Short-term Frequency Stability Research Articles

Challenges in the system engineering of a Precise Timing Facility for NavIC

AbstractAt the heart of the NavIC/IRNSS ground segment is the IRNSS Network Timing (IRNWT) facility, a precise timing facility (PTF), responsible for the generation, maintenance and dissemination of the IRNSS system time. This paper dwells on the challenges in the system engineering of such a complex system.A PTF has two major applications namely metrological timekeeping and navigation timekeeping for precise orbit determination and time synchronization (OD&TS). These two different objectives in turn translate to two different sets of requirements such as long‐term frequency stability and accuracy for metrological timekeeping, while short and medium term frequency stability and high availability of timescale for navigation.At first, these high level requirements need to be translated to a comprehensive design with minute level operational and performance specifications. The design needs to ensure high availability of the system by creating an ensemble of different kinds of atomic clocks while at the same time maintain frequency stability and optimization for various noise processes dominant at different averaging intervals. The design also need to ensure accuracy of the generated timescale with respect to a desired reference such as UTC needs to be ensured with regular time transfers either by Common‐view or Two‐way satellite time and frequency transfer. In the next step, the design is implemented with the appropriate selection of hardware and software elements. The system engineering of a PTF thus involves varied and multi‐disciplinary facets such as selection of atomic clocks, development of ensemble algorithms, steering the generated timescale signal to the desired reference, monitoring and control of all the hardware and software involved and designing of facility including appropriate environmental conditions.The next step is the verification and validation of the realized system. This step needs to ensure that the system is tested for a sufficiently long period of times to assess both short term and long term performance of the system before it is declared operational. Three such systems have now been made operational in India for NavIC.

Electromagnetically induced absorption scheme for vapor-cell atomic clock.

A dual-frequency light field scheme, composed of counterpropagating pump and probe light waves with equal circular polarizations and different intensities, is proposed for the detection of subnatural-linewidth electromagnetically induced absorption (EIA) resonances. In this scheme, the bright-type EIA resonance is obtained at fixed static magnetic field by tuning the frequency difference between both optical fields and can be used as a frequency reference in an atomic clock. Using a 5-mm long buffer-gas-filled Cs vapor cell, an EIA-based atomic clock with a short-term fractional frequency stability of 5.8 × 10-12τ-1/2 until 20 s integration time is reported. These performances are found to be in correct agreement with the signal-to-noise/linewidth ratio of the resonance. The proposed EIA scheme can be considered as an alternative approach to the coherent population trapping (CPT) technique for the development of compact atomic clocks and sensors.

Improved Generic Model of Variable Speed Wind Turbines for Dynamic Studies

Fast growth of wind power generation and its contribution in power systems dynamic performance has highlighted the importance of developing generic models for wind turbines. Following the former efforts, an enhanced version of standard generic wind turbine model is proposed in this article. The enhancements are aimed to make the model applicable for unbalanced Root Mean Square (RMS), short-term frequency stability, and low-voltage ride-through (LVRT) studies. Moreover, fidelity of the overall responses of the model is increased. To achieve these goals, five new blocks are designed and added to the base model and three existing blocks are modified. The new blocks are negative-sequence generator/converter model, inertial controller, LVRT controller, dc-link and the Line Side Converter (LSC), and the natural flux models. Responses of the enhanced model are compared with the results of both the base model and a detailed model, and validity of the proposed model is verified by different transient scenarios.

Internal resonance between the extensional and flexural modes in micromechanical resonators

Internal resonance between different vibration modes in micromechanical devices has been widely studied due to its promising application prospects in microelectromechanical systems (MEMS) resonators and oscillators. In this paper, we investigated the 2:1 internal resonance between the extensional and flexural modes in a micromechanical cantilever beam resonator using open and closed loop testing methods. In the open loop test, energy transfer from the extensional mode to the flexural mode induced by internal resonance is directly observed. Amplitude saturation and internal resonance bandwidth change in the extensional mode are experimentally studied and theoretically verified with numerical simulation. In the closed loop system, internal resonance produces a bistable self-oscillation frequency. The oscillation frequency of the extensional mode will be locked to one of the two peaks induced by internal resonance. In addition, obvious improvement in short-term frequency stability of the closed loop system is observed with the help of internal resonance. The dynamic characteristics studied in this research can be potentially used to enhance the performance of MEMS vibration devices by internal resonance.

