Digital Phase-locked Loop Research Articles

Identifying Arnold's tongue for digital oscillators through event-based control in phase-locked loops.

Digital phase-locked loops (PLLs) are essential feedback circuits for synchronizing signals in digital communication systems. While amplitude and phase vary continuously in analog oscillators, the amplitude remains constant in digital oscillators with dynamical variations manifesting exclusively through changes in the timing of signal transitions. In this work, we introduce a novel analytically solvable event-based model for phase-locking in digital PLLs that leverages the discrete nature of digital signals. By employing a sampled control strategy, we demonstrate one-to-one and higher ratios of frequency locking under positive and negative feedback. By discretizing the continuous control signal, we drive a discrete iterative map, which we then use to derive analytical expressions for bifurcation curves, analogous to Arnold's tongue in analog oscillators. This mathematical framework provides an analytical approach for the analysis of synchronization and phase-locking in digital oscillators. Furthermore, the event-based control presented in this work for digital oscillators paves the way for energy-efficient circuit design and optimized control strategies for future digital communication systems.

A Fully Synthesizable Fractional-N Digital Phase-Locked Loop with a Calibrated Dual-Referenced Interpolating Time-to-Digital Converter to Compensate for Process–Voltage–Temperature Variations

This paper presents advancements in the performance of digital phase-locked loop (DPLL)s, with a special focus on addressing the issue of required gain calibration in the time-to-digital converter (TDC) within phase-domain DPLL structures. Phase-domain DPLLs are preferred for their simplicity in implementation and for eliminating the delta–sigma modulator (DSM) noise inherent in conventional fractional-N designs. However, this advantage is countered by the critical need to calibrate the gain of the TDC. The previously proposed dual-interpolated TDC(DI-TDC) was proposed as a solution to this problem, but strong spurs were still generated due to the TDC resolution, which easily became non-uniform due to PVT variation, degrading performance. To overcome these problems, this work proposes a DPLL with a new calibration system that ensures consistent TDC resolution matching the period of the digitally controlled oscillator (DCO) and operating in both the foreground and background, thereby maintaining consistent performance despite PVT variations. This study proposes a DPLL using a calibrated dual-interpolated TDC that effectively compensates for PVT variations and improves the stability and performance of the DPLL. The PLL was fabricated in a 28-nm CMOS process with an active area of only 0.019 mm2, achieving an integrated phase noise (IPN) performance of −17.5 dBc, integrated from 10 kHz to 10 MHz at a PLL output of 570 MHz and −20.5 dBc at 1.1 GHz. This PLL operates within an output frequency range of 475 MHz to 1.1 GHz. Under typical operating conditions, it consumes only 930 µW with a 1.0 V supply.

On the equivalence between steady-state Kalman filter and DPLL

Fundamental results in the literature showed that a class of Kalman filters (KF) converges to a digital phase lock loop (DPLL) structure. Results were proved for second- and third-order KFs. We extend these results to KFs of any order and derive in closed form the equivalent loop filter constants as a linear combination of the steady-state Kalman gains. We also give the inverse relation. Both closed-form relations involve Stirling numbers of the first or second kind. We implement both filters in a global navigation satellite system (GNSS) receiver and illustrate their equivalence with real-world data. These extended theoretical results provide a deeper understanding of the equivalence between KF and DPLL and may be of practical interest in highly dynamic scenarios to design and tune tracking filters.

Fast synchronization with enhanced switching control for grid-tied single-phase square wave inverter using FPGA

Research on grid synchronization has been conducted worldwide by researchers in conjunction with the development of innovative technologies, such as dedicated short-range communication (DSRC) and cellular vehicle-to-everything (C-V2X). However, grid-connected inverters face several challenges, mainly the mismatch in voltage amplitude, frequency, and phase angle, as well as grid voltage disturbance and grid faults. Thus, the control algorithm of this research mainly focused on a half-cycle algorithm to design an enhanced digital switching control for fast synchronization using an FPGA. The control algorithm was developed based on zero-crossing detection (ZCD) and digital phase-locked loop (PLL) modeling techniques using the hardware description language (HDL) and a combination of digital logic blocks in Quartus II software, where the proposed switching was applied using the square-wave switching technique through a 300-watt full-bridge experimental prototype. The performance of the proposed technique was studied, where the total harmonic distortion (THD) for voltage and current resulted in a percentage reduction of 89.29% and 78.05% for voltage and current, respectively, after filter implementation. Also, the resulting signal synchronized in every half cycle and matched the voltage amplitude, frequency, and phase angle of the grid signal in 10 ms.

