Reference Frequency Research Articles

A 0.9-V 28-MHz Highly Digital CMOS Dual-RC Frequency Reference With ±200 ppm Inaccuracy From −40 °C to 85 °C

This article presents an energy-efficient dual- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RC$ </tex-math></inline-formula> frequency reference intended for wireless sensor nodes. It consists of a digital frequency-locked loop (FLL) in which the frequency of a digitally controlled oscillator (DCO) is locked to a temperature-independent phase shift derived from two different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RC$ </tex-math></inline-formula> poly-phase filters (PPFs). Phase shifts with complementary temperature coefficients (TCs) are generated by using PPFs made from different resistor types (p-poly and silicided p-poly). The phase shift of each filter is determined by a zero-crossing (ZC) detector and then digitized by a digital phase-domain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula> modulator ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \Sigma \text{M}$ </tex-math></inline-formula> ). The results are then combined in the digital domain via fixed polynomials to produce a temperature-independent phase shift. This highly digital architecture enables the use of a sub-1-V supply voltage and enhances energy and area efficiency. The 28-MHz frequency reference occupies 0.06 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in a 65-nm CMOS process. It achieves a period jitter of 7 ps ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\sigma $ </tex-math></inline-formula> ) and draws <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$142~\mu \text{W}$ </tex-math></inline-formula> from a 0.9-V supply, which corresponds to an energy consumption of 5 pJ/cycle. Furthermore, it achieves ±200 ppm inaccuracy from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 40\,\,^\circ \text{C}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$85~^\circ \text{C}$ </tex-math></inline-formula> after a two-point trim.

A 500 kHz to 150 MHz Multi-Output Clock Generator Using Analog PLL and Open-Loop Fractional Divider with 0.13 μm CMOS

Clocks are widely used in multimedia and electronic devices, and they usually have different frequency demands. This paper presents the design of a multi-output clock generator using an analog integer-N phase-locked loop (PLL) and open-loop fractional dividers. The PLL based on a three-stage ring voltage-controlled oscillator (VCO) is used to transform the lower frequency reference into a high-frequency intermediate clock (600 MHz–900 MHz). Then, relying on the open-loop fractional divider, a wide frequency range of 500 kHz to 150 MHz can be generated. Due to the open-loop control characteristic, the clock generator has instantaneous frequency switching capability. In addition, phase-adjusting circuits added to the divider greatly improved the jitter performance of the output clock; its RMS jitter is 5.2 ps. This work was conducted with 0.13 μm CMOS technology. The open-loop divider occupies an area of 0.032 mm2 and consumes 7.7 mW from a 1.2 V supply.

High-precision Microwave Frequency Measurement Based on Stimulated Brillouin Scattering With Simple Configuration

We propose and implement a microwave frequency measurement (MFM) scheme based on stimulated Brillouin scattering (SBS) and an apodized fiber Bragg grating (AFBG), achieving high accuracy in a wide range of measurement with a highly simplified configuration. By sweeping a reference frequency during SBS process, a frequency-to-power mapping between the reference frequency and the monitored output optical power of the MFM system is established. Unknown frequencies can be identified through a specific numerical relationship among the unknown frequency, reference frequency, and Brillouin frequency shift (BFS). The transmission and reflection properties of the AFBG are exploited to offer pump light and probe light simultaneously for SBS process, thereby reducing complexity of the MFM system. It can be derived theoretically that all frequencies larger than one BFS can be measured except for 3/2 BFS. This measurement blind spot can be eliminated by utilizing two segments of single-mode fibers with different BFSs. A measurement error of less than ±1 MHz within 10.68 GHz to 20 GHz is achieved in a proof-of-concept experiment of the proposed MFM approach. This method has also been proved to be applied to dual microwave frequency measurements.

