Phase-locked Oscillator Research Articles

Binding of cortical functional modules by synchronous high-frequency oscillations.

Whether high-frequency phase-locked oscillations facilitate integration ('binding') of information across widespread cortical areas is controversial. Here we show with intracranial electroencephalography that cortico-cortical co-ripples (~100-ms-long ~90 Hz oscillations) increase during reading and semantic decisions, at the times and co-locations when and where binding should occur. Fusiform wordform areas co-ripple with virtually all language areas, maximally from 200 to 400 ms post-word-onset. Semantically specified target words evoke strong co-rippling between wordform, semantic, executive and response areas from 400 to 800 ms, with increased co-rippling between semantic, executive and response areas prior to correct responses. Co-ripples were phase-locked at zero lag over long distances (>12 cm), especially when many areas were co-rippling. General co-activation, indexed by non-oscillatory high gamma, was mainly confined to early latencies in fusiform and earlier visual areas, preceding co-ripples. These findings suggest that widespread synchronous co-ripples may assist the integration of multiple cortical areas for sustained periods during cognition.

Study on phase-locked out-of-step fault characteristic analysis and protection of VSPSU

Abstract The variable-speed pumped storage unit (VSPSU) adopts flexible three-phase AC excitation, and the control dominant characteristics of the equipment are significant, which deeply affects the out-of-step (OOS) fault law and stability mechanism of VSPSU. Aiming at the OOS fault of VSPSU, this paper first defines the power angle of VSPSU and analyzes the influence of a phase-locked loop on the power angle stability of the unit. Then, the fault characteristics of the power angle instability of VSPSU are further studied. It is found that the traditional lens impedance protection scheme based on measuring the number of sliding poles has the problem that the phase-locked OOS oscillation cannot be responded to or the response is not timely. Combined with the research on the fault characteristics of power angle instability of VSPSU, an OOS protection method based on a bilateral annular blocker is proposed. The simulation results show that the proposed protection method can quickly and accurately reflect the phase-locked OOS fault of VSPSU, and meet the requirements of VSPSU for the reliability of OOS protection.

Edge scanning reflectometry for density profile measurement on the SPARC tokamak.

Edge scanning reflectometry (ESRL) on the SPARC tokamak aims to measure the electron density profile from the far scrape-off layer to the top of the typical H-mode pedestal and provide real-time data for plasma control. ESRL uses a standard frequency-modulated continuous wave technique from 18 to 90GHz. By implementing both the O-mode and left-hand-cutoff X-mode, it covers densities from ∼4 × 1018 to ∼4 × 1020m-3 at B0 ∼12T. A voltage-controlled oscillator acts as the frequency sweep source. Phase-locked dielectric resonator oscillators and bandpass filters generate base signals ∼9-15GHz. The signals are then frequency multiplied and amplified to reach the K (18-26GHz), Ka (26-40GHz), U (40-60GHz), and E (60-90GHz) bands. Multi-band signals are combined via the quasi-optical technique. ESRL plans to use oversized waveguides (∼20m one-way) and a bi-static arrangement to minimize signal losses and distortions while allowing system flexibility. A COMSOL Multiphysics RF model in 2D has been set up to simulate the reflectometry process and help decide the layout of the horn antennas. Engineering analyses of the key parts of the system have been carried out in support of its preliminary design.

Binding of cortical functional modules by synchronous high frequency oscillations.

Whether high-frequency phase-locked oscillations facilitate integration ('binding') of information across widespread cortical areas is controversial. Here we show with intracranial EEG that cortico-cortical co-ripples (~100ms long ~90Hz oscillations) increase during reading and semantic decisions, at the times and co-locations when and where binding should occur. Fusiform wordform areas co-ripple with virtually all language areas, maximally from 200-400ms post-word-onset. Semantically-specified target words evoke strong co-rippling between wordform, semantic, executive and response areas from 400-800ms, with increased co-rippling between semantic, executive and response areas prior to correct responses. Co-ripples were phase-locked at zero-lag over long distances (>12cm), especially when many areas were co-rippling. General co-activation, indexed by non-oscillatory high gamma, was mainly confined to early latencies in fusiform and earlier visual areas, preceding co-ripples. These findings suggest that widespread synchronous co-ripples may assist the integration of multiple cortical areas for sustained periods during cognition.

