Second-order Phase-locked Loop Research Articles

On the limit behavior of second-order analog phase-locked loops

The study of limit behavior of a dynamical system is necessary for nonlinear analysis and computation of the exact boundary of global stability in the parameters’ space. For phase-locked loops (PLLs), a problem of its global stability is equal to a problem of a pull-in range calculation, which is one of the key stability characteristics of a PLL. In this paper, we consider a model of a second-order analog PLL and show that it can exhibit a wide range of limit behavior, including cycles and polycycles of the first and second kind.

Design of Noncoherent and Coherent Receivers for Chirp Spread Spectrum Systems

LoRaWAN is a prominent communication standard to enable reliable low-power, long-range communications for the Internet of Things (IoT). The modulation technique used in LoRaWAN, commonly known as LoRa modulation, is based on the principle of chirp spread spectrum (CSS). The main objective of this article is to design a practical, low-complexity coherent receiver for a recently proposed CSS-based modulation scheme, called phase-shift keying CSS (PSK-CSS), that embeds extra information bits in the starting phases of conventional CSS symbols. To this end, a novel method is proposed to perform coarse timing and frequency synchronization that makes use of a preamble consisting of both up and down chirps and the shape of the pulse shaping and/or receive (matched) filters. Furthermore, to enable fine synchronization, timing, and phase loop filters are designed as simple first-order and second-order phase-locked loop (PLL) circuits with dynamic gain control. A natural outcome of our design is a practical noncoherent receiver that can be used for the conventional LoRa/CSS system and has better performance and/or lower computational complexity as compared to other existing designs. Extensive simulation results are presented to demonstrate the excellent performance and merits of the proposed design. In particular, the bit-error-rate (BER) performance of the higher-rate PSK-CSS system obtained with the proposed coherent receiver is only 0.25 dB worse than that obtained with the ideal co-coherent receiver, whereas it enjoys about 0.75-dB power gain over the noncoherent detection performance of the conventional CSS system. Thanks to the extra information bits carried by the phases of CSS symbols, the PSK-CSS system implemented with quadrature phase-shift keying (QPSK) delivers additional 23.44% and 18.75% data rate as compared to the conventional CSS system for the spreading factors (SFs) of 8 and 10, respectively.

A 0.8–3.2 GHz PLL with wide frequency division ratio range

An improved phase-locked loop (PLL) with a wide frequency division ratio range is presented. A digital to analog converter (DAC) is used to separate the proportional path and integral path, thus the dynamic performance of PLL can be flexibly adjusted by DAC and the current-controlled oscillator (CCO). As the resistor in the second-order PLL is replaced by an equivalent circuit, the implemented PLL is insensitive to the process, voltage, and temperature (PVT) variation. Decoupling the relationship between loop bandwidth ωb and division ratio N improves the overall performance over a wide dynamic output frequency range. The PLL was implemented in TSMC 22 nm CMOS process and the chip occupies an area of 0.04 mm2. The measured output frequency is ranged from 0.8 GHz to 3.6 GHz. The phase noise is −107.3dBc@1 MHz and the integrated RMS jitters at 1.92 GHz is 3.36ps. The total power consumption at 1.92 GHz is 4.2 mW.

PLL Position and Speed Observer With Integrated Current Observer for Sensorless PMSM Drives

In this article, a phase-locked loop (PLL) rotor position and speed observer, including an integrated decoupled stator current observer, is proposed for wide-speed-range sensorless control of permanent magnet synchronous motor (PMSM) drives. This new PLL scheme consists of two interconnected observers: 1) a second-order PLL position observer using the direct current error as correction term and 2) a third-order extended Luenberger speed observer, based on the mechanical model of the drive, using the quadrature current error as the correction term. The estimated speed is just an unrefined reference for the position integrator, and it is further corrected by the PLL. The current observer is a subsystem integrated as a PLL phase detector. Key relations between the current errors and the position and speed errors are proven, and a practical two-step observer design method is presented. A method for real-time identification of the stator resistance at low speeds and of the permanent magnet flux at high speeds is proposed, using the current errors in the current reference frame. Experimental results for a 0.5-kW surface-mounted PMSM drive confirm the effectiveness, excellent dynamic performance, and robustness of the new PLL observer. Stable motor and generator operation at 15 r/min (0.01 p.u.) with ramp and step speed reversals, high-speed operation, and stator resistance adaptation is shown.

Synthetic baseline navigation using phase-coherent acoustic communication signals.

