Reference Frequency Research Articles

Advanced Hyperpolarized 13C Metabolic Imaging Protocol for Patients with Gliomas: A Comprehensive Multimodal MRI Approach.

This study aimed to implement a multimodal 1H/HP-13C imaging protocol to augment the serial monitoring of patients with glioma, while simultaneously pursuing methods for improving the robustness of HP-13C metabolic data. A total of 100 1H/HP [1-13C]-pyruvate MR examinations (104 HP-13C datasets) were acquired from 42 patients according to the comprehensive multimodal glioma imaging protocol. Serial data coverage, accuracy of frequency reference, and acquisition delay were evaluated using a mixed-effects model to account for multiple exams per patient. Serial atlas-based HP-13C MRI demonstrated consistency in volumetric coverage measured by inter-exam dice coefficients (0.977 ± 0.008, mean ± SD; four patients/11 exams). The atlas-derived prescription provided significantly improved data quality compared to manually prescribed acquisitions (n = 26/78; p = 0.04). The water-based method for referencing [1-13C]-pyruvate center frequency significantly reduced off-resonance excitation relative to the coil-embedded [13C]-urea phantom (4.1 ± 3.7 Hz vs. 9.9 ± 10.7 Hz; p = 0.0007). Significantly improved capture of tracer inflow was achieved with the 2-s versus 5-s HP-13C MRI acquisition delay (p = 0.007). This study demonstrated the implementation of a comprehensive multimodal 1H/HP-13C MR protocol emphasizing the monitoring of steady-state/dynamic metabolism in patients with glioma.

Adaptive bearing fault diagnosis using reference frequency and modified scalogram

Previous studies on the diagnosis of natural faults in rolling element bearings have primarily concentrated on detecting an increase in the frequency amplitude across a broad frequency spectrum within the measured signal when a fault occurs in the bearing. However, this study introduces an adaptive method centered on the conspicuous distinction in frequency amplitude between the shaft and bearing fault frequencies as the bearing fault progresses. Specifically, we propose a bearing fault diagnosis approach leveraging the shaft frequency amplitude as a constant reference independent of prevailing conditions, as it consistently maintains a relatively steady level regardless of the presence of bearing faults. Moreover, we devised a modified scalogram to enhance the diagnostic performance for bearing faults by consistently and prominently visualizing information pertinent to faults. We comprehensively assessed fault diagnosis accuracy between a convolutional neural network employing the scalogram and one employing the modified scalogram to verify the diagnostic performance of the adaptive method. This analysis yielded accuracies of 93.6% and 99.3%, respectively. Furthermore, the relationship between the bearing fault diagnosis results and the visualized fault-related information in the scalogram and modified scalogram was analyzed using gradient-weighted class activation mapping, providing evidence supporting improved fault diagnosis performance using the adaptive method.

Massive black hole binaries as sources of low-frequency gravitational waves and X-shaped radio galaxies

ABSTRACT We present the study of multimessenger signatures of massive black hole (MBH) binaries residing in the centres of galaxy merger remnants. In particular, we first focus on the gravitational wave background (GWB) produced by an ensemble of MBH binary inspirals in the frequency range probed by the Pulsar Timing Array (PTA) experiments. The improved estimates of the characteristic strain were obtained with the inclusion of environmental effects on the MBH binary orbital decay within the galaxy merger remnants, added in post-processing to the semi-analytical model of galaxy formation and evolution SHARK. Secondly, we explore two, intriguing in terms of the MBH binary evolution studies, hypotheses aiming to explain the origins of X-shaped radio galaxies – a peculiar type of objects with double lobe structures, constituting approximately 6–10 per cent of known radio loud galaxies. The two considered scenarios involve either an abrupt change in the jet direction after an MBH merger (a spin-flip) or an unresolved close binary, where each of the two components produces a jet. We find that the estimated GWB amplitude at the reference frequency $f_0=1 \, {\rm yr}^{-1}$ is in the range of $A_{\rm { yr^{-1}}} = 1.20\times 10^{-15}{\!-\!}1.46\times 10^{-15}$, which is 50 per cent lower than the strain of the signal detected by the PTA experiments. We also show that the spin-flip scenario considered in gas-poor mergers reproduces the observed properties of X-shaped radio galaxies well in terms of flip angle, redshift, and luminosity distributions.