Coherent homodyne detection for amplified cross-beam electric-field induced second harmonic

The electric-field induced second harmonic (E-FISH) signal sensing is commonly used as a nonlinear optical technique to probe electric fields inside a plasma region. Cross-beam E-FISH is being investigated to improve spatial resolution by defining the interaction volume via a controlled geometry of two overlapping noncolinear optical beams. This drastic reduction in interaction length of the electric field and laser region results in a significant signal reduction. To overcome this signal reduction, we introduce coherent amplification of the cross-beam E-FISH signal by mixing the low E-FISH signal with a phase-locked bright local oscillator. We demonstrate enhancement of the signal. By introducing a local oscillator we can now derive the polarity of the measured electric field through the phase of the homodyne signal. To illustrate the technique, we, for the first time, to the best of our knowledge, measure the magnitude and the direction of the electric field in a cold atmospheric pressure plasma jet, which dynamically follows the profile of the applied bias current.

Dissemination of UTC(NIST) over 20 km of commercial optical fiber with active phase stabilization.

We demonstrate the transfer of a cesium frequency standard steered to UTC(NIST) over 20 km of dark telecom optical fiber. Our dissemination scheme uses an active stabilization technique with a phase-locked voltage-controlled oscillator. Out-of-loop characterization of the optical fiber link performance is done with dual-fiber and single-fiber transfer schemes. We observe a fractional frequency instability of 1.5 × 10-12 and 2 × 10-15 at averaging intervals of 1 s and 105 s, respectively, for the link. Both schemes are sufficient to transfer the cesium clock reference without degrading the signal, with nearly an order of magnitude lower fractional frequency instability than the cesium clocks over all time scales. The simplicity of the two-fiber technique may be useful in future long-distance applications where higher stability requirements are not paramount, as it avoids technical complications involved with the single-fiber scheme.

Sensory Drive Modifies Brain Dynamics and the Temporal Integration Window.

Perception is suggested to occur in discrete temporal windows, clocked by cycles of neural oscillations. An important testable prediction of this theory is that individuals' peak frequencies of oscillations should correlate with their ability to segregate the appearance of two successive stimuli. An influential study tested this prediction and showed that individual peak frequency of spontaneously occurring alpha (8-12 Hz) correlated with the temporal segregation threshold between two successive flashes of light [Samaha, J., & Postle, B. R. The speed of alpha-band oscillations predicts the temporal resolution of visual perception. Current Biology, 25, 2985-2990, 2015]. However, these findings were recently challenged [Buergers, S., & Noppeney, U. The role of alpha oscillations in temporal binding within and across the senses. Nature Human Behaviour, 6, 732-742, 2022]. To advance our understanding of the link between oscillations and temporal segregation, we devised a novel experimental approach. Rather than relying entirely on spontaneous brain dynamics, we presented a visual grating before the flash stimuli that is known to induce continuous oscillations in the gamma band (45-65 Hz). By manipulating the contrast of the grating, we found that high contrast induces a stronger gamma response and a shorter temporal segregation threshold, compared to low-contrast trials. In addition, we used a novel tool to characterize sustained oscillations and found that, for half of the participants, both the low- and high-contrast gratings were accompanied by a sustained and phase-locked alpha oscillation. These participants tended to have longer temporal segregation thresholds. Our results suggest that visual stimulus drive, reflected by oscillations in specific bands, is related to the temporal resolution of visual perception.

An Adaptive Phase Locked Oscillator to Improve the Performance of Fault Recovery from Commutation Failure in LCC-Based HVDC Systems

An adaptive control of phase lock oscillator (PLO) is proposed to increase the ability of LCC-based HVDC systems to successfully recover from commutation failure, where the dynamic performance during the recovery process is improved. The phase lock oscillator is one of the most important parts of the control system, which is used to trace the phase angle of commutating voltage. However, the PLO with constant parameters cannot provide accurate information under both steady-state operation and large disturbances. In our work, the control parameters of PLO can be adaptively adjusted, following the states of commutating voltage. When the system is operating in a steady state, the PLO selects parameters that exhibit improved small-signal stability, while parameters prioritizing dynamic behaviors with high-tracing accuracy are adopted during large disturbances. Case studies based on simulations in PSCAD/EMTDC and RT-LAB show that the proposed control strategy can improve the performance of fault recovery from CF.

