Jérôme Juillard

Analysis of Mutually Injection-Locked Oscillators for Differential Resonant Sensing

The potential benefits of oscillator synchronization are receiving increased interest in the resonant MEMS community, for clocking or sensing applications. In this paper, we explore the possibilities of differential resonant sensing applications based on the phase-difference between two injection-locked resonators, strongly coupled through an electronic mixer. A general model of such oscillators is established, and their static and dynamic performance is determined. The design space offered by the mixing scheme is then investigated at the system-level, in the weak and strong coupling cases. The practical implementation of the corresponding architectures in the context of a MEMS application is discussed. The theoretical results are supported by simulations and experimental data.

Temperature-drift rejection and sensitivity to mismatch of synchronized strongly-coupled M/NEMS resonators

This paper describes a strongly-coupled resonant architecture in which two M/NEMS resonators are synchronized through their actuation voltage. In the context of a sensing application, this architecture theoretically enables environmental drift rejection (e.g. temperature, humidity) and ultra-sensitive measurement by monitoring a phase difference rather than a frequency. Experiments prove the efficiency of the proposed scheme, with respect to temperature-drift rejection and sensitivity to mismatch.

Impact of output metric on the resolution of mode-localized MEMS resonant sensors

In this paper, we investigate how additive noise, e.g. thermomechanical noise, impacts the resolution of mode-localized resonant sensing architectures based on two weakly-coupled resonators. Existing work suggests that the resolution of these sensors can be improved by decreasing the coupling coefficient of the resonators. The present work gives an analytical proof that this result does not hold when the ratio of the motional amplitudes of the resonators is used as an output metric, and that, in this case, the sensor resolution is actually independent of the coupling strength. We then extend our proof, supported by transient simulations of a simple model, to other output metrics.

Monolithic integration of mutually injection-locked CMOS-MEMS oscillators for differential resonant sensing applications

Differential architectures based on two injection-locked MEMS oscillators are a promising technique for high-end resonant sensing applications since they enable environmental drift rejection and high sensitivity. But properly coupling two M/NEMS resonators together is challenging. In order to eliminate drift, the resonators must be fabricated very close to each other and to be as well-matched as possible. To this end, both resonators and the circuitry can be monolithically-integrated on a single chip. However this leads to parasitic coupling and feedthrough, which affect the performances. This paper explains how, block by block, our architecture and our chip are designed to minimize these spurious couplings. The improvements resulting from the optimization of the ASIC are illustrated by simulated and experimental results.

Impact of the closed-loop phase shift on the frequency stability of capacitive MEMS oscillators

Phase noise is a clue performance indicator for MEMS-based resonant sensors. The optimal resolution achievable with these sensors is limited by the close-to-the-carrier phase noise resulting from the modulation of noise sources by the mechanical resonator. In this paper, we focus on the effect of a white noise input source on a one-sided capacitive MEMS resonator. We study how the closed-loop phase shift affects its frequency stability. Our study reveals the existence of optimal points, with phase noise minimization and SNR maximization, which cannot be predicted by a traditional third-order Taylor-Series approach. We reveal that, due to the modulation of the actuation force by the electrostatic nonlinearity, tuning the closed-loop phase shift to improve the oscillator frequency stability is especially relevant.

A further study of reduced-order modeling techniques for nonlinear MEMS beams

This paper gives a further look at reduced-order modeling (ROM) techniques that can be applied to MEMS beams subject to nonlinear forces. It is focused on the popular method which consists in multiplying the equation governing the displacement of the beam by the displacement-dependent denominator of the nonlinear (electrostatic) force before modal projection is performed. Having already shown that in the case of 1-mode, 1-harmonic analysis, this method can lead to dramatically wrong results, we propose another choice of multiplicative coefficient, with much improved behavior. This method is illustrated, discussed and compared to other approaches in terms of simplicity, accuracy and range of validity.