Phase-locked Frequency Research Articles

Enhanced spectral resolution in mid-infrared dual-comb spectroscopy via synchronous offset frequency tuning.

Mid-infrared dual-comb spectroscopy offers significant advantages by combining the high sensitivity of mid-infrared spectroscopy with the high spectral resolution and rapid acquisition of the dual-comb method. However, its effective resolution, constrained by the inherent comb line spacing, hinders its ability to resolve narrow absorption features, common in critical applications such as sub-Doppler spectroscopy, low-pressure gas analysis, and construction of the atmospheric profile. To address this challenge, we present a synchronous offset frequency tuning method for the mid-infrared dual-comb system to improve effective resolution far beyond comb line spacing. In our system, the mid-infrared dual-comb source is generated from a near-infrared dual-comb source and a continuous-wave pump laser via difference frequency generation in a single periodically poled lithium niobate bulk. By adjusting the phase-lock frequency of the pump laser to one of the near-infrared combs, we synchronously tune the offset frequencies of both mid-infrared combs without changing the near-infrared dual-comb source. We demonstrated that this method enabled the high resolution of overlapped spectral lines of ethane around 3000 cm-1, achieving a uniform spectral sampling interval of 10 MHz in the interleaved spectrum and a 25-fold enhancement in effective resolution. This approach allows for sub-MHz spectral resolution in mid-infrared dual-comb spectroscopy without any modifications to the data acquisition system, offering possibilities for high-precision spectral analysis.

Dynamic characteristics of the high-speed frequency synthesizer architecture of the indirect synthesis method

Frequency synthesizers of the indirect synthesis method (based on phase-locked frequency tuning systems, PLL) are widely used in the construction of transceivers of radio communication systems and digital information transmission systems, including as part of software-defined radio platforms and systems on a chip. This is due to a set of required parameters: tuning in the octave/super octave frequency range, high frequency resolution and "purity" of the spectrum of the generated signal, low power consumption and the possibility of microcircuit implementation in the microwave frequency range. At the same time, one of the significant disadvantages is the relatively low frequency tunning speed of such devices, in comparison with direct synthesis methods, due to the characteristics of the PLL system structure used in them with charge pumping (Charge-pump phase lock loop, CPPLL). As a result, it is relevant to search for methods to increase the performance of frequency synthesizers based on PLL systems. One of such solutions is the structure of a frequency synthesizer proposed by the authors based on a globally linearized synchronization system (GLSS), which also belongs to the class of PLL systems. In this paper carry out a comparative analysis of the dynamic characteristics of microwave frequency synthesizers made on the basis of a charge-pumped PLL system – CPPLL and on the basis of the proposed high-speed structure – GLSS, under conditions of different values of loop parameters and the magnitude of the frequency adjustment step. Using simulation modeling methods, the results of the operation of models of two structures for discrete frequency steps of various sizes in the entire operating frequency range are presented. The problem of changing the dynamics of structures due to shifts in the values of loop parameters is considered. The obtained dependences of the synchronization time on the relative initial frequency disorder demonstrate a gain in the speed of the GLSS compared to the CPPLL, reaching an order of magnitude or more. The results of the work can be used in the design of modern high-speed microwave frequency synthesizer chips of the indirect synthesis method.

Near-Field Probing of Microwave Oscillators with Josephson Microscopy.

Voltage-controlled oscillators, serving as fundamental components in semiconductor chips, find extensive applications in diverse modules such as phase-locked loops, clock generators, and frequency synthesizers within high-frequency integrated circuits. This study marks the first implementation of superconducting Josephson probe microscopy for near-field microwave detection on multiple voltage-controlled oscillators. Focusing on spectrum tracking, various phenomena, such as stray spectra and frequency drifts, were found under nonsteady operating states. Parasitic electromagnetic fields, originating from power supply lines and frequency divider circuits, were identified as sources of interference between units. The investigation further determined optimal working states by analyzing features of the microwave distributions. Our research not only provides insights into the optimization of circuit design and performance enhancement in oscillators but also emphasizes the significance of nondestructive near-field microwave microscopy as a pivotal tool in characterizing integrated millimeter-wave chips.

