Bit error ratio is quoted everywhere and actionable nowhere. This maps it to the things you can measure — Q-factor, random and deterministic jitter, horizontal eye opening — and to the one thing people always underestimate: how long a BERT has to run to prove the claim.
| Target BER | Q | Total jitter | Eye left | Bits to prove it | Time at this rate |
|---|
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Every SerDes datasheet quotes a bit error ratio, every standard sets one, and on its own it is not actionable. What you can actually measure is jitter, eye opening and noise — and what you can actually run is a BERT for some finite length of time. This tool maps between all of them.
BER = Q(q) = ½ erfc(q/√2) ·
TJ(BER) = DJ + 2 · q(BER) · RJrmseye opening = UI − TJ(BER) ·
bits to prove = λ(N, CL) / BERThis is the relationship that makes the whole subject behave counter-intuitively. Deterministic jitter is bounded — it has a peak-to-peak value and that is the end of it. Random jitter is Gaussian and unbounded, so the deeper the BER you demand, the further out on the tail you are sampling and the more of it you have to allow for.
The multiplier is roughly 14 at 10−12 and roughly 16 at 10−15. So tightening a specification by three decades of BER costs you about two extra RJ of jitter budget — and nothing at all in DJ. A link that fails at 10−15 but passes at 10−12 has an RJ problem, essentially by definition.
Change the target in the table above and watch which column moves.
This is the number people underestimate by orders of magnitude. To claim a BER with statistical
confidence you have to observe enough bits that, had the true BER been worse than your claim, you
would probably have seen an error. With no errors observed the requirement is
−ln(1 − CL) / BER bits — about 3/BER for 95% confidence.
At 10 Gbps that is five minutes for 10−12. For 10−15 it is over three days of continuous error-free running, and for 10−18 it is longer than most product programmes. This is precisely why deep BER claims are extrapolated from a bathtub curve measured at shallow BER rather than measured directly — and why "we ran it overnight and saw no errors" is a much weaker statement than it sounds.
Seeing errors makes it worse, not better: the tool takes an error count and recomputes the bits required, because a run that saw two errors needs substantially more data to support the same claim than a clean one.
The curve plots BER against where in the unit interval you sample. Near the centre the error ratio collapses to nothing; near the edges it rises to 0.5, which is a coin toss. The flat-bottomed region is the eye, and the width of that region at your target BER is your real timing margin — shaded green above.
The two walls are Gaussian tails, which is why the curve is straight on a log axis in those regions. Extrapolating those straight sections is exactly how instruments report BER values they could not possibly have measured, and it is legitimate provided the jitter really is Gaussian out there. It often is not: crosstalk, bounded periodic jitter and data-dependent effects all put structure in the tail that a dual-Dirac extrapolation does not see.
A link has two independent ways to fail, and effort spent on the wrong one is wasted. The
horizontal axis is jitter against the unit interval; the vertical is eye height against noise, with
its own Q of eye / 2σ. The tool computes both and says which one is limiting.
An amplitude-limited link needs less loss, better equalisation or a quieter receiver — the channel loss budget is where that starts. A timing-limited link needs less jitter, and the usual suspects are the reference clock, supply noise on the PLL, and crosstalk. They are different problems with different fixes, and the datasheet BER hides which one you have.
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