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本文讨论在卫星通信、遥控遥测等领域中用作同步的锁相环在有噪声作用时的非线性分析。文中从估计理论观点论证了锁相环路是一个最佳非线性相位估计器。并用福克—普朗克(Focker-Planck)方法分析了在观测噪声为白高斯过程时锁相环的统计特性。详细推导了三阶锁相环的稳态相位误差的概率密度,导出了锁相环在统计稳态时的失锁概率和跳周平均时间。
This article discusses the non-linear analysis of phase-locked loops used as synchronization in the fields of satellite communications, telemetry, and the like, under noisy conditions. The article proves that the phase-locked loop is the best non-linear phase estimator from the viewpoint of estimation theory. The statistical characteristics of PLL are analyzed with Focker-Planck method when the observed noise is white Gaussian. The probability density of the steady-state phase error of the third-order phase-locked loop is deduced in detail, and the probability of lock-out and the average time of the jump in the steady-state of the PLL are deduced.