Improved Phase-Locked Loop Performance with Adaptive Phase Comparators

A major problem in phase-locked loop (PLL) design is to meet the requirements of both fast signal acquisition and good synchronous mode performance. This relation is reviewed for different types of phase comparators. As a result a new phase-and-frequency comparator is proposed. This comparator is based on an up-down counter principle and can be considered as an adaptive acquisition control circuit. The analysis of a PLL with the proposed phase comparator is based on an exact calculation method for the pull-in time. It is shown that fast signal acquisition is possible without affecting the filtering properties of the loop. Experimental results are given of the acquisition behavior of a second-order type-2 loop which show a good correspondence with the theoretical analysis.     

Stability Criterion for a Hybrid Phase-Locked Loop Range Tracker

A currently tested high-performance electronic range tracker operating in a linear region and tracking a nearly stationary target can be modeled as a hybrid or gated phase-locked loop. A relationship for stability in this system is developed. The relationship is applicable to both Type I and Type II second-order hybrid phase-locked loop trackers.     

Graphical Analysis of a Digital Phase-Locked Loop

Under the assumption of negligible quantization error effect and no noise, a nonuniform sampling first-order digital phase-locked loop (DPLL) is analyzed by a graphical method which displays limit cycles and the cycle slipping phenomenon. The analysis suggests an upper bound to the model gain and, consequently, to the pull-in range. Moreover, this method enables one to obtain a closed-form expression of the acquisition time, accurate enough for the cases of practical interest.     

Noise Performance of a Gated Phase-Locked Loop

The objectives of this paper are two. The first is to show that a gated phase-locked loop (GPLL) is a tracking device whose operation approximates that of a maximum likelihood estimator of the phase of a pulsed sinusoid imbedded in noise. The second is to determine the behavior of theb loop in the presence of noise. It is found that the loop performance is equivalent to that of a continuous phase-locked loop driven by the same noise, plus a continuous sinusoid which has the same power as the pulsed sinusoid at the input of the GPLL.     

Phase Detector Data Distortion in Phase-Lock Loop Receivers

The nonlinear characteristic of a sinusoidal phase detector can create an additional loop suppression factor and cause distortion of any phase-modulated data that is to be extracted in a phase-lock loop receiver. The distortion caused by the phase detector's sinusoidal characteristic will degrade the phase-lock loop parameters and decrease the amplitude of the phase-modulated data.     

Dynamics of the Phase-Locked Loop without a Limiter

The general (nth order) phase-locked loop is analyzed, of which the amplitude is not constant. The input carrier signal is amplitude-modulated by wide-band stationary Gaussian noise, and the signal, superposed with the additive white stationary Gaussian noise, enters the nonlimited phase-locked loop. Under the above assumptions the loop can be shown to constitute an n-dimensional vector Markov process, so that the process satisfies the n-dimensional Fokker-Plank equation. The probability density function depends on the effective loop signal-to-noise ratio and the effective modulation power.     

Pull-In Performance of a Piecewise Linear Phase-Locked Loop

This is part of a study concerned with the analysis of phase-locked loops (PLL's). The broad objective throughout this work is to improve upon our general understanding in this important area. More particularly, ly, we are seeking quantitative results indicative of the pull-in behavior of PLL's. In the present paper, we point out some results in foreign publications and focus attention on a paper by Kapranov [1] which is devoted to the study of the pull-in frequency of second-order PLL's with a symmetric phase comparator. We apply the same approach and present results, in closed form, in the more general case where the phase comparator possesses an asymmetric triangular characteristic. Special cases of this phase comparator are the sawtooth and symmetric triangular comparators. It can also be viewed as an approximation to the Tanlock phase comparator. The RC filter case is treated.     

Noise Dynamics of the Phase-Locked Loop with Signal Clipping

Employing techniques similar to the averaging methods of Krylov and Bogoliubov, an approximate noise analysis of the phase-locked loop with signal clipping is presented. The validity of the method is demonstrated by comparing the stationary probability density function for the phase error, generated by a system simulation, with the derived theoretical results. The latter portion of the paper discusses the relation of the phase-locked loop to Kalman-Bucy filter theory and presents a demodulator design that illustrates the self-adaptive properties attainable in phase-locked loops with signal clipping.     

An Extension of Viterbi's Analysis of the Cycle Slipping in a First-Order Phase-Locked Loop

The phenomenon of cycle slipping in a first-order phase-locked loop is reconsidered and a simple expression for the expected number ? of cycles slipped per second is given in the form of a rapidly converging series. In this way the computation of ? becomes much easier than with previously known formulas. A formula allowing the computation of the expected number of cycles gained or lost per second is also given. These results are obtained by extending a technique used by Viterbi. The outcome of experimental verifications of the theory is also reported.     