Broadband High-Linear FMCW Light Source Based on Spectral Stitching

The key to realizing a high-performance frequency-modulated continuous wave (FMCW) laser frequency-sweeping light source is how to extend the frequency-swept bandwidth and eliminate the effect of nonlinearity. To solve these issues, this paper designs a broadband high-linear FMCW frequency-sweeping light source system based on the combination of fixed temperature control and digital optoelectronic phase-locked loop (PLL), which controls the temperatures of the two lasers separately and attempts to achieve the coarse spectral stitching based on a time-division multiplexing scheme. Furthermore, we uses the PLL to correct the frequency error more specifically after the coarse stitching, which achieves the spectrum fine stitching and, meanwhile, realizes the nonlinearity correction. The experimental results show that our scheme can successfully achieve bandwidth expansion and nonlinearity correction, and the sweeping bandwidth is twice as much as that of the original single laser. The full-width half-maximum (FWHM) of the FMCW output is reduced from 150 kHz to 6.1 kHz, which exhibits excellent nonlinear correction performance. The relative error of the FMCW ranging system based on this frequency-swept light source is also reduced from 1.628% to 0.673%. Therefore, our frequency-swept light source with excellent performance has a promising application in the FMCW laser ranging system.

A Series Impedance Reshaping Control Method Considering PLL Dynamics for Grid-Connected Inverters Under Weak Grid Conditions

Grid-connected inverters are the key part in renewable energy power generation systems. Usually, phase-locked loop (PLL) is adopted in grid-connected inverters to achieve synchronization. However, prior-art works have revealed that the negative resistance behavior in the low-frequency band caused by PLLs may lead to system instability under weak grids. In this paper, first, a comprehensive small-signal output impedance modeling of the LCL-filtered single-phase grid-connected inverter is derived for stability analysis, where the digital control delays and PLL dynamics have been taken into account. Then, a simple but effective virtual series based impedance reshaping method is proposed. With that, the inverter system can operate stably even under a very weak grid (e.g., short-circuit ratio (SCR) is as low as 1.2). Compared with the traditional grid impedance compensation by virtually increasing grid resistance or reducing the grid inductance, the proposed method does not require grid impedance estimation and is robust against system parameter variations. Thus, its feasibility is improved. Finally, experimental tests are carried out on a single-phase 5-kW prototype, validating the effectiveness of the proposed scheme.

Multi-frequency signal acquisition and phase measurement in space gravitational wave detection.

To enhance the accuracy of phase measurement and to prevent tracking errors, it is crucial to effectively read the multi-frequency signal in space gravitational wave detection. In this paper, a novel signal acquisition method called the multi-frequency acquisition algorithm is proposed and implemented. Different from the traditional single-frequency acquisition, the signal characteristics of amplitude and frequency are both considered to better distinguish different frequency components. A phasemeter integrated with the acquisition method and narrow-bandwidth digital phase-locked loop is constructed for the method test and verification. The results show that the multi-frequency acquisition unit can capture all the frequencies of an input signal in several milliseconds. The precision is better than ±200Hz under a low SNR (signal-to-noise ratio) of 0 dB. The phase noise can reach 2 µrad/Hz1/2 in the frequency range of 0.1-1Hz and satisfy the requirement of the space gravitational wave detection in all frequency ranges.

Research on Pulsar Time Steered Atomic Time Algorithm Based on DPLL

In today’s society, there is a wide demand for high-precision and high-stability time service in the fields of electric power, communication, transportation and finance. At present, the time standard in various countries is mainly based on atomic clocks, but the frequency drift of atomic clocks will affect the long-term stability performance. Compared with atomic clocks, millisecond pulsars have better long-term stability and can complement with the excellent short-term stability of atomic clocks. In order to improve the long-term stability of the atomic timescale, and then improve the timing accuracy, this paper proposes an algorithm for steering the atomic clock ensemble (ACE) by ensemble pulsar time (EPT) based on digital phase locked loop (DPLL). First, the ACE and EPT are generated by the ALGOS algorithm, then the ACE is steered by EPT based on DPLL to calibrate the long-term frequency drift of the atomic clock, so that the generated steered atomic time follows both the short-term stability characteristics of ACE and the long-term stability characteristics of EPT, and finally, the steered atomic time is used to calibrate the local cesium clock. The experimental results show that the long-term stability of atomic time after steering is improved by 2 orders of magnitude compared with that before steering, and the daily drift of a local cesium clock after calibration is less than 9.47 ns in 3 yr, 3 orders of magnitude higher than that before calibration on accuracy.

