Automated Signal Integrity Analysis Framework for High-Speed Interconnects in the PPCB-1347-MuPix11 Probe Card

A.E. McDougall; A.J.A. Knight; A.S. Rotelli; D. Bortoletto; D M S Sultan; J. Vossebeld; R. Plackett

Automated Signal Integrity Analysis Framework for High-Speed Interconnects in the PPCB-1347-MuPix11 Probe Card

T0 review · 4 major / 7 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper shows that a reusable MATLAB pipeline can turn four-port S-parameter data into link-level signal-integrity evidence, and that applying it to the PPCB-1347/MuPix11 probe card's four 1.25 Gbps routes demonstrates path length…

desk verdict A competent, reusable signal-integrity pipeline for four MuPix links, with the honest caveat that the input CST S-parameters are unvalidated at the reflection ports. read the letter →

arxiv 2608.09462 v2 pith:HRIAMJX7 submitted 2026-08-10 hep-ex cs.SYeess.SY

D M S Sultan , R. Plackett , A.E. McDougall , A.J.A. Knight , A.S. Rotelli , J. Vossebeld , D. Bortoletto This is my paper · ORCID

classification hep-excs.SYeess.SY

keywords signalintegrityS-parametersmixed-modeconversionhigh-speedlinkmodelingprobecardMuPix11eyediagrambiterrorrate

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a four-port S-parameter file, whether from a simulator or a calibrated VNA, can be turned into a full link-level signal-integrity assessment by an automated MATLAB pipeline, and that doing so for the four 1.25 Gbps differential routes of the PPCB-1347/MuPix11 probe card shows all four routes retain similar modeled margin while none is uniformly 'best.' The authors build this case by converting each route's S-parameters to mixed-mode form, loading the channel with a causal receiver model, propagating a complete PRBS-31 record, and reporting eye, BER, and 8b10b-coded-link projections separately from finite-record observations. The key comparative result is that route length alone does not rank signal quality: DP3 has the lowest Nyquist insertion loss, DP1 the strongest differential-to-common isolation, and DP4 the largest modeled eye, even though the modeled FEB-input eye varies by only 2 mV across the four routes. A sympathetic reader would care because the framework offers a traceable pre-fabrication bridge between raw electromagnetic data and receiver-relevant decisions, with uncertainty and model assumptions kept visible.

What carries the argument

The load-bearing machinery is a power-normalized mixed-mode transformation (sum/difference waves of equations 2.1-2.2) applied to four-port Touchstone data, followed by a route-length-aware loss decomposition over $\sqrt{f}$, $f$, $f^2$, and $f^4$ bases and a causal rational-model loaded channel driven by a full PRBS-31 waveform. A context-resolved Gaussian/BER model keeps deterministic ISI inside the sampled voltage levels while combining the stated 2 mV receiver noise and 2 ps aperture jitter as independent Gaussian terms; the same decision record feeds eye, bathtub, rate-sweep, and 8b10b checker projections. The framework's stated function is to keep route-dependent waveform behavior, model projections, and finite-record observations distinct throughout.

What would settle it

A calibrated, de-embedded VNA measurement of DP1-DP4 on a fabricated PPCB-1347 card, or an independent full-wave solver with explicitly defined reference planes, that reports a Nyquist $S_{DD21}$ range wider than the modeled 0.05 dB, a differential insertion loss outside -0.350 to -0.300 dB at 0.625 GHz, or FEB-input eye openings outside 0.586-0.588 V under the same launch and receiver assumptions would falsify the paper's modeled margin claim.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is a workflow that converts compatible four-port S-parameter data into traceable link-level evidence, and the demonstration that no single route descriptor ranks the four probe-card links. At 1.25 Gbps (Nyquist 0.625 GHz), DP1-DP4 show differential insertion loss $S_{DD21}$ between -0.350 and -0.300 dB, differential-to-common conversion from -31.038 to -28.236 dBc, and modeled FEB-input eye openings from 0.586 to 0.588 V. The paper reports the mean FEB-input eye as $0.5867 \pm 0.001$ V and a Nyquist $S_{DD21}$ range of only 0.05 dB, which it reads as robust modeled differential margin under the stated transmitter and receiver assumptions. The comparative finding is that DP3 minimizes Nyquist insertion loss, DP1 provides the strongest differential-to-common isolation, and DP4 has the largest modeled eye, so physical length is not a sufficient proxy for link quality and acceptance criteria must name the metric being controlled. The paper also establishes that all analytical BER values lie below the $10^{-15}$ reporting floor and therefore do not support a BER-based ranking.

