Interferences in Phase-Locked Loops

An analysis of the behavior of a second-order phase-locked loop is presented when an unwanted signal is added to the useful signal. Both signals are sinusoidal and unmodulated, and the analysis is made in the absence of additive noise. When the loop remains locked on the useful signal, a parasitic signal exists at the phase detector output. This signal produces a parasitic phase modulation of the VCO and a static phase error in the loop. The parasitic signal amplitude, the parasitic phase modulation index, and the static phase error are calculated. A necessary condition for the loop to remain in lock is derived. When the loop is initially unlocked, locking can occur either on the useful signal or on the unwanted signal, depending on the amplitude ratio and the frequency difference of the two signals. A formula allowing one to compute the pull-in time is obtained. When the loop locks on the useful signal, acquisition can be slower or faster than in the absence of an unwanted signal. The same phenomenon is observed when the loop locks on the unwanted signal.     

基于DDS驱动PLL结构的X波段雷达信号频率综合器

给出了一种基于DDS驱动PLL的频率综合器结构。该结构采用AD9854DDS芯片产生低频的参考信号,然后驱动锁相环和VCO产生X波段射频信号。实验和测量结果表明,该频率综合器具有较宽的工作带宽和较低的相位噪声,可以用来产生连续波、线性调频信号和频率捷变信号用于X波段雷达信号的仿真。     

Carrier loop architectures for tracking weak GPS signals

The performance of various carrier recovery loop architectures (phase lock loop (PLL), Doppler-aided PLL, frequency lock loop (FLL), and Doppler-aided FLL) in tracking weak GPS signals are analyzed and experimentally validated. The effects of phase or frequency detector design, oscillator quality, coherent averaging time, and external Doppler aiding information on delaying loss of lock are quantified. It is shown that for PLLs the metric of total phase jitter is a reliable metric for assessing low C/N performance of the tracking loop provided the loop bandwidth is not too small (~> 5 Hz). For loop bandwidths that are not too small, total phase jitter accurately predicts carrier-to-noise ratio (C/N) at which loss of lock occurs. This predicted C/N is very close to the C/N predicted by bit error rate (BER). However, unlike BER, total phase jitter can be computed in real-time and an estimator for it is developed and experimentally validated. Total phase jitter is not a replacement for BER, since at low bandwidths it is less accurate than BER in that the receiver loses lock at a higher C/N than predicted by the estimator. Similarly, for FLLs operating at small loop bandwidths, it is found that normalized total frequency jitter is not a reliable metric for assessing loss of lock in weak signal or low C/N conditions. At small loop bandwidths, while total frequency jitter may indicate that a loop is still tracking, the Doppler estimates provided by the FLL will be biased.     

基于FPGA的硅微机械陀螺仪数字化驱动电路研究

为了进一步提高硅微机械陀螺仪的性能,提出了一种基于FPGA数字信号处理来实现控制的数字化驱动电路。该设计方案通过AGC环路稳定了驱动幅度,并用SPLL对相位进行了控制以跟踪谐振频率。两主要环路以FPGA为硬件基础,用软件编程实现,相较模拟驱动电路在实际应用中更具灵活性。实验给出了该电路的驱动幅度和频率漂移曲线,证明了该电路可以较好的实现硅微机械陀螺仪的驱动。     

Analysis of interference effects on monopulse radars

The complete numerical analysis of angle-tracking performance of a coherent amplitude-comparison monopulse radar system in a two-target situation is described. This system, equipped with automatic gain control (AGC) and phase-locked loop (PLL), was originally invented for improving the target-tracking performance in multiple-target situation. The general behavior depends on Doppler separation of the targets relative to the bandwidths of AGC and PLL. The performance of this system has previously been roughly analyzed by using linear approximation for four extreme cases: wideband and narrowband AGC in combination with wideband and narrowband PLL. In this study, the author performs nonlinear analysis of the same system for all bandwidths of AGC and PLL, because Doppler separation varies over a wide range in actual tracker, and therefore it is indispensable to know the total system behavior. A special numerical technique called the Galerkin method is used. As a result of this analysis, the extensive target-tracking performance for all intermediate bandwidths of AGC and PLL has been clarified. The result is useful for actual target tracker design     

Transient Frequency-Error Statistics in Acquisition of Noiseless First-Order Phase Lock Loop

After a certain time interval from the appearance of a reference signal in a synchronizing system employing a first-order phase lock loop (PLL), the probability that the output frequency error will be higher than a maximum tolerated value is determined. The system is assumed to be noise free.     

