The fourth rule, and the one the previous three quietly depend on being false only a little: timing noise and amplitude noise are not separable. On the channel this series works against, the separation stops being safe at about ten gigabits per second.
Everything in the three previous decks treats jitter as a one-dimensional problem: transitions move horizontally, and the question is by how much. Look at an eye diagram and the assumption is obviously incomplete. The noise on it is visible in both directions, and the two are not independent.
The voltage noise that reduces the signal-to-noise ratio does not only cause amplitude errors. It also moves the instant at which the waveform crosses its threshold, which is jitter by any definition. Equally, phase noise does not only cause timing errors — at a fixed sampling instant on a sloping edge it produces an amplitude error.
With infinitely fast edges, jitter would be caused by phase noise alone and amplitude noise would cause no timing error whatever. Separating the two would then be exact rather than convenient.
Real transitions have finite slope. A vertical displacement therefore produces a horizontal one, in a ratio set entirely by that slope — and the slope, on a lossy channel, is set by the channel rather than by the transmitter.
Stephens's formulation is that jitter analysis considers one dimension of a two-dimensional problem, and that this is useful rather than correct. The purpose of this deck is to find where it stops being useful, which turns out to be a computable question with an uncomfortable answer.
The conversion is geometric and immediate. A waveform displaced vertically by $\delta V$ crosses its threshold earlier or later by that displacement divided by the slope it crosses at:
$$\delta t \approx \frac{\delta V}{dV/dt}.$$
Three things follow, and none of them is obvious from the one-dimensional picture.
The slower the transition, the more timing error a given voltage disturbance produces. An equaliser that restores amplitude without restoring the edge does not help with this term.
Not the transmitter. Past the channel's bandwidth the received edge stops getting faster however hard the driver is pushed, so the conversion factor is a property of the board.
Receiver noise, crosstalk, supply ripple, reflections: each has a jitter equivalent, and adding them in the voltage budget and again in the timing budget double-counts, while adding them in only one under-counts.
The vocabulary extends in the obvious way. Random jitter has a counterpart in random noise, deterministic jitter in deterministic noise, data-dependent jitter in data-dependent noise; and each can be split further into the part contributed by phase noise and the part contributed by amplitude noise — written RJ(h) and RJ(v) for the horizontal and vertical contributions.
The slope is measured from the equalised pulse response of the same 28.8-inch backplane the rest of this series uses, so the conversion factor below is that channel's, not a generic one.
Here is the result that makes this deck worth computing. Hold the transmitter's amplitude and the receiver's voltage noise fixed, and let the symbol rate rise on the same physical channel.
It is tempting to assume the edge scales with the rate, in which case the amplitude-induced jitter would stay a constant fraction of the unit interval and nothing interesting would happen. That assumption is wrong, and it is wrong in the direction that matters: the channel sets the received rise time, and the channel's bandwidth does not improve because the data rate went up.
Deck 07 introduced bounded uncorrelated jitter as the category the industry uses for organising its ignorance. Crosstalk is its best example, and it earns the place by failing every other classification.
It is an exact, deterministic function of the aggressor's data. Nothing about it is stochastic; there is no underlying Gaussian process.
It is a function of somebody else's data, which the victim's receiver has never seen and cannot predict. So the equaliser, which removes data-dependent jitter by construction, does nothing about it.
By the aggressor's swing, so it cannot grow without limit the way a Gaussian can. That is what puts it on the deterministic side of the tree despite being unpredictable.
Several uncorrelated aggressors with random data sum towards a bell shape, which is exactly the condition deck 08 showed inflates the fitted random jitter. Crosstalk is therefore routinely counted as random and multiplied by fourteen on its way into the total.
This is why the decomposition tree has a branch that is defined by what it is not. The category is an admission that the measurement cannot separate these contributions, and the remedy is experimental rather than analytical: measure with the aggressors quiet, then with them driven.
Deck 06 computed the crosstalk on this channel as a voltage: four near-end aggressors at three trace widths on an inner layer, combining in power. Rule four says that voltage has a timing equivalent, and the slew rate of slide 03 converts it.
The same physical disturbance now appears in two budgets. It must be counted once, not twice — and which budget it belongs in depends on where the receiver's margin is tightest. A receiver limited by its voltage threshold should carry it as voltage; one limited by its sampling window should carry it as timing. Carrying it in both is the commonest way a budget comes out pessimistic by a factor that nobody can locate afterwards.
The resolution, when the one-dimensional treatment stops being trustworthy, is to stop projecting. Instead of an eye opening measured horizontally at a fixed voltage or vertically at a fixed time, the honest object is a two-dimensional region of the time-voltage plane within which the error ratio is acceptable.
It stops the double-counting of the previous slide, because each disturbance is placed once in the plane rather than projected onto both axes. And it makes visible the fact that the worst case is usually a diagonal — a bit that is both late and low — rather than either extreme.
Two dimensions of measurement instead of one, so the observation time for a given confidence goes up sharply; and a specification language that most standards do not have. This is why the industry still specifies jitter and amplitude separately even where everyone agrees it is an approximation.
The channel operating margin of deck 17 is a partial answer: it combines the noise terms into a single signal-to-noise ratio at the sampling instant, which is a projection onto the voltage axis after the timing terms have been converted into voltage through the slope. That is the same conversion as slide 02, run in the opposite direction, and it is why that calculation carries a jitter term at all.
Compliance testing of a receiver applies a deliberately degraded signal and checks that the error ratio is still met. The stress is specified as a list: so much sinusoidal jitter, so much random jitter, so much bounded uncorrelated jitter, a defined amount of intersymbol interference, and an amplitude.
Adding crosstalk to that list is comparatively recent and it changes the test in a way the list format hides. The other impairments are one-dimensional by construction — sinusoidal jitter is purely timing, an amplitude reduction is purely voltage. Crosstalk is neither, and calibrating it means calibrating a two-dimensional disturbance with instruments that report projections.
The stress has to be verified at the receiver's pins, through the test fixture, with the aggressors driven. Every impairment interacts with the fixture, and the fixture has to be de-embedded — which is deck 16.
A receiver that passes with one-dimensional stress and fails with crosstalk is a common outcome, because its adaptation loops can converge on a setting that is optimal for the clean case and poor for the noisy one.
The amount of crosstalk to apply is a judgement about the systems the part will be used in, not a measurement. Deck 17 shows the crosstalk assumption moving a compliance verdict further than any receiver parameter does.
| Idea | Statement | Consequence |
|---|---|---|
| Rule 4 | Timing and amplitude noise are not separable | Useful, not correct; find where it fails |
| Conversion | $\delta t \approx \delta V / (dV/dt)$ | Every voltage term has a timing equivalent |
| Who sets the slope | The channel, not the transmitter | Past the channel bandwidth the edge stops improving |
| Where it fails | Around 10 Gb/s on this channel | Rise time overtakes the unit interval; see slide 04 |
| Crosstalk | Bounded, uncorrelated, looks Gaussian | Counted as random jitter and multiplied by 14 |
| Double counting | One disturbance, two budgets | Count it once, in whichever budget is tighter |
| The honest object | A region of the time-voltage plane | The worst case is a diagonal, not an axis |
| Tolerance testing | Crosstalk is two-dimensional stress | Calibration, not generation, is the hard part |
Deck 10 of eleven in Signal Integrity & High-Speed Digital Design. Every figure on this page is computed by si_models/deck10 and embedded as data; nothing is typed in by hand.
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