Load-bearing premise

The core assumption is that the computer-simulated electrical descriptions of the four probe-card routes supplied by the PCB vendor match the real card, including the definition of the reference planes at the connectors; if that simulation is wrong, the reported signal margins and route rankings would not describe the physical hardware.

Editorial extensions

If this is right

All four routes (DP1-DP4) retain a modeled FEB-input eye between 0.586 and 0.588 V at 1.25 Gbps, so the shared probe-card layout preserves vertical margin under the stated transmitter and receiver assumptions.
Because Nyquist $S_{DD21}$ spans only 0.05 dB across a 23.9 mm path-length spread, physical length is not a sufficient proxy for differential insertion loss at the operating point.
No single route is 'best': DP3 has the least-negative Nyquist $S_{DD21}$, DP1 the strongest differential-to-common isolation, and DP4 the largest modeled eye, so acceptance criteria must explicitly choose a metric.
Analytical BER and 8b10b checker projections for all routes sit below the declared $10^{-15}$ and $1.25 \times 10^{-6}$ events/s reporting floors, so these outputs are reported as bounds rather than rankings or hardware measurements.
Any compatible four-port Touchstone response, from EM simulation or calibrated VNA, can be passed through the same checked pipeline, making the method transferable to other high-speed interconnects.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An immediate testable extension is to apply the same pipeline to post-fabrication VNA measurements of the PPCB-1347 card; agreement with the modeled $S_{DD21}$ range of 0.05 dB would validate the pre-fabrication margin claim, while a wider spread would localize the discrepancy to the CST model or its reference planes.
The paper's 4.94 dB disagreement on reflection terms between the PTSL-reported CST values and its own re-analysis suggests that reference-plane definition, not trace loss, is the least constrained part of the input; a reader prioritizing reflections would want those planes pinned down before trusting route rankings.
The framework's separation of model projections from finite-record observations generalizes beyond this probe card: the same reporting-floor discipline could be applied whenever sub-$10^{-15}$ Gaussian tails are produced from a finite simulated record, preventing over-interpretation of floating-point underflow as measured zero-error operation.
Because the loss decomposition bases are correlated over a finite band, the zero dielectric proxies and non-zero higher-order coefficients for some routes should not be read as physical material differences; a coupon or de-embedded fixture measurement would be needed to separate conductor, dielectric, and radiation terms.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Read the PPCB-1347/MuPix11 probe card SI paper. The useful contribution is the automated MATLAB framework that turns four-port Touchstone files into route-resolved link evidence, and the demonstration on the four 1.25 Gbps routes. The numbers in Table 2 are internally consistent, and the paper is unusually disciplined about separating model projections from finite-record observations, and about reporting BER values as inequalities below a 1e-15 floor rather than pretending they are measured. The main conclusion — that no single metric like path length or insertion loss ranks the routes — is well supported by the data as presented.

What is actually new is the specific comparison: DP3 has best Nyquist insertion loss, DP1 best differential-to-common isolation, DP4 largest eye, and these do not coincide. That is a legitimate engineering result for the Mu3e collaboration, though the general maxim is not new.

The soft spot is exactly the one you flagged. The whole chain rides on PTSL's CST S-parameters. The paper admits a 4.94 dB SDD11 discrepancy with its own re-evaluation of the same Touchstone files, and there is no VNA measurement or independent solver to break the tie. This matters for the time-domain eye because reflections feed the impulse response. The reported 2 mV eye spread across routes could easily be swamped by reference-plane or export issues. The authors are transparent about this, and they defer final verification to hardware, which is honest, but it does cap what the paper can claim right now: these are model projections, not characterizations of the physical card.

Also, no code or data are released, so the 'reusable framework' claim is not testable by a third party. The loss decomposition is explicitly non-unique, and they say so. That is fine.