Optimum Acquisition of the Idling First-Order Phase-Locked Loop

Acquisition of the idling first-order phase-locked loop (PLL) is investigated. An analytical solution for the Fokker-Planck equation is found if the noise term is neglected. Furthermore, the modulation signal that optimizes the acquisition is obtained by use of phase-plane techniques and Pontryagin's minimum principle.     

Random Characteristics of the Type II Phase-Locked Loop

The results of a study of the characteristics of the second-order Type II phase-locked loop with a Gaussian noise input, and obtained by digital computer simulation, are presented. The digital simulation is described and the random state variables are defined such that their characteristics can be interpreted in terms of existing phase portraits of autonomous phase-locked loops. The statistics associated with the state variables, which are phase error and a measure of frequency error, and those associated with the number of cycles skipped and the mean time to unlock, are given.     

基于锁相环的光电振荡器频率稳定化研究

通过构建小数分频锁相环,将一个工作于X波段的OEO(OptoElectronic Oscillator,光电振荡器)与OCXO(Oven-Controlled Crystal Oscillator,恒温晶体振荡器)进行锁相,得到了输出信号相位噪声和长期频率稳定度的提升。从PLL(Phase-Locked Loop,锁相环)环路传输特性出发,理论分析了PLL输出信号环路带宽内相位噪声水平和作用范围。为降低OEO整体的相位噪声,采用SIL(Self-Injection-Locking,自注入锁定)使OEO在10Hz~10kHz频偏处的相位噪声得到20dB以上的抑制。在此基础上将此SIL OEO与一个频率为100 MHz的OCXO锁相,获得了频率为9.95GHz、相位噪声为-55dBc/Hz@10Hz和-124dBc/Hz@10kHz的微波信号输出,其频率的重叠阿伦方差在100s平均时间内达到1.14×10~(-11),证明了提出的方案对提升OEO频率稳定性具有一定的实际意义。     

On Uniform Sampling of Amplitude Modulated Signals

For a bandpass waveform produced by the amplitude modulation of a low-pass signal, it is shown that the corresponding bandpass signal may be recovered from its samples taken at a uniform rate which is equal to or less than half the sampling rate called for in applying the classical bandpass sampling theorem.     

Square-Wave Correlation Phase Detector with VLF Atmospheric Noise

Correlation phase detectors often include hard limiting of both received and reference signals. The characteristics of such " square-wave" correlation detectors for both Gaussian and impluse noise are derived as functions of both phase and carrier-to-noise ratio. Decoding algorithms and accuracy are discussed.     

The Counting Phase Detector with VLF Atmospheric Noise

The counting detector offers a simple means of making and averaging digital measurements of signal phase. However, use of the averages can lead to erroneous estimates if the signal has a low carrier-to-noise ratio. How to overcome this problem by using multiple counters is shown here. Characteristics for both Gaussian and impulsive noise are derived, and algorithms for estimating both phase and carrier-to-noise ratio are presented.     

S频段小数分频锁相环频率合成器实现与应用

传统的整数分频锁相环频率合成技术无法在单个环路实现高频率、低分辨率和低相噪的目标,小数分频锁相环在提高鉴相频率的同时减小分频计数值,从而降低相位噪声。针对USB统一测控系统的需要,本文提出基于单片小数分频锁相环的微波频率合成方法。实验结果表明,小数分频锁相环频率合成器具备良好的信号输出特性,可以为测控系统提供低成本频率合成方案。     

HVDC直流场强仪相敏检波器分析与设计

地面合成电场是高压直流（HVDC）输电线路电磁环境的一个重要指标,测量该电场时需要同时测量其大小和极性。一般测量电场极性的方法是使用相敏检波器。传统的相敏检波器存在因相位不同步而导致检波误差较大的问题,影响了测量结果的准确性。本文从直流场强仪的原理出发,针对传统方式的弊端,设计了相敏检波器电路,基于该电路的工作原理分析了相位不同步所引起的检波误差,并采用全通滤波器补偿相位差。实验证明,该电路能够灵活、准确地补偿相位误差,从而解决传统设计方法中相位不同步的问题,实现了全波检波,进而分辨电场极性,满足了地面合成电场测量的需求。     

Effects of Automatic Gain Control on Phase-Locked Loop Behavior in the Presence of Interference

The behavior of a second-order phase-locked loop (PLL) in the presence of an interfering signal has been analyzed by different authors with different results. The discrepancy is attributed to the presence or absence of an automatic gain controlled amplifier preceeding the PLL. Simulation results verify that the presence of the automatic gain controlled amplifier reduces the tendency of the PLL to break lock from the desired signal in favor of the interfering signal     

Phase Locked Loop Acquisition for a Noisy FM Signal

A method based upon the quasi-linearization technique of evaluating the pull-in characteristics of a phase locked loop for an angle modulated signal corrupted with Gaussian noise is presented. Experimental results along with formulas for calculating the locking range and locking time are also presented and they are in good agreement with the theoretical results. Some new findings regarding the dependence of the locking range and locking time on the modulating frequency are also incorporated.