A General Spectral Analysis of Time Jitter Produced in a Regenerative Repeater

A general theory is presented for evaluating the spectral density of time jitter produced in a self-timed regenerative repeater. The timing circuit consists of a general memoryless nonlinear device followed by a narrow-band tank circuit tuned as close as possible to the symbol rate; the signal (timing wave) at the output of the circuit has both amplitude and phase modulations that cause the timing error (jitter). The theory includes the cases of arbitrary pattern statistics, pulse waveform, and nonlinear processing, in contrast to previous work which is strongly limited to the assumptions of pattern symbol independence and particular nonlinearities. The time jitter is treated as a discrete-parameter random process and its spectral density is finally related to the input message statistics, pulse waveform, and timing circuit parameters. In most cases the spectral density turns out to be a rational function of exp (j2),fbeing the frequency andTthe symbol period. Hence, a spectral factorization can be obtained that leads to a useful linear equivalent circuit of the timing (nonlinear) circuit (NLC). This last feature is illustrated by three examples.