I would send this to peer review. It is a solid, careful engineering analysis with a clear scope, and the referee can push for the S-parameter validation to be resolved or at least for the claims to be softened accordingly. It is not a groundbreaking methods paper, but it is useful and competently done.

The paper is for detector front-end and interconnect engineers, not a general physics audience. I would not cite it myself in the next year, but I would point a student working on similar probe cards to it.

Recommendation: engage. Conditional acceptance with request for external validation of the input S-parameters.

Referee Report

4 major / 7 minor

Summary. The manuscript presents a reusable MATLAB signal-integrity (SI) framework that converts four-port S-parameter data (from VNA or electromagnetic simulation) into a set of link-level analyses: power-normalized mixed-mode transformation, route-length-aware loss decomposition, causal loaded channel modeling, full PRBS-31 waveform propagation, eye-diagram extraction, conditional BER, and 8b10b coded-link event-rate projections. The framework is demonstrated on four 1.25 Gbps differential routes (DP1-DP4) of the PPCB-1347-MuPix11 probe card, using PTSL-supplied CST-simulated S-parameters. The main results are that the modeled FEB-input eye openings are 0.586-0.588 V across the four routes, the Nyquist SDD21 spans only -0.350 to -0.300 dB, and the routes differ in differential-to-common isolation (-31.038 to -28.236 dBc) and common-mode transfer (SCC21 -1.244 to -0.520 dB). The authors conclude that physical path length alone is not a sufficient ranking variable and that acceptance criteria must specify which metric is controlled.

Significance. If the underlying S-parameters are trustworthy, the framework is a valuable methodological contribution to detector-instrumentation signal-integrity analysis: it is automated, reusable, and carefully separates model projections from finite-record observations and from hardware measurements. The decision to report sub-floor BER as inequalities, the explicit listing of transmitter and receiver assumptions, and the avoidance of cross-route S-parameter averaging are genuine strengths. The engineering conclusion that route length is not a sufficient proxy for link quality is plausible and useful. However, the demonstration rests entirely on a single set of vendor-provided simulated S-parameters with an acknowledged internal reflection discrepancy, and the numerical eye-height reporting contains an unresolved inconsistency. The significance is therefore conditional: the framework may be transferable, but the specific probe-card rankings and margin claims require independent validation or clearly stated limits of validity.

major comments (4)

[Section 4] The manuscript reports that the Oxford mixed-mode re-evaluation agrees with PTSL SDD21 within 0.06 dB but disagrees on SDD11 by up to 4.94 dB and on SDD22 by up to 4.79 dB, and states that 'a direct numerical comparison must identify the exact Touchstone export and reference planes.' Since the loaded channel model, impulse response, eye openings, and BER projections in Sections 5 and 6 are all computed from these S-parameters, the unresolved reflection discrepancy is load-bearing for the quantitative route rankings in Tables 2-4. The paper should either reconcile the discrepancy with an independent solver or VNA measurement, or restrict the central claims to SDD21-based quantities, which agree between the two evaluations.
[Section 5 / Section 6] The text in Section 5 states that 'At 1.25 Gbps data rate, the eye height remains 0.593V' and that with 2 mV noise and 2 ps jitter 'the operating point remains limited to ~13 mV,' while Section 6, Table 2 lists RX eye heights of 0.586-0.588 V for all four routes. The relationship among the free-running eye, the noisy eye, the '13 mV' quantity, and the Table 2 values is undefined and numerically inconsistent. Since the central conclusion of robust modeled differential margin depends on these eye values, the authors must correct the numbers and define exactly which eye metric is reported in each location.
[Section 3.2 / Section 3.5] Section 3.2 states that 'The diagnostic level-spread proxy is excluded from production BER because treating deterministic multimodal ISI as independent Gaussian noise creates false BER structure,' while Section 3.5 states that 'The retained receiver BER is the maximum of the context-resolved Gaussian tail, the robust level-spread/ISI term, and any deterministic decision errors.' Section 5 then reports both the context tail (2.225e-308) and the robust level-spread term (2.281e-297) for DP4, showing that the level-spread term is indeed included in the raw BER before the floor is applied. The manuscript must clarify whether the level-spread proxy is part of the reported BER; this affects the interpretation of all sub-floor BER statements.
[Section 3.1 / Table 2] Equation (2.4) is explicitly non-unique, and the text acknowledges that correlated bases over a finite band make the decomposition non-unique. Yet Table 2 reports conductor, dielectric, and higher-order contributions to three decimal places (e.g., DP1: 0.303, 0.000, 0.020 dB), and Section 6 converts these into per-meter values for DP3 and DP4 with two-to-three significant digits. The caveats in the text mitigate this, but the tabular presentation gives the basis coefficients an apparent physical precision that is not supported. A footnote or a less precise reporting format is needed.

