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.     

Noise analysis of a digital tanlock loop

The noise performance analysis of a nonuniform digital phase-locked loop (DPLL), called the digital tanlock loop (DTL), is investigated by both analytic and computer-simulation methods. The results are presented in terms of phase error probability mass function and mean time to skip cycle versus input signal-to-noise ratio (SNR). These results are compared to the ones obtained with the conventional sinusoidal DPLL loop (DPLL). It is found that, for low-to-moderate input SNR, the DTL has only a slight improvement over the DPLL. The DTL, however, has larger linear characteristics than the conventional DPLL, which makes it attractive for applications that require an increased tracking range or as a first stage in carrier tracking systems based on optimum estimation procedures such as a Kalman smoother     

Digital accumulators in phase and frequency tracking loops

Results on the effects of digital accumulators in phase and frequency tracking loops are presented. Digital accumulators or summers are used extensively in digital signal processing to perform averaging or to reduce processing rates to acceptable levels. For tracking the Doppler of high-dynamic targets at low carrier-to-noise ratios, it is shown through simulation and experiment that digital accumulators can contribute an additional loss in operating threshold. This loss was not considered in any previous study and needs to be accounted for in performance prediction analysis. Simulation and measurement results are used to characterize the loss due to the digital summers for three different tracking loops: a digital phase-locked loop, a cross-product automatic frequency tracking loop, and an extended Kalman filter. The tracking algorithms are compared with respect to their frequency error performance and their ability to maintain lock during severe maneuvers at various carrier-to-noise ratios. It is shown that failure to account for the effect of accumulators can result in an inaccurate performance prediction, the extent of which depends highly on the algorithm used     

一种低噪声和高精度的频率合成技术

介绍了锁相环(PLL)技术和直接数字式频率合成(DDS)技术的基本工作原理,给出了一种提高DDS输出频率精度及减小其相位截断误差的方法。     

Performance analysis of GPS carrier phase observable

The accuracy analysis of Global Positioning System (GPS) carrier phase observable measured by a digital GPS receiver is presented. A digital phase-locked loop (DPLL) is modeled to extract the carrier phase of the received signal after a pseudorandom noise (PRN) code synchronization system despreads the received PRN coded signal. Based on phase noise characteristics of the input signal, the following performance of the first, second, and third-order DPLLs is analyzed mathematically: (1) loop stability and transient process; (2) steady-state probability density function (pdf), mean and variance of phase tracking error; (3) carrier phase acquisition performance; and (4) mean time to the first cycle-slipping. The theoretical analysis is verified by Monte Carlo computer simulations. The analysis of the dependency of the phase input noise and receiver design parameters provides with an important reference in designing the carrier phase synchronization system for high accuracy GPS positioning     

Coherent Square Wave Demodulation of Ideal Limiter Output

An ideal limiter may be used to single-bit quantize a noisy sinusoidal signal. This digitization is particularly economical if the signal is to be recorded. lt might then be desired to obtain phase coherence with the limited input signal. A single-bit digital phase-locked loop. utilizing a square wave reference, could be used for this purpose. The effects of coherent square wave demodulation on the signal-to-noise ratio and the (signal-to-noise spectral density) ratio are discussed. The latter result is directly applicable to the performance of the digital phase-locked loop.     

Adaptive Maximum Likelihood Receiver for Direct-Ranging Applications

Recent interest in direct-ranging navigation methods has prompted new research into practical receiver structures which provide improved signal processing. Maximum likelihood receivers are compared with conventional phase-locked receivers by theoretical and simulation methods as phase estimators based on signal measurements only. Signal-to-noise ratio (SNR) enhancement is examined and filter recommendations made. An adaptive maximum likelihood receiver is then developed which uses both signal measurements and a priori data to improve phase estimation accuracy. Simulation results indicate a 33.3 dB processing gain yielding a ranging error standard deviation of ±15 feet for zero dB received SNR. Nonadaptive and adaptive receivers are fabricated, flight tested, and experimental results reported.     

机动飞行目标的数学模型与仿真算法研究

描述系统运动的状态方程所含的状态理越多,其数学模型就越准确,但其数字仿真时的算法实现也越困难。困此,采用“当前”统计模型建立机动飞行目标的空间运动方程,并结合桥函数级数理论求解,实现了对机动飞行目标稳定、准确、实时地仿真计算。以典型机动目标为例,进行了数字仿真,通过对各主要状态量的计算结果分析,验证了该方法的有效性。     

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.     

