= Pulse timing jitter
{title2=$\sigma_t$}
\b[Pulse timing jitter] describes variation of pulse arrival times relative to a stated timing reference. Choose a reproducible pulse feature and reference instants $t_j^{\rm ref}$; define errors $e_j=t_j-t_j^{\rm ref}$. One measure is their <standard deviation> $\sigma_t$. Edge-time error relative to an ideal reference differs from variation of successive periods or cycle-to-cycle differences; the primary timing guide distinguishes these measurements.<Digital Design Debugging Guide by Tektronix>[Picking out Jitter, Diagram5 and statistical discussion, printedpp.12–14]{ref}
For an original distribution, let each error equal $500\,\mathrm{ps}+\epsilon$, where $\epsilon$ is equally likely to be $+100$ or $-100\,\mathrm{ps}$. The mean delay is $500\,\mathrm{ps}$ and $\sigma_t=100\,\mathrm{ps}$. The <root mean square> error about zero is instead $\sqrt{500^2+100^2}\approx510\,\mathrm{ps}$. A fixed delay changes the mean without increasing the spread. None of these numbers is the individual pulse's duration.
A fast <photodetector>, reference timing signal and <oscilloscope> can measure a selected arrival feature. A fixed electrical threshold can also turn amplitude/readout noise into an apparent time change, producing <threshold timing noise from amplitude noise>. Specify the reference, feature, observation duration and measurement response. A fitted or recovered reference can absorb some timing variation, changing the reported residual.
Timing variation can become gated-energy variation even at constant full pulse energy. The <Gaussian gate centring error> provides one quantitative model, distinct from <pulse-to-pulse energy fluctuation> of complete pulses.
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