minor comments (7)

[Table of contents / Section 2.1] The table of contents lists '2.1 Mixed-mode representation' but the body uses '3. Mixed-mode representation' and later sections are numbered 4 onward; the numbering should be made consistent throughout.
[Section 4] The phrase 'the third harmonic of 1.25 GHz (3.75 GHz)' is confusing; for a 1.25 Gbps NRZ signal with a repetitive 1010 pattern, the fundamental is 0.625 GHz, so the relevant third harmonic is 1.875 GHz, not 3.75 GHz.
[Section 4] The text contains a typo: 'PTSL ST Microwave 3D-Solver' should be 'PTSL CST Microwave 3D-Solver'.
[Section 5] Equation (4.1) is referenced before it is displayed, and the equation number '4.1' is inconsistent with the section numbering (Section 5); renumber the equation or move it earlier.
[Section 3.5] In Equation (2.10), the denominator is written as N, but the interpretation of N (number of contexts vs number of bits in a context) is not defined; please define N explicitly.
[Section 3.3] The 'configured fitting tolerance' for the rational approximation is not stated; reporting the tolerance and the number of poles for at least one route would improve reproducibility.
[Section 6] The sentence about 'DP4 differential data pair spTAB bonded alone for the Mu3e outer pixel detector HDI-flex [9]' cites Reference [9] (a general Mu3e technical design) which may not contain this specific detail; please verify the citation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported eyes, BER floors, and route rankings are deterministic consequences of the supplied S-parameters under fixed transmitter/receiver assumptions; the only fit is an explicitly non-unique loss-descriptor decomposition, not a prediction.

full rationale

The paper's central derivation chain is self-contained with respect to its own equations and stated inputs. The four-port S-parameters from PTSL are external inputs; the mixed-mode transform (Eqs. 2.1-2.2) is an algebraic re-parameterization, not a fit. The channel impulse response is obtained by rational approximation of the loaded S-parameter transfer function, and the received waveform is the convolution (Eq. 2.6) of a fixed PRBS-31 launch with that impulse response. Eye height (Eq. 2.7), conditional BER (Eqs. 2.8-2.10), and the upper-bound confidence model (Eq. 2.11) are all computed from this propagated waveform and declared receiver noise/jitter assumptions, with no parameter tuned to match the reported eyes or BER values. The only fitted quantities are the loss-basis coefficients in Eq. 2.4; the paper explicitly states that 'Correlated bases over a finite band make the decomposition non-unique' and labels the components 'descriptors, not direct measurements of material loss tangent or radiated power.' These fit coefficients are used to describe the same SDD21 curve, not to predict an independent target, so no fitted input is renamed as a prediction. The paper also carefully separates model projections from finite-record observations, reporting analytical BER only as below the 1e-15 floor and giving zero-count upper bounds separately. The unresolved SDD11/SDD22 discrepancies with PTSL (0.02-4.94 dB) are an external validation gap concerning whether the supplied electromagnetic model represents the physical card; they are acknowledged in the text and do not constitute a circular derivation. No load-bearing step reduces by construction to its own inputs, and no self-citation chain is used to force a conclusion. The route rankings and margin claims are conditional on the supplied S-parameters; that conditionality is a completeness limitation, not circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central analysis relies on four classes of input: PTSL CST S-parameters, assumed transmitter and receiver parameters, standard mixed-mode and statistical formulas, and per-route loss fits. The first two are unverified premises; the loss fits are fitted to the same data they describe. No new physical entities are introduced.

