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本文讨论有噪声的二阶锁相环路的非线性性能。环路滤波器是比例-加-积分控制型。此滤波器符合于相位相干通信系统的实现中为了载波跟踪通常使用的一种。文章基本上由两部分组成:第一部分介绍关于相位误差的概率分布的分析结果。因为这些分析结果是近似值,仅仅是对于一定的信噪比范围有效,它们由在试验室内模拟销相环路系统得到的试验结果补充。用来测量环路性能的统计特性的试验技术以及相应的结果构成文章的第二部份。系统相应误差分布的近似分析式首先是由采用 Fokker-Planck仪器获得的,其次是假设锁相环性能为很窄的带通渗滤器。这些近似值是有效的信噪比范围是将分析式与从试验行来的相应误差分布用曲线图进行比较得到的。此外,与相位误差方差相关的测量与线性锁相环理论计的那些以及由近似解计算的方并进行了比较。最后,对于在线性锁相环理论没有应用的范围内的信噪比,给出了周之间时间间隔的概率分布的试验结果。具体地说希望环路可能保持在锁定之中的最大时间长度作为环路带宽中信噪比的函数用曲线图说明。
This article discusses the non-linear performance of noisy second-order phase-locked loops. Loop filter is proportional - plus - integral control type. This filter conforms to the one commonly used for carrier tracking in the implementation of phase coherent communication systems. The article basically consists of two parts: The first part introduces the analysis results of the probability distribution of phase error. Because the results of these analyzes are approximations that are valid only for a limited range of signal-to-noise ratios, they are supplemented by experimental results from analog pin-phase loop systems in the laboratory. The experimental techniques used to measure the statistical properties of loop performance and the corresponding results form the second part of the article. The approximate analytical expression for the corresponding error distribution of the system is first obtained using a Fokker-Planck instrument followed by a bandpass percolator assuming a very narrow PLL performance. These approximations are valid for the range of signal-to-noise ratios obtained by comparing the analytical and the corresponding error distribution from the experimental line with a graph. In addition, measurements related to the phase error variance are compared with those of the linear phase locked loop theory and those calculated by the approximate solution. Finally, the experimental results of the probability distribution of the time interval between weeks are given for the signal-to-noise ratio in the range that is not applicable to linear phase-locked loop theory. Specifically, the maximum length of time the loop is expected to remain in lockout is illustrated graphically as a function of signal-to-noise ratio in the loop bandwidth.