The development of a synthetic baseline navigation technique that self-localizes an autonomous underwater vehicle (AUV) using intermittent acoustic communications signals received by a single transducer is described, along with field results from in-ocean tests. The method uses the phase measurement at the output of a second-order phase-locked loop to create fine-scale pseudorange estimates in addition to, or in the absence of, a one-way travel time measurement based on the arrival time of the acoustic data packet. These range measurements are incorporated by an adaptive particle filter. This technique allows the vehicle navigation system to take advantage of multiple phase-derived range measurements made over the duration of a communication packet. These measurements, when incorporated with an appropriate filter and vehicle kinematic model, improve vehicle navigation at no additional cost in navigation-specific acoustic transmissions. This approach was demonstrated and evaluated with data collected at-sea using a REMUS 100 AUV (Hydroid, Inc., Pocasset, MA).

Design-Oriented Transient Stability Analysis of PLL-Synchronized Voltage-Source Converters

Differing from synchronous generators, there are lack of physical laws governing the synchronization dynamics of voltage-source converters (VSCs). The widely used phase-locked loop (PLL) plays a critical role in maintaining the synchronism of current-controlled VSCs, whose dynamics are highly affected by the power exchange between VSCs and the grid. This paper presents a design-oriented analysis on the transient stability of PLL-synchronized VSCs, i.e., the synchronization stability of VSCs under large disturbances, by employing the phase portrait approach. Insights into the stabilizing effects of the first- and second-order PLLs are provided with the quantitative analysis. It is revealed that simply increasing the damping ratio of the second-order PLL may fail to stabilize VSCs during severe grid faults, while the first-order PLL can always guarantee the transient stability of VSCs when equilibrium operation points exist. An adaptive PLL that switches between the second-order and the first-order PLL during the fault-occurring/-clearing transient is proposed for preserving both the transient stability and the phase tracking accuracy. Time-domain simulations and experimental tests, considering both the grid fault and the fault recovery, are performed, and the obtained results validate the theoretical findings.

A Study of Phase Noise and Frequency Error of a Fractional-N PLL in the Course of FMCW Chirp Generation

This paper presents the theoretical and experimental results on the phase noise spectrum and the rms frequency error of a fractional-N phase-locked loop (PLL) under frequency-modulated continuous-wave (FMCW) chirp generation. The phase noise spectrum under modulation is analytically calculated for a second-order charge pump PLL with a feedback divider ratio linearly changing over time. This is followed by an analysis of the steady-state rms frequency error of the output frequency after PLL settling is achieved during chirp generation. A fractional-N PLL with integrated frequency ramp generator is presented. Phase noise and jitter measurements on the PLL under modulation are performed at the output of the programmable feedback divider. The resulting low-frequency rms jitter is reduced by about 9dB with doubling the charge pump current, and reduced by about 6dB with halving the ramp slope. The rms frequency error under FMCW modulation is measured at the modulated voltage-controlled oscillator output. The dependence of the frequency error on the loop filter capacitance for various ramp slopes is given. A frequency error of 112kHz is achieved with a ramp slope of 1.28GHz/80 μs at a carrier frequency of 62GHz. The noise measurements are in good agreement with the developed phase noise model. A programmable loop filter capacitance is suggested to accommodate the static phase offset and the resulting noise performance to the ramp slope.

New Nonlinear Second-Order Phase-Locked Loop with Adaptive Bandwidth Regulation

Synchronization of large acquisition bandwidth brings great challenges to the traditional second-order phase-locked loop (PLL). To address the contradiction between acquisition bandwidth and noise suppression capability of the traditional PLL, a new second-order PLL coupled with a nonlinear element is proposed. The proposed nonlinear second-order PLL regulates the loop noise bandwidth adaptively by the nonlinear module. When a large input–output phase error occurs, this PLL reduces the frequency offset quickly by taking advantage of the large bandwidth. When the phase error is reduced by the loop control, the proposed PLL suppresses noises by using the small bandwidth to increase the tracking accuracy. Simulation results demonstrate that the tracking speed of the proposed PLL is increased considerably, and its acquisition bandwidth is increased to 18.8 kHz compared with that of the traditional second-order PLL (4 kHz).

Accidental phase modulation in second-order phase-locked loops

The phase-locked loop, essential element for phase synchronization in communications and control, is studied for several types of application. However, some cases urge for more accurate models, mainly regarding to the accidental phase modulation, an unavoidable phenomenon provoked by imperfections of circuits and transmission media, causing oscillations around the synchronous state, even when this state is reached. In this work, this problem is treated by distinguishing two different cases: jitter (high frequency) and wander (low frequency). In addition, the perturbation origins are modeled, dividing the problem into deterministic and random signal perturbations showing how they affect the equilibrium even with the loop operating in the pull-in range.