free parameters (3)

Loss-basis coefficients (A_fixture, a_c, a_d, a_2, a_4) = Not listed as coefficients; per-route dB contributions in Table 2
Fitted per route to the smooth attenuation over 0.1 to 0.8 GHz in Eq. 2.4; the paper calls the decomposition non-unique due to correlated bases.
Receiver noise and jitter parameters = 2 mV RMS noise; 2 ps RMS aperture jitter
Chosen by hand as FEB assumptions and explicitly stated as not measured Arria V input specifications; they set sigma_k in Eq. 2.8 and drive the BER tails.
Transmitter launch parameters = 0.700 Vpp differential; 180 ps edge; -0.08 post-cursor
Assumed MuPix-like launch; the eye height and BER results depend on this assumed waveform shape.

assumptions (5)

domain assumption The PTSL CST simulations correctly represent the physical probe-card channel (Section 4).
All subsequent eye and BER results are computed from these S-parameters; the paper states final verification requires hardware validation, so this is an unverified premise.
domain assumption The stated receiver model (100 ohm termination, 0.35 pF input, 2 mV RMS noise, 2 ps RMS jitter) is appropriate for the Mu3e FEB.
Section 1 explicitly states these are assumptions, not measured Arria V specifications; they set the noise and jitter terms in Eqs. 2.8 to 2.10.
standard math Standard mixed-mode S-parameter relations from Bockelman and Eisenstadt [7] apply to the four-port Touchstone data.
Used in Eq. 2.2; the paper numerically cross-checks SDD21 against PTSL values within 0.06 dB.
standard math The Gaussian tail Q-function models decision errors for the conditional BER (Eq. 2.10).
This is a conventional assumption; the paper flags that sub-1e-15 tails are not resolvable and should not be read as measured BER.
ad hoc to paper The non-negative loss basis in Eq. 2.4 is an adequate descriptor of channel attenuation over 0.1 to 0.8 GHz.
The paper itself cautions that correlated bases make the decomposition non-unique and that a zero dielectric proxy does not imply a lossless dielectric.

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Cite this review

Pith. "Pith review of Automated Signal Integrity Analysis Framework for High-Speed Interconnects in the PPCB-1347-MuPix11 Probe Card." pith.science (2026). https://pith.science/paper/HRIAMJX7

@misc{pith2026260809462,
  author       = {Pith},
  title        = {Pith review of: Automated Signal Integrity Analysis Framework for High-Speed Interconnects in the PPCB-1347-MuPix11 Probe Card},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HRIAMJX7}},
  note         = {Machine review of arXiv:2608.09462}
}

read the original abstract

A reusable MATLAB signal-integrity (SI) framework is presented that converts compatible four-port S-parameter data, measured by VNA or obtained from electromagnetic simulation, into traceable link-level evidence rather than a single loss metric. The framework is demonstrated on the four 1.25 Gbps differential routes (DP1-DP4) of the PPCB-1347/MuPix11 probe card using PTSL CST Microwave 3D-Solver-derived four-port S-parameters and a virtual time-domain solver. The automated pipeline preflights file structures, performs a power-normalized mixed-mode transformation, applies route-length-aware loss decomposition, constructs a causally loaded channel model, and propagates full PRBS-31 sequences into eye-diagram, conditional-BER, and 8b10b-coded-link analyses. At the 1.25 Gbps data rate (Nyquist 0.625 GHz), DP1-DP4 exhibit differential insertion loss (SDD21) from -0.350 to -0.300 dB, differential-to-common conversion from -31.038 to -28.236 dBc, and modeled FEB-input eye openings from 0.586 to 0.588 V. The comparison shows that path length alone is not an adequate SI ranking variable: DP3 has the lowest Nyquist insertion loss, DP1 the strongest differential-to-common isolation, and DP4 the largest modeled eye. All analytical BER values remain below the reporting floor and therefore do not support a BER ranking. By preserving the distinction between route-dependent waveform behavior, model projections, and finite-record observations, the framework provides an extensible basis for comparative high-speed-interconnect SI analysis from design review through calibrated VNA measurement interpretation.