Phase Drift Research Articles

Transition of synchronization state during the quasiperiodic route to chaos in coupled friction-induced continuous oscillators

Friction-induced vibration, particularly associated with the squealing problem in disk brake systems, has been a longstanding challenge in the automotive industry. In our research, we employed the synchronization theory to gain insights into the interaction between two coupled cantilever beams attached with tip masses. This proposed model emulates the dynamics of a mountain bike disk brake assembly. The work explores a range of collective behaviors, including synchronized periodic, multi-periodic, quasiperiodic, as well as desynchronized chaotic and quasiperiodic oscillations. Despite numerous studies reported on the synchronization phenomenon in discrete friction-induced oscillatory systems, there appears to be a lack of similar research on continuous systems. This work stands as the first of its kind in exploring the dynamics of synchronization between two coupled continuous systems exhibiting a quasiperiodic route to chaos. A bifurcation study is conducted utilizing the Poincaré points corresponding to the local maxima of oscillation amplitude with respect to the zero-velocity crossing. The results showed the existence of narrow multi-periodic windows during the quasiperiodic route at several locations. Additionally, the existence of multiple quasiperiodic attractors exhibiting different states of synchronization for the same set of parameters is observed. We analyzed the time evolution of the cumulative instantaneous phase difference between the coupled signals and identified distinct states of synchronization possessed by the system. The coupled system undergoes interesting phenomena such as complete phase lock, intermittent phase lock, and phase drifting. Moreover, the transition occurring to the state of synchronization during the quasiperiodic route to chaos is studied employing the phase locking value, the Pearson linear correlation coefficient, and the relative mean frequency. Notably, our findings revealed that while the Pearson correlation can effectively identify both the mode and strength of synchronization, other measures such as phase lock value and relative mean frequency only reflect synchronization strength.

Two-tone RF signal phase drift measurement system

Modern electronic circuits designed for various applications, such as telecommunications, radar systems, and high-energy physics experiments, require increasing performance of RF signal phase (propagation delay) drift in the signal chain reaching millidegree (or femtosecond) stability levels at hundreds of MHz or GHz frequencies. Therefore, long-term phase change measurements are getting difficult and sensitive to effects rarely considered in earlier designs. Consequently, new and more precise techniques for phase drift measurements and compensation must be developed.This paper presents the concept of a novel RF signal phase drift measurement system based on a unique two-tone approach to accurately measure the phase drift, providing an improved alternative to traditional measurement methods. The idea can be used in systems with digital signal processing of measurement signals. An auxiliary (2nd tone) signal is introduced in the RF chain to allow for extracting phase changes introduced by the system components.The principles of the system are explained, including mathematical basics. Next, a detailed description of a sample system, illustrating how the concept can be practically implemented, is presented. The measured test system achieved a temperature coefficient of a signal propagation delay of just 0.67 fs/°C @ RF frequency of 162.5 MHz. The paper concludes by discussing the system’s performance and highlighting its strengths and limitations. Furthermore, the authors outlined plans for future research and potential improvements to the system.

Delay drift compensation of an optoelectronic oscillator over a large temperature range through continuous tuning

Phase noise reduces target sensitivity in radar and increases bit error rate in telecommunications systems. Optoelectronic oscillators are known for using optical fibre technology to realise the large delay required to attain superior phase noise performance compared to conventional microwave source technology. However, the long fibre is vulnerable to environmentally induced phase perturbations, while conventional phase shifters have insufficient range to compensate for the phase drift over the operational temperature range without the use of a temperature-controlled enclosure. Here we introduce a vector modulator controlled by a Stuart-Landau integrator, as a solution to non-efficient tuning for the phase shift. The concept is verified by simulation and experimentally demonstrated using an optoelectronic oscillator phase-locked to a system reference. Phase lock is maintained over four free spectral ranges equivalent to a tuning phase range of 1440° when the optoelectronic oscillator is cycled over a 10 °C to 85 °C temperature range. These demonstrations highlight the practical potential of our continuous tuning method.