Differential cortical activation patterns: pioneering sub-classification of tinnitus with and without hyperacusis by combining audiometry, gamma oscillations, and hemodynamics.

The ongoing controversies about the neural basis of tinnitus, whether linked with central neural gain or not, may hamper efforts to develop therapies. We asked to what extent measurable audiometric characteristics of tinnitus without (T) or with co-occurrence of hyperacusis (TH) are distinguishable on the level of cortical responses. To accomplish this, electroencephalography (EEG) and concurrent functional near-infrared spectroscopy (fNIRS) were measured while patients performed an attentionally demanding auditory discrimination task using stimuli within the individual tinnitus frequency (fTin) and a reference frequency (fRef). Resting-state-fMRI-based functional connectivity (rs-fMRI-bfc) in ascending auditory nuclei (AAN), the primary auditory cortex (AC-I), and four other regions relevant for directing attention or regulating distress in temporal, parietal, and prefrontal cortex was compiled and compared to EEG and concurrent fNIRS activity in the same brain areas. We observed no group differences in pure-tone audiometry (PTA) between 10 and 16 kHz. However, the PTA threshold around the tinnitus pitch was positively correlated with the self-rated tinnitus loudness and also correlated with distress in T-groups, while TH experienced their tinnitus loudness at minimal loudness levels already with maximal suffering scores. The T-group exhibited prolonged auditory brain stem (ABR) wave I latency and reduced ABR wave V amplitudes (indicating reduced neural synchrony in the brainstem), which were associated with lower rs-fMRI-bfc between AAN and the AC-I, as observed in previous studies. In T-subjects, these features were linked with elevated spontaneous and reduced evoked gamma oscillations and with reduced deoxygenated hemoglobin (deoxy-Hb) concentrations in response to stimulation with lower frequencies in temporal cortex (Brodmann area (BA) 41, 42, 22), implying less synchronous auditory responses during active auditory discrimination of reference frequencies. In contrast, in the TH-group gamma oscillations and hemodynamic responses in temporoparietal regions were reversed during active discrimination of tinnitus frequencies. Our findings suggest that T and TH differ in auditory discrimination and memory-dependent directed attention during active discrimination at either tinnitus or reference frequencies, offering a test paradigm that may allow for more precise sub-classification of tinnitus and future improved treatment approaches.

A Novel Frequency Reference Compensation Method in Decentralized Secondary Frequency Control for Parallel Operation of Multiple Generators in an Islanded Microgrid

A Novel Frequency Reference Compensation Method in Decentralized Secondary Frequency Control for Parallel Operation of Multiple Generators in an Islanded Microgrid

Terahertz microcomb oscillator stabilized by molecular rotation

Controlling the coherence between light and matter has enabled the radiation of electromagnetic waves with a spectral purity and stability that defines the Système International (SI) second. Transitions between hyperfine levels in atoms are accessible in the microwave and optical domains, but faithfully transferring such stability to other frequency ranges of interest requires additional components such as optical frequency combs. Such spectral purity and stability are specifically sought out for the terahertz domain for both scientific and commercial applications, including precision studies of molecular physics, next-generation wireless communications, quantum sensors, and terahertz frequency standards. Currently, there is a lack of native frequency references in this spectral range, which is essential for the consistency of measurements and traceability. Small-scale terahertz oscillators, which leverage dissipative Kerr soliton microcombs, present a promising avenue for the generation of terahertz waves that rival the spectral purity of electronic alternatives. Here, we experimentally demonstrate the rotational spectroscopy of nitrous oxide (N2O) with a microcomb-based oscillator. To mitigate the frequency drift encompassed in such waves, we lock the frequency of the microcomb terahertz oscillator to that of a rotational transition of N2O, reducing the fractional frequency stability to a level of 5 × 10−12 at 10 s of averaging time. These results constitute a high performance terahertz oscillator that can be scaled down to a compact size while circumventing the need for frequency multiplication or division of frequency standards. This demonstrates a foundational component needed for future terahertz applications.

