Frequency Stability Of Oscillators Research Articles

Stress Fields Distribution and Simulation in 3C-SiC Resonators

In this paper the stress field distribution in 3C-SiC (111) resonators has been studied by micro-Raman measurements and COMSOL simulations. The measurements show that the asymmetry of the anchor points configuration produce an asymmetry in the stress filed distribution. This behavior has been confirmed also by the simulations. Furthermore, from the simulations the importance of the reduction of the under etching of the anchor points of the resonators has also been observed. In fact the reduction of this under etch produces a decrease of the stress in the double clamped beams, a small reduction of the resonance frequency, and a large reduction of the Q-factor and then of the oscillation frequency stability of the resonators in closed-loop operation.

Dark solitons and their bound states in a nonlinear fiber with second- and fourth-order dispersion

We study the excitations of dark solitons in a nonlinear optical fiber with the second- and fourth-order dispersion, and find the emergence of striped dark solitons (SDSs) and some multi-dark-soliton bound states. The SDSs can exhibit time-domain oscillating structures on a plane wave, and they have two types: the ones with or without the total phase step, while the multi-dark-soliton bound states exhibit different numbers of amplitude humps. By the modified linear stability analysis, we regard the SDSs as the results of the competition between periodicity and localization, and analytically give their existence condition, oscillation frequency, and propagation stability, which show good agreements with numerical results. We also provide a possible interpretation of the formation of the existing striped bright solitons (SBSs), and find that SBS will become the pure-quartic soliton when its periodicity and localization carry equal weight. Our results provide the theoretical support for the experimental observation of striped solitons in nonlinear fibers, and our method can also guide the discovery of striped solitons in other physical systems.

Actuators linearization of a large volume environmental simulation chamber via pulse code modulation

Ultra-stable room-sized environmental chambers may involve significant power variations leading to hysteresis and nonlinearities of the stabilization system. This paper describes utilization of a pulse code modulation control which significantly reduces observed nonlinearity of the chamber actuation system. Stability of environmental conditions for temperature ΔT=±25 mK (15–35 °C dynamic range), relative humidity ΔRh=±0.1% (3%–95% dynamic range), and pressure ΔP=±12 Pa (±500 Pa dynamic range) was achieved within 27 m3 chamber volume, which is two orders of magnitude better than the corresponding stabilization achievable using a standard linear proportional–integral–derivative (PID) controller. Utilizing this chamber we have demonstrated two orders of magnitude improvement of the operational relative frequency stability of ultrastable quartz oscillators (USO), reaching 2×10−13 stability at 1-105 s averaging time.

Ultra-long-distance distribution of low-phase-noise reference lightwave for optical communications.

The remote delivery of optical reference with highly stable oscillation frequency and carrier phase can eliminate the need of digital signal processing for the estimation of these parameters in optical communication. The distribution distance of the optical reference has been limited, however. In this paper, an optical reference distribution over 12,600 km is achieved while maintaining low-noise characteristics, using an ultra-narrow-linewidth laser as a reference source and a fiber Bragg grating filter for noise removal. The distributed optical reference enables 10 GBaud, 5 wavelength-division-multiplexed dual-polarization 64QAM data transmission without using carrier phase estimation, which significantly reduces off-line signal processing time. In the future, this method can enable all coherent optical signals in the network to be synchronized to a common reference ideally, thereby improving overall energy efficiency and cost.

Improvement of Absorption and Emission Phenomena of 1.55µm Quantum Dot Laser using Indium Nitride

This paper presents the improvement of emission and absorption phenomena of 1.55µm quantum dot laser by enhancing the stability of oscillation frequency and minimizing absorption loss. Among the key parameters related to these absorption and emission phenomena, the effective density of state, rate of change of carrier mobility, and optical feedback level were extensively investigated to reduce the fluctuation of the oscillation frequency of the emitted light as well as the absorption loss. These phenomena were investigated through mathematical analysis and numerical simulation using AlN, GaN, and InN quantum dots as the active material of the laser structure. The numerical results were compared, confirming that the InN quantum dot in the active layer significantly improved the absorption and emission phenomena of the quantum dot laser. At the same time, InN is capable of emitting light at a wavelength of 1.55µm due to its band gap of 0.7eV. Consequently, InN has a superior potentiality to other existing materials to fabricate the quantum dot laser operating at the 1.55µm wavelength, which is the window of an optical fiber communication system that offers the lowest attenuation. Therefore, the InN quantum dot laser is expected to be a promising candidate not only in the field of semiconductor technology but also in the field of optical communication in the imminent future.

