Thomas W. Kenny

We demonstrate a non-ovenized Temperature Compensated Synthesized Oscillator (TCSO) that maintains <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\pm 10$</tex> parts-per-billion (ppb) fractional frequency stability over large dynamic temperature transients between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10-70^{\circ} \mathrm{C}$</tex>. In still air, this TCSO exhibits 40 parts-per-trillion (ppt) fractional frequency stability for integration times <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau=600 \mathrm{s}$</tex> and 160 ppt at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau=10^{4} \mathrm{s}$</tex>. The system simultaneously provides a temperature readout with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$154 \mu \mathrm{K}$</tex> resolution for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau=1.15 \mathrm{s}$</tex>. This dual functionality offers a versatile solution for timing and sensing applications where power constraints preclude ovenization, yet stringent stability requirements must still be satisfied.

This paper presents a dual-mode ovenized MEMS resonator clock that achieves a fractional frequency stability of 21 parts per trillion at 7.5 hours of averaging time. The device incorporates a micro-oven in-chip heater that thermally isolates and maintains the suspended MEMS resonator at its turnover temperature. The ultra-stable performance is enabled by leveraging a machine-learning algorithm to dynamically compensate for residual environmental perturbations within the frequency tracking electronics.

We present, for the first time ever, a disk resonator made from (100) single-crystalline silicon (SCS) in which the two conjugate vibration modes are frequency-matched. This mode matching is achieved by shaping the disk as a smooth-quatrefoil, where the uneven distribution of inertia balances the inherent anisotropic elasticity of SCS. The average diameter of the disk is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$400 \ \mu \mathrm{m}$</tex> and it is supported by concentric stems that allow free in-plane vibrations, yielding a quality factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q=9.7\times 10^{5}$</tex>. The measured average frequency of the two conjugate modes is 9.737 MHz, and the mismatch is 105 Hz (a relative mismatch of 11 ppm). For comparison, in a circular disk resonator made from (100) SCS, the mismatch between the two conjugate modes is ~24% (a relative mismatch of 248,647 ppm).

We experimentally demonstrate a novel frequency tracking system for ultra-high stability MEMS frequency references. The technique relies on probing the amplitude response at two points to infer the resonance frequency and is implemented using a direct digital synthesizer (DDS) and PID controller system. This approach eliminates sensitivity to the gain and phase of the measurement electronics, which can otherwise lead to undesirable frequency drifts due to aging and temperature variations. This approach is extremely valuable for frequency references that require parts-per-trillion level stability.

This paper presents a fully integrated MEMS oscillator incorporating a low-noise high gain TIA, tunable phase shifter, and drive control circuit. It is fabricated in 65 nm CMOS and features a 115–134 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{dB}\Omega, 81\text{fA}/\sqrt{\text{Hz}}$</tex> TIA, a 360° phase shifter, and a 10mV - 200 mV drive control circuit. Leveraging a high Q electrostatic MEMS resonator, the oscillator achieves -90 dBc/Hz phase noise at a 10Hz offset.

Capacitively transduced micromechanical resonators for timing reference applications are overwhelmingly measured from the current output at their sensing electrodes, using a transimpedance amplifier (TIA). Continuous time floating-voltage measurement in capacitive resonators has not found its reach due to various reasons, the primary drawback being picking up of stray charges through stray/unknown capacitances linked to the electrically floating electrode. In this paper, we introduce a novel concept of bias tuning electrodes which alleviates this issue. Through theoretical modelling and experimental evidence, we show that voltage measurement performed at electrically-floating sensing-electrode using a voltage-amplifier (VA) is superior to TIA topology in terms of robustness, noise performance, and bandwidth. Furthermore, we introduce a new electrical circuit equivalent model for resonator devices with a bias tuning electrode in lieu of the standard Mason and Butterworth-Van Dyke (BVD) models which are unsuitable for our new topology. This new model also offers better insights for the combined system of resonator and sensing-unit. The theoretical and experimental work was carried out using a Epi-seal encapsulated DETF device wherein the superior performance of VA topology in key parameters and equivalent performance in other measures is demonstrated. This work is readily extendable to any general capacitively transduced device.[2024-0156]

We demonstrate a MEMS-enabled clock that sets a new record 53 parts-per-trillion (ppt) fractional frequency stability at 8 hours averaging time, and stays below 100 ppt up to 12 hours. This is achieved using a dual-mode temperature stabilization approach along with a TCXO-inspired compensation scheme that corrects for residual errors in the frequency tracking system. These results represent more than 40x improvement from the previous record [1].

We demonstrate the first MEMS-only differential gyrator using a single Lamé mode electrostatic resonator. A gyrator is a two-port device that produces a pure non-reciprocal phase response and is considered a universal element from which isolators and circulators can be derived. We demonstrate in this work that gyration can be achieved using any electrostatic resonator, through very simple time-modulated biasing, without the need for any auxiliary spatio-temporal switching elements.

Researchers experimentally test various protocols for finding the most stable state of two coupled Kerr parametric oscillators. The result can help in the endeavor to use such networks as simulation hardware for solving complex optimization problems.

Phononic frequency combs represent the mechanical analog of optical frequency combs. Several independent experimental studies have demonstrated the onset and evolution frequency comb response in a variety of micro- and nanoelectromechanical devices in recent years. A theoretical basis for exploring and understanding the conditions for comb generation and evolution with varying driving parameters is essential to enable future practical applications. Here, we present the comparison between modeling and experimental results on the generation and evolution mechanism of phononic frequency combs in a nonlinear micromechanical resonator from the perspective of coherent energy transfer between two mechanical modes. Phononic frequency combs emerge in a strong coupling regime involving nonlinear resonances when the amplitudes and phases of two coupled mechanical modes are modulated via coherent energy transfer. The spacing and number of comb teeth can be analytically estimated based on modeling the nature of the interaction of the coupled modes under the specified driving conditions. As the driving conditions are varied, the phononic frequency comb evolves into different forms and a phenomenological model for the system is established to accurately predict the evolution of phononic frequency combs. The alignment between experiment and model provides a basis for the engineering of this phenomenon in future device applications.