Investigation of support transducer enabled higher-order radial bulk mode MEMS resonator and low phase noise oscillator

This work reports the successful excitation of a novel bulk acoustic mode whose actuation and sensing are facilitated by the support transducer topology (STT). The design methodology concurrently supports low motional impedance and high energy confinement features which are crucial for frequency reference components in Radio Frequency communication. A conventional bulk mode operating in the width extension (WE) mode is deployed to efficiently excite the higher-order radial mode using the STT design feature of resonant frequency matching. The thin-film piezoelectric on substrate support transducers excited in a WE mode is mechanically coupled to the bulk silicon allowing the acoustic energy of the MEMS resonator to be stored maximally in the high-quality factor (Q) resonant tank, thereby alleviating the overall losses due to low-Q of the piezoelectric thin film and electrode material. The resonator exhibits a Q of 19 728 at 63.56 MHz resonant frequency with a motional resistance (R m) of 368 Ω when measured in vacuum at a power level of 0 dBm. Under cryogenic measurement conditions, the device recorded a Q of 24 153 at 15 K. A standalone WE resonator is studied to put a spotlight on the quality factor enhancement technique using the STT. The STT enabled novel bulk mode enhances the overall Q by 320% and halves the R m. When implemented as an oscillator, its performance exceeds the Global System for Mobile communication standards phase noise (PN) requirements. PN of −136.95 dBc Hz−1 and −161.52 dBc Hz−1 at 1 kHz and 1 MHz offset, respectively, were recorded when normalized to a carrier frequency of 13 MHz.

Laser-written vapor cells for chip-scale atomic sensing and spectroscopy.

We report the fabrication of alkali-metal vapor cells using femtosecond laser machining. This laser-written vapor-cell (LWVC) technology allows arbitrarily-shaped 3D interior volumes and has potential for integration with photonic structures and optical components. We use non-evaporable getters both to dispense rubidium and to absorb buffer gas. This enables us to produce cells with sub-atmospheric buffer gas pressures without vacuum apparatus. We demonstrate sub-Doppler saturated absorption spectroscopy and single beam optical magnetometry with a single LWVC. The LWVC technology may find application in miniaturized atomic quantum sensors and frequency references.

Experimental Research on Reducing Flow-Induced Cavity Resonance with a Narrowband Active Noise Control System

In this paper, active control of flow-induced cavity resonance noise is addressed. A hybrid numerical method is presented to predict the resonance frequency and, instead of traditional active flow control, a narrowband active noise control system is utilized to suppress the resonance. A duct system is built up at low Mach numbers and experiments are carried out to validate the proposed methods. The results have shown that the resonance frequency could be predicted with 1.5% errors and the flow-induced narrowband noise could be effectively suppressed at both the fundamental frequency and its first harmonic. More than 10 dB global attenuations could be achieved for the fundamental resonance frequency without noise enhancements at other frequencies. Further, it was also found that the optimal reference frequency of the narrowband active noise control system could be largely biased from the original resonance frequency, which indicates a nonlinear mechanism of the control system.

Model Predictive Displacement Control Tuning for Tap-Water-Driven Artificial Muscle by Inverse Optimization with Adaptive Model Matching and its Contribution Analyses

The tap-water-driven McKibben artificial muscle has many advantages and is expected to be applied in mechanical systems that require a high degree of cleanliness. However, the muscle has strong asymmetric hysteresis characteristics that depend on the load, and these problems prevent its widespread use. In this study, a novel control method, model predictive control with a servomechanism based on inverse optimization with adaptive model matching, was developed. This control method was applied to the muscle by using a high-precision mathematical model employing an asymmetric Bouc-Wen model. The experimental results show that the proposed approach achieved a high tracking performance for a given reference frequency, with a mean absolute error of 0.13 mm in the steady-state response and with easier controller tuning. Furthermore, the contributions of the controller elements of the proposed method were evaluated. The results show that the contribution of the adaptive system was higher than that of the servo system. Furthermore, the effectiveness of adaptive model matching was verified.

