A Simple Frequency Formulation for the Tangent Oscillator

The frequency of a nonlinear vibration system is nonlinearly related to its amplitude, and this relationship is critical in the design of a packaging system and a microelectromechanical system (MEMS). This paper proposes a straightforward frequency prediction method for nonlinear oscillators with arbitrary initial conditions. The tangent oscillator, the hyperbolic tangent oscillator, a singular oscillator, and a MEMS oscillator are chosen to elucidate the simple solving process. The results, when compared with those obtained by the homotopy perturbation method, exhibit a good agreement. This paper introduces a very convenient procedure for attaining quick and accurate insight into the vibration property of a nonlinear vibration system.

A 6.89-MHz 143-nW MEMS Oscillator Based on a 118-dBΩ Tunable Gain and Duty-Cycle CMOS TIA

This article presents a 6.89 MHz MEMS oscillator based on an ultra-low-power, low-noise, tunable gain/duty-cycle transimpedance amplifier (TIA) and a bulk Lamé-mode MEMS resonator that has a quality factor (Q) of 3.24 × 106. Self-cascoding and current-starving techniques are used in the TIA design to minimize the power consumption and tune the duty-cycle of the output signal. The TIA was designed and fabricated in TSMC 65 nm CMOS process technology. Its open-loop performance has been measured separately. It achieves a tunable gain between 107.9 dBΩ and 118.1 dBΩ while dissipating only 143 nW from a 1 V supply. The duty-cycle of the output waveform can be tuned from 23.25% to 79.03%. The TIA has been interfaced and wire bonded in a series-resonant oscillator configuration with the MEMS resonator and mounted in a small cavity standard package. The closed-loop performance of the whole oscillator has been experimentally measured. It exhibits a phase noise of −128.1 dBc/Hz and −133.7 dBc/Hz at 1 kHz and 1 MHz offsets, respectively.

A fast estimation of the frequency property of the microelectromechanical system oscillator

A nonlinear oscillator with zero initial conditions is considered, which makes some effective methods, for example, the variational iteration method and the homotopy perturbation method, invalid. To solve the bottleneck, this paper suggests a simple transform to convert the problem into a traditional case so that He’s frequency formulation can be effectively used to solve its approximate solution. An microelectromechanical system (MEMS) oscillator is used as example to show the solution process, and a good result is obtained.

Integrating Resonator to Enhance Magnetometer Microelectromechanical System Implementation with ASIC Compatible CMOS 0.18 μm Process

In this study, a multi-function microelectromechanical system (MEMS) was integrated with a MEMS oscillator, using the resonant frequency oscillation characteristics of the oscillator to provide the Lorentz current of the magnetometer to enhance a large dynamic range of reading, which eliminates the off-chip clock and current generator. The resonant frequency can be adjusted by adjusting the bias voltage of the oscillator to further adjust the sensitivity of the magnetometer. With the mechanical Q value characteristic, a great dynamic range can be achieved. In addition, using the readout circuit of the nested chopper and correlated double-sampling (CDS) to reduce the noise and achieve a smaller resolution, the calibration circuit compensates for errors caused by the manufacturing process. The frequency of the tuning range of the proposed structure is 17,720–19,924 Hz, and the tuning range of the measurement result is 110,620.36 ppm. The sensitivities of the x-, y-, and z-axes of the magnetometer with driving current of 2 mA are 218.3, 74.33, and 7.5 μV/μT for ambient pressure of 760 torr. The resolutions of the x-, y-, and z-axes of the magnetometer with driving current of 2 mA are 3.302, 9.69, and 96 nT/√Hz for ambient pressure of 760 torr.

Phase-delay Induced Variation of Synchronization Bandwidth and Frequency Stability in a Micromechanical Oscillator

Phase feedback is commonly utilized to set up a synchronized MEMS oscillator for high performance sensor applications. It's a consensus that the synchronization region varies with phase delay with a `Anti-U' mode within 0 to pi and phase delay is typically fixed on pi/2 to achieve maximum synchronization range and best frequency stability. In this paper, phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator is investigated analytically and experimentally. A self-sustained oscillator is built by applying phase feedback to an electrostatically actuated micro-beam resonator and synchronization phenomenon is observed after coupling it to a weak external periodic excitation. The analytical expression for predicting the synchronization bandwidth with phase delay is derived based on the dynamic model, from which three different types (`U', `Anti-U' and `M') of variation pattern of synchronization bandwidth are observed as feedback tuning. The variation of frequency stability along phase delay is also studied. The synchronization bandwidth and the frequency stability have exactly opposite variation pattern with phase delay in linear oscillators while they are totally consistent in nonlinear oscillators. Experimental tests in vacuum environment are carried out to validate the analytical observations. Our work presented here provides a precise way for achieving best performance of a synchronized MEMS oscillator in the sensor application.