Ultrafast generation and detection of coherent acoustic phonons in SnS0.91Se0.09

The rapid growth of attention to tin sulfide (SnS) is due to its efficient application in the field of thermoelectricity, and its doping product SnS0.91Se0.09 can obtain a high average thermoelectric figure of merit (ZTave≈ 1.25). Although many efforts have been made to reveal the mechanisms associated with electron transport and heat conduction, the role of lattice vibration remains poorly understood. Here, we studied the coherent vibration dynamics in SnS0.91Se0.09 bulk single crystal by using the femtosecond two-color pump-probe optical reflectivity technique. The oscillation signal in the time domain of SnS0.91Se0.09 is considered to be an electron–phonon interaction. The coherent dynamics of longitudinal acoustic phonons in this coupling behavior is closely related to probe polarization and excitation power. The stability of oscillation frequency reveals the microscopic mechanism of phonon conduction, and further understands the lattice nonharmonic caused by electron–phonon interaction in light-induced.

Enhanced Frequency Stability of SAW Yarn Tension Sensor by Using the Dual Differential Channel Surface Acoustic Wave Oscillator.

This paper presents a 60 MHz surface acoustic wave (SAW) yarn tension sensor incorporating a novel SAW oscillator with high-frequency stability. A SAW delay line was fabricated on ST-X quartz substrate using the unbalanced-split electrode and bi-directional engraving slots. The dual differential channel delay linear acoustic surface wave oscillator is designed and implemented to test yarn tension, which can effectively remove the interference of temperature, humidity, and other peripheral factors through differential design. The yarn tension sensor using the surface acoustic wave has high-precision characteristics, and the SAW delay line oscillator is designed to ensure the test system’s stable operation. The effect of time and tension on oscillator frequency stability is studied in detail, and the single oscillator and the dual differential channel system were tested, respectively. After using the dual differential channel system, the short-term frequency stability from is reduced from 1.0163 ppm to 0.17726 ppm, the frequency accuracy of the tension sensor is improved from 134 Hz to 27 Hz, and the max frequency jump steady is reduced from 2.2395 ppm to 0.45123 ppm.

Microgrid Stability Improvement Using a Deep Neural Network Controller Based VSG

In order to support the inertia of a microgrid, virtual synchronous generator control is a suitable control method. However, the use of the virtual synchronous generator control leads to unacceptable transient active power sharing, active power oscillations, and the inverter output power oscillation in the event of a disturbance. This study aims to propose a deep neural network controller which combines the features of a restricted Boltzmann machine and a multilayer neural network. To initialize a multilayer neural network in the unsupervised pretraining method, the restricted Boltzmann machine is applied as a very important part of the deep learning controller. The Lyapunov stability method is used to update the weight of the deep neural network controller. The proposed method performs power oscillation damping and frequency stabilization. The experimental and simulation results are presented to assess the usefulness of the suggested method in damping oscillations and frequency stabilization.

Stability Analysis of Grid-Connected VSC Dominated by PLL Using Electrical Torque Method

The instability issue of the grid-connected Voltage Source Converter (VSC) dominated by Phase-lock loop (PLL) is investigated using the electrical torque method in this paper. The system dynamic model and steady-state relationship of variables are first established. Then, a basic two-order model representing the PLL natural oscillation mode is extracted. The impacts of the current control loop and altering current grid (ACG) on the PLL oscillation mode are derived using the electrical torque method. As a result, analytical expressions of the system synchronous and damping coefficients are obtained. Based on the derived synchronous and damping coefficient, qualitative evaluations of the impacts of the system parameters on the oscillation frequency and system stability can be achieved. It is drawn that a small PLL time constant, low infinite source voltage, heavy load, reactive power absorption, and long electrical distance will deteriorate system stability. Moreover, a sufficient analytical stability criterion for the grid-connected VSC is derived from the damping coefficient. The system stability can be directly evaluated through the operation points and system parameters, and the quantitative evaluation of the system stability is achieved. The eigenvalue analysis and electromagnetic transient simulation have verified the reliability and effectiveness of the theoretical analysis.

Theoretical Analysis of Frequency Stabilization and Pulling Effects in a Gyrotron with Delayed Reflection

The effect of delayed reflection on frequency stabilization and pulling in a gyrotron oscillator is studied. Simple theoretical formulas for start-oscillation current, oscillation frequency, and frequency stabilization rate are derived in the framework of the linear (or small-signal) theory and verified by numerical simulation for the gyrotron with fixed axial profile of the RF field. Capabilities of increasing frequency stability are analyzed. A possibility of expanding frequency tunability range owing to excitation of high-order axial modes is demonstrated.

