Jitter is not a quantity a system has; it is a quantity defined against an error ratio you nominate. Everything awkward about measuring it follows from that, and so does the one instrument that can do it honestly.
Jitter attracts acronyms faster than almost any other topic in this field, and it is easy to end up fluent in the vocabulary while losing track of what any of it is for. Ransom Stephens's remedy is a short list of rules that the acronyms have to serve, and this section of the series is organised around them.
The first and the last are the same rule, which is the point of stating it twice. We care about jitter for exactly the reason we care about signal-to-noise ratio: a poor one means a high error rate. Voltage noise causes errors when the signal fluctuates vertically across the sampling point; jitter causes errors when the transition fluctuates horizontally across it. Anything said about jitter that cannot be connected back to an error ratio is decoration.
The first and fifth are this deck. The second is slide 03 and everything about the dual-Dirac model in deck 08, which exists because the honest measurement is too slow. The third is deck 09, on clock recovery and the reference clock. The fourth — that timing noise and amplitude noise are not really separable — is deck 10, and it is the one this series would most easily have got wrong, because the separation is so convenient that it is rarely questioned.
The quantity that links jitter to errors is total jitter at a specified error ratio, written TJ(BER). It is the amount by which the eye has closed horizontally by the time the error ratio reaches the value you nominate, and it changes with that value — which is why quoting a total jitter without the error ratio it belongs to says very little.
The construction is straightforward. Sweep the sampling instant across the unit interval and record the error ratio at each position. Near the middle it is vanishingly small; approaching either crossing it climbs. The horizontal distance between the two flanks at a chosen level is the eye opening at that level, and the total jitter is the unit interval minus that opening:
$$\mathrm{TJ(BER)} = T_b - \text{eye opening at that BER}.$$
Read backwards, this is a design criterion: a link works at a given error ratio if the total jitter at that error ratio is less than one bit period. Read forwards, it says something less comfortable — the eye may be wide open at $10^{-6}$ and entirely closed at $10^{-15}$, and the two statements describe the same signal.
The multiplier on the random part of the jitter grows only slowly with the error ratio, which is both a mercy and a trap: three extra decades of reliability cost less than one unit of Q, so the budget is insensitive far from the target and very sensitive near it.
The second rule is the awkward one. Total jitter at a low error ratio can only be measured on a bit error ratio tester, because measuring an error ratio means counting errors, and counting enough of them to believe the number means transmitting on the order of ten divided by that ratio.
Everything else — every oscilloscope, every time-interval analyser, every fast estimate a bit error ratio tester itself offers — produces an estimate, obtained by measuring what can be measured quickly and extrapolating with a model. Deck 08 is about that model and what it costs.
Before any arithmetic, a collision of notation worth flagging explicitly, because it genuinely catches engineers who work across both domains — and the two meet inside this very topic.
The argument of the complementary error function: a signal-to-noise ratio measured in standard deviations, so that the error ratio is $\tfrac{1}{2}\,\mathrm{erfc}(Q/\sqrt{2})$. Dimensionless, normally between three and eight, and larger is better. Every budget in this series uses it.
Energy stored divided by energy dissipated per radian: a property of a tuned circuit, normally between ten and several thousand. Larger is also better, and it means something entirely different.
They meet in a chain that makes the confusion harder rather than easier to avoid. The resonator Q of an inductor-capacitor oscillator's tank sets its phase noise; the phase noise integrates to the random jitter; the random jitter is part of the noise in the denominator of the communications Q. A sentence about a high-Q tank improving Q is therefore not nonsense — but it needs both words defined, and a reviewer who works across both will ask.
The reason to decompose jitter at all is that the components combine differently and are fixed by different purchases. Bounded quantities add arithmetically, unbounded ones in quadrature, and a budget that mixes the rules passes on the bench and fails in the field.
The standard tree splits total jitter into random and deterministic; splits deterministic into data-dependent, periodic and bounded uncorrelated; and puts intersymbol interference and duty-cycle distortion under data-dependent, with a dotted line between them because duty-cycle distortion changes how much intersymbol interference there is.
The last column is the one that earns the decomposition its keep. A budget reporting a single total jitter figure cannot tell you whether to buy a better oscillator, a longer equaliser, a quieter regulator or more spacing — and those are four different conversations with four different departments.
One branch of the tree deserves its own slide because it is honest about being a residue. Stephens describes bounded uncorrelated jitter as the category the industry uses for organising its ignorance: it is everything bounded that is not correlated with the victim's own data, which in practice means everything we do not know how to measure separately.
