Nonlinear effects in single-crystal silicon microresonators are analyzed with the focus on mechanical nonlinearities. The bulk acoustic wave (BAW) resonators are shown to have orders-of-magnitude higher energy storage capability than flexural beam resonators. The bifurcation point for the silicon BAW resonators is measured and the maximum vibration amplitude is shown to approach the intrinsic material limit. The importance of nonlinearities in setting the limit for vibration energy storage is demonstrated in oscillator applications. The phase noise calculated for silicon microresonator-based oscillators is compared to the conventional macroscopic quartz-based oscillators, and it is shown that the higher energy density attainable with the silicon resonators can partially compensate for the small microresonator size. Scaling law for microresonator phase noise is developed.

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Nonlinear limits for single-crystal silicon microresonators

An increasing number of calibration and metrology laboratories now employ a Global Positioning System disciplined oscillator (GPSDO) as their primary standard for frequency. GPSDOs have the advanta...

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The Use of GPS Disciplined Oscillators as Primary Frequency Standards for Calibration and Metrology Laboratories

The jamming robustness of frequency hopping (FH) systems with M-ary frequency shift keying (MFSK) modulation may be potentially neutralized by a follower partial-band jammer. In this paper, a maximum likelihood (ML)-based algorithm that uses a two-element array is proposed for joint follower jamming rejection and symbol detection in slow FH/MFSK systems over quasi-static flat Rayleigh fading channels. The algorithm is derived by treating both the received jamming components and the unknown data symbols as deterministic quantities to be jointly estimated in an integrated ML operation. In addition, an approximate expression for the symbol error rate (SER) of the proposed scheme is derived when BFSK signaling is employed in a jamming dominant scenario. Analytical and simulated results show that the proposed approach is able to remove jamming and outperform the conventional and sample matrix inversion (SMI)-based beam-formers in the presence of a follower partial-band jammer.

ML-based follower jamming rejection in slow FH/MFSK systems with an antenna array

Studies of structural and dielectric properties of lead-free perovskite K05Na05NbO3 (KNN) ceramics obtained by the substitution of 5 at% of La and Ti for ions in the A-site and B-site, respectively, and sintered at different temperatures between 1100°C and 1190°C, are presented X-ray diffraction patterns show the successful formation of an orthorhombic perovskite phase similar to that of pure KNN The effect of doping and sintering temperature on the dielectric properties of the resulting ceramics is discussed Simultaneous substitution of La and Ti into the KNN (KNNLaTi) causes a shift in the ferroelectric–paraelectric phase transition temperature from that of pure KNN (420°C) to considerably lower ones (81 to 110°C) for the modified compounds A particularly important result is the appearance of a single peak in the permittivity vs temperature curve associated with the ferroelectric–paraelectric phase transition, where the KNNLaTi compound changes from orthorhombic to cubic structure, instead of the two reported for pure KNN This transition exhibits the characteristics of a normal diffuse phase transition with an incipient relaxer behavior

Structural and dielectric properties of La- and Ti-modified K 0.5 Na 0.5 NbO 3 ceramics

Electrostatic tuning of the frequency in micromachined Si-SiO2 composite resonators for temperature compensation is demonstrated and analyzed. Electrostatic tuning exploits the bias voltage dependence of frequency for the compensation. Si-SiO2 composite resonators have intrinsically small frequency variation over temperature, thus being appropriate for electrostatic tuning. We developed a tuning procedure and applied it to a flexural-mode composite resonator. Experimental results show ±2.5-ppm stability over a 90°C-wide temperature range.

Electrostatic Tuning to Achieve Higher Stability Microelectromechanical Composite Resonators

: The objective of the program was to explore advanced concepts in the design and manufacture of frequency control devices. The program was designed to lead to low cost mass production, high performance components, increased levels of communication system circuit integration, and a significant size reduction of radios and other communication system elements. The proposed approach was to adapt advanced microelectronic material processing, piezoelectric thin films, and micromachining of single crystal plates to achieve wafer scale integration and production of a wide class of frequency control devices.

K. M. Lakin

Papers

Frequency Control Devices.