Seventeen decks in five sections on getting a signal from one chip to another intact — the physics of the channel, the mechanisms that close an eye, and the arithmetic a standard uses to decide a channel is legal.
Every number on every slide is computed by a model in si_models and embedded as data. Nothing is asserted by hand, and the models are checked against published worked examples wherever one exists.
What a transmission line is, where the return current flows, what the materials do to the signal, and what happens at the one feature made by drilling.
When a trace stops being a wire, where the fifty-ohm convention comes from, and what a reflection actually is.
Every signal current is a loop. Where the other half of it flows, and what happens when the board will not let it.
Copper roughness, dielectric loss, and why a constant dielectric constant describes a material that cannot exist.
The only part of a channel made by drilling, and the one that decides whether the link runs at 28 gigabaud.
Why every fast link is differential, and the one impairment no equaliser can remove.
Why every fast link is differential, what tight coupling really costs, and how symmetry is lost.
The impairment no equaliser can remove, and the one place near-end and far-end coupling genuinely differ.
Organised around Ransom Stephens's five rules: it is about the bit error ratio, total jitter can only be measured on a bit error ratio tester, measurement is always a comparison against a reference clock, and timing noise and amplitude noise are not really separable.
Why jitter is defined against an error ratio, what a bit error ratio tester does that nothing else can, and the decomposition tree done properly.
Five assumptions, a fitting parameter that is not the peak-to-peak deterministic jitter, and the tails a measurement cannot reach.
Every jitter measurement compares a test clock against a reference. Which reference, how much it tracks, and what the tolerance mask is really testing.
Timing noise and amplitude noise are not separable, the separation fails above about ten gigabits per second, and crosstalk is where it fails first.
The power delivery network as an impedance, as an ecology of resonances, as something that has to be measured in milliohms, and finally as a source of signal-integrity failures.
Target impedance and what the rule is worth, real capacitors, and why the number of parts is set by inductance rather than by capacitance.
Spreading inductance, cavity resonances, and the Bandini Mountain — the peak the board cannot reach because it is behind the package.
Why a reflection measurement stops at about an ohm, how the two-port shunt-through method reaches a milliohm, and the ground loop that ruins it.
The routes by which a disturbance on the supply becomes an error at a receiver — switching noise, cavity coupling, and supply-induced jitter.
Whether the timing closes, whether the measurements can be believed, and how a standard turns all of it into a pass or a fail.
Flight time is not propagation delay, and the arithmetic that ended the wide parallel bus.
Where S-parameters come from, how they are damaged, and what correlation honestly means.
How a standard decides a channel is legal, run on the same channel the equalisation deck could not close.
A model that agrees only with itself is not worth much. Every cross-check the series makes against an independently published result is listed here, with the disagreement. The last rows, marked internal, are not checks against anybody else: they are places where two different computations in the series have to agree with each other, and the quoted worst disagreement excludes them. The worst is 2.44 per cent.
| Quantity | This series | Reference value | Difference | Source |
|---|---|---|---|---|
| zdiff w0.15 s0.15 | 102.62 | 102.44 | +0.18 % | Cohn 1955, exact coupled-stripline result |
| zdiff w0.15 s0.30 | 112.32 | 112.39 | -0.06 % | Cohn 1955, exact coupled-stripline result |
| zdiff w0.20 s0.20 | 93.189 | 93.282 | -0.10 % | Cohn 1955, exact coupled-stripline result |
| f rough onset | 1.348e+09 | 1.34e+09 | +0.59 % | Hall & Heck, Advanced Signal Integrity, ch. 5 |
| hammerstad rac ratio | 1.7144 | 1.7284 | -0.81 % | Hall & Heck, Advanced Signal Integrity, ch. 5 |
| huray factor | 1.9579 | 1.95 | +0.40 % | Hall & Heck, Advanced Signal Integrity, ch. 5 |
| huray sphere area um2 | 160.9 | 161 | -0.06 % | Hall & Heck, Advanced Signal Integrity, ch. 5 |
| weave five inch ghz | 19.511 | 20 | -2.44 % | Hall & Heck, example 7-2 |
| weave ten inch ghz | 9.7557 | 10 | -2.44 % | Hall & Heck, example 7-2 |
| return within 3h | 0.79517 | 0.8 | -0.60 % | Johnson sec 5.2; Hall & Heck eq (5-15) |
| C | 6.917e-11 | 6.91e-11 | +0.10 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| L | 6.917e-07 | 6.91e-07 | +0.10 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| critical length m | 1.977 | 1.97 | +0.35 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| f diel | 4.9889e+08 | 4.98e+08 | +0.18 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| f lc | 9.5873e+06 | 9.58e+06 | +0.08 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| f skin | 2.7152e+07 | 2.71e+07 | +0.19 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| f wg | 1.423e+11 | 1.42e+11 | +0.21 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| r ac f0 | 76.742 | 76.74 | +0.00 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| r dc | 12.645 | 12.64 | +0.04 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| v0 | 1.4457e+08 | 1.4457e+08 | +0.00 % | Johnson & Graham, Advanced Black Magic 2003, sec 3.10 |
| droop vs zpeak | 23.241 | 24.876 | -6.57 % | internal: deepest transient droop per amp against the peak of the impedance profile (time domain vs frequency domain) |
The same material as a written report: Signal_Integrity.pdf. It carries the continuous argument where the decks carry the interactive models, and it is generated from the same computations, so a number cannot differ between the two.
Most decks are worked against one channel — the 28.8 inch backplane characterised in Equalisation in High-Speed Serial Links — so the numbers in one deck can be set against the numbers in another.
| Repository | How it relates |
|---|---|
| Equalisation in High-Speed Serial Links | The worked channel this series keeps returning to, taken from S-parameters to a closed link budget |
| Matrix Methods in Network Parameters | The S-, Z- and Y-parameter algebra behind every cascade here |
| Matrix Concepts in Digital Filters | The optimal-tap theory behind every equaliser |
| Kramers–Kronig Relations | The causality constraint decks 03 and 16 both lean on |
| High-Speed Serial Links — interview preparation | The written companion: notes and worked problems on the same ground |
| LPDDRx Layout — interview preparation | The parallel-bus side of deck 15 |
| Modern SoC Design | The silicon side: its deck 04 on SerDes, 09 on power delivery, 13 on clocks |
| Hardware | The index this series sits in |