现代飞机尾旋平衡点的分析和预测

 本文提出了两种近似估计稳态尾旋平衡点的方法。一种是通过忽略一些对稳态尾旋影响不大的参数,理论上得出了稳态尾旋时各量的近似值;另一种方法是通过计算机,运用最优化方法——DFP变尺度法,算出平衡点的值,从而大大缩短了尾旋运动的数字仿真时间,为改进尾旋的研究提供了方便。     

Statistical Analysis of Digital Phase-Locked Loops Fading Channiels

Statistical analyses of zero-crossing sampling first- and second order digital phase-locked loops in fading channls (DPLFC) are presented. A DPLFC is defined as one where the incoming signal is not only corrupted by additive Gaussian noise channel (AGN) but also by a fading communication channel. The three fading channels considered are the log-normal, Rayleigh, and Rician channels. The performance degradation of the DPLFC operation is characterized by the steady-state phase-error process probability density function and phase-error variance. Approximate analytic expressions for the phase-error statistics of a first-order DPLFC for both phase-step and frequency-step inputs are obtained by solving the Chapman-Kolmogorov equation associated with the phase-error process. The second-order DPLFC is analyzed for a frequency-step input. Numerical and simulation results are provided confirming the analyses presented for the three fading channels considered.     

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。     

一种基于螺旋桨部件特性的螺旋桨建模方法

通过缩比法,利用螺旋桨通用部件特性获得期望研究的螺旋桨部件特性,提出了飞行速度不为零条件下的螺旋桨数学模型建模算法,同时,借鉴缩比后螺旋桨部件特性、螺旋桨定桨叶角工作性能曲线以及螺旋桨空气动力学原理,分析了静拉力状态下的螺旋桨功率系数、拉力系数、桨叶角、螺旋桨静态推力进距比阈值以及螺旋桨几何设计参数的相互作用关系,提出了静拉力状态下的螺旋桨数学模型建模算法。所述算法与Gas Turbine Simulation Program (GSP)软件仿真数据进行了数字仿真对比验证。结果表明:所提出的螺旋桨建模算法具有有效性,在前进状态下,螺旋桨拉力相对误差最大不超过6.6059×10-6，需求功率相对误差最大不超过5.5098×10-6，效率相对误差最大不超过6.6955×10-6。      

数字闭环光纤陀螺死区机理研究与抑制

在数字闭环光纤陀螺中,死区产生及其附近噪声特性恶化的主要因素可以归结于施加在相位调制器上信号的串扰。根据死区产生机理的不同,提出了偏置相位调制和阶梯波反馈调制两种死区串扰误差因素的观点。通过对这两种死区误差机理的分析和比较,提出了采用模拟相加反馈方案可以避免偏置相位调制死区误差的观点。采用速率转台法测试了光纤陀螺的死区特性,验证了理论仿真和计算的正确性。最后,通过采用三角波相位抖动抑制死区误差技术,将一种高精度光纤陀螺0.08(°)/h的死区误差抑制到0.001(°)/h以下。     

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.     

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。     

一种基于输出误差观测的冗余MEMS-IMU标定技术研究

针对传统六位置标定存在标定步骤复杂、标定时间长等问题，同时随着MEMS器件冗余数目增加和冗余配置结构复杂化，利用分立标定技术实现器件误差参数辨识的难度进一步增大，且不同配置结构所采用的标定方法存在通用性较差的问题。因此提出了一种基于Kalman滤波的冗余MEMS-IMU分立标定方案。该方案首先采用小角度建模法实现安装误差的精确建模；然后针对直接以转台三轴角速率为观测值，导致部分状态量不可观的问题，提出了以器件的输出误差值作为观测量、以器件误差参数作为状态量设计Kalman滤波器；最后设计了高精度三轴转台转位编排方式，并利用四陀螺冗余结构进行标定仿真试验。仿真结果表明：该标定方法与六位置标定方案相比，标定精度平均提高了11.37%，可实现MEMS器件误差参数的快速辨识，对实际工程实践具有一定参考价值。     

基于DSP的测试转台控制系统研究与设计

以锁相环控制为基础研究了转台速率控制系统的设计,利用数字信号处理芯片DSP、高速A/D和D/A芯片(AD7865和AD7836)以及FPGA技术完成了系统硬件电路设计,和关键逻辑电路——指令脉冲发生器、精密移相器、鉴相器的设计,并设计了控制器,给出了软件设计流程和仿真结果。实际运行表明系统稳定可靠,满足了转台的设计性能要求。     

A Comparison of Second, Third, and Fourth Order Phase-Locked Loops

This paper presents data describing various performance characteristics of phase-locked loops, which were obtained for the purpose of determining an optimum selection of system order in view of typical operating conditions. With the functions optimized with respect to particular performance characteristics, calculations of the integrated square error and peak error with polynomial inputs are presented in terms of the noise bandwidth; and the generalized error coefficients are also provided in terms of the bandwidth with consideration for the use of both perfect and imperfect integrators. With specific input functions as provided by signals transmitted from earth satellites, an improved performance is demonstrated with the use of the higher order loops, and experimental results verify the calculations and also demonstrate the feasibility of the fourth order loop design.     

On the Acquisition Time for an Apollo Ranging Code

An Apollo ranging system is considered whose phase reference is obtained by a phase-locked loop for bit synchronization. The bit phase reference is noisy, and the error probability for the ranging code is shown to depend on the input signal energy per bit to noise density ratio. The procedure of computing the acquisition time for the ranging code is then presented and the acquisition time for a lunar ranging code is plotted versus the input signal-to-noise density ratio.