GNSS IF Signal Simulation Considering Oscillator Phase Noise

Oscillator phase noise has a negative effect on the tracking performance of Global Navigation Satellite System (GNSS) receivers. To provide GNSS software receivers with real test environments, this paper proposes a method to simulate the GNSS Intermediate Frequency (IF) signal, taking the oscillator phase noise effect into consideration. The oscillator parameters are first measured via a pseudolite transmitter and receiver system. According to the measured oscillator parameters, an oscillator-induced frequency fluctuation is then generated, and added to the digital IF signal. Further simulation experiments are conducted that attempt to measure the oscillator phase noise effect on a second-order Phase Lock Loop (PLL) performance. Results indicate that the IF signal simulator considering the oscillator phase noise is able to provide software receivers with real signal dynamics, helping to evaluate the performance of signal processing algorithms on a software platform.

A Novel FLL-Assisted PLL With Fuzzy Control for TC-OFDM Carrier Signal Tracking

The time and code division-orthogonal frequency-division multiplexing (TC-OFDM) signal is a promising wireless positioning signal, which multiplexes the China mobile multimedia broadcasting signal and pseudorandom noise codes in the same frequency band. The drastic change of carrier-to-noise ratio can increase carrier tracking error of the TC-OFDM receiver and may lead to the loss of lock. To address this problem, a novel frequency-lock loop (FLL)-assisted phase-lock loop (PLL) with fuzzy control is proposed, and the effect of signal strength on the carrier tracking loop is analyzed. The proposed algorithm uses the outputs of the phase and frequency discriminator as measured residuals of the Kalman filter (KF), and a KF-based second-order FLL-assisted three-order PLL carrier tracking loop is designed. Moreover, fuzzy control is applied to the designed loop. It can automatically switch between pure KF-based PLL, pure KF-based FLL, and KF-based FLL-assisted PLL, and automatically adjust the noise bandwidth. Simulation and experimental results show that, compared with the existing carrier tracking algorithms, the proposed algorithm can effectively avoid the divergence of the tracking loop and improve the robustness of the TC-OFDM receiver.

Soft direct-adaptation based bidirectional turbo equalization for MIMO underwater acoustic communications

This paper proposes a soft direct-adaptation based bidirectional turbo equalizer for multiple-input multiple-output underwater acoustic communication systems. Soft, rather than hard, direct-adaptation based equalizer combined with the fast self-optimized least mean square algorithm is employed to achieve a faster convergence rate, and the second-order phase-locked loop is embedded into the equalizer to track the time-varying channel. Meanwhile, by utilizing a weighted linear combining scheme, the conventional soft direct- adaptation based equalizer is combined with the time-reversed soft direct-adaptation based equalizer to exploit bidirectional diversity and mitigate error propagation. Both the simulation and experimental results demonstrate that the soft direct-adaptation based bidirectional turbo equalizer outperforms the single-direction soft direct-adaptation based turbo equalizer, and achieves a faster convergence rate than the hard direct-adaptation based bidirectional turbo equalizer.

Stability improvement of PV‐BESS diesel generator‐based microgrid with a new modified harmony search‐based hybrid firefly algorithm

Using a new improved harmony search-based hybrid firefly algorithm (IHBFA), a comprehensive controller gain parameter estimation of all distributed resources-based microgrid is proposed. To ensure a fast convergence and to endeavour less randomisation to conventional firefly algorithm (FA), diversity of population is increased by an improved harmony search (HS) algorithm. To decrease local optima searching delay, a linear incremental pitch adjustment rate and exponential decaying bandwidth is considered for proposed HS-based hybrid FA. Photovoltaic (PV), an auxiliary battery energy storage system (BESS) with the second-order phase-locked loop control, is considered as a primary DG ( DG 1) for the proposed microgrid. Pade approximation delay-based governor control is used for the diesel generator unit, considered as a secondary DG ( DG 2). The overall gain optimisation improves the dynamic stability limits by minimising low-frequency network behaviour. The effectiveness of proposed IHBFA in terms of power oscillation damping and improved stability limits is clearly demonstrated for microgrid applications.

Modeling and verifying the impact of time delay on INS-aided GNSS PLLs

The timing error between global navigation satellite system (GNSS) and inertial navigation system (INS) processes limits the integration performance in GNSS/INS integrated systems. In a deeply coupled system, this timing error affects not only the integrated navigation solution, but also the GNSS signal tracking. We propose a time-domain model of INS-aided second-order phase-locked loops (PLLs) in consideration of the INS aiding delay, and analyze the effect of INS aiding delay on the tracking errors in details. In addition, an integrated hardware deeply coupled system platform was developed to verify the impact of time delay on INS-aided PLLs. Simulation and field vehicles testing results demonstrate that the tracking error of the INS-aided PLL caused by aiding delay increases with the lengthening of the delay time, the compression of the bandwidth, and the increase in the acceleration. Testing results verify the proposed model.