Towards a compact, optically interrogated, cold-atom microwave clock

Abstract A compact platform for cold atoms opens a range of exciting possibilities for portable, robust and accessible quantum sensors. In this work, we report on the development of a cold-atom microwave clock in a small package. Our work utilises the grating magneto-optical trap and high-contrast coherent population trapping in the lin ⊥ $\perp $ lin polarisation scheme. We optically probe the atomic ground-state splitting of cold 87Rb atoms using a Ramsey-like sequence whilst the atoms are in free-fall. We have measured a short-term fractional frequency stability of 5 × 10 − 11 / τ $5{\times}{10}^{-11}/\sqrt{\tau }$ with a projected quantum projection noise limit at the 10 − 13 / τ ${10}^{-13}/\sqrt{\tau }$ level.

Supercapacitor to Provide Ancillary Services With Control Coordination

This paper proposes a dynamic frequency support scheme of a supercapacitor energy storage system (SCESS) in coordination with run-of-the-river-based pumped storage hydropower (PSH) to enhance the short-term frequency stability in a power system that has a high penetration of renewable energy. To achieve this, the proposed coordinated frequency controller (CFC) enables the SCESS and PSH plant to provide the frequency response. The CFC scheme employs a dynamic droop characteristic in parallel with an integral controller and a distribution function. The dynamic droop characteristic determines the power production for frequency regulation employing a variable gain, which varies with the total capacity of the frequency control units and magnitude of the system frequency error with time; the gain increases with the frequency error, and thereby, arresting the frequency nadir at a higher level than in the conventional droop characteristic. In addition, the distribution function dispatches the power from the dynamic droop and integral controller to the control units in proportion to their headrooms; furthermore, the distribution function considers a sudden loss of generation from an SCESS by its operational constraint during the frequency support. Thus, the proposed dynamic frequency support scheme can enhance the short-term frequency stability for a frequency event.

Development of the integrated integrating sphere cold atom clock**Project supported by the Youth Innovation Promotion Association of the Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant Nos. 61875215, 61727821, and 11604353).

We develop an integrated integrating sphere cold atom clock (ISCAC), which mainly consists of physical package, laser system, microwave source, and electronics. This compact system is more stable and reliable than the previous version. The experimental results show that the short term frequency stability of and 2.9 × 10−15 at 1-day integrating time are achieved.

Experimental study of the application feasibility of a novel chip-scale atomic clock scheme.

We report on research into a microfabricated 87Rb vapor cell with differential detection. Elliptically polarized light is used to interact with alkali atoms to generate coherent population trapping (CPT) resonance, and the CPT signal is obtained by detecting the Faraday rotation effect with differential detection technology. To move closer to an actual chip-scale atomic clock (CSAC), we reduce the volume of the experimental apparatus and use a divergent laser beam to interact with the atoms. We obtain the short-term frequency stability of the CSAC based on the differential detection scheme and compare it with that of a conventional CSAC. The results show that the frequency stability is more than two times better than that of current commercial CSAC devices with the same power consumption and volume.

Methane microwave optical master oscillator for fountain references

We have demonstrated a microwave master oscillator operating on optical principles and based on a He – Ne/CH4 optical frequency standard (λ = 3.39 μm) and femtosecond fibre laser system ( λ = 1.54 μm). The output signal spectrum of the oscillator has the form of an equidistant frequency comb in the range 60 MHz to 10 GHz with a 60-MHz step. Comparison of the frequencies of two master oscillators shows that the short-term output frequency instability for the comb components in the range 0.8 – 1.5 GHz is under 1 × 10−14 at an averaging time of 1 s. We have tested microwave signals from the oscillator using apparatus in the reference facility at the State Time and Frequency Service, All-Russia Research Institute of Physical and Radio Engineering Measurements. A signal at a nominal frequency of 100 MHz synthesised from one comb component was compared to signals from two hydrogen masers with enhanced short-term stability in the reference facility. The short-term frequency stability of the synthesised signal has been shown to be twice better than the stability of the masers and to be limited by the intrinsic instability of the commercial synthesiser of a 100-MHz nominal frequency. Our experiments confirm that the proposed microwave optical master oscillator is potentially attractive for use in systems with increased requirements for short-term frequency stability, in particular in time and frequency fountain references.

Micromechanical vibration absorber for frequency stability improvement of DETF oscillator

This article explores a novel way to improve the frequency stability of micromechanical double-ended tuning fork (DETF) resonators. The aim of this work is to use a non-linear vibration absorber to improve the frequency stability of the oscillator. A vibration absorption device is set up on the oscillator to absorb part of the energy of the oscillator. The influence of the vibration absorber on the frequency stability is studied. The short-term frequency stability of the DETF oscillator can be improved from 378 ppb to 202 ppb by coupling it to a mechanical vibration absorber.