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     

A Semi-Empirical Approach to the PLL Threshold

This correspondence considers the response of the PLL near threshold to an input consisting of a modulated carrier and white, Gaussian noise. For high input signal-to-noise power ratios ?, the output noise power is Gaussian with a parabolic spectrum. As ? is decreased, the PLL tends to lose lock which gives rise to impulses or ?spikes? in the output with a resulting white power spectrum. The additional output noise due to these ?spikes? causes a threshold in the output signal-to-noise ratio. Unfortunately the loss of lock rate in the PLL depends on the modulation as well as the noise power. A semiempirical approximate expression for the loss of lock rate as a function of the noise and sinusoidal frequency modulation is presented and is used to determine the optimum design procedure for PLL's to demodulate FM signals of varying modulation indexes, ?.     

GPS/SINS超紧组合导航的性能分析

GPS接收机在高动态环境下很容易失锁,特别是载体的高动态造成的应力对接收机载波跟踪环影响很大。为了解决高动态环境下的组合导航,分析了GPS接收机载波跟踪环的测量误差和跟踪门限,采用惯导速度辅助GPS接收机跟踪环路的超紧组合结构。超紧组合需要涉及到GPS接收机跟踪环内部编排及高动态环境下的实验数据,难度较大。针对超紧组合仿真专门开发了GPS实时软件接收机、高动态GPS中频信号仿真器和惯导模拟器并构建了一个完整的GPS/SINS超紧组合仿真系统。仿真结果表明,该超紧组合导航系统可以跟踪50g的加速度和10倍音速。     

带通限幅器对锁相环噪声性能的影响

锁相环路中,在鉴相器前加上AGC（自动增益控制）,可以使环路性能在输入信噪比发生变化时保持稳定,带通限幅器也可以起到类似作用。尽管有一些文章对限幅器的性能作了研究,但是在PLL（锁相环）闭环条件下,鲜有文章分析其对环路噪声性能的影响。因此,文章以基本PLL环路的数学模型为基础,推导出PLL中分别加入相干AGC和带通限幅器后新的环路数学模型,以一阶PLL为例,计算和比较不同控制方式下环路相位误差均方值的变化,最后说明应当根据飞行任务的不同选择对环路更有利的控制方式。     

北斗导航接收机高增益相干积分算法

近年来,针对弱信号的高灵敏度接收机已逐渐成为国内外的研究热点。加长相干积分时间可以提高信噪比,从而跟踪到更弱的信号。但是,北斗导航接收机跟踪环路并不可以无限加长相干积分时间,相干积分时间的长短和功效还受到卫星导航电文比特跳变的限制。为了消除导航电文比特跳变对相干积分的影响,提出了一种改进的基于最大似然估计的北斗信号位同步方法,完成位同步后再利用先猜后检的方法便可以实现长相干积分。利用软件接收机进行编程设计,仿真结果表明：该长相干积分算法能够稳定可靠地实现对弱信号的跟踪,20ms相干积分环路信噪比约提升12dB,40ms相干积分环路信噪比约提升15dB,80ms相干积分环路信噪比约提升17dB,提高了北斗导航接收机的灵敏度。     

GPS软件接收机的捕获与跟踪算法

研究了GPS软件接收机的捕获与跟踪算法。分析了时域串行滑动相关捕获算法和频域基于FFT的并行相关捕获算法,设计了适合GPS软件接收机的并行算法,实现了对空中可见卫星的捕获。针对GPS信号的特点,设计了基于DLL与PLL相结合方法的GPS跟踪算法。利用实测中频信号对上述捕获与跟踪算法进行了验证分析,测试结果表明,基于FFT的并行相关捕获算法能够有效增强软件接收机的捕获能力,采用DLL与PLL相结合的方法能够实现对GPS信号的有效跟踪。     

一种用于深空测距的数字化锁相环设计

在深空测距中,扩大锁相环捕获范围与提高锁相环对微弱信号检测能力是一对矛盾。为解决这一矛盾,本文提出一种基于频率引导与二次混频的数字化锁相环结构,并对其性能进行理论分析和计算机仿真。仿真结果表明,该锁相环可以很好地在较大范围内实现对微弱测距信号的捕获锁定。该结构已在实际测距接收机中使用。     

Phase-Locked Loop Behavior near Threshold

The phase-locked loop behavior is analyzed following the quasilinearization Booton's method. When the loop is locked on an unmodulated input signal with a static phase error, the phase detector nonlinearity produces an interaction between the static phase error and the voltage-controlled-oscillator (VCO) noise phase fluctuations. Formulas allowing one to compute the static phase error increase and the VCO phase variance increase are derived. When the input signal is phase modulated, there is an interaction between the static phase error, the VCO noise phase fluctuations, and the input signal phase modulation. Formulas are obtained that allow one to compute the loop loss of performances (static phase error increase and VCO phase variance increase) and the coherent phase demodulator output signal-to-noise ratio decrease. Finally, a slight modification to Booton's procedure is proposed, leading to results in better agreement with experimental data.     