Robust continuous-variable quantum key distribution in the finite-size regime

Quantum key distribution (QKD) has been proven to be theoretically unconditionally secure. However, any theoretical security proof relies on certain assumptions. In QKD, the assumption in the theoretical proof is that the security of the protocol is considered under the asymptotic case where Alice and Bob exchange an infinite number of signals. In the continuous-variable QKD (CV-QKD), the finite-size effect imposes higher requirements on block size and excess noise control. However, the local local oscillator (LLO) CV-QKD system cannot be considered time-invariant under long blocks, especially in cases of environmental disturbances. Thus, we propose an LLO CV-QKD scheme with time-variant parameter estimation and compensation. We first establish an LLO CV-QKD theoretical model under the temporal modes of continuous-mode states. Then, a robust method is used to compensate for arbitrary frequency shift and arbitrary phase drift in CV-QKD systems with longer blocks, which cannot be achieved under traditional time-invariant parameter estimation. Besides, the digital signal processing method predicated on high-speed reference pilots can achieve a time complexity of O(1). In the experiment, the frequency shift is up to 89.05 MHz/s and phase drift is up to 3.036 Mrad/s using a piezoelectric transducer (PZT) to simulate the turbulences in the practical channel. With a signal-to-interference ratio (SIR) of −51.67 dB, we achieve a secret key rate (SKR) of 0.29 Mbits/s with an attenuation of 16 dB or a standard fiber of 80 km. This work paves the way for future long-distance field-test experiments in the finite-size regime.

Research on Phase Stabilization Algorithm of Femtosecond Timing System

This paper presents the design, implementation, and validation of a femtosecond timing system aimed at achieving precise time control and phase synchronization for large particle accelerators. A prototype system utilizing a continuous wave laser was developed, focusing on minimizing timing jitter and long-term phase drift. Key components include an optical delay line for coarse adjustments and a fiber stretcher for fine-tuning, achieving an adjustment precision of 1 femtosecond. The system incorporates a phase detection module with a non-In-phase/Quadrature downconversion approach, enabling high-accuracy phase measurements. A collaborative algorithm was designed to optimize the interplay between the optical delay line and the fiber stretcher, utilizing a proportional-integral-derivative (PID) control algorithm to enhance adjustment precision. A Field Programmable Gate Array (FPGA) served as the core interface converter, facilitating data communication and real-time phase information acquisition. Experimental results demonstrated significant improvements in phase stability, with average phase deviation reduced from 1374.104 fs to 15.782 fs, showcasing the effectiveness of the proposed system in achieving high precision and stability in phase control. This research provides a solid foundation for future advancements in timing systems for high-frequency reference signals.

A Precessing Stellar Disk Model for Superorbital Modulations of the Gamma-Ray Binary LS I+61° 303

Gamma-ray binary LS I+61° 303 consists of a neutron star orbiting around a Be star with a period of P orb ≃ 26.5 days. Apart from orbital modulations, the binary shows long-term flux variations with a superorbital period of Psup≃4.6yr as seen in nearly all wavelengths. The origin of this superorbital modulation is still not well understood. Under the pulsar wind–stellar outflow interaction scenario, we propose that the superorbital modulations of LS I+61° 303 could be caused by the precession of the Be disk. Assuming X-rays arise from synchrotron radiation of the intrabinary shock, we develop an analytical model to calculate expected flux modulations over the orbital and superorbital phases. The asymmetric two-peak profiles in orbital light curves and sinusoidal-like long-term modulations are reproduced under the precessing disk scenario. The observed orbital phase drifting of the X-ray peak and our fitting of long-term X-ray data indicate that the neutron star is likely orbiting around the star with a small eccentricity and periastron phase around Φp ∼ 0.6. We compare the Corbet diagrams of LS I+61° 303 with other Be/X-ray binaries, and the linear correlation in the Psup–Porb diagram suggests that the precession of the Be disk in LS I+61° 303 is induced by the tidal torque of its neutron star companion.

Wake Three-Dimensionality of Profiled Blunt Trailing Edge Bodies with Varying Chord Length

This paper investigates experimentally the structure of turbulent blunt trailing edge body wakes with varying boundary-layer thicknesses controlled through the freestream velocity and the chord length. The intrinsic effect of transition to turbulence on the vortex-shedding frequency, strength, and its three-dimensional structure is explored. At large-scales, the vortex shedding is characterized by significant phase variations along the span, which vary stochastically and are punctuated by vortex dislocations when the phase differences grow large. These features of the vortex shedding are quantitatively examined in a streamwise–spanwise plane of the wake with particle image velocimetry. When the point of transition shifts upstream due to an increasing Reynolds number, greater phase variations in the vortex shedding along the span and more frequent dislocation events are produced. These changes are linked to the spanwise correlation of the streamwise velocity in the wake. In the turbulent boundary-layer regime, it is found that the phase drift does not change significantly. The decline in the spanwise correlation with increasing boundary-layer thickness in this regime is instead linked to the relative strength of the vortex shedding compared to the random turbulent fluctuations in the wake.