Resonant fiber-optic thermometry with high resolution and wide range.

We report a high-resolution and wide-range thermometer using a fiber Bragg grating Fabry-Perot cavity (FBG-FP) combined with beat frequency interrogation. Two distributed feedback (DFB) lasers are locked to the FBG-FP sensing head and a hydrogen cyanide H13C14N (HCN) gas cell, respectively, both using the Pound-Drever-Hall (PDH) technique. The light beams from two lasers are brought together to interfere on a photodetector producing a beat frequency signal which provides a measure of the temperature change. Our sensor exhibits a dynamic range of ∼109 °C, a high resolution of 2×10-4 °C with an averaging time of 1 s. By introducing the reference frequency, the sensor has demonstrated good long-term stability. This sensor provides a useful tool for those fields where resolving slight temperature changes is crucial, such as deep ocean temperature measurement.

Inferring spin tilts at formation from gravitational wave observations of binary black holes: Interfacing precession-averaged and orbit-averaged spin evolution

Two important parameters inferred from the gravitational wave signals of binaries of precessing black holes are the spin tilt angles, i.e., the angles at which the black holes' spin axes are inclined with respect to the binary's orbital angular momentum. The LIGO-Virgo parameter estimation analyses currently provide spin tilts at a fiducial reference frequency, often the lowest frequency used in the data analysis. However, the most astrophysically interesting quantities are the spin tilts when the binary was formed, which can be significantly different from those at the reference frequency for strongly precessing binaries. The spin tilts at formally infinite separation are a good approximation to the tilts at formation in many formation channels and can be computed efficiently for binary black holes using precession-averaged evolution. Here, we present a new code for computing the tilts at infinity that combines the precession-averaged evolution with orbit-averaged evolution at high frequencies and illustrate its application to GW190521 and other binary black hole detections from O3a. We have empirically determined the transition frequency between the orbit-averaged and precession-averaged evolution to produce tilts at infinity with a given accuracy. We also have regularized the precession-averaged equations in order to obtain good accuracy for the very close-to-equal-mass binary parameters encountered in practice. This additionally allows us to investigate the singular equal-mass limit of the precession-averaged expressions, where we find an approximate scaling of $1/(1 - q)$ with the mass ratio $q$.

A low power clock generator 400–1800 MHz for ADPLL

This paper describes a low-power all-digital clock generator (ADCG) designed for reading and processing signals from detectors of large physical experiments. The clock generator operates with a reference clock frequency of 10 to 50 MHz and generates an output signal ranging from 400 to 1800 MHz in 10 MHz steps. The clock generator has been approved in 28 nm CMOS technology of TSMC. The power consumption and chip area of the block are 1.5 mW and 80 × 80 μm2 correspondingly. A wide range of reference and output frequencies makes this block versatile in application.

Multirate Timestamp Modeling for Ultralow-Jitter Frequency Synthesis: A Tutorial

In this tutorial brief, we introduce a unified wideband phase-noise theory framework of frequency synthesis based on a multirate timestamp modeling with “two <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> -variables”. We apply it to model and analyze two types of ultra-low jitter (i.e., sub-50fs) phase-locking techniques: 1) high-bandwidth PLLs with high phase-detector gain (with emphasis on all-digital PLLs), and 2) injection locking (IL) or recently proposed charge-sharing locking (CSL), serving as a unified guide on achieving the sub-50 fs jitter. All analytical results are numerically verified through time-domain behavioral simulations, demonstrating that the theoretically maximum bandwidths are around 30% and 44% of the reference frequency in PLLs and IL, respectively.

