Timing jitter

Timing jitter is the error in when something happens: a data transition, a laser pulse, a sampling instant, or a detector's output edge, measured against an ideal reference time. In the frequency domain the same quantity is phase noise; jitter is the integral of the phase noise spectrum over a stated offset range, converted to time, and a jitter figure without that range is incomplete.

In a data link, jitter closes the eye diagram from the sides. It is divided into random jitter, unbounded and usually taken as Gaussian with an rms value, and deterministic jitter, bounded, from causes such as intersymbol interference, duty-cycle distortion and crosstalk. Because random jitter has no peak, total jitter is defined at a target bit error ratio: in the common dual-Dirac model, $TJ = DJ + 2Q\,RJ_\text{rms}$, where $Q$ = 7.03 at a ratio of $10^{-12}$. With 3 ps of deterministic jitter and 0.5 ps rms of random jitter, total jitter at $10^{-12}$ is 10.0 ps, which is 27% of the 37.6 ps unit interval at 26.5625 GBd and 53% of the 18.8 ps interval at 53.125 GBd. The same jitter budget becomes twice as expensive each time the symbol rate doubles, which is why jitter specifications tighten with each generation and why receiver clock recovery is designed to track and remove the slow part of it.

In sampling systems, a clock with rms jitter $\sigma_t$ limits the signal-to-noise ratio for a sine wave of frequency $f$ to $-20\log_{10}(2\pi f \sigma_t)$ dB. A 10 GHz signal sampled by a clock with 100 fs rms jitter can be digitized no better than 44.0 dB, about seven effective bits, whatever the converter's nominal resolution. Mode-locked lasers, whose pulse trains can have jitter of femtoseconds or less, are used as sampling clocks in photonic analog-to-digital converters and as timing references for that reason.

Photon-counting detectors have a jitter of their own: the spread in delay between a photon's arrival and the output edge. It sets the timing resolution of time-correlated single-photon counting and of time-of-flight ranging; tens of picoseconds is typical for thin silicon SPADs and single-digit to tens of picoseconds for SNSPDs.

Measurement follows the application. Real-time and sampling oscilloscopes decompose jitter into its components from the edges of a long pattern; phase-noise analyzers integrate the spectrum of a clock; and for optical pulse trains, cross-correlation or the phase noise of a photodetected harmonic is used when the jitter is too small for an oscilloscope.

References: M. P. Li, Jitter, Noise, and Signal Integrity at High-Speed (Prentice Hall, 2007); R. H. Walden, IEEE J. Sel. Areas Commun. 17, 539 (1999).