The reason the category exists at all is an assumption: that the only unbounded contribution is the Gaussian random part. Everything else must be bounded, so anything bounded that cannot be attributed to the data or to a known tone gets swept here.
Deterministic — it is an exact function of the aggressor's data — but that data is not the victim's, so nothing in the victim's receiver can predict it. Bounded by the aggressor's swing. The best example of the category, and the subject of deck 10.
Most techniques for extracting random jitter assume that anything smooth and wide in the tails is Gaussian. Bounded uncorrelated jitter is often both, so it is counted as random — and random jitter is multiplied by fourteen at $10^{-12}$ while bounded jitter is not.
Measure with the aggressors quiet and again with them driven. The difference is the contribution that the acronyms cannot name, and it is usually easier to obtain than to argue about which branch of the tree it belongs on.
Data-dependent jitter is the one branch that can be computed exactly rather than measured, because it is a deterministic function of the preceding bits and the channel's own pulse response. Enumerating every pattern of a given depth and finding the zero crossing for each gives the distribution outright.
It is worth looking at, because it is emphatically not two impulses, which is what the model in deck 08 will assume it is.
Every jitter measurement, and every model built on one, assumes the process is stationary — that a measurement taken over a suitable interval gives the same answer whenever it is started. It is listed as one of the five assumptions behind the dual-Dirac model and it is almost never mentioned in a specification.
It is also the assumption most obviously untrue of a real system.
A rail that droops when a neighbouring core wakes up. A spread-spectrum clock, deliberately modulated. A thermal drift over minutes. A link that retrains. A fan that changes speed. Each makes the jitter distribution a function of when you looked.
Extrapolating to $10^{-12}$ means claiming to know a distribution's behaviour a long way past where it was sampled. If the distribution itself moves on a timescale comparable with the measurement, the extrapolated tail is not a tail of anything — it is a mixture of several distributions, which is broader than any of them.
The practical consequence is that a jitter number should carry its observation interval alongside its error ratio, and that a measurement repeated at a different time is worth more than the same measurement continued for longer.
The word "frequency" does two jobs in this subject and mixing them produces confident nonsense.
The harmonic content of the waveform itself: the spectrum whose Nyquist frequency is half the symbol rate, whose loss is the subject of deck 03, and which the equaliser shapes. For a 28 GBd lane this domain runs to tens of gigahertz.
The spectrum of the deviations from the ideal phase — the single-sideband phase-noise spectrum. Its axis is the offset from the carrier, and the interesting region runs from kilohertz to tens of megahertz: six orders of magnitude below the other one.
A clock recovery circuit's bandwidth is a frequency in the second domain. It says nothing about the signal's bandwidth and everything about which part of the phase-noise spectrum reaches the sampler. That distinction is the whole of deck 09, and getting it wrong is how a perfectly good oscillator comes to be blamed for a problem it has no part in.
If a statement about jitter would change meaning when the data rate changed but the oscillator did not, it is probably about the first domain. If it would change when the clock recovery loop changed but the data rate did not, it is about the second.
| Idea | Statement | Consequence |
|---|---|---|
| Rule 1 and 5 | It is about the bit error ratio | Anything not connected to an error ratio is decoration |
| Rule 2 | Total jitter can only be measured on a BERT | Everything else is an estimate from a model |
| Rule 3 | Measurement compares a test clock with a reference | Deck 09: which reference decides the answer |
| Rule 4 | Timing and amplitude noise are not separable | Deck 10: the separation fails above about 10 Gb/s |
| Total jitter | $\mathrm{TJ(BER)} = T_b - \text{opening}$ | A function of the error ratio, not a number |
| Measurement time | $\approx 10/\mathrm{BER}$ bits | Six minutes at $10^{-12}$ and 28 GBd; four days at $10^{-15}$ |
| Random | Unbounded, Gaussian, adds in quadrature | Multiplied by $2Q$; fixed by a better oscillator |
| Deterministic | Bounded, adds arithmetically | Enters once, whatever the error ratio |
| BUJ | Bounded, uncorrelated, unmeasured | Usually crosstalk; usually counted as random by mistake |
| Stationarity | Assumed everywhere, stated nowhere | Repeat the measurement rather than lengthen it |
Deck 7 of eleven in Signal Integrity & High-Speed Digital Design. Every figure on this page is computed by si_models/deck07 and embedded as data; nothing is typed in by hand.
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