METHOD FOR CALCULATING THE RELIABILITY OF QUARTZ RESONATORS

In the process of developing a thermocompensated quartz generator, it was necessary to calculate the reliability indicators of such an important element of the circuit as a quartz resonator for a failure-free period of 15 000 hours. The main parameter that can be used to evaluate the reliability of the quartz resonator is the stability of the nominal oscillation frequency. It is the stability of the nominal frequency of the resonator that formed the basis of the new developed technique. The method includes rules for constructing a probabilistic and statistical model of the dependence of the resonator frequency change on the test time. The article describes the work done on the accelerated evaluation of the reliability of piezoelectric resonators RK563 on the basis of probabilistic and statistical modeling of the behavior of the frequency from the test time. The method of mathematical modeling is based on the results of incomplete tests for a period of 30…50 % of the set value of the minimum operating time.

Low-Voltage Gate-Leakage-Based Timer Using an Amplifier-Less Replica-Bias Switching Technique in 55-nm DDC CMOS

Energy-efficient timer circuits are required in numerous applications for periodic operations, such as performing measurements and communicating data. In this paper, we present a gate-leakage-based timer that utilizes an amplifier-less replica-bias switching technique to generate a stable frequency, which can operate at a low supply voltage. To guarantee a stable oscillation frequency in a small circuit area, the proposed design adopts an architecture that discharges a pre-charged capacitor through a resistive element (gate-leaking MOS capacitor) with a low-leakage switch. In the proposed switching technique, the low-voltage timer operates by tracking the discharging terminal of the capacitor and biasing the reference voltage of the switch unit, thereby enabling the minimization of the leakage current without the need for analog amplifier circuits. The high supply sensitivity of the timer is addressed by regulating the supply voltage using a native NMOS header (NNH). The proposed design is fabricated using the 55-nm deeply depleted channel (DDC) CMOS technology, which has a strong body coefficient and occupies an active circuit area of 0.0022 mm2. The measurements show that the proposed design can achieve an energy-per-cycle value of 25 pJ/cycle at a supply voltage of 350 mV when body biasing is applied. The measured Allan deviation floor is 200 ppm at room temperature. The timer exhibits an average temperature sensitivity of 810 ppm/°C for four samples. Moreover, a reduction in the supply sensitivity by a factor of 26 using the NNH is demonstrated in an active circuit area of 0.0034 mm2.

Low offset frequency 1/f flicker noise in spin-torque vortex oscillators

Low-frequency noise close to the carrier remains little explored in spin-torque nano-oscillators. However, it is crucial to investigate as it limits the oscillator's frequency stability. This work addresses the low offset frequency flicker noise of a spin-torque vortex oscillator in the regime of large-amplitude steady oscillations. We first phenomenologically expand the nonlinear auto-oscillator theory, aiming to reveal the properties of this noise. We then present a thorough experimental study of the oscillator's $1/f$ flicker noise and discuss the results based on the theoretical predictions. Thereby, we connect the oscillator's nonlinear dynamics with the concept of flicker noise and furthermore refer to the influence of a standard $1/f$ noise description based on the Hooge formula, taking into account the nonconstant magnetic oscillation volume, which contributes to the magnetoresistance.

Simulation of plasma dynamics during discharge ignition in Hall thruster

Because of the lack of effective methods to measure the evolution of plasma in the channel of a Hall thruster, the dynamic behavior of the Hall thruster, the ignition process, was investigated by a two-dimensional axisymmetric fully kinetic particle-in-cell/Monte Carlo collision model. The corresponding evolutions of plasma density, electric potential, and neutral density during the ignition process are discussed. The results which show a pulse duration of 15 μs, a peak current value of 142 A and a stable oscillation frequency of 20 kHz, indicate that during the ignition process, the anode current rises rapidly with the increase of the plasma density, the consumption of the neutrals, and the change of the position where the main potential drops. The model can provide a new and valid method to analyze the ignition of the Hall thruster.

Stable and Low-Spurs Optoelectronic Oscillators: A Review

An optoelectronic oscillator (OEO) is an optoelectronic hybrid oscillator which utilizes ultra-low-loss fiber as an electro-magnetic energy storage element, overcoming the limits of traditional microwave oscillators in phase noise performance. Due to their ability to generate ultra-low phase noise microwave signal, optoelectronic oscillators have attracted considerable attentions and are becoming one of the most promising and powerful microwave signal sources. In this paper, we briefly introduce the operation principle and discuss current research on frequency stability and spurious suppression of optoelectronic oscillators.

