Analysis of Mutually Injection-Locked Oscillators for Differential Resonant Sensing

Jerome, J. Terrence Jose; Prache, Pierre; Barniol, N.

doi:10.1109/tcsi.2016.2553298

Cited by 21 publications

(46 citation statements)

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“…Our theoretical analyses [3,10] have highlighted that the large parametric sensitivity of PM or AM WCRs is commensurate with their sensitivity to thermomechanical noise. This restatement of the classical result [11] that coupling noisy resonators may at most yield a √ improvement in signal-to-noise ratio was experimentally verified on a PM MILO in [12].…”

Section: Introductionmentioning

confidence: 93%

“…In the rest of the paper, we refer to the terms appearing on the right-hand side of (3-a) or (3-c) as "in phase" terms, whereas those appearing on the right-hand side of (3-b) or (3-d) are "quadrature" terms. As our previous analyses have shown, the first term on the left-hand side of quadrature equations and the first 2 terms on the left-hand side of the in-phase equations have little influence on the slow dynamics of amplitude and phase and can be neglected [3]. By assumption, ̇,̇≪ Ω, the quadrature equations become:…”

Section: Introductionmentioning

confidence: 98%

“…The last few years have seen a growing interest in resonant MEMS sensors based on weakly-coupled resonators (WCRs). Such sensors consist in two or more resonators [1][2][3][4], that are coupled in such a way that a small change of one mechanical parameter (typically the stiffness or the mass of one resonator) induces a large change of an electrically-measurable output metric. Another interesting property of such sensors is their robustness to drift, since their typical output metrics are intrinsically differential, as illustrated in [4][5].…”

Section: Introductionmentioning

confidence: 99%

“…In "mode-localized" sensors (MOLOs), the ratio of the oscillation amplitudes of (two of) the resonators is the output metric of choice [1][2]5], but other amplitude-based metrics have also been proposed [7][8]. In "mutually injection-locked oscillators" (MILOs) based on two synchronized oscillators, the phase-difference between the two oscillating structures is usually preferred as output metric [3][4], although it was recently shown that, in some MILO architectures, amplitude ratio could also be used [9].…”

Section: Introductionmentioning

confidence: 99%

“…Equation 1can be studied by averaging [25] or harmonic balance techniques [26]. For example, a slowly-varying amplitude and phase model can be established as follows, with the same approach as in [3]. We first assume that ( ) = ( ) sin(Ω + ( )), ( ) = ( ) sin (Ω + ( )) (2) where ( ), ( ), ( ) and ( ) are assumed to vary on a time-scale much slower than the steady-state period 2 /Ω of the system.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Operation of Resonant Sensors Based On Weakly Coupled Resonators: Theory and Modeling

Jerome

Mostafa

Ferreira

2019

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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This theoretical work investigates the properties of nonlinearlyoperated weakly-coupled resonators (WCRs) for resonant sensing applications. We propose an analysis framework for mutually injection-locked oscillators (MILOs) and mode-localized oscillators (MOLOs), subject to nonlinear restoring and damping forces. Under some simplifying assumptions, three sensor architectures are investigated and compared, highlighting several common features such as: (i) the insensitivity of the amplitude ratio output metric to the Af effect, (ii) the instability of one oscillation state above a threshold amplitude. These results are illustrated and validated using transient simulations. Their range of validity is then discussed with respect to finite perturbations, finite bandwidth, measurement noise and nonlinear dissipation-fluctuation. While nonlinear operation of WCRs has been experimentally investigated in [9, 14-15], and nonlinear coupling of FM resonant sensors or oscillators was covered in [16], there is little theoretical background against which experimental results obtained with nonlinear WCRs can be tested. Our own work on this subject [9, 17] has highlighted that some MILOs may benefit from nonlinear operation. In particular, the increase of the measurement range of MILOs, with a trade-off in sensitivity, was theoretically and experimentally proven in [9]. Most interestingly, the analysis in [17] showed the resolution of a MILO based on two similar Duffing resonators may not be limited by the A-f effect [18] provided amplitude-ratio was used as an output metric instead of phasedifference. To this day, no similar study has been performed on MOLOs. Furthermore, the results in [17] are limited to a narrow framework: a specific MILO architecture, only nonlinear restoring forces and quasi-static perturbations being considered. With this paper, we establish the fundamental limitations of WCRs in the nonlinear regime, aiming at a general, qualitative description of their behavior, rather than at particular results. The analysis of WCRs presented in section II may be used for MILOs or MOLOs; it is slightly simplified compared to the one in [17], but is more general in the sense that it captures dynamic system fluctuations (i.e. finite sensor bandwidth). Furthermore, it is not only valid for resonators with nonlinear restoring forces (e.g stress-stiffening, or electrostatic softening [19]), but also with nonlinear damping forces. Nonlinear damping is ubiquitous in MEMS sensors: for instance, it may result from the squeezed-film phenomenon [20], from anchor loss [21], or from coupling to an undesired vibration mode [22]. A global outlook on the nonlinear properties of WCRs with quadratic stiffness and damping coefficients is derived in sections III and IV. In section III, three WCR architectures are investigated, and their properties are established with further simplifying assumptions. We find that the insensitivity of AM WCRs to the A-f effect holds in all the studied cases. In section IV, these results are illustrated and ...

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 98%