Integer-locking condition for stable dual-comb interferometry in situations with fluctuating frequency-comb repetition rates

To make dual-comb interferometry usable in a wide range of applications, it is important to achieve reproducible measurement results even in non-ideal environments that affect the repetition-rate stability. Here, we consider dual-comb interferometry based on a pair of fully referenced optical frequency combs (OFCs) and investigate the impact of fluctuations in the OFC repetition frequencies on the peak position of the center burst in the interferogram. We identify a phase-locking scheme that minimizes the impact of these fluctuations through choosing a special combination of phase-locked frequencies, and the resulting type of operating condition is termed integer-locking condition. Under the integer-locking condition, the number of sampling points in each interferogram remains constant regardless of repetition-rate variations, and this enables more stable phase-resolved measurements in non-ideal environments. We demonstrate the application of this approach using absolute path-length measurements and discuss the accuracy limit imposed by the integer-locking condition. Our findings offer a strategy for robust dual-comb interferometry outside metrology laboratories.

Implementation And Comparison of Different Stages of Current Starved CMOS Ring Oscillator – A Study

The ring oscillators serves as the fundamental building blocks in both digital and analog circuit design, as its extensive use is found in various electrical systems, including phase-locked loops, frequency dividers, and clock generators. This study gives a general overview of the ring oscillator circuit, including its workings, uses, and important design considerations. The ring oscillator generates timing signals for synchronous operation and is often employed as a clock generator in digital systems. It may also be used as a frequency divider to separate higher frequencies into lower ones. A closed loop is used to connect an odd number of inverting stages to create the ring oscillator circuit. An inverter, which is often built using complementary metal-oxide-semiconductor (CMOS) technology, is a component of every stage. By adding a delay to each step, the ring oscillator creates a self-sustaining oscillation. The development and comparison of 3, 5, and 7 stage ring oscillators for different performance metrics, as well as corner analysis for propagation delay and the effect of temperature on the operation of the ring oscillator was performed using Cadence Virtuoso with 90nm technology. This comparison of several phases of a current-starved (CS) ring oscillator offers an advantage to the best design with innovation based on the technology employed and outcomes from the corner analysis, which hasn't been done in any of the more recent researches.

An Investigation of All Fiber Free-Running Dual-Comb Spectroscopy.

A dual-comb spectroscopy (DCS) system uses two phase-locked optical frequency combs with a slight difference in the repetition frequency. The spectrum can be sampled in the optical frequency (OF) domain and reproduces the characteristics in the radio frequency (RF) domain through asynchronous optical sampling. Therefore, the DCS system shows great advantages in achieving precision spectral measurement. During application, the question of how to reserve the mutual coherence between the two combs is the key issue affecting the application of the DCS system. This paper focuses on a software algorithm used to realize the mutual coherence of the two combs. Therefore, a pair of free-running large anomalous dispersion fiber combs, with a center wavelength of approximately 1064 nm, was used. After the signal process, the absorption spectra of multiple species were simultaneously obtained (simulated using the reflective spectra of narrow-bandwidth fiber Bragg gratings, abbreviated as FBG). The signal-to-noise ratio (SNR) could reach 13.97 dB (25) during the 100 ms sampling time. In this study, the feasibility of the system was first verified through the simulation system; then, a principal demonstration experiment was successfully executed. The whole system was connected by the optical fiber without additional phase-locking equipment, showing promise as a potential solution for the low-cost and practical application of DCS systems.

Unexpected phase-locked Brillouin Kerr Frequency comb in fiber Fabry Perot resonators

We report the observation of a stable and broadband optical frequency comb in a high-Q fiber Fabry Perot resonator. We evidence it arises from an unexpected mode-locking phenomena.

Triggerless data acquisition in asynchronous optical-sampling terahertz time-domain spectroscopy based on a dual-comb system.

By using two mutually phase-locked optical frequency combs with slightly different repetition rates, we demonstrate asynchronous optical-sampling terahertz time-domain spectroscopy (ASOPS THz-TDS) without using any trigger signals or optical delay lines. Due to a tight stabilization of the repetition frequencies, it was possible to accumulate the data over 48 minutes in a triggerless manner without signal degradation. The fractional frequency stability of the measured terahertz signal is evaluated to be ∼8.0 × 10-17 after 730 s. The frequency accuracy of the obtained terahertz spectrum is ensured by phase-locking the two frequency combs to a frequency standard. To clarify the performance of our system, we characterized the absorption line of water vapor around 0.557 THz. The good agreement of the measured center frequency and linewidth with the values predicted from the HITRAN database verifies the suitability of our ASOPS THz-TDS system for precise measurements.

A Precise Closed-Loop Controlled ZnO Nanowire Resonator Operating at Room Temperature.