HEARING LOSS AND FATIGUE IN MIDDLE-AGED AND OLDER ADULTS

Abstract Fatigue is associated with worse cognitive and physical functioning, psychosocial wellbeing, and quality of life. Hearing loss may be a risk factor for fatigue, perhaps through greater cognitive demand to compensate for degraded auditory signal. However, prior studies are predominantly in audiology clinical samples, which may be oversampled for individuals experiencing hearing-loss-related fatigue. We conducted a cross-sectional analysis including 3,031 participants from the National Health and Nutrition Examination Survey (NHANES) 2015-18. Fatigue was based on self-reported frequency of feeling tired or having little energy over the past 2 weeks. Hearing loss was defined as better-ear 4-frequency (0.5, 1, 2, 4 kilohertz) pure-tone average >25 decibels hearing level. Multivariable-adjusted multinomial logistic regression was used to model the relative risk ratios (RRR) of reporting a higher vs. reference frequency category of fatigue associated with hearing loss, adjusting for age, sex, race/ethnicity, education, smoking, drinking, occupational and off-work noise exposure, body mass index, comorbidities, and depressive symptoms. In this nationally representative sample of middle-aged and older adults (40-80 years, 48% male, 10% Black), 713 (24%) had hearing loss. When compared to normal-hearing participants, hearing-loss participants were more likely to report fatigue for more than half the days (RRR=2.16, 95% confidence interval [CI]: 1.24, 3.75) and nearly every day (RRR=2.09, 95% CI: 1.24, 3.52) relative to not feeling fatigue at all. Hearing loss is associated with fatigue at the population level. Public health efforts to manage hearing loss might improve fatigue and associated downstream health outcomes.

A genomic mutational constraint map using variation in 76,156 human genomes.

The depletion of disruptive variation caused by purifying natural selection (constraint) has been widely used to investigate protein-coding genes underlying human disorders1-4, but attempts to assess constraint for non-protein-coding regions have proved more difficult. Here we aggregate, process and release a dataset of 76,156 human genomes from the Genome Aggregation Database (gnomAD)-the largest public open-access human genome allele frequency reference dataset-and use it to build a genomic constraint map for the whole genome (genomic non-coding constraint of haploinsufficient variation (Gnocchi)). We present a refined mutational model that incorporates local sequence context and regional genomic features to detect depletions of variation. As expected, the average constraint for protein-coding sequences is stronger than thatfor non-coding regions. Within the non-coding genome, constrained regions are enriched for known regulatory elements and variants that are implicated in complex human diseases and traits, facilitating the triangulation of biological annotation, disease association and natural selection to non-coding DNA analysis. More constrained regulatory elements tend to regulate more constrained protein-coding genes, which in turn suggests that non-coding constraint can aid the identification of constrained genes that are as yet unrecognized by current gene constraint metrics. We demonstrate that this genome-wide constraint map improves the identification and interpretation of functional human genetic variation.

A Study on the High Reliability Audio Target Frequency Generator for Electronics Industry

The frequency synthesizer performs a simple function of generating a desired frequency by manipulating a reference frequency signal, but stable and precise frequency generation is essential for reliable operation in mechanical equipment such as communication, control, surveillance, medical, and commercial fields. Frequency synthesis, which is commonly used in various contexts, has been used in analog and digital methods or hybrid methods. Especially in the field of communication, a precise frequency synthesizer is required for each frequency band, from very low-frequency AF (audio frequency) to high-frequency microwaves. The purpose of this paper is to design and implement a highly reliable frequency synthesizer for application to a railway track circuit systems using AF frequency only with the logic circuit of an FPGA (field programmable gate array) without using a microprocessor. Therefore, the development trend of analog, digital, and hybrid frequency synthesizers is examined, and a method for precise frequency synthesizer generation on the basis of the digital method is suggested. In this paper, the generated frequency generated by applying the digital frequency synthesizer using the ultra-precision algorithm completed by many trials and errors shows the performance of generating the target frequency with an accuracy of more than 99.999% and a resolution of mHz, which is much higher than the resolution of 5 Hz in the previous study. This highly precise AF-class frequency synthesizer contributes greatly to the safe operation and operation of braking and signaling systems when used in transportation equipment such as railways and subways.