Doppler Parameters Estimation Using Digital PLL Based on SWIFT & αSWIFT Structures

A digital phase-locked loop (DPLL) based on sliding window infinite Fourier transform (SWIFT) and αSWIFT is proposed to extract the vibration and velocity parameters from the phase-modulated carrier signal. The phase of a carrier signal gets modulated when it is reflected from a vibration object due to the Doppler effect. Therefore, the phase-modulated carrier signal contains the Doppler signal that has the vibration information. The SWIFT or αSWIFT structure is designed from sliding discrete-time Fourier transform (DTFT) where the exponential window provides higher weightage to recent samples. It acts as a phase detector in the proposed DPLL, and its bandwidth can be varied based on the values of the time-constant. A controller unit, along with a bi-quad oscillator, is introduced in the proposed DPLL structure to remove any leakages in the system and to synchronize the system units in the parameter estimation. The proposed scheme is implemented in MATLAB/SIMULINK environment and validation for real-time applications is done using dSPACE 1202 MicrolabBox.

Transponder-type laser interferometer prototype for spaceborne gravitational wave detectors.

Transponder-type laser interferometry is essential in spaceborne gravitational wave detection missions. This paper presents a transponder-type laser interferometer prototype for potential noise calibration of spaceborne gravitational wave detectors. Using a digital optical phase-locked loop, we successfully locked the phase of the slave laser to the master laser (∼200p W). Once the link between the master laser and the slave laser is established, the two satellites (essentially two lasers) form a transponder-type laser interferometer. We carefully analyze the measurement stability and noise characteristics of the interferometer, and the results show that the Allan deviation of the zero drift can reach 243.2pm at t=0.429s, while the noise spectral density has a typical 1/f line shape with a floor of 21p m/H z 1/2 at 1Hz. The coherence analysis shows that the temperature drift is an important factor limiting the performance of the interferometer below 2mHz, while the frequency noise of the master laser is not dominant in the experiment. Transponder-type laser interferometers have a wide range of applications in intersatellite communication and measurement. Our design can serve as a valuable reference for gravitational wave detection missions such as LISA.

A Novel Frequency and Positive Sequence Detector for Utility Applications and Power Quality Analysis.

Based on multi-dimensional representation and vector calculus definitions, this paper proposes two novel and quite simple algorithms for utility applications and power quality analysis. The first one is a synchronizing procedure, based on a digital PLL (Phase Locked Loop). Its design and dynamic behavior are analyzed for single and three-phase systems. The second one is a positive sequence detector, which uses the proposed PLL to ensure that the positive sequence components can be calculated even under distorted waveform conditions or frequency variations. Since it is not based on Fortescue’s classical decomposition and no special input filtering are needed, its dynamic response may be as fast as one fundamental cycle. In order to validate the proposed models, simulations are shown and experimental results were obtained by means of a DSP-based system and a prototype of Power Quality Monitor. Furthermore, the PLL algorithm was implemented in a selective active filter to confirm the expectations in a closed-loop application.

Canceling Fundamental Fractional Spurs Due to Self-Interference in a Digital Phase-Locked Loop

Canceling Fundamental Fractional Spurs Due to Self-Interference in a Digital Phase-Locked Loop

A Low-Jitter and Compact-Area Fractional-N Digital PLL With Fast Multi-Variable Calibration Using the Recursive Least-Squares Algorithm

A Low-Jitter and Compact-Area Fractional-<i>N</i> Digital PLL With Fast Multi-Variable Calibration Using the Recursive Least-Squares Algorithm

A 6.5-to-8-GHz Cascaded Dual-Fractional-$N$ Digital PLL Achieving $-$52.79-dBc Fractional Spur With 50-MHz Reference

A 6.5-to-8-GHz Cascaded Dual-Fractional-$N$ Digital PLL Achieving $-$52.79-dBc Fractional Spur With 50-MHz Reference

Research on an Active Hydrogen Maser Digital Circuit Control System Based on FPGA.

A hydrogen maser is a high-precision time measurement instrument with high frequency stability and low frequency drift, which is widely used in satellite navigation, ground time keeping, frequency measurement, and other fields. An active hydrogen maser (AHM) is better than the current space passive hydrogen maser (PHM) in orbit in terms of its frequency stability and drift rate, but it has the disadvantages of large volume and weight. To further reduce the volume and weight of the circuit, this paper demonstrates a digital circuit control system based on a field-programmable gate array (FPGA). It uses digital temperature control, digital detectors, digital down-conversion, digital phase-locked loops, and other digital methods for temperature control, cavity auto-tuning, and crystal phase locking, which improve the integration and flexibility of the circuit system. Meanwhile, a tuning method based on hydrogen flow is proposed, which effectively solves the problem of fluctuations in hydrogen maser resonance frequency with changes in the external environment. Our experimental results show that the designed digital circuit control system meets the requirements of an oven-controlled crystal oscillator (OCXO) loop and a cavity loop. Its frequency stability can reach 2.6×10-13/1 s and 1.4×10-15/10,000 s, which is close to the stability index of ground active hydrogen maser. This scheme has certain practical engineering value, and can be used in the design of hydrogen masers for next-generation space navigation satellites, deep space exploration, and space stations.

