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引言用环路工作的线性理论无法预测也无法解释在锁相接收机中观察到的跳周现象。文献[1]能解一个福克-普朗克方程,获得一阶环路从锁定到跳周的预期时间,不过,到目前为止尚不能将此法推广到高阶环路。文本表明:一个任意阶环路的预期初跳时间满足一可以简化为一阶的线性微分方程,对于此方程至少很容易得到某形式上的解。此推导可由一个不限于马尔柯夫过程的随机游动模型直接得出。计算精确的解涉及到能否计算某一条件期望,要计算此期望通常需要一个关于相位误差过程概率密度的先验解,然而,
INTRODUCTION The linear theory of working with loops is unpredictable and unable to explain the jumps observed in phase-locked receivers. In [1], a Foucault-Planck equation can be solved for the expected time of first-order loop from lock-in to jump-skip. However, this method has not been extended to higher-order loops so far. The text shows that the expected initial jump time for an arbitrary order loop satisfies a linear differential equation that can be reduced to first order, at least for some easy solution to this equation. This derivation can be directly derived from a random walk model that is not limited to the Markov process. Computationally exact solutions involve the possibility of calculating a conditional expectation. To calculate this expectation usually requires a priori solution to the probability density of the phase error process. However,