Design and implementation of a frequency synthesizer using PLL

An investigation has been made to find the new frequency from a reference frequency such is done for the beneficial of day-to-day rapid increase in the technology and its uses. The effect of such is derived from the comparison of analog circuits and digital circuits to find the better result. A software analysis is also done to verify the result. Mainly for the regular use of wireless technology this work is done and compared for the analysis of better result. Phase lock loop is used to get the better frequency response from the crystal oscillator used as a reference frequency. It is a very essential component for modern technology

Intelligent voltage and frequency control of islanded micro-grids based on power fluctuations and communication system uncertainty

Control of critical micro-grid factors such as voltage/frequency is complex and challenging in power distribution networks that include micro-grids. Therefore, providing an efficient and optimal control framework to maintain stability and control the critical factors of the network significantly affects the development of micro-grids goals. The present study proposed the intelligent voltage/frequency control scheme in primary and secondary micro-grids. Micro-grid voltage/frequency restoration was planned based on the PSO-Fuzzy control algorithm in the primary control. In addition to optimizing the members of the fuzzy controller, the PSO optimization algorithm was also used to calculate the voltage/ frequency deviation based on the voltage error factors and the violation of the deviation from the frequency reference. The PSO-Fuzzy structure was provided to optimize hybrid energy storage units' charge and discharge thresholds. Moreover, an intelligent artificial neural network algorithm was presented based on Lyapunov stability equations and a communication system platform to compensate for the voltage/frequency deviation in the secondary control. The proposed algorithm had optimal and efficient performance in different scenarios, such as the effect of load dynamic and its type, power fluctuations, and communication system delays.

Ultra-Stable Fiber Laser Based on Intracavity Dual Mode Self-Reference Mechanism

Ultra-stable lasers serve as the backbone for the most advanced optical metrology scientific experiments, enabling the ability to laser interferometry or atomic spectroscopy at the highest levels of precision, thanks to the rapid development of laser wavelength stabilization techniques based on optical or electrical feedback from an external reference such as absorption line or optical cavity. With the increasing interest in making these scientific systems portable and applying it outside of the laboratory, it still remains an open question as to how to realize a laser source that can reach the high wavelength stabilization and still remain sufficiently compact and portable for field use. Here, we describe a wavelength stabilization fiber laser with intracavity reference mechanism, by utilizing the beat note of dual modes inside the laser cavity as the laser wavelength drift reference signal. A laser wavelength drift less than 5 kHz and ADEV 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−13</sup> level at integration time scales from 0.01s to 1000s is achieved, which is to-date the best results for the laser wavelength stabilization without the external frequency reference. The outcome of this work presents a new way to achieve an ultra-stable laser with a simpler, lower cost feature. It offers new insights to promote the highest precision optical metrology scientific application outside of the laboratory, and also gives the possibilities of applying the ultra-stable laser source into a wider range of industrial application.

Uncertain frequency response analysis of clamp-pipe systems via the coordinate transformed polynomial chaos expansion

The frequency response function (FRF) that links structural responses and external excitations is required to realize the dynamic analysis of a clamp-pipe system. Due to random geometry and stiffness parameters, the FRF becomes a stochastic quantity that is represented by a surrogate model based on the polynomial chaos expansion (PCE) in this paper. Considering that an FRF trajectory is mainly controlled by resonance and anti-resonance frequencies, a reference frequency coordinate characterized by the controlling frequencies associated with a nominal value of input random variables is first determined. By reserving the original amplitude, an FRF sample is projected to the reference coordinate through a linear transform. Then, a PCE surrogate model with coefficients estimated by the Gauss-quadrature scheme is obtained, and the utility of an inverse transform allows one to obtain the predicted FRF result in the original domain. Together with estimations on the confidence intervals and extreme boundary results, engineering applications are demonstrated by the uncertain FRF analysis of straight and L-shape clamp-pipe systems.