Real‐time optimisation of emergency demand response and HVDC power modulation to improve short‐term frequency stability of the receiving‐end power systems

In recent years, large-capacity high-voltage direct currents (HVDCs) have been employed to transfer electricity from the west to the east of China. However, the frequent frequency drops due to HVDC blockings seriously threaten the short-term frequency stability of receiving-end power systems. The existing emergency frequency control strategy is not adaptive to the varying operation conditions and may cause excessive or deficient actions, which could result in inefficient control or high risk of frequency instability. Therefore, a real-time coordinated control strategy is proposed in this study based on the online-updated frequency response model. The model is designed to incorporate multiple types of generators and to reflect the dynamic frequency response of loads. The new control strategy combines multiple control resources, including the emergency demand response and HVDC power modulation, to improve the short-term frequency stability after HVDC failures. By online data preparation and cubic fitting, the nadir of the frequency is expressed as an analytic function of the control variables. A real-time optimisation of emergency controls is achieved to improve the short-term frequency dynamics. Case studies show that the proposed scheme is robust to the varying operation conditions and has lower control cost than the existing control strategy.

A 0.35-μm CMOS-MEMS Oscillator for High-Resolution Distributed Mass Detection.

This paper presents the design, fabrication, and electrical characterization of an electrostatically actuated and capacitive sensed 2-MHz plate resonator structure that exhibits a predicted mass sensitivity of ~250 pg·cm−2·Hz−1. The resonator is embedded in a fully on-chip Pierce oscillator scheme, thus obtaining a quasi-digital output sensor with a short-term frequency stability of 1.2 Hz (0.63 ppm) in air conditions, corresponding to an equivalent mass noise floor as low as 300 pg·cm−2. The monolithic CMOS-MEMS sensor device is fabricated using a commercial 0.35-μm 2-poly-4-metal complementary metal-oxide-semiconductor (CMOS) process, thus featuring low cost, batch production, fast turnaround time, and an easy platform for prototyping distributed mass sensors with unprecedented mass resolution for this kind of devices.

Development of low phase noise microwave frequency synthesizers for reducing Dick effect of Cs fountain clocks

The Dick effect is one of the main factors limiting the short-term frequency stability of Cs fountain clocks, which is especially decided by the phase noise of the local oscillator at smaller offset frequency. Here we report on the development of a 9.192 GHz microwave frequency synthesizer with low phase noise to be used as the local oscillator for Cs fountain clocks. The synthesizer is based on frequency multiplication and synthesis from an ultra-low phase noise 5 MHz Oven Controlled Crystal Oscillator (OCXO). The key component of the frequency multiplication is a non-linear transmission-line (NLTL) as a frequency comb generator. Based on the principle of the NLTL, we carefully optimized the input power, the input and output impedances of the NLTL to suppress its excess phase noise. The measured results show that the absolute phase noises of 9.192 GHz signal are -64 dBc/Hz, -83 dBc/Hz, -92 dBc/Hz and -117 dBc/Hz at 1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The residual phase noise of the synthesizer is − 82 dBc/Hz at 1 Hz offset frequency. The frequency stability limit due to the absolute phase noise via Dick effect is theoretically estimated to be 7.0 × 10−14τ−1/2.

Suppression of Dick Effect in Ramsey-CPT Atomic Clock by Interleaving Lock.

The Dick effect is one of the main limitations of short-term frequency stability for most atomic clocks operating in the pulsed mode. Rather than employing better local oscillators with ultralow phase noise, using the interleaving lock technique to eliminate the dead time is a promising approach to suppress the Dick effect. In this paper, we demonstrate the suppression of the Dick effect by the interleaving lock technique in a pulsed Ramsey-coherent population trapping clock with two identical Cs atomic ensembles. The Dick effect is expected to be reduced by a factor of 24 theoretically. The measured short-term Allan deviation is improved from at 1 s to at 1 s. What is even more remarkable is that the Allan deviation curve exhibits slope from 0.01 to 2 s.

In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms

Atomic clocks based on laser-cooled atoms are widely used as primary frequency standards. Deploying such cold atom clocks (CACs) in space is foreseen to have many applications. Here we present tests of a CAC operating in space. In orbital microgravity, the atoms are cooled, trapped, launched, and finally detected after being interrogated by a microwave field using the Ramsey method. Perturbing influences from the orbital environment on the atoms such as varying magnetic fields and the passage of the spacecraft through Earth’s radiation belt are also controlled and mitigated. With appropriate parameters settings, closed-loop locking of the CAC is realized in orbit and an estimated short-term frequency stability close to 3.0 × 10−13τ−1/2 has been attained. The demonstration of the long-term operation of cold atom clock in orbit opens possibility on the applications of space-based cold atom sensors.