The design of LLRF system for STCF storage ring

The Super Tau Charm Facility (STCF) is a new generation of high brightness electron–positron collider planned by China, designed to achieve a center of mass collision energy is 2–7[Formula: see text]GeV and a peak brightness is 0.5–[Formula: see text][Formula: see text]cm[Formula: see text]s[Formula: see text]. The digital low-level RF control system (LLRF), as the essential equipment of the storage ring RF system, is usually responsible for maintaining the stability of the cavity field. This paper presents the design scheme of LLRF for cavity in STCF storage ring, which mainly includes the hardware structure and software design of the system. We perform simulation analysis on the STCF RF system to evaluate the influence of delay and control parameters on the stability of the system and the influence of control parameters on the suppression of two kinds of noise. Desktop testing on the existing prototype demonstrates that the adopted direct-sampling architecture introduces less phase drift compared to the down-conversion architecture. Under the direct-sampling architecture, non-IQ demodulation offers better SNR and stability in both amplitude and phase. Specifically, direct-sampling in non-IQ mode achieves open-loop RMS short-term stability of 0.019% for amplitude and 0.021∘ for phase. Long-term stability in the closed-loop setting measures 0.027% for amplitude and 0.024∘ for phase.

Investigation of 3D Bipedal Spring-Loaded Inverted Pendulum Human Walking Model on Laterally Vibrating Surfaces in the Case of Phase Drift, Phase Pulling, and Synchronization

Investigation of 3D Bipedal Spring-Loaded Inverted Pendulum Human Walking Model on Laterally Vibrating Surfaces in the Case of Phase Drift, Phase Pulling, and Synchronization

Simultaneous frequency and phase corrections of single-shot MRS data using cross-correlation.

The objective of this study was to propose a novel preprocessing approach to simultaneously correct for the frequency and phase drifts in MRS data using cross-correlation technique. The performance of the proposed method was first investigated at different SNR levels using simulation. Random frequency and phase offsets were added to a previously acquired STEAM human data at 7 T, simulating two different noise levels with and without baseline artifacts. Alongside the proposed spectral cross-correlation (SC) method, three other simultaneous alignment approaches were evaluated. Validation was performed on human brain data at 3 T and mouse brain data at 16.4 T. The results showed that the SC technique effectively corrects for both small and large frequency and phase drifts, even at low SNR levels. Furthermore, the mean square measurement error of the SC algorithm was comparable to the other three methods used, with much faster processing time. The efficacy of the proposed technique was successfully demonstrated in both human brain MRS data and in a noisy MRS dataset acquired from a small volume-of-interest in the mouse brain. The study demonstrated the availability of a fast and robust technique that accurately corrects for both small and large frequency and phase shifts in MRS.

Field-domain rapid-scan EPR at 240 GHz for studies of protein functional dynamics at room temperature

We present field-domain rapid-scan (RS) electron paramagnetic resonance (EPR) at 8.6T and 240GHz. To enable this technique, we upgraded a home-built EPR spectrometer with an FPGA-enabled digitizer and real-time processing software. The software leverages the Hilbert transform to recover the in-phase (I) and quadrature (Q) channels, and therefore the raw absorptive and dispersive signals, χ′ and χ′′, from their combined magnitude (I2+Q2). Averaging a magnitude is simpler than real-time coherent averaging and has the added benefit of permitting long-timescale signal averaging (up to at least 2.5×106 scans) because it eliminates the effects of source-receiver phase drift. Our rapid-scan (RS) EPR provides a signal-to-noise ratio that is approximately twice that of continuous wave (CW) EPR under the same experimental conditions, after scaling by the square root of acquisition time. We apply our RS EPR as an extension of the recently reported time-resolved Gd-Gd EPR (TiGGER) [Maity et al., 2023], which is able to monitor inter-residue distance changes during the photocycle of a photoresponsive protein through changes in the Gd-Gd dipolar couplings. RS, opposed to CW, returns field-swept spectra as a function of time with 10ms time resolution, and thus, adds a second dimension to the static field transients recorded by TiGGER. We were able to use RS TiGGER to track time-dependent and temperature-dependent kinetics of AsLOV2, a light-activated phototropin domain found in oats. The results presented here combine the benefits of RS EPR with the improved spectral resolution and sensitivity of Gd chelates at high magnetic fields. In the future, field-domain RS EPR at high magnetic fields may enable studies of other real-time kinetic processes with time resolutions that are otherwise difficult to access in the solution state.