To realize the real-time measurement of masses of nanoparticles, virus molecules, organic macromolecules, and gas molecules, and to analyze their physical and chemical properties, a ZnO nanowire (NW) resonator operating at room temperature with an ultrahigh resonant frequency, real-time detection, and high precision was designed and developed in this study. The machining method is simple and easy to integrate into an integrated circuit. A closed-loop detection system based on a phase-locked loop (PLL) and frequency modulation technology (FM) was used to perform closed-loop testing of electromagnetically excited ZnO NW. The first-order resonance frequency of the resonator was 10.358 MHz, the quality factor Q value was about 600, the frequency fluctuation value fRMS was about 300 Hz, and the FM range could reach 200 kHz. The equivalent circuit model of the resonator was established, the parasitic parameters during the test were obtained, and the frequency accuracy and phase noise of the resonator were analyzed and tested. The experimental results show that the closed-loop system can automatically control the resonator in a wide range of frequency bands, with good tracking performance of the resonant frequency, small frequency fluctuation, and low phase noise level.

JOINT TRACKING GPS AND LEO SIGNALS WITH ADAPTIVE VECTOR TRACKING LOOP IN CHALLENGING ENVIRONMENTS

Abstract. Navigation from LEO satellites own many merits and attracts increasing popularity recently. In addition to increasing the signal availability, the low signal strength loss and fast satellite geometry change from LEO satellite are particularly appealing in challenging environments. Recently, a few researchers attempt to navigate with non-cooperative signals from LEO satellites with pure phase lock loop (PLL) or frequency lock loop (FLL), while a more practical solution to utilizing LEO navigation is joint positioning with the existing GNSS signals which has not been seriously studied. In this study, we proposed a joint GPS and LEO navigation signal tracking strategy that employs a vector tracking loop (VTL) with fully considering the high dynamic characteristics of the LEO signals. In order to solve the high dynamics problem, the second-order deviation parameters were considered in the extended Kalman filter, which is more adaptive to the non-linear variation of the signal acceleration. In addition, a carrier-to-noise ratio (C/N0) based observation noise determination strategy is employed to adapt different observation conditions. The proposed method was verified with different simulation data and the results indicate the adaptive vector tracking loop is capable of tracking GPS and LEO signals simultaneously and robustly. The benefit is particularly in the weak signal scenarios. The experiment results also reveal that the joint vector tracking loop improves positioning accuracy in GNSS challenging environments.

Features of an acousto-optical two-channel laser displacement interferometer with multi-frequency photodetectors with subpycometer resolution

The article discusses the issues of improving acousto-optical (AO) heterodyne laser displacement interferometers (LDI) by using two independent multi-frequency photodetectors: high- frequency (HF) and low-frequency (LF) low-noise, working with "fast inaccurate" and "slow accurate" measuring channels, respectively. The "fast inaccurate" channel allows you to measure displacements with high velocity peed movements. The scheme of the "slow accurate" channel is based on the joint operation of a phase-locked frequency system and a small-range phase meter, providing high resolution for low velocity. Such a scheme of AO LDI most fully implements its capabilities in the control of start-stop cyclic movements of objects, providing high resolution at the initial and final stages of movements with low velocity. A metrological analysis of the "slow accurate" channel is carried out, the possibilities and conditions for achieving AO LDI at low velocity of subpicometer resolution are shown.

Quantum optics of soliton microcombs

Soliton microcombs -- phase-locked microcavity frequency combs -- have become the foundation of several classical technologies in integrated photonics, including spectroscopy, LiDAR, and optical computing. Despite the predicted multimode entanglement across the comb, experimental study of the quantum optics of the soliton microcomb has been elusive. In this work, we use second-order photon correlations to study the underlying quantum processes of soliton microcombs in an integrated silicon carbide microresonator. We show that a stable temporal lattice of solitons can isolate a multimode below-threshold Gaussian state from any admixture of coherent light, and predict that all-to-all entanglement can be realized for the state. Our work opens a pathway toward a soliton-based multimode quantum resource.