Optical frequency reference based on a cryogenic silicon resonator

We present the development and in-depth characterization of an optical reference based on a 1.5 μm laser stabilized to a cryogenic silicon optical resonator operated at 1.7 K. The closed-cycle cryostat is equipped with a cryogenic passive vibration isolation. At τ = 1 s integration time the frequency instability is 2 × 10−14, predominantly due to residual vibrations. At τ = 100 s the frequency instability is 6.2 × 10−15. The lowest instability of 3.5 × 10−16 occurs at τ = 6000 s, and is limited by the stability of the hydrogen maser used in the comparison. The mean fractional frequency drift rate over 190 days was −3.7 × 10−20/s. In conjunction with a frequency comb and a GNSS receiver this optical reference would be suitable to provide optical frequencies with accuracies at the low 10−14 level. We show that residual vibrations affect the resonator and the optical fiber delivering the laser light to it, and that laboratory temperature variations contribute to frequency instability at short and medium integration times. Mitigation of these issues might in the future allow for demonstration of the thermal-noise-limited performance of the resonator.

Enhanced Detection Precision of the Taiji Program by Frequency Setting Strategy Based on a Hierarchical Optimization Algorithm

For space-based gravitational wave detection, a laser interferometric measurement system composed of a three-spacecraft formation offers the most rewarding bandwidth of astrophysical sources. There are no oscillators available that are stable enough so that each spacecraft could use its own reference frequency. The conversion between reference frequencies and their distribution between all spacecrafts for the synchronization of the different metrology systems is the job of the inter-spacecraft frequency setting strategy, which is important for continuously acquiring scientific data and suppressing measurement noise. We propose a hierarchical optimization algorithm to solve the frequency setting strategy. The optimization objectives are minimum total readout displacement noise and maximum beat-note frequency feasible range. Multiple feasible parameter combinations were obtained for the Taiji program. These optimized parameters include lower and upper bounds of the beat note, sampling frequency, pilot tone signal frequency, ultrastable clock frequencies, and modulation depth. Among the 20 Pareto optimal solutions, the minimum total readout displacement noise was 4.12 pm/Hz, and the maximum feasible beat-note frequency range was 23 MHz. By adjusting the upper bound of beat-note frequency and laser power transmitted by the telescope, we explored the effects of these parameters on the minimum total readout displacement noise and optimal local laser power in greater depth. Our results may serve as a reference for the optimal design of laser interferometry system instrument parameters and may ultimately improve the detection performance and continuous detection time of the Taiji program.

Temperature compensation of fiber optic unbalanced interferometers for high resolution static strain sensing

Accurate temperature compensation challenges the use of fiber optic unbalanced interferometers in static strain sensing. We propose a temperature compensation theory and scheme of unbalanced interferometers using sensing fibers with different temperature coefficients, aiming at resolving the temperature disturbance of optical fibers and achieving high strain resolution. For the first time, we comprehensively analyze the thermal response of interferometers due to different temperature coefficients, different thermal behaviors, and inconsistent temperature disturbances in the optical fiber arms. A sensing combination and a reference combination are designed. The sensing combination measures a strain and compensates for the temperature disturbance of the sensing arm, and the reference combination provides a reference to compensate for the temperature disturbance of the reference arm and frequency drift of the interferometer in the sensing combination. The proposed scheme can compensate for the temperature disturbances of interferometers in the sensing combination completely. To verify the theory and scheme, bend-insensitive single-mode fibers and Boron/Germanium co-doped fibers are used as sensing fibers in the experiment. The experimental results show that the temperature resolution of the sensing arm is about 3.43 × 10−4 °C, and the static strain resolution of the unbalanced interferometer within 24 h after temperature compensation is about 2.55 nε. The temperature-compensated strain resolution of ∼nε indicates that the proposed temperature compensation theory and scheme can be used in high-resolution, long-term, low-frequency, and static strain sensing, such as crustal deformation observation in geophysical applications.