Impact of excitation waveform on the frequency stability of electrostatically-actuated micro-electromechanical oscillators

In this paper, the frequency stability of high-Q electrostatically-actuated MEMS oscillators with cubic restoring forces, and its relation with the amplitude, the phase and the shape of the excitation waveform, is studied. The influence on close-to-the carrier frequency noise of additive processes (such as thermomechanical noise) or parametric processes (bias voltage fluctuations, feedback phase fluctuations, feedback level fluctuations) is taken into account. It is shown that the optimal operating conditions of electrostatically-actuated MEMS oscillators are highly waveform-dependent, a factor that is largely overlooked in the existing literature. This simulation-based study covers the cases of harmonic and pulsed excitation of a parallel-plate capacitive MEMS resonator.

Picosecond-precision multichannel autonomous time and frequency counter.

This paper presents the design, implementation, and test results of a multichannel time interval and frequency counter developed as a desktop instrument. The counter contains four main functional modules for (1) performing precise measurements, (2) controlling and fast data processing, (3) low-noise power suppling, and (4) supplying a stable reference clock (optional rubidium standard). A fundamental for the counter, the time interval measurement is based on time stamping combined with a period counting and in-period two-stage time interpolation that allows us to achieve wide measurement range (above 1 h), high precision (even better than 4.5 ps), and high measurement speed (up to 91.2 × 106 timestamps/s). The frequency is measured up to 3.0 GHz with the use of the reciprocal method. Wide functionality of the counter includes also the evaluation of frequency stability of clocks and oscillators (Allan deviation) and phase variation (time interval error, maximum time interval error, time deviation). The 8-channel measurement module is based on a field programmable gate array device, while the control unit involves a microcontroller with a high performance ARM-Cortex core. An efficient and user-friendly control of the counter is provided either locally, through the built-in keypad or/and color touch panel, or remotely, with the aid of USB, Ethernet, RS232C, or RS485 interfaces.

Effects of two‐area variable inertia on transient stabilisation in interconnected power system with DFIG‐based wind turbines

This study investigates a novel operating method of the interconnected power grid to improve dynamic stability using variable inertia control of large wind farms. In this scheme, the system inertia is considered as an adjustable operating parameter which can be regulated for inter-area power oscillation control and frequency support. Based on the linear state equations derived from a two-area interconnected power system, the effect of the controlled inertia on power oscillation damping is evaluated theoretically considering the different cases of power feeding and receiving networks. The respective wind turbine variable inertia control strategies for the feeding and receiving regional networks are proposed to enhance both inter-area power oscillation damping and frequency stability. A typical two-area interconnected power system with a high 30% wind penetration is simulated, which consists of four conventional power plants and two doubly fed induction generator (DFIG)-based wind farms. The results demonstrate that by using the proposed control scheme, the frequency stability and the inter-area oscillation damping are both significantly improved for the more effective inertia support in the interconnected power system.

Design and implementation of a low-power hybrid capacitive MEMS oscillator

This paper reports on the design and implementation of a low power MEMS oscillator based on capacitively transduced silicon micromachined resonators. The analysis shows how design parameters of MEMS resonator impact on the power requirement of the oscillator, particularly with a view towards informing the impact of device and interface parasitics. The analysis is based on resonators fabricated in a 2-μm gap SOI-MEMS foundry process. The sustaining circuit, which is based on a Pierce topology, is fabricated in a standard 0.35μm process. An automatic gain control (AGC) is adopted to suppress the mechanical non-linearity so as to improve oscillator frequency stability. The 110-kHz MEMS and CMOS dies are assembled within a standard ceramic package and electrically integrated through wire bonds. The oscillator core consumes 400nA (900nA with parasitic readout loading) at 1.2-V dc supply while demonstrating a frequency stability of less than 0.5ppm. The work provides a thorough analysis and design guidelines for both MEMS and CMOS circuit design with a view towards minimizing overall power consumption. The implications of the results reported in this paper are towards enabling a new class of low power resonant MEMS sensors that utilize the oscillator as a front-end building block.

Introduction to the Special Issue on Celebrating the 50th Anniversary of the Allan Variance.

The papers in this special issue focus on the Allan Variance (also referred to as two-sample variance), a measurement technique that determeines the frequency stability in amplifiers, clocks, and oscillators.