Optimal nonlinear filtering of M-PSK signals against a background of harmonic interference with a random initial phase

Objectives. The widespread use of radio data transmission systems using signals with multiposition phase shift keying (MPSK) is due to their high noise immunity and the simplicity of constructing the transmitting and receiving parts of the equipment. The conducted studies have shown that the presence of non-fluctuation interference, in particular, harmonic interference, in the radio channel significantly reduces the noise immunity of receiving discrete information. The energy loss in this case, depending on the interference intensity, can range from fractions of dB to 10 db or more. Therefore, interference suppression is an important task for such radio systems. The aim of the work is to synthesize and analyze an algorithm for optimal nonlinear filtering of MPSK signals against a background of harmonic interference with a random initial phase.Methods. The provisions of the theory of optimal nonlinear signal filtering and methods of statistical radio engineering are used.Results. The synthesis and analysis of the algorithm of optimal nonlinear filtering of MPSK signals against the background of harmonic interference with a random initial phase are carried out. The synthesized receiver contains a discrete symbol evaluation unit, two phase-locked frequency circuits of reference generators that form evaluation copies of the signal and interference, and cross-links between them. Analytical expressions are obtained that allow calculating the dependences of the bit error probability on the signal-to-noise ratio and the interference intensity µ. It is established that uncompensated fluctuations of the initial phase of the useful signal have a greater effect on the receiver noise immunity than similar fluctuations of the phase of harmonic interference, especially with low positional signals.Conclusions. Comparison of the obtained results with the results obtained in the case when there are no harmonic interference compensation circuits shows that the use of the obtained phase filtering algorithms allows for almost complete suppression of harmonic interference. Thus, if µ = 0.5 and the probability of error is 10−2, the energy gain at M = 2 is about 2.5 dB, at M = 4 – about 6 dB, at M = 8 and M = 16 – at least 10 dB.

An ultra-wideband ultra-low phase noise frequency synthesizer

In order to solve the problems of frequency band expansion in direct frequency synthesis method and serious additional deterioration of phase noise in phase-locked frequency synthesis method, a mixer phase-locked frequency synthesizer combining direct analog frequency synthesis and phase-locked frequency synthesis is designed. In order to reduce the frequency multiplication times of the phase detector and optimize the phase noise of the output signal, the frequency synthesizer uses a comb spectrum generator to excite an offset signal with ultra-low phase noise for mixing. In the meantime, the error-lock problem is solved in ultra-wideband mixing phase-locked loop (PLL). An ultra-wideband frequency synthesizer with frequency band 12 GHz–24 GHz and step of 100 MHz is designed in this paper. The experimental test of the frequency synthesizer shows that the phase noise of the frequency synthesizer is better than -116 dBc/Hz@1 kHz at low frequency 12 GHz, and −109 dBc/Hz@1 kHz at high frequency 24 GHz. This phase noise is basically the same as the direct analog frequency synthesis method and is 20 dB better than the conventional phase-locked scheme. The frequency synthesis method has the advantages of ultra-wideband and ultra-low phase noise, and it can be used in the high performance electronic equipment.

Novel phase-locked loop-based resonant frequency tracking control for linear reciprocating compressor

Abstract The paper presents a novel phase-locked loop (PLL)-based resonant frequency tracking method for linear compressors with oscillatory motions. The proposed method achieves the phase-locked control between two signals by using PLL, which includes a multiplier, and a low-pass filter to obtain the phase signal difference. Consequently, based on the phase signal difference, the electrical frequency of the power supply can be adjusted through a PI (proportional-derivative) regulator such that the phase signal difference converges to 90° and the linear compressor works under the resonant frequency conditions. The analytical expression of the resonant frequency condition is proposed for the linear compressor. Then, the detailed design and procedure of the proposed method are presented. The designed method and the resonant frequency characteristics are verified by using the simulation experiment. The simulated results demonstrate that the proposed algorithm has faster response speed and higher convergence accuracy to step load change in comparison with the other commonly used algorithms.

Routes to Synchronization in a pitch–plunge aeroelastic system with coupled structural and aerodynamic nonlinearities

The present study aims to investigate the synchronization characteristics of a pitch–plunge aeroelastic system subjected to coupled structural free-play and dynamic stall-induced aerodynamic nonlinearities. The semi-empirical Leishman–Beddoes (LB) aerodynamic model is used to capture the dynamic stall phenomena at large angles-of-attack (AoA). A bifurcation analysis, considering the flow-speed as the control parameter, reveals that the free-play nonlinearity is primarily responsible for the dynamical transition in the presence of the attached flow. In this case, a pitch and plunge frequency coalescence takes place through an aperiodic to periodic signature transition. Furthermore, by tracking the flow specific variables estimated using the LB model, it is observed that the onset of the dynamic stall plays a pivotal role in the bifurcation scenario at high flow speed regimes, marking the presence of stall flutter. The framework of synchronization is used to discern the response dynamics at low speed and high speed flow regime by estimating the pitch and plunge modal frequencies and their corresponding phase components. The routes to synchronization are identified to be through phase-locking (frequency coalescence) and through suppression of the plunge mode by the dominance of pitching frequency in the regimes before and after the onset of dynamic stall, respectively. Finally, it is shown that the different synchronization routes can possibly be a useful tool to identify the presence of stall flutter oscillations in a coupled aeroelastic system.

