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The resolution of resonant sensors is fundamentally limited by the presence of noise. Thermomechanical noise, intrinsic to the resonator, sets the ultimate sensor performance when all other noise sources have been eliminated. For linear resonators, the sensing resolution can always be further improved by increasing the driving power. However, this trend cannot continue indefinitely, since at sufficiently high driving powers non-linear effects emerge and influence the noise performance. As a consequence, the resonator's non-linear characteristics play an inextricable role in determining its ultimate resolution limits. Recently, several works have studied the characteristic performance of non-linear resonators as sensors, with the counter intuitive conclusion that increasing the quality factor of a resonator does not improve its sensing resolution at the thermomechanical limit. In this work we further analyze the ultimate resolution limits, and describe different regimes of performance at integration times below and above the resonator's decay time. We provide an analytical model to elucidate the effects of Duffing non-linearity on the resolution of closed-loop sensors, and validate it using numerical simulations. In contrast to previous works, our model and simulations show that under certain conditions the ultimate sensing resolution of a Duffing resonator can be improved by maximizing its quality factor. With measurements on a nanomechanical membrane resonator, we experimentally verify the model and demonstrate that frequency resolutions can be achieved that surpass the previously known limits., Comment: 15 pages, 5 figures

Resonant sensors determine a sensed parameter by measuring the resonance frequency of a resonator. For fast continuous sensing, it is desirable to operate resonant sensors in a closed-loop configuration, where a feedback loop ensures that the resonator is always actuated near its resonance frequency, so that the precision is maximized even in the presence of drifts or fluctuations of the resonance frequency. However, in a closed-loop configuration, the precision is not only determined by the resonator itself, but also by the feedback loop, even if the feedback circuit is noiseless. Therefore, to characterize the intrinsic precision of resonant sensors, the open-loop configuration is often employed. To link these measurements to the actual closed-loop performance of the resonator, it is desirable to have a relation that determines the closed-loop precision of the resonator from open-loop characterisation data. In this work, we present a methodology to estimate the closed-loop resonant sensor precision by relying only on an open-loop characterization of the resonator. The procedure is beneficial for fast performance estimation and benchmarking of resonant sensors, because it does not require actual closed-loop sensor operation, thus being independent on the particular implementation of the feedback loop. We validate the methodology experimentally by determining the closed-loop precision of a mechanical resonator from an open-loop measurement and comparing this to an actual closed-loop measurement., Comment: Accepted version of publication in IEEE Sensors Journal

This work presents a new class of micro-electro-mechanical system (MEMS) resonators toward Ka band (26.5-40GHz) for fifth-generation (5G) wireless communication. Resonant frequencies of 21.4 and 29.9 GHz have been achieved using the fifth and seventh order asymmetric (A5 and A7) Lamb-wave modes in a suspended Z-cut lithium niobate (LiNbO3) thin film. The fabricated device has demonstrated an electromechanical coupling (kt2) of 1.5% and 0.94% and extracted mechanical Qs of 406 and 474 for A5 and A7 respectively. The quality factors are the highest reported for piezoelectric MEMS resonators operating at this frequency range. The demonstrated performance has shown the strong potential of LiNbO3 asymmetric mode devices to meet the front-end filtering requirements of 5G., Comment: 5 pages, 7 figures, 2018 IEEE International Frequency Control Symposium

This work demonstrates the first non-reciprocal network based on switched low-loss acoustic delay lines. The 4-port circulator is built upon a recently reported frequency-independent, programmable, non-reciprocal framework based on switched delay lines. The design space for such a system, including the origins of the insertion loss and harmonic responses, is theoretically investigated, illustrating that the key to better performance and low-cost modulation signal synthesis lies in a large delay. To implement a large delay, we resort to in-house fabricated low-loss, wide-band lithium niobate (LiNbO3) SH0 mode acoustic delay lines employing single-phase unidirectional transducers (SPUDT). The 4-port circulator, consisting of two switch modules and one delay line module, has been modularly designed, assembled, and tested. The design process employs time-domain full circuit simulation and the results match well with measurements. A 18.8 dB non-reciprocal contrast between insertion loss (IL = 6.6 dB) and isolation (25.4 dB) has been achieved over a fractional bandwidth of 8.8% at a center frequency 155 MHz, using a record low switching frequency of 877.19 kHz. The circulator also shows 25.9 dB suppression for the intra-modulated tone and 30 dBm for IIP3. Upon further development, such a system can potentially lead to future wide-band, low-loss chip-scale nonreciprocal RF systems with unprecedented programmability., Comment: 13 pages, 23 figures

This work demonstrates the first non-reciprocal network based on switched low-loss acoustic delay lines. A 21 dB non-reciprocal contrast between insertion loss (IL=6.7 dB) and isolation (28.3 dB) has been achieved over a fractional bandwidth of 8.8% at a center frequency 155MHz, using a record low switching frequency of 877.22 kHz. The 4-port circulator is built upon a newly reported framework by the authors, but using two in-house fabricated low-loss, wide-band lithium niobate (LiNbO3) delay lines with single-phase unidirectional transducers (SPUDT) and commercial available switches. Such a system can potentially lead to future wide-band, low-loss chip-scale nonreciprocal RF systems with unprecedented programmability., Comment: 4 pages, 7 figures