Equivalent Model of a Clock Recovery Circuit

In previous work a jitter model has been used to predict the growth of the timing errors along a chain of PCM regenerators. According to this model each regenerator behaves as a combination of a low-pass filter and a source of noise. The former accounts for the smoothing effect of the time constants of the regenerator, and the latter represents timing errors associated with the clock recovery process. This theory has been brought out under restrictive hypotheses either on the width of the pulses (often assumed very short) or on the form of the nonlinearity in the clock recovery system. In this paper we show that the theory is still valid for any reasonable form of nonlinearity and for pulses wider than the symbol spacing. A method is also given to compute the filter transfer function and the spectral density of the noise.