An integrated wavemeter based on fully-stabilized resonant electro-optic frequency comb

Optical frequency combs provide a powerful tool for precise measurement of the optical frequency, holding significant importance in fields such as spectroscopy, optical communication and optical clock. The frequency stability of the comb line determines the precision of the frequency measurement, but the delicate interplay between high precision, low power consumption and integration still needs to be optimized. To this aim, here we demonstrate a frequency measurement scheme based on a fully stabilized electro-optic comb, in which the pump laser frequency and repetition rate are independently locked to the atomic transition and microwave signal. The measurement precision of the demonstrated wavemeter can reach sub-kHz-level, and the parallel measurement of multiple wavelengths can be performed. Therefore, by combining the technical scheme reported here with advanced integrated functional devices, our system is expected to provide a feasible solution for chip-scale frequency precision measurement and reference.

Analysis on the Effect of Phase Noise on the Performance of Satellite Communication and Measurement System

An oscillator is a key component of a satellite communication measurement and control system, performing symmetry precisely as a time frequency reference. At the same time, the phase noise index has a close coupling relationship with the overall performance of the entire system, while persistently breaking the symmetry property of the oscillator during work. It is very important to study and reasonably allocate the phase noise index. According to the theoretical formula of phase noise, this paper analyzes the power law spectral model in the frequency domain and the noise jitter characteristics in the time domain. Using the carrier tracking loop in the measurement system, the frequency domain transfer model of phase noise is established, and typical analysis results are given. A discrete fractional integration algorithm is proposed, which can generate the phase noise time domain sequence under the given power law spectral model coefficients. The proposed algorithm is more realistic compared with the previous numerical calculation method, and has sufficient accuracy compared with the results of the instrument. After frequency domain conversion, the RMS deviation between the simulated noise sequence in the frequency domain and the measured single sideband power spectral density is less than 2.5 dB, indicating that the phase noise sequence can reflect the frequency domain characteristics more completely. A communication measurement simulation system is built, and a discrete sequence simulation analysis method combining frequency domain and time domain is provided, and the coupling relationship of key indicators such as phase noise, thermal noise, communication data rate, modulation method and bit error rate is synthesized. The results show that the BER of the QPSK/BPSK communication system will not be significantly reduced if the phase jitter RMS caused by the phase noise is less than 5 degrees, so 5 degrees can be used as a reference for the decomposition of the carrier SSB phase noise index. The simulation results have been successfully applied to a satellite inter-satellite link system, which has universal practical application value.

Remote Residual Instability Evaluation of Comb-Based Precise Frequency Transmission for Optical Clock

Optical clocks can be used as the absolute frequency reference due to their high accuracy and stability. In a precise optical clock transmission system, the instability loss of the link is usually evaluated by beating the remote optical signal with the reference clock, which is not suitable for real frequency distribution applications. Therefore, it is necessary to assess the performance directly at the remote site for the optical frequency transfer, because the two sites of the link are usually not co-located. In this paper, we proposed a comb-based remote residual instability evaluation scheme. Two coherent optical combs with different wavelengths were extracted from a frequency stable comb and transmitted after multiplexing. The residual instability was evaluated directly at the remote site by measuring the phase fluctuation difference between the two combs. We achieved 8.61 × 10−19 at 40,000 s over a 10 km fiber link, reaching the instability of optical clocks. These results revealed that our scheme can evaluate optical clock frequency transmission directly at the remote site, which made the method truly practical.

COMPASSO mission and its iodine clock: outline of the clock design

One of the limiting factors for GNSS geolocation capabilities is the clock technology deployed on the satellites and the knowledge of the satellite position. Consequently, there are numerous ongoing efforts to improve the stability of space-deployable clocks for next-generation GNSS. The COMPASSO mission is a German Aerospace Center (DLR) project to demonstrate high-performance quantum optical technologies in space with two laser-based absolute frequency references, a frequency comb and a laser communication and ranging terminal establishing a link with the ground station located in Oberpfaffenhofen, Germany. A successful mission will strongly improve the timing stability of space-deployable clocks, demonstrate time transfer between different clocks and allow for ranging in the mm-range. Thus, the technology is a strong candidate for future GNSS satellite clocks and offers possibilities for novel satellite system architectures and can improve the performance of scientific instruments as well. The COMPASSO payload will be delivered to the international space station in 2025 for a mission time of 2 years. In this article, we will highlight the key systems and functionalities of COMPASSO, with the focus set to the absolute frequency references.

