37-EFT.WP.EDX.HighSpeed v1.0 | Chapter 1 — Scope & Aims

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Chapter 1 — Scope & Aims

I. Chapter Objectives & Structure

1. Objective: Integrate dispersion, radiation, and layout–process factors of high-speed interconnects into a unified path → arrival → kernels → weights → impedance framework; provide verifiable metrology and design gates; align seamlessly with EFT.WP.EDX.Current v1.0.
2. Structure: This chapter states the boundaries, core assumptions, minimal equations & recording dialect, baselines, and falsifiability criteria, and points to the cross-chapter closure path.
3. Shared time-of-arrival dialect (two equivalent forms; record delta_form; explicit gamma(ell) / d ell):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

II. Symbols & Domain

• High-frequency variables: alpha(omega) (Np·m⁻¹), beta(omega) (rad·m⁻¹), k(omega)=alpha+i·beta, Z_c(omega), Sij(omega), T_group(omega)=d/domega( arg Z_eft ), E_phase, GDR.
• Paths & weights: gamma(ell), d ell, w_p(omega), ΔT_arr.
• Radiation correction: ΔZ_rad(omega) with Re{ΔZ_rad} ≥ 0, E_rad(omega,r), H_rad(omega,r).
• Material & conductor: n_eff(omega), sigma_eff(omega), Σ_eff.
• Band & objects: microstrip/stripline, differential interconnects, connectors/launches, vias/plane transitions, cable transitions; frequency span covers the target coherence window and its neighborhood.
• Out of scope: antenna far-field design, EMC regulation text, and whole-system methodology; only interfaces to measurements and design gates consistent with this framework are provided.

III. Axioms / Minimal Relations / Mappings (P10-HF- / S20-HF- / S50-HF-*)**

• P10-HF-1 (coherence-window linear phase): within the chosen coherence window, arg Z_eft(omega) admits a first-order approximation omega·T_arr + φ_T(omega) with controlled curvature.
• P10-HF-2 (positive-real radiation correction): when boundary discontinuities or open returns activate radiation, Z_eft = Z_ref + ΔZ_T + ΔZ_rad, with Re{ΔZ_rad} ≥ 0 and K–K consistency.
• P10-HF-3 (slowly varying weights): in-band w_p(omega) varies slowly under small perturbations; path switching appears primarily as linear phase translation via ΔT_arr.
• P10-HF-4 (two-dialect agreement): for the same gamma(ell) and n_eff, the two T_arr writings agree within u(T_arr).
• S20-HF-1 (group-delay definition): T_group(omega) = d/domega( arg Z_eft(omega) ).
• S20-HF-2 (dispersion relation): beta(omega) · L ≈ omega · T_arr + φ_T(omega).
• S50-HF-1 (S↔Z mapping & port normalization): the mapping from multiport Sij(omega) to Z_eft(omega) preserves passivity and causality; deviations in Z_c(omega) must be explicitly recorded.

IV. Engineering Implementation & Records (minimum execution dialect)

• Mandatory records: arrival{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form}, binding_ref, deemb, sync(Δt_sync), qa_gates{check_dim, passivity, KK}, and HF increments {alpha_per_m, beta_per_m, Z_c(omega), E_phase, GDR, ΔZ_rad(omega)}.
• Phase correction: arg Z_corr(omega) = arg Z_raw(omega) - ( omega · Δt_sync ).
• Compliance snippet (fragment):
• highspeed:
• band_GHz: [f_min, f_max]
• coherence_window: {w1: ω1, w2: ω2}
• arrival: {form:"n_over_c", gamma:"explicit", measure:"d_ell", c_ref:299792458.0, Tarr_s:..., u_Tarr_s:..., delta_form:"n_over_c"}
• dispersion: {alpha_per_m:[...], beta_per_m:[...], T_group_s:[...]}
• radiation_gate: {Re_Zrad_min: 0.0, KK_consistency: "pass"}
• weights: {w_main:[...], w_side:[...]}
• qa_gates: ["check_dim","passivity(Re{Z}≥0)","KK_consistency"]

V. Baselines & Reference Cases (reproducible)

1. Baseline fixtures:
   • Differential microstrip pair (equal length A/B, guards/return differ) — for Δarg Z slope vs ΔT_arr consistency.
   • Via & plane-transition board (tunable stub and returns) — for w_p(omega) drift and E_phase/GDR degradation.
   • Reference-plane gap/aperture board (seal-able) — for Re{ΔZ_rad} non-negativity and post-sealing decrease.
2. Each baseline includes dataset_card / pipeline_card / env_lock plus reference outputs, serving as regression and release-gate exemplars.

VI. Falsifiability Criteria (volume-level)

• J-HF-1 (path-switching criterion): within the coherence window, Δarg Z(omega) vs omega slope k_φ satisfies k_φ ≈ ΔT_arr, with R^2 ≥ 0.98 and residuals ≤ 3·u(arg Z); otherwise reject the binding or w_p hypothesis.
• J-HF-2 (small-perturbation criterion): under smooth sweeps of n_eff (temperature/bias), |Z|/arg Z renormalize smoothly, Re{Z_eft} ≥ 0, and K–K passes; otherwise reject dispersion or kernel priors.
• J-HF-3 (radiation positive-real criterion): after sealing gaps/shortening stubs, Re{ΔZ_rad} and |E_rad|/|I_CM| decrease together; otherwise reject the radiation-channel model.
• J-HF-4 (two-dialect agreement): if the two T_arr dialects differ beyond u(T_arr), reject release.

VII. Cross-Chapter Links & Closure

• Upstream dependencies: EFT.WP.EDX.Current v1.0 Chapter 8 (Paths & Arrival), Chapter 12 (High-Speed Interconnects & Dispersion), Chapter 9 (Metrology Chain), Chapter 10 (Experimental Design).
• This volume’s flow: Chapter 2 (Terms & Symbols) → Chapter 4 (Dispersion Minimal Equations) → Chapter 5 (Radiation Correction) → Chapter 7 (Coherence-Window KPIs) → Chapter 12 (Layout & Process Rules) → Chapter 16 (Design Protocols & Engineering Checklist).
• Fixed cross-volume citation form: “See companion white paper Energy Filament Chapter x S/P/M/I…”. Numbering in this volume uses P10-HF-* / S20-HF-* / I30-HF-* / M10-HF-*.