Real‐time optimisation of short‐term frequency stability controls for a power system with renewables and multi‐infeed HVDCs

Short-term frequency stability (STFS) is becoming a great concern for a regional receiving-end power system such as the East China Power Grid (ECPG) mainly for two reasons: (i) the increasing percentage of power injected from multi-infeed (ultra-) high-voltage DCs (HVDCs) with the skyrocketed capacities; (ii) the replacement of traditional generation by the continuously growing inertia-less renewables. However, the existing emergency control is not adaptive enough to maintain STFS under varying operation conditions. In this study, a real-time optimised control is proposed to solve the issue more efficiently. It combines emergency power boosting (EPB) of HVDC and emergency demand response (EDR) in a coordinated way. The optimal control problem is formulated based on the online-updated models that reflect the current state of the system and the dynamic responses of multiple types of generators. By converting the non-linear constraint into a linear matrix inequality, the allocation of EPB and EDR can be optimised in a real-time and coordinated way. The performance of the proposed control and its advantages over the existing one are verified by simulation studies on the model of ECPG with low, normal and high penetrations of renewables.

Two-tone frequency modulation saturation spectroscopy for tunable frequency offset locking of a single laser

The two-tone frequency modulation spectroscopy (TTFMS) is widely used for gas trace detection with its low noise absorption signal. In this paper we propose and implement the TTFMS scheme for frequency offset locking a single diode laser to an atomic resonance line by using its dispersion signal. The TTFMS theory is first discussed under the assumption that the intermediate modulation frequency is comparable to the linewidth of the absorption feature, and the dependence of the TTFMS absorption and dispersion features on the intermediate modulation frequency and modulation index are investigated theoretically. Based on a fiber-coupled electro-optic modulator (EOM) with two-tone modulation, we experimentally demonstrated the performance of the frequency offset locking method. The result shows a short-term frequency stability of the frequency offset locked laser reached around 1.1 × 10−11, with an averaging time of 2 s. This method can find wide applications in fields requiring widely tunable frequency offset locking a single laser to the atomic resonance line, like precision spectroscopy and Raman optics for atom interferometers.

Toward a High-Stability Coherent Population Trapping Cs Vapor-Cell Atomic Clock Using Autobalanced Ramsey Spectroscopy

The next generation of alkali-vapor-cell atomic clocks are under development in labs around the world, with prototypes already demonstrating short-term fractional frequency stabilities one or two orders of magnitude better than for commercial clocks. However, stability is often spoiled at medium time scales (>100 s) by light-power-induced frequency-shift effects. The authors tackle this problem by applying autobalanced Ramsey interrogation, recently demonstrated on a Yb${}^{+}$ clock, to coherent-population-trapping systems---an approach that could really boost the development of vapor-cell clocks with white-noise-limited frequency stability over greatly extended time scales.

Frequency stability of a pulsed optically pumped atomic clock with narrow Ramsey linewidth.

In general, the linewidth of the Ramsey central fringe (RCF) is equal to 1/(2T), where T is the Ramsey free-evolution time. We demonstrate that the RCF linewidth of a pulsed optically pumped (POP) atomic clock with orthogonal polarization detection based on the magneto-optical rotation effect can be narrowed down to 1/(4T). The Allan deviation of the POP atomic clock decreases from 2.4×10-13τ-1/2 to 1.4×10-13τ-1/2. This corresponds to an improvement in the frequency stability by about 60%. We also estimate the main noise sources that limit the short-term frequency stability of the POP atomic clock.

Stability characterization of vacuum encapsulated MEMS resonators with Au–Sn solder bonding

This paper presents a vacuum encapsulation technique and stability characterization for MEMS resonator. Sn-rich Au–Sn solder bonding is used to achieve reliable hermetic packaging with high shear strength. Simple planar feedthrough structure is utilized to achieve electrical interconnection and low cost of packaging. The stabilities of the encapsulated resonator are systematically studied, including frequency stability, temperature stability, long-term hermeticity, and mechanical reliability. The short-term and medium-term frequency stability are ± 0.4 and ± 3 ppm, respectively. The temperature cycle test is introduced between − 20 and 80 °C, and the resonant-frequency drift of the packaged resonator is within ± 4 ppm between 40 temperature cycles. Furthermore, the packaged resonator is temperature compensated by micro-oven, which obtained a frequency stability range of ± 13 ppm between 20 and 100 °C. The packaged resonator shows favorable long-term stability of the Q-factor over 200 days and average shear strength of 43.93 MPa among 12 samples.