation introduced in this work is the use of passive transmission lines in the loop filter of a bandpass continuous-time Sigma-Delta modulator instead of the conventional solution with gm-C or LC resonators. As long as transmission lines are used as replacement of a LC resonator in RF technology, it seems compelling that transmission lines could improve bandpass continuous-time Sigma-Delta modulators. The analysis of a Sigma- Delta modulator using distributed resonators has led to a completely new family of Sigma- Delta modulators which possess properties inherited both from continuous-time and discretetime Sigma-Delta modulators. In this thesis we present the basic theory and the practical design trade-offs of this new family of Sigma-Delta modulators. Three demonstration chips have been implemented to validate the theoretical developments. The first two are a proof of concept of the application of transmission lines to build lowpass and bandpass modulators. The third chip summarizes all the contributions of the thesis. It consists of a transmission line Sigma-Delta modulator which combines subsampling techniques, a mismatch insensitive circuitry and a quadrature architecture to implement the IF to digital stage of a receiver

A New Method to Synthesize and Optimize Band-Pass Delta-Sigma Modulators for Parallel Converters

An analysis and synthesis method for continuoustime (CT) band-pass delta-sigma modulators, applicable in parallel converters is presented in this paper. This method makes the design of band-pass delta-sigma modulators possible in a wide range of central frequencies and high DAC+ADC delays. This method is also applicable for narrow-band deltasigma converters in order to improve their performances

Design of Electronic Control Circuit of Piezo-Electric Resonators for sigma delta Modulator Loop in AMS Bi-CMOS 0.35μm

Most of the recent design methodologies of continuous-time sigma-delta modulators use piezo-electric resonators as loop filters. Compared with classical resonators (Gm-c,Gm-LC and etc), piezo-electric resonators have the advantage of high quality factor and accurate resonance frequency. However, they suffer from anti-resonance frequency and impedance adaptation issues with connected electronic circuits. Therefore, their performance is in practice deteriorated. Compatible electronic control circuit is required to achieve expected performance. In this study, the specifications of the electronic control circuit are studied and this circuit is designed in AMS Bi-CMOS 0.35μm technology. the simulations are done at layout-level

Continuous-time cascaded ΣΔ modulators for VDSL: A comparative study

This paper describes new cascaded continuous-time ΣΔ modulators intended to cope with very high-rate digital subscriber line specifications, i.e 12-bit resolution within a 20-MHz signal bandwidth. These modulators have been synthesized using a new methodology that is based on the direct synthesis of the whole cascaded architecture in the continuous-time domain instead of using a discrete-to-continuous time transformation as has been done in previous approaches. This method allows to place the zeroes/poles of the loop-filter transfer function in an optimal way and to reduce the number of analog components, namely, transconductors and/or amplifiers, resistors, capacitors and digital-to-analog converters. This leads to more efficient topologies in terms of circuitry complexity, power consumption and robustness with respect to circuit non-idealities. A comparison study of the synthesized architectures is done considering their sensitivity to most critical circuit error mechanisms. Time-domain behavioral simulations are shown to validate the presented approach.Ministerio de Educación y Ciencia TEC2004-01752/MI

Pulsed digital oscillators

The objective of this paper is to collect the main latest results on pulsed digital oscillators. Rigorous and experimental results are presented that show what kind of sequences are at their output, the relation between these sequences and those of first-order sigma-delta modulators and how is their performance in practical applications. A new variation of the standard topology of PDOs, on which the feedback variable is not position but the velocity of the resonator, is also presented. The first preliminary results obtained with a PDO working with a MEMS cantilever for chemical sensing are presented, which show that it is possible to infer the oscillation frequency directly from the bitstream at the output of the oscillator. Finally, the dependence of the oscillation frequency as a function of the initial conditions of the resonator are also analyzed with simulations.Peer ReviewedPostprint (published version

Small-size MEMS accelerometer encapsulated in vacuum using Sigma-Delta modulation

A vacuum encapsulated MEMS accelerometer using Sigma-Delta modulation is here presented. Three different modulation orders (second, third, and fourth) were implemented in a field-programable gate array (FPGA), enabling flexibility for tuning the loop parameters in real-time. Three devices were measured, and the results are in good agreement with simulations performed in Simulink. A noise figure of 123 μg/√Hz for a bandwidth of 400 Hz and a range of at least ±1 g was experimentally measured. A figure of merit considering device size and bandwidth is proposed, highlighting the relevance of the results for the current state of the art.FCT - Fundação para a Ciência e a Tecnologia (PDE/BDE/114563/2016

Extended frequency-band-decomposition sigma–delta A/D converter

Parallelism can be used to increase the bandwidths of ADC converters based on sigma–delta modulators. Each modulator converts a part of the input signal band and is followed by a digital filter. Unfortunately, solutions using bandpass sigma–delta modulators are very sensitive to the position of the modulators' central frequencies. This paper shows the feasibility of a frequency-band-decomposition (FBD) ADC using continuous time bandpass sigma–delta modulators, even in the case of large analog mismatches. The major benefit of such a solution, called extended-frequency-band-decomposition (EFBD) is its low sensitivity to analog parameters. For example, a relative error in the central frequencies of 4% can be accepted without significant degradation in the performance (other published FBD ADCs require a precision of the central frequencies better than 0.1%). This paper will focus on the performance which can be reached with this system, and the architecture of the digital part. The quantization of coefficients and operators will be addressed. It will be shown that a 14 bit resolution can be theoretically reached using 10 sixth-order bandpass modulators at a sampling frequency of 800 MHz which results in a bandwidth of 80 MHz centered around 200 MHz (the resolution depends on the effective quality factor of the filters of the analog modulators)