Low-noise phase-sensitive optical parametric amplifier with lossless local pump generation using a digital dither optical phase-locked loop.

The low noise figure of phase-sensitive amplifiers (PSAs) is attractive for optically pre-amplified measurement and communication systems. However, a major practical implementation difficulty pertains to the requirement of phase-locked signal, idler, and pump waves. Previously, injection locking to a co-propagating weak pump pilot or tapping portions of the received signal (lossy) for carrier re-generation have been used. Here we present a novel, lossless approach without any pump pilot, that generates a phase-locked receiver-local pump within the PSA using a digital dither-based optical phase-locked loop. We experimentally demonstrate a 2 dB noise figure with a low 0.3 dB penalty due to imperfect locking. By comparing the phase-locking performance in a PSA to that in a 50/50-coupler, we discuss and predict potential performance improvements connected to loop delay and laser phase characteristics.

Virtual Space-Time DiversityTurbo Equalization Using Cluster Sparse Proportional Recursive Least Squares Algorithm for Underwater Acoustic Communications

The oceanic positioning, navigation and timing (PNT) network requires high-quality underwater acoustic message transmission. Turbo equalization technology has exhibited superior performance for underwater acoustic (UWA) communications compared with conventional channel equalizers. To overcome the performance reduction caused by severe doubly selective UWA channels, the virtual space-time diversity soft direct-adaptation turbo equalization is proposed for UWA communications. The proposed scheme improves the ability of the typical turbo equalizer to deal with both Doppler and multipath effects for time varying channels. We utilize a fractionally spaced soft interference cancellation equalizer (FS-SE) instead of a hard decision to constitute the soft-input soft-output (SISO) equalizer. Combined with another virtual time-reversal mirror equalizer component, we can obtain virtual space and time diversity with only a single receiving transducer and mitigate the error propagation phenomenon of the feedback filter. To satisfy the sparse UWA channel, the ℓp,q-PRLS algorithm is applied to adaptive updates for FS-SE. In the proposed scheme, an adjustable interpolator and digital phase-locked loop are embedded into the equalizer to overcome the residual Doppler frequency shift and recover the timing distortion. Results of simulations and field lake trial show that the proposed scheme achieves better performance than existing ones under the same equalizer order.

Hybrid Multibeamforming Receiver With High-Precision Beam Steering for Low Earth Orbit Satellite Communication

A hybrid multibeamforming receiver for low Earth orbit (LEO) satellite communication in the Ku-band is designed and tested. The proposed receiver is implemented with eight channels to enable multibeam control. The proposed receiver, including both analog and digital beamforming structures, is capable of multibeam reception using both analog and digital beamforming techniques simultaneously or selectively. Analog beamforming is implemented by employing a local oscillator phase shifter using direct digital synthesis and phase-locked loop (PLL) structures. In digital beamforming, a software-defined radio can control the phase of the signal in the digital baseband. The multibeam received using the proposed hybrid multibeamforming receiver was measured at 11.7 GHz and 12.7 GHz in an anechoic chamber. The phase-control resolutions of analog and digital beamforming were 0.022° and 0.72°, respectively. Analog beam-switching speed is slower than digital beamforming because it depends on the settling time of the PLL circuit, but it has a high phase-control resolution. Therefore, by using analog and digital beamforming when precise beam tilting and fast beam switching are required, respectively, the proposed hybrid multibeamforming is shown to be suitable in accordance with the communication situation.

Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers.

Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of z-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained.

A Novel Pilot-Aided Timing Recovery Algorithm With High Tolerance to Impairments for OQAM-Based Digital Multi-Band Systems

Timing recovery (TR) plays an important role in the digital signal processing (DSP) of coherent receivers. In TR, timing error (TE) is extracted by the timing recovery algorithm (TRA) and fed back to adjust the clock sampling phase. However, widely-used Gardner and Godard TRAs are sensitive to spectral roll-off factor and differential group delay (DGD), and more importantly, are inapplicable to the offset quadrature amplitude modulation (OQAM) system. In this paper, we propose a novel pilot-aided TRA for the OQAM-based digital multi-band (OQAM-DMB) system, which is robust to different impairments including rotation of state of polarization (RSOP), DGD, spectral roll-off, residual chromatic dispersion (rCD), residual carrier frequency offset (RFO), and laser linewidth. 1.12-Tbit/s simulations and 320-Gbit/s experiments show that OQAM-DMB based on the proposed algorithm works properly for all spectral roll-off factors and exhibits excellent tolerance against DGD, RSOP, rCD, RFO, and laser linewidth, and outperforms QAM-DMB using conventional TRAs. The digital phase-lock loop can be locked for the clock frequency offset within ±80 ppm and all initial sampling phase offsets. Although investigated in OQAM-DMB, the proposed algorithm is also applicable to conventional QAM-DMB.