A phase-locked transit time oscillator operated with low external guiding magnetic field

A phase-locked coaxial transit time oscillator is designed for microwave sources with a small volume and low magnetic field in high-power microwave coherent combining. The oscillator achieves controlled output phase through pre-modulation of electron beams. To improve the phase-locked performance with low magnetic fields, a reentrant input cavity is used to ensure the stability and uniformity of the electric field. Electric field uniformity of the buncher and extractor is also improved. To reduce the device volume, a reflector with pre-modulation function is used to reduce the axial size of the device. Particle-in-cell simulation shows that 5 kW input power is sufficient to lock-in a 610 MW output microwave, with a conversion efficiency of 40.6% at 0.66 T. The input power ratio reaches −50.8 dB. Simulation results demonstrate that the device can still achieve phase locking with a magnetic field as low as 0.5 T.

A low-noise X-band microwave source with digital automatic frequency control for electron paramagnetic resonance spectroscopy

We report a new design of microwave source for X-band electron paramagnetic resonance spectrometer. The microwave source is equipped with a digital automatic frequency control circuit. The parameters of the digital automatic frequency control circuit can be flexibly configured for different experimental conditions, such as the input powers or the quality factors of the resonator. The configurability makes the microwave source universally compatible and greatly extends its application. To demonstrate the ability of adapting to various experimental conditions, the microwave source is tested by varying the input powers and the quality factors of the resonator. A satisfactory phase noise as low as −135 dBc/Hz at 100-kHz offset from the center frequency is achieved, due to the use of a phase-locked dielectric resonator oscillator and a direct digital synthesizer. Continuous-wave electron paramagnetic resonance experiments are conducted to examine the performance of the microwave source. The outstanding performance shows a prospect of wide applications of the microwave source in numerous fields of science.

Partial locking in phase-oscillator populations with heterogenous coupling.

We consider a variant of the mean-field model of coupled phase oscillators with uniform distribution of natural frequencies. By establishing correlations between the quenched disorder of intrinsic frequencies and coupling strength with both in- and out-coupling heterogeneities, we reveal a generic criterion for the onset of partial locking that takes place in a domain with the coexistence of phase-locked oscillators and drifters. The critical points manifesting the instability of the stationary states are obtained analytically. In particular, the bifurcation mechanism of the equilibrium states is uncovered by the use of frequency-dependent version of the Ott-Antonsen reduction consistently with the analysis based on the self-consistent approach. We demonstrate that both the manner of coupling heterogeneity and correlation exponent have influence on the emergent patterns of partial locking. Our research could find applicability in better understanding the phase transitions and related collective phenomena involving synchronization control in networked systems.

Periodic, Quasi-Periodic and Phase-Locked Oscillations and Stability in the Fiscal Dynamical Model with Tax Collection and Decision-Making Delays

In this paper, we consider the complex dynamics of a fiscal dynamical model, which was improved from Wolfstetter classical growth cycle model by Sportelli et al. The main work of the present paper is to study the impact of fiscal policy delays on the national income adjustment processes using a dynamical method, such as double Hopf bifurcation analysis. We first use DDE-BIFTOOL to find the double Hopf bifurcation points of the system, and draw the bifurcation diagrams with two bifurcation parameters, i.e. the tax collection delay [Formula: see text] and the public expenditure decision-making delay [Formula: see text]. Then we employ the method of multiple scales to obtain two amplitude equations. By analyzing these amplitude equations, we derive the classification and unfolding of these double Hopf bifurcation points. And three types of double Hopf bifurcations are found. Finally, we verify the results by numerical simulations. We find complex dynamic behaviors of the system via the analytical method, such as stable equilibrium, stable periodic, quasi-periodic and phase-locked solutions in respective regions. The dynamical phenomena can help policy makers to choose a proper range of the delays so that they could effectively formulate fiscal policies to stabilize the economy.