Erbium-Doped LiYF4 as a Potential Solid-State Frequency Reference: Eligibility and Spectroscopic Assessment

Time and frequency metrology is a key enabler for both forefront science and innovation. At the moment, atomic frequency standards (AFSs) are based on atoms either in the vapor phase or trapped in magneto-optical lattices in a vacuum. Finding a solid-state material that contains atoms suitable to be used as a frequency reference would be an important step forward in the simplification of the setup of AFSs. Lanthanide-doped inorganic crystals, such as Er-doped LiYF4, have been studied for several decades, and their intrashell 4f transitions are usually identified as ultra-narrow. Nevertheless, a systematic characterization of these transitions and their linewidths with a correlation to the dopant’s concentration and isotopic purity at low temperatures is lacking. In this work, we studied Er-doped LiYF4 as a potential benchmark material for solid-state frequency references. We chose Er as it has a set of transitions in the telecom band. The influence of Er concentrations and isotope purity on the transition linewidth was systematically studied using high-resolution optical spectroscopy at 5 K. The results indicate that the material under study is an interesting potential candidate as a solid-state frequency reference, having transition linewidths as low as 250 MHz at ~1530 nm.

A Wideband and Low Reference Spur PLL with Clock Feedthrough Suppressed and Low Current Mismatch Charge Pump and Symmetrical CML Divider

This paper presents the design and performance analysis of a wideband charge-pump phase-locked loop (CPPLL) characterized by low reference spur and low phase noise. The proposed CPPLL, operating as a wideband phase-locked loop (PLL) with a reference frequency of 100 MHz, achieves a wide tuning range of 40% from 2.0 GHz to 3.0 GHz. A clock feedthrough suppressed charge pump with additional bias current branches is used to reduce the PLL’s loop reference spur. The 4-stage current mode logic (CML) divide-by-2/3 circuit is utilized in the frequency divider to achieve high-speed frequency division. The circuit of an AND gate and latch in the 2/3 divider adopts a full differential symmetric structure to minimize the phase error of high-frequency differential signals. The voltage-controlled oscillator (VCO) is designed to provide a wide tuning range while optimizing the trade-off between the phase noise and power consumption. The fabricated PLL is implemented using a 0.13 µm CMOS process. Experimental measurements reveal a reference spur of −74.39 dBc at an oscillation frequency of 2.4 GHz. Moreover, the CPPLL achieves phase noise of −102.55 dBc/Hz@100 kHz and −127.15 dBc/Hz@1 MHz, while consuming 33.6 mW under a 1.2 V supply voltage. The integrated root-mean-square (rms) jitter, measured from 10 kHz to 10 MHz, is 340.99 fs, and the figure-of-merit (FoM) is −234.08 dB at a carrier frequency of 2.4 GHz, highlighting the potential of the proposed PLL for integrated circuit applications.

The second data release from the European Pulsar Timing Array

We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). A robust GWB detection is conditioned upon resolving the Hellings-Downs angular pattern in the pairwise cross-correlation of the pulsar timing residuals. Additionally, the GWB is expected to yield the same (common) spectrum of temporal correlations across pulsars, which is used as a null hypothesis in the GWB search. Such a common-spectrum process has already been observed in pulsar timing data. We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of 4%. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of 60 and a false alarm probability of about 0.1% (≳3σ significance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The latest EPTA data from new generation observing systems show non-negligible evidence for the GWB. At the same time, the inferred spectrum is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of (2.5 ± 0.7) × 10−15 at a reference frequency of 1 yr−1. Further investigation of these issues is required for reliable astrophysical interpretations of this signal. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years.

The characterisation of a phase micro-stepper

The frequency steering of the local standard time is a common procedure for the timekeeping. The local radiofrequency reference output is modified by a phase and frequency offset generator to corresponds to the global timescales such as the International Atomic Time and Coordinated Universal Time timescales. The phase and frequency offset generator, also known as the phase micro-stepper, is used for such timescales for many years but it has not been very well characterized. It will be shown for a particular type of the phase micro-stepper that its phase delay error can exceed 10 ps and its frequency offset error can be relatively more than 10−16 of the reference frequency.