Methodology for evaluating the quality of a digital channel of a satellite communication system based on an integral indicator and a fuzzy logical conclusion

The problem of evaluating the quality of digital channels of satellite communication systems (DCSCS) is considered. It is shown that two quality assessment strategies are used in practice: the first is an assessment of quality from the position of consumers of services and specialists in the provision of communication services in the market; the second is an assessment of quality from the position of specialists in technical operation. It is concluded that the first strategy does not allow to identify the degradation of DCSCS quality. It is suggested that it is advisable to use the second strategy. A reasonable choice of particular quality indicators was made: error probability, jitter and phase drift, slippage, signal transmission delay, reliability, relative transmission rate, energy reserve, error vector modulus. A quality assessment criterion is proposed that forms three possible outcomes: satisfactory quality, marginal quality, and unsatisfactory quality. A single integral indicator is proposed, formed on the basis of particular quality indicators and fuzzy logical inference. The structure of a fuzzy expert quality assessment system is considered. An illustrative example is given.

Push the Limit of Highly Accurate Ranging on Commercial UWB Devices

Ranging plays a crucial role in many wireless sensing applications. Among the wireless techniques employed for ranging, Ultra-Wideband (UWB) has received much attention due to its excellent performance and widespread integration into consumer-level electronics. However, the ranging accuracy of the current UWB systems is limited to the centimeter level due to bandwidth limitation, hindering their use for applications that require a very high resolution. This paper proposes a novel system that achieves sub-millimeter-level ranging accuracy on commercial UWB devices for the first time. Our approach leverages the fine-grained phase information of commercial UWB devices. To eliminate the phase drift, we design a fine-grained phase recovery method by utilizing the bi-directional messages in UWB two-way ranging. We further present a dual-frequency switching method to resolve phase ambiguity. Building upon this, we design and implement the ranging system on commercial UWB modules. Extensive experiments demonstrate that our system achieves a median ranging error of just 0.77 mm, reducing the error by 96.54% compared to the state-of-the-art method. We also present three real-life applications to showcase the fine-grained sensing capabilities of our system, including i) smart speaker control, ii) free-style user handwriting, and iii) 3D tracking for virtual-reality (VR) controllers.

Coherent feedback enhanced quantum-dense metrology in a lossy environment.

Quantum dense metrology (QDM) performs high-precision measurements by a two-mode entangled state created by an optical parametric amplifier (PA), where one mode is a meter beam and the other is a reference beam. In practical applications, the photon losses of meter beam are unavoidable, resulting in a degradation of the sensitivity. Here, we employ coherent feedback that feeds the reference beam back into the PA by a beam splitter to enhance the sensitivity in a lossy environment. The results show that the sensitivity is enhanced significantly by adjusting the splitting ratio of the beam splitter. This method may find its potential applications in QDM. Furthermore, such a strategy that two non-commuting observables are simultaneous measurements could provide a new way to individually control the noise-induced random drift in phase or amplitude of the light field, which would be significant for stabilizing the system and long-term precision measurement.