Stable microwave LO distribution via a phase-locked OEO assisted by passive compensation

We present a stable microwave local oscillator (LO) distribution scheme based on a phase-locked optoelectronic oscillator (OEO) assisted by passive compensation. By injecting the LO reference into the phase-locked OEO and locking it with the oscillation signal, a microwave LO with a low phase noise can be tapped at the remote site. Meanwhile, a frequency-mixing-based passive compensation system is utilized to efficiently prevent the remote LO signal from the slow phase drift caused by the temperature susceptibility of fiber. In the experiment, a 10.8 GHz LO signal is stably distributed along a 6.8-km ring fiber to the remote site that is 1.8 km away from the local site. The frequency stability of 3.8 × 10−14 at 1s and 2.3 × 10−17 at 10000 s can be attained. The single-sideband (SSB) phase noise of the received signal at the remote site is up to –110 dBc/Hz at 10 kHz offset frequency with the root-mean-square phase jitter of 0.023 rad.

3D-Printed Liquid Cell Resonator with Piezoelectric Actuation for In-Line Density-Viscosity Measurements.

The in-line monitoring of liquid properties, such as density and viscosity, is a key process in many industrial areas such as agro-food, automotive or biotechnology, requiring real-time automation, low-cost and miniaturization, while maintaining a level of accuracy and resolution comparable to benchtop instruments. In this paper, 3D-printed cuboid-shaped liquid cells featuring a rectangular vibrating plate in one of the sides, actuated by PZT piezoelectric layers, were designed, fabricated and tested. The device was resonantly excited in the 3rd-order roof tile-shaped vibration mode of the plate and validated as a density-viscosity sensor. Furthermore, conditioning circuits were designed to adapt the impedance of the resonator and to cancel parasitic effects. This allowed us to implement a phase-locked loop-based oscillator circuit whose oscillation frequency and voltage amplitude could be calibrated against density and viscosity of the liquid flowing through the cell. To demonstrate the performance, the sensor was calibrated with a set of artificial model solutions of grape must, representing stages of a wine fermentation process. Our results demonstrate the high potential of the low-cost sensor to detect the decrease in sugar and the increase in ethanol concentrations during a grape must fermentation, with a resolution of 10 µg/mL and 3 µPa·s as upper limits for the density and viscosity, respectively.

Time-delayed Kuramoto model in the Watts-Strogatz small-world networks.

We study the synchronization of small-world networks of identical coupled phase oscillators through the Kuramoto interaction and uniform time delay. For a given intrinsic frequency and coupling constant, we observe synchronization enhancement in a range of time delays and discontinuous transition from the partially synchronized state with defect patterns to a glassy phase, characterized by a distribution of randomly frozen phase-locked oscillators. By further increasing the time delay, this phase undergoes a discontinuous transition to another partially synchronized state. We found the bimodal frequency distributions and hysteresis loops as indicators of the discontinuous nature of these transitions. Moreover, we found the existence of Chimera states at the onset of transitions.

On the VCO/Frequency Divider Interface in Cryogenic CMOS PLL for Quantum Computing Applications

The availability of quantum microprocessors is mandatory, to efficiently run those quantum algorithms promising a radical leap forward in computation capability. Silicon-based nanostructured qubits appear today as a very interesting approach, because of their higher information density, longer coherence times, fast operation gates, and compatibility with the actual CMOS technology. In particular, thanks to their phase noise properties, the actual CMOS RFIC Phase-Locked Loops (PLL) and Phase-Locked Oscillators (PLO) are interesting circuits to synthesize control signals for spintronic qubits. In a quantum microprocessor, these circuits should operate close to the qubits, that is, at cryogenic temperatures. The lack of commercial cryogenic Design Kits (DK) may make the interface between the Voltage Controlled Oscillator (VCO) and the Frequency Divider (FD) a serious issue. Nevertheless, currently this issue has not been systematically addressed in the literature. The aim of the present paper is to investigate the VCO/FD interface when the temperature drops from room to cryogenic. To this purpose, physical models of electronics passive/active devices and equivalent circuits of VCO and the FD were developed at room and cryogenic temperatures. The modeling activity has led to design guidelines for the VCO/FD interface, useful in the absence of cryogenic DKs.

Generation of ultra-low jitter radio frequency phase pulses by a phase-locked oscillator.

We demonstrate a novel, to the best of our knowledge, method for mode locking of an oscillator, which is based on the injection of a strong sinusoidal signal from an external source into the cavity. The oscillator generates a low phase noise carrier signal with a train of ultra-low jitter, short 2π phase pulses at a repetition period equal to the cavity round-trip time. Both the carrier signal and phase pulses are phase-locked to the external source. We demonstrate the effect in an optoelectronic oscillator that generates a train of short phase pulses at a high carrier frequency with the broadband spectrum of a dense RF frequency comb. The phase pulses can be converted to short, ultra-low jitter intensity RF pulses by beating the oscillator signal with the external source, used for locking.

