Electrostatic Frequency Tuning of Bulk Acoustic Wave Disk Gyroscopes

Bulk acoustic wave gyroscopes have been researched for potential benefits such as immunity to shock and vibration and the high Q factors achievable with the bulk modes. This paper outlines an approach to address mode matching in bulk acoustic wave (BAW) disk gyroscopes using electrostatic frequency tuning. Electrostatic frequency tuning is achieved by varying the potential difference between the body of the resonator and electrodes surrounding the disk resonator. Tuning of the frequencies of both drive and sense modes is demonstrated in this work as a means to achieving mode matching. The experimental results are also compared to COMSOL simulations reporting mode matching

Model Predictive Control for Signal Temporal Logic Specification

We present a mathematical programming-based method for model predictive control of cyber-physical systems subject to signal temporal logic (STL) specifications. We describe the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness. For synthesis, we encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of a receding horizon control framework. We prove correctness of our algorithms, and present experimental results for controller synthesis for building energy and climate control

Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds

Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of quantifier-free Presburger formulas in which most linear constraints are difference (separation) constraints, and the non-difference constraints are sparse. This class has been observed to commonly occur in software verification. We derive a new solution bound in terms of parameters characterizing the sparseness of linear constraints and the number of non-difference constraints, in addition to traditional measures of formula size. In particular, we show that the number of bits needed per integer variable is linear in the number of non-difference constraints and logarithmic in the number and size of non-zero coefficients in them, but is otherwise independent of the total number of linear constraints in the formula. The derived bound can be used in a decision procedure based on instantiating integer variables over a finite domain and translating the input quantifier-free Presburger formula to an equi-satisfiable Boolean formula, which is then checked using a Boolean satisfiability solver. In addition to our main theoretical result, we discuss several optimizations for deriving tighter bounds in practice. Empirical evidence indicates that our decision procedure can greatly outperform other decision procedures.Comment: 26 page

A Silicon MEMS Disk Resonator Oscillator Demonstrating 36 ppt Frequency Stability

This paper reports experimental results demonstrating excellent short-term frequency stability of 45.6 µLHz (36 [email protected] s integration time) for a bulk acoustic wave (BAW) silicon disk resonator oscillator. The n=4 radial mode of a BAW disk resonator demonstrates an extremely high-quality factor of 1.8*10^6 at 1.25 MHz. The disk is designed with anchors aligned with nodal locations to minimize anchor damping. The results on the measured short-term frequency stability reported here benchmark favourably relative to the state-of-the-art.Engineering and Physical Research Council UK, Silicon Microgravity and Innovate UK

Intrinsic Noise of the Single Electron Box

We quantify the intrinsic noise of the Single Electron Box arising from stochastic cyclic electron tunnelling between a quantum dot and a resevoir driven by a periodic gate voltage. We use both a master equation formalism and Markov Monte Carlo simulations to calculate the gate noise current, and find it to be generated by a cyclostationary process which displays significant spectral correlations at large excitation amplitudes and high tunnel rates. We model noise filtering through an electrical resonator and detection via synchronous demodulation to evaluate the effective noise spectral density in rf-reflectometry qubit readout applications, and determine the conditions under which the intrinsic noise limit could be measured experimentally. Our results have implications in the ultimate sensitivity of SEBs for fast, high-fidelity readout of spin qubits.Comment: 6 pages, 4 figure

Extending the lifetime of resonant atmospheric particulate mass sensors with solvent rinses

The cleaning of a collection-based sensor extends its lifetime and reduces its effective cost. Existing cleaning regimes for silicon-based devices typically require access to large laboratory equipment. A simple cleaning method based on solvent rinses is presented here for the application of microresonator atmospheric particulate mass sensors. The suggested approach is intended for scenarios with limited access to laboratory equipment. Two piezoelectric resonator topologies (in-plane bulk mode and out-of-plane flexural) collected particles via impaction for an hour before rinsing. The solvent rinses reset the resonant frequency and quality factor of each resonator to within 0.4% and 10% of their original values, respectively. Subsequent mass collections were largely repeatable despite fluctuations in particle concentration and deposition location. The presented method provides a straightforward but effective cleaning method for soluble particulate removal. A physical cleaning method is required after substantial insoluble particle adsorption

Effects of spatial sensitivity on mass sensing with bulk acoustic mode resonators

The spatial sensitivity of bulk acoustic mode resonators can influence calibrations when they are implemented as accurate mass sensors of surface-bound particles. A new spatial sensitivity model based on images of the resonator surface is introduced from early principles. The adsorption of particles was studied empirically by repeatedly drying particle laden droplets on the surface of two 3.14 MHz bulk acoustic mode resonators. Theoretical and experimental results were compared to identify three scenarios over the course of consecutive droplet evaporation with varying spatial sensitivity influences. Examining different surface treatments for the resonators revealed the hydrophilic surface to have a higher rate of particle stacking and conglomeration.ATZ thanks the Natural Sciences and Engineering Research Council of Canada, the Sir Winston Churchill Society of Edmonton, and the Cambridge Trust for funding of the PhD degree.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.sna.2015.11.00

Nonlinear cancellation in weakly coupled MEMS resonators

© 2017 IEEE. For the first time, this paper demonstrates the cancellation of nonlinear response in weakly coupled resonators. It has been observed that by working in the region where the mechanical nonlinearity of the resonators and the electrical nonlinearity of the electrostatic coupling cancel, the output current amplitudes are increased by 4x while the trend of vibration amplitude variation upon stiffness perturbations is preserved as seen in the linear regime of the resonators

Closed-loop tracking of amplitude and frequency in a mode-localized resonant MEMS sensor

In this paper, the amplitude and frequency stability of a mode-localized sensor are characterized in a closed loop setup. The system describes an absolute amplitude ratio sensitivity of 5250 to stiffness perturbations in linear operation. A stability of 432ppm at 500s integration time is observed for amplitude ratio measurements. A resolution of 85ppb corresponding to normalised stiffness perturbations in amplitude ratio measurements is thus demonstrated at 500s integration time. Comparisons to frequency shift sensing within the same device shows that amplitude ratio sensing provides higher accuracies for long term measurements due to intrinsic common mode rejection properties in a mode-localized system

A Portable System with 0.1-ppm RMSE Resolution for 1-10 MHz Resonant MEMS Frequency Measurement

This article presents a portable and programmable frequency measurement system (PrO-FMS) with 0.1-ppm RMSE resolution over a measurement time interval of 33.2 s for bulk-acoustic resonator applications. PrO-FMS has a feature of choosing a frequency estimation method and accordingly the sampling frequency, which is programmable. Five frequency estimation methods, Candan, Djukanovic, Prony, M-Pisarenko, and zero crossing interpolation methods, are reviewed for high-resolution frequency measurement. PrO-FMS can also be reconfigured to select a particular resonance mode over a range of 1-10 MHz. Measurement results are provided for two different commercial quartz crystals and a microfabricated in-plane bulk acoustic resonator in two different modes of resonance. The results of these estimation methods are compared with a standard commercial tabletop frequency counter. Measurement results show that PrO-FMS can achieve a resolution of 0.1 ppm RMSE. For the same gate time, PrO-FMS provides better resolution than standard tabletop frequency counter. This article also provides a study on the behavior of the five different frequency estimation methods for short-and long-term measurements for quartz crystals and bulk acoustic resonator in two different modes