Time jitter caused by noise in trigger circuits

This paper deals with the time jitter caused by noise in a trigger circuit; specifically with its probability density (PD). The model adopted for the circuit assumes that the initiation of switching occurs at the instant when the front of the input signal crosses some reference level. The time jitter is defined as the fluctuation of the initiation time due to the presence of an additive noise. It is shown that, when the corrupted signal has one crossing at the reference level, the PD of the jitter is given by the crossing rate at the same level. This rate, in turn, is known in the case of a general uncorrupted signal added to a stationary Gaussian noise. Hence, the PD is determined for various examples of uncorrupted signals. In many cases, the PI) tends rapidly to the Gaussian law as the signal-to-noise ratio (SNR) becomes larger. In other cases the deviation from the Gaussian law remains significant even for large SNRs. It is also shown that the one-crossing situation occurs in most cases of practical interest, specifically when the SNR is fairly large and the noise is spectrally of the same order of magnitude as the signal. Finally, the case is considered where the signal and the additive noise are prefiltered by low-pass systems.