Subharmonic Oscillations Induced by Continuous Wave Electromagnetic Interference on a Microwave Phase-Locked Loop

This paper presents measurements, simulations, and a theoretical basis to support the observation of spurious peaks on the output spectrum of a microwave phase-locked loop (PLL) exposed to a continuous wave electromagnetic interference (EMI). It is shown that high-power EMI combined to nonlinear characteristics of the PLL may induce subharmonic oscillation phenomena, which provoke the appearance of spurious peaks on the output spectrum. Measurements show that in addition to their dependence on the EMI power and frequency, these spurious peaks depend also on the natural frequency of the PLL and on its stability. Transient circuit simulations of the PLL allowing the prediction of these spurious peaks are presented. Finally, a theoretical explanation based on an analysis of a second-order PLL is given.

Complex Amplitudes Tracking Loop for multipath channel estimation in OFDM systems under slow to moderate fading

This paper deals with multipath channel estimation for Orthogonal Frequency-Division Multiplexing systems under slow to moderate fading conditions. Most of the conventional methods exploit only the frequency-domain correlation by estimating the channel at pilot frequencies, and then interpolating the channel frequency response. More advanced algorithms exploit in addition the time-domain correlation, by employing Kalman filters based on the approximation of the time-varying channel. Adopting a parametric approach and assuming a primary acquisition of the path delays, channel estimators have to track the complex amplitudes of the paths. In this perspective, we propose a less complex algorithm than the Kalman methods, inspired by second-order Phase-Locked Loops. An error signal is created from the pilot-aided Least-Squares estimates of the complex amplitudes, and is integrated by the loop to carry out the final estimates. We derive closed-form expressions of the mean squared error of the algorithm and of the optimal loop coefficients versus the channel state, assuming a Rayleigh channel with Jakes' Doppler spectrum. The efficiency of our reduced complexity algorithm is demonstrated, with an asymptotic mean squared error lower than the first-order auto-regressive Kalman filters reported in the literature, and almost the same as a second-order Kalman-based algorithm.

Exact laser line-width requirements evaluation for optical PSK homodyne communication systems with Dither loop

The laser line-width required in PSK homodyne communication systems with Dither phase-locked loop receivers are exactly evaluated. It is shown that second-order phase-locked loops require at least 0.2pW of signal power per every Hz of laser line-width (this number refers to the system with the detector responsivity 0.94 A/W, damping ratio 0.707, and the phase error standard deviation 10°). This signal power is used for phase locking, and is, therefore lost from the data receiver. This study for the first time shows the imperfect-phase-recovery-induced power penalty as a function of laser line-width. It can be estimated from the theoretical result that an optimal dither phase locked-loop receiver requires the laser line-width as Δυ≤3.14×10−5×Rb, where Rb is the system bit rate. This number refers to the system with power penalty of 1dB at BER=10−10.

An Analytical Approximation for the Pull-Out Frequency of a PLL Employing a Sinusoidal Phase Detector

The pull-out frequency of a second-order phase lock loop (PLL) is an important parameter that quantifies the loop's ability to stay frequency locked under abrupt changes in the reference input frequency. In most cases, this must be determined numerically or approximated using asymptotic techniques, both of which require special knowledge, skills, and tools. An approximating formula is derived analytically for computing the pull-out frequency for a second-order Type II PLL that employs a sinusoidal characteristic phase detector. The pull-out frequency of such PLLs can be easily approximated to satisfactory accuracy with this formula using a modern scientific calculator.

An Analytical Approximation for the Pull-Out Frequency of a PLL Employing a Sinusoidal Phase Detector

The pull-out frequency of a second-order phase lock loop (PLL) is an important parameter that quantifies the loop's ability to stay frequency locked under abrupt changes in the reference input frequency. In most cases, this must be determined numerically or approximated using asymptotic techniques, both of which require special knowledge, skills, and tools. An approximating formula is derived analytically for computing the pull-out frequency for a second-order Type II PLL that employs a sinusoidal characteristic phase detector. The pull-out frequency of such PLLs can be easily approximated to satisfactory accuracy with this formula using a modern scientific calculator.

Three Parametric Model Third-Order Software Phase-Locked Loop and its Application in Range Measuring System

In order to improve the precision of side tone range measuring and realize the range measuring process by software, one kind of three parametric model third-order software phase-locked loop (SPLL) is designed based on three parametric loop filter model and the predominant closed-loop poles theory, which can apply the parameter setting principles of the second-order phase-locked loop; this kind of third-order SPLL is realized through C++ language programming and used as the range measuring system’s side tone phase-locked loop(PLL) to process the experiment data. The results indicates that the precision of phase measuring and capture time satisfy the system’s index.