Research on the application of nanometre fiso interferometer for phase and phase element detection signal processing

The use of nanometre fiso interferometer to measure heterodyne interference signals at the same time for phase and phase element detection and phase-locked frequency multiplication counting is employed here. After a certain logic mixing, a set of measurement results with a certain degree of redundancy can be obtained; the test results can be measured and resolved. The rate is better than 0.1 nm, and the measurement range is not limited by the λ/2 period, thus overcoming the previous problems that is the measurement range of the phase measurement method is limited to one period and the resolution of the phase-locked frequency multiplication counting method is not easy to improve.

Comparison of the Segmentation Results of Two Carrier Tracking Loop Types and Analysis of Theoretical Influencing Factors

This paper proposes an accurate quantitative segmentation method by analyzing the probability distribution of tracking variance and strict derivation based on the tracking loop theory. The segmentation points are taken as characteristics of phase lock loop (PLL) and frequency lock loop (FLL) performances, and the two factors that cause the performance difference are discriminator gain and filtering coefficient, which denote proportional and integration coefficients, respectively. The filtering coefficients lead to a difference of 2.5 dB-Hz between the FLL and PLL. Moreover, through the analysis of the normalized bandwidth and phase margin, it is found that the integration time and bandwidth need a dynamic balance to achieve the best performance. Finally, the simulation results and real data are in good agreement with the theoretical analysis results. The minimum mean error rate of the deviation between the real data and the theoretical data is only 1.8%. In the proposed method, the influence of external hardware factors on the tracking loop is removed, and the loop design factors are modeled directly. Instead of testing the denoising performance based on the ranging and angle measuring error after location calculation, the filter coefficient is proposed to evaluate the processing performance of the tracking loop objectively and directly at the theoretical level, which proposes a new performance evaluation method at the theoretical level. The results presented in this study provide theoretical support for the design of a new-type tracking loop with enhanced performances.

Impedance Reshaping Control Strategy for Improving Resonance Suppression Performance of a Series-Compensated Grid-Connected System

In the series-compensated grid-connected system (SCGCS), there is an impedance interaction between the inverter impedance and the grid impedance that is prone to cause resonance in the SCGCS. In this paper, firstly, considering the effects of the phase-locked loop (PLL), current-loop, and frequency coupling, the broadband impedance model of the SCGCS is established. The stability of the SCGCS is analyzed by the impedance-based Nyquist stability criterion. It is found from the stability analysis that the impedance interaction between the inverter impedance and the grid impedance is the leading cause of the resonance. An impedance reshaping based resonance suppression method is proposed to suppress the resonance. The phase characteristics of the inverter equivalent output impedance are reshaped from the perspective of impedance. The phase margin at the intersection frequency of the inverter impedance and the grid impedance is improved. The proposed resonance suppression approach mainly consists of reshaping the current loop impedance and the novel phase-locked loop impedance. Finally, simulations and experiments are used to verify the feasibility of the resonance analysis and the effectiveness of the proposed control strategy.

Achieving Precise Spectral Analysis and Imaging Simultaneously with a Mode-Resolved Dual-Comb Interferometer.

In this paper, we report a scheme providing precise spectral analysis and surface imaging, simultaneously, based on a high-coherence dual-comb interferometer. With two tightly phase-locking frequency combs, we demonstrate a high-coherence dual-comb interferometer (DCI) covering 188 to 195 THz (1538.5 to 1595.7 nm) with comb-tooth resolution and a max spectral signal-to-noise ratio (SNR) of 159.7. The combination of the high-coherence dual-comb spectrometer and a reference arm simultaneously enables gas absorption spectroscopy and for the absolute distance information to be obtained in one measurement. As a demonstration, we measure the spectrum of CO2 and CO. From the same interferograms, we demonstrate that distance measurement, by time-of-flight (TOF), can be resolved with an rms precision of 0.53 μm after averaging 140 images and a measurement time of 1 s. Finally, we demonstrate that non-contact surface imaging, using 2D mechanical scanning, reaches lateral resolution of 40 μm. The longitudinal precision is 0.68 μm with a measurement time of 0.5 s. It verifies that DCS has the potential to be applied in standoff detection, environmental pollution monitors, and remote sensing.