Timing Errors in a Chain of Regenerative Repeaters, II

We showed in a previous discussion that the pulse displacements at the output of a chain of repeaters may he represented by a linear transformation of the pulse displacements at the output of the first repeater.* The linear transformation turns out to be a simple function of a basic operator T which, in essence, represents the action of the repeater on I he incoming jitter. Though the operator T depends directly on the manner in which the repeater extracts its timing information from the incoming pulse train, it is believed that there would be no basic difference in the major results obtained or in the method of analysis for different timing extractors. We have assumed that the timing information extractor is a tuned circuit with a finite but fairly high Q and the source of jitter is the mistiming in the tuned circuit. Other sources of jitter often lend themselves to a similar mode of investigation. The rest of the discussion in Part I concerned the class of periodic pulse trains. The problem reduces, in such cases, to a consideration of linear transformations in a finite dimensional space. For a periodic pulse train with period m, it was shown that the variance of the jitter remains bounded for an indefinitely long string of repeaters. * We shall assume t h a t the reader is familiar with the contents of P a r t I of this paper: B. K. Kinariwala, Timing Errors in a Chain of Regenerative Repeaters, I, this issue, pp. 17G9-1780. 1781