Low-Phase-Noise CMOS Relaxation Oscillators for On-Chip Timing of IoT Sensing Platforms

The design of low-phase-noise fully integrated frequency references is often a critical aspect in the development of low-cost integrated circuits for communication interfaces, sensing platforms, and biomedical applications. This work first discusses relaxation oscillator topologies and design approaches aimed at minimizing the phase noise; then, a single-comparator low-phase-noise RC relaxation oscillator is proposed, featuring a novel comparator self-threshold-adjustment technique. The oscillator was designed for a 10 MHz oscillation frequency. Electrical simulations performed on a 0.18 μm CMOS design confirmed that the proposed technique effectively rejects the flicker component of the comparator noise, allowing for a 152 dBc/Hz figure of merit at a 1 kHz offset frequency. The standard deviation of the jitter accumulated across 10k oscillation cycles is lower than 4 ns. The simulated current consumption of the circuit is equal to 50.8 μA with a 1.8 V supply voltage. The temperature sensitivity of the oscillation frequency is also notably low, as its worst-case value across process corners is equal to −20.8 ppm/°C from −55 °C to 125 °C.

A Power-Efficient TVC-Based Fast Auto-Frequency Calibration for PLLs

This brief presents a low-power, time-to-voltage converter (TVC)-based auto-frequency calibration (AFC) technology for phase-locked loops (PLLs). Instead of using power-hungry counters and finite-state machine (FSM), the proposed AFC uses TVC and comparator circuits to get the frequency information. Relying on a simple digital operable divide-by-3 (O-Div3) circuit, sampling procedure of TVCs is easy to be realized, which avoids the accumulation of multiple reference periods. Meanwhile, reference frequency is reused, that reduces the cost of extra clock. Beyond that, a binary-like search algorithm is proposed without frequency error. The 4.7-6.8-GHz PLL is implemented in 65-nm CMOS process. The total AFC setting time is less than 750 ns under 20-MHz reference, and consumes below 0.1 mW. Simultaneously, the adopted PLL achieves &#x2212;116.2-dBc/Hz&#x0040;1MHz phase noise when generating 4.89-GHz output.

Creating an Optical Comb of Reference Frequencies in an Optoelectronic Oscillator

Creating an Optical Comb of Reference Frequencies in an Optoelectronic Oscillator

Research on BG characteristics of a new multi-bandgap PnC

The bandgap (BG) of a phononic crystal (PnC) can suppress the propagation of elastic waves and has great potential in suppressing vibration. In this paper, a new type of multi-BG PnC is studied, which has many BGs in the low frequency. The eigenfrequency and displacement vector field distribution of the structure are calculated using the finite element method, and the influence of geometric parameters and material parameters on the first BG is analyzed. In addition, the BG ratio is defined to describe the coverage ability of multiple BGs in the reference frequency range. The results show that there are many flat bands in the dispersion curve of the structure. The BG covers almost all frequencies below 4000 Hz. In the range of 0–4000 Hz, the BG width accounts for more than 95% coverage, which can effectively suppress the propagation of elastic waves in the low frequency.

Grid-Forming Operation of Energy-Router Based on Model Predictive Control with Improved Dynamic Performance

The focus of this study is on the grid-forming operation of the Energy Router (ER) based on Model Predictive Control (MPC). ER is regarded as a key component of microgrids. It is a converter that interfaces the microgrid (s) with the utility grid. The ER has a multiport structure and bidirectional energy flow control. The ER concept can be implemented in Nearly Zero-Energy Buildings (NZEB) to provide flexible energy control. A concept is proposed where the ER works as a single grid-forming converter. The challenge is to keep the predefined reference voltage and frequency inside the NZEB in all possible modes, including the idle operation mode, current sources, and nonlinear load control. To gain stability and output voltage quality, the MPC is proposed. The design of the modified MPC algorithm with improved dynamics performance is explained. PLECS software is utilized to verify the proposed algorithm. The results demonstrate the suitable performance of the proposed control method in terms of total harmonic distortion of the output voltage. The influence of weighting coefficiencies is evaluated, showing the higher impact of the capacitor filter voltage on lowering the total harmonics distortion of the output voltage. Finally, the capability of the control system toward step change in the reference value is evaluated.