Forced synchronization of self-excited chaotic thermoacoustic oscillations

We experimentally investigate the forced synchronization of a self-excited chaotic thermoacoustic oscillator with two natural frequencies, $f_1$ and $f_2$ . On increasing the forcing amplitude, $\epsilon _f$ , at a fixed forcing frequency, $f_f$ , we find two different types of synchronization: (i) $f_f/f_1 = 1:1$ or $2:1$ chaos-destroying synchronization (CDS), and (ii) phase synchronization of chaos (PSC). En route to $1:1$ CDS, the system transitions from an unforced chaotic state ( ${\rm {CH}}_{1,2}$ ) to a forced chaotic state ( ${\rm {CH}}_{1,2,f}$ ), then to a two-frequency quasiperiodic state where chaos is destroyed ( $\mathbb {T}^2_{2,f}$ ), and finally to a phase-locked period-1 state ( ${\rm {P1}}_f$ ). The route to $2:1$ CDS is similar, but the quasiperiodic state hosts a doubled torus $(2\mathbb {T}^2_{2,f})$ that transforms into a phase-locked period-2 orbit $({\rm {P2}}_f)$ when CDS occurs. En route to PSC, the system transitions to a forced chaotic state ( ${\rm {CH}}_{1,2,f}$ ) followed by a phase-locked chaotic state, where $f_1$ , $f_2$ and $f_f$ still coexist but their phase difference remains bounded. We find that the maximum reduction in thermoacoustic amplitude occurs near the onset of CDS, and that the critical $\epsilon _f$ required for the onset of CDS does not vary significantly with $f_f$ . We then use two unidirectionally coupled Anishchenko–Astakhov oscillators to phenomenologically model the experimental synchronization dynamics, including (i) the route to $1:1$ CDS, (ii) various phase dynamics, such as phase drifting, slipping and locking, and (iii) the thermoacoustic amplitude variations in the $f_f/f_1$ – $\epsilon _f$ plane. This study extends the applicability of open-loop control further to a chaotic thermoacoustic system, demonstrating (i) the feasibility of using an existing actuation strategy to weaken aperiodic thermoacoustic oscillations, and (ii) the possibility of developing new active suppression strategies based on both established and emerging methods of chaos control.

Filterless Frequency Octupling Microwave Photonic Phase Shifter Based on Cascaded Mach–Zehnder Modulators

ABSTRACT In this paper, we propose a microwave photonic phase shifter (MPPS) without optical filtering to generate a frequency octupling microwave photonic (MWP) signal with 360º phase-shifting based on two cascaded Mach–Zehnder modulators (MZMs). Theoretical analysis is given to realize the high-quality frequency octupling MPPS by eliminating the undesired optical carrier and sidebands using an optical coupler (OC). Simulations show that the generated MMW signal has an electrical spurious suppression ratio (ESSR) higher than 33 dB. The impact of the non-ideal modulation index, extinction ratio, and phase drift is discussed and analyzed. Furthermore, the influence of different center frequencies, power, and linewidths of the laser is also analyzed.

Correction of phase drifts in two-wavelength digital holographic microscopy using secondary reference waves

We present a two-wavelength digital holographic microscopy setup for surface topography measurement with single-point illumination and a method for correction of unwanted phase drifts using secondary reference waves.

Sub-Terahertz Channel Characterization in a Lecture Room from Measurements with Phase Drift by a Rotating Horn Antenna

Sub-Terahertz Channel Characterization in a Lecture Room from Measurements with Phase Drift by a Rotating Horn Antenna

Downlink Performance Analysis of CF-MMIMO With RCEs and LO Phase Drift: A Stochastic Geometry Approach

Downlink Performance Analysis of CF-MMIMO With RCEs and LO Phase Drift: A Stochastic Geometry Approach

Tuner Loop Based on FPGA for Petra Cavity at TPS Booster Ring

The low-level radio frequency system of the Taiwan Photon Source, TPS, booster ring was replaced by the digital low-level RF system, DLLRF, in 2018. After that, the phase drift compensation loop for energy-saving operation and the tuner loop were also implemented in the DLLRF system sequentially. We used Altera-DE3 to build the core of DLLRF and handle the high-speed ADC/DAC procedure for RF signal sampling. As we con-sider the response time of the tuner, we choose an-other low-cost board, Altera-DE0-Nano, to develop the tuner loop for 5-Cell-Petra-Cavity. It has an eight-channel 12-bits-ADC, 150 ksps, ADC128S022, to detect the positions of two tuners and two transmitted powers sampled from two cells of the 5-Cell-Petra-Cavity for a power balance function. The phase information of for-ward power and cavity gap voltage will come from the Altera-DE3 to tell the tuner loop in the Altera-DE0-Nano whether the cavity is on resonance or not. The tuner loop controls the cavity to work not only at the resonance frequency but also with a balanced electric field distribution. This study presents the tuner loop’s architecture, including the locking resonance frequency and field balance functions. The performance of the field balance function is observed by the archive data of the two tuners positions and two transmit power signals.