Emergence of Stripe-Core Mixed Spiral Chimera on a Spherical Surface of Nonlocally Coupled Oscillators

We report on a stripe-core mixed spiral chimera in a system of nonlocally coupled phase oscillators, located on the spherical surface, where the spiral wave consisting of phase-locked oscillators is separated by a stripe-type region of incoherent oscillators into two parts. We analyze the existence and stability of the stripe-core mixed spiral chimera state rigorously, on the basis of the Ott–Antonsen reduction theory. The stability diagram for the stationary states including the spiral chimeras as well as incoherent state is presented. Our stability analysis reveals that the stripe-core mixed spiral chimera state emerges as a unique attractor and loses its stability via the Hopf bifurcation. We verify our theoretical results using direct numerical simulations of the model system.

Statistical analysis of periodic data in neuroscience

Many experimental paradigms in neuroscience involve driving the nervous system with periodic sensory stimuli. Neural signals recorded using a variety of techniques will then include phase-locked oscillations at the stimulation frequency. The analysis of such data often involves standard univariate statistics such as T-tests, conducted on the Fourier amplitude components (ignoring phase), either to test for the presence of a signal, or to compare signals across different conditions. However, the assumptions of these tests will sometimes be violated because amplitudes are not normally distributed, and furthermore weak signals might be missed if the phase information is discarded. An alternative approach is to conduct multivariate statistical tests using the real and imaginary Fourier components. Here the performance of two multivariate extensions of the T-test are compared: Hotelling’s T2 and a variant called Tcirc2. A novel test of the assumptions of Tcirc2 is developed, based on the condition index of the data (the square root of the ratio of eigenvalues of a bounding ellipse), and a heuristic for excluding outliers using the Mahalanobis distance is proposed. The Tcirc2 statistic is then extended to multi-level designs, resulting in a new statistical test termed ANOVAcirc2. This has identical assumptions to Tcirc2, and is shown to be more sensitive than MANOVA when these assumptions are met. The use of these tests is demonstrated for two publicly available empirical data sets, and practical guidance is suggested for choosing which test to run. Implementations of these novel tools are provided as an R package and a Matlab toolbox, in the hope that their wider adoption will improve the sensitivity of statistical inferences involving periodic data.

Photonic microwave synthesizer based on optically referenced sub-sampling phase-locked optoelectronic oscillator

Wideband and low phase noise microwave synthesizers are of critical significance for various applications. Phase-locked loop (PLL) based microwave synthesizers are widely used. Normally, the phase noise of the PLL based microwave synthesizer is limited by the phase noise of the reference, phase detector, frequency divider and voltage-controlled oscillator (VCO). It is challenging to achieve a pure electronic microwave synthesizer with wide frequency coverage and low phase noise, simultaneously. Here, we propose a photonic microwave synthesizer which incorporates an ultra-low phase noise fiber mode-locked laser (MLL) based reference and a wideband frequency tunable optoelectronic oscillator (OEO) based VCO in a hybrid optoelectronic sub-sampling PLL. The frequency of the OEO can be locked to the harmonics of the repetition-rate of the fiber MLL, which combines the distinct advantages of the low phase noise of MLL and the wideband frequency tuning of OEO. A sub-sampling phase detector formed by a balanced optical microwave phase detector (BOMPD) eliminates the use of RF frequency divider and maintains low residual phase noise. We attain an X- and Ku-band photonic microwave synthesizer with over an octave frequency coverage from 8 GHz to 18 GHz, frequency synthesis step of 60.74 MHz and phase noise of -80 dBc/Hz at 100 Hz offset and -100 dBc/Hz at 1 kHz offset for 10 GHz output. The characteristics of the optoelectronic sub-sampling phase detector, the phase-locking dynamics of the hybrid optoelectronic PLL, and the phase noise of the synthesized RF signals are both theoretically and experimentally investigated. The experimental results agree well with the theoretical models. Our approach is promising to achieve wideband and low phase noise microwave synthesis.