一种基于参数控制的低轨星载接收机载波跟踪算法CSCD

低轨星座接收机面临大多普勒频移及频繁快速换星等设计约束,对其载波跟踪环路设计提出了较高的动态适应性与跟踪精度要求。针对以上问题,提出了一种基于参数控制的载波跟踪算法。该算法引入环路控制因子参数,将环路滤波器分为牵引和跟踪两阶段。基于理论建模推导环路控制因子的最优参数配置原则,指导实现牵引和跟踪两种状态滤波器的协同配合,在牵引阶段有效引导大多普勒信号快速入锁,在跟踪阶段精确估计载波频移参数,实现基于低轨星载平台的GNSS信号快速准确跟踪。理论与仿真结果均表明基于参数控制的载波跟踪算法能够有效提升环路的动态适应性与跟踪精度,满足低轨星载接收机的设计需求。与传统算法相比,该算法在保证信号跟踪精度的同时,能够将收敛时间缩短78%,且环路设计简单,易于硬件实现。     

Low C/N_0 Carrier Tracking Loop Based on Optimal Estimation Algorithm in GPS Software Receivers

Suppressing jitter noises in a phase locked loop(PLL) is of great importance in order to keep precise and continuous track of global positioning system(GPS) signals characterized by low carrier-to-noise ratio(C/N0).This article proposes and analyzes an improved Kalman-filter-based PLL to process weak carrier signals in GPS software receivers.After reviewing the optimal-bandwidth-based traditional second-order PLL,a Kalman-filter-based estimation algorithm is implemented for the new PLL by decorrelating the model error noises and the measurement noises.Finally,the efficiency of this new Kalman-filter-based PLL is verified by experimental data.Compared to the traditional second-order PLL,this new PLL is in position to make correct estimation of the carrier phase differences and Doppler shifts with less overshoots and noise disturbances and keeps an effective check on the disturbances out of jitter noises in PLL.The results show that during processing normal signals,this improved PLL reduces the standard deviation from 0.010 69 cycle to 0.007 63 cycle,and for weak signal processing,the phase jitter range and the Doppler shifts can be controlled within ±17° and ±5Hz as against ±25° and ±15 Hz by the traditional PLL.     

Optimum Strategies for Minimum Time Frequency Transitions in Phase-Locked Loops

Pontryagin's maximum principle is applied to minimize the time for a phase-locked loop to lock to a step change in frequency. In particular, a Type II phase-locked loop is considered in detail. Phase control and frequency control of the input signal are analyzed with the nonlinearity of the phase detector taken into consideration. It is shown that application of Pontryagin's maximum principle offers a decided advantage in shortening this time by proper control.     

Interference in Frequency-Locked Doppler Tracking Loops

The effects of interference on frequency-locked Doppler tracking loops are investigated. Conditions for jump from locking on the desired signal to locking on the interfering signal are established. Parasitic frequency modulation of the desired signal results when the other signal interferes with it. The index of this parasitic modulation as a function of the interference-to-desired signal amplitude ratio is computed. Both critical amplitude ratio and critical parasitic modulation index at the occurrence of jump are derived. Comparing frequency-locked loops with phase-locked loops with phase-locked loops in the presence of interference shows the former performs better for most cases of practical importance in Doppler tracking systems.     

高码率导航电文引起的跟踪环路失锁及其解决方法

卫星信号的多普勒频移会引起导航数据跳变点在1ms中频采样数据中的相对位置发生滑动,当跳变点处于采样数据段的中间位置时,相关器输出接近于零,造成环路失锁。本文在详细分析这一问题的基础上,针对“北斗II”信号提出了一种改进的环路跟踪方法。新方法通过在连续的两段1ms数据中找出不包含数据位跳变点的数据段,将该段数据的鉴相结果用于2ms环路更新。仿真和GNSS模拟器的实验验证了该方法的有效性。     

Sampling Bandpass Signals

In a recent paper [1], Brown examined the sampling of a real finiteenergy bandpass signal having an (angular) bandwidth ? (in radians per second) at the theoretically minimum (average) rate of ?/? samples per second. Following Grace and Pitt's [2] quadrature sampling, a particular case of Kohlenberg's second-order sampling [3, 4], Brown has proved the feasibility of a separate interpolation of the in-phase and quadrature components of the signal when ?o = k?/2 (Brown's condition), where ?o is the center (angular) frequency of the signal and k is an arbitrary positive integer. Here the problem is reconsidered from a general point of view, introducing, under Brown's condition, an interpolation formula which includes that of Grace and Pitt and which extends a theorem of Populis [5-7]. We indicate the necessary and sufficient conditions to obtain a separate interpolation, offering closed formulas to obtain the interpolation functions. We also discuss the minimum oversampling rate needed whenBrown's condition is not verified.