37-EFT.WP.EDX.HighSpeed v1.0 | Chapter 2 — Terms & Symbols (EDX High-Speed Specialization)

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Chapter 2 — Terms & Symbols (EDX High-Speed Specialization)

I. Sources & Applicability

1. This chapter fixes the terminology and symbol dialect for EDX.HighSpeed, covering dispersion, radiation, and S-parameter to impedance mapping for high-frequency/high-speed interconnects.
2. Section headings use Roman numerals in bold; bullet items use “- space”; numbered lists use “1. space”.
3. All symbols/formulae are in English and wrapped in backticks; any expression with division/integrals/composed operators must use parentheses and explicitly declare the path gamma(ell) and measure d ell.
4. Shared time-of-arrival dialect (two equivalent forms; path/measure explicit; record delta_form):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
5. Use omega as the frequency variable; if using f_Hz, state explicitly omega = 2π f_Hz.
6. SI units throughout; key equalities must pass check_dim = pass; passivity and K–K consistency are hard release gates.

II. Master Glossary (anchor at first occurrence)

• alpha(omega): attenuation constant, Np·m⁻¹ (material/conductor/radiation combined loss).
• beta(omega): phase constant, rad·m⁻¹.
• k(omega) = alpha(omega) + i·beta(omega): complex propagation constant.
• Z_c(omega): characteristic impedance (Ω), potentially frequency/modal dependent.
• Sij(omega): multiport S-parameters (complex); i,j are port indices.
• Z_eft(omega): tension-landscape impedance (Ω), Z_eft = Z_ref + ΔZ_T [+ ΔZ_rad].
• ΔZ_T(omega): tension-induced correction (Ω).
• ΔZ_rad(omega): radiation/leakage positive-real correction (Ω), require Re{ΔZ_rad} ≥ 0.
• T_group(omega) = d/domega( arg Z_eft(omega) ): group delay (s).
• E_phase: phase linearity error (rad), coherence-window KPI.
• GDR: group-delay ripple (s), coherence-window KPI.
• gamma(ell): propagation path (geometric curve; ell is arclength); d ell: path measure (m).
• w_p(omega): path/mode weights (0…1, Σ_p w_p ≤ 1).
• n_eff(omega): effective refractive index (—); sigma_eff(omega) / Σ_eff: effective conductivity (S·m⁻¹ / tensor).
• c_ref: reference propagation limit (m·s⁻¹); delta_form: arrival-dialect tag ("n_over_c" or "one_over_c_times_n").
• Δt_sync: timebase misalignment (s), time equivalent of phase correction.

III. Symbols & Units (minimal set)

IV. Forbidden Aliases & Conflicts (mandatory)

• T_fil (tension) ≠ T_trans (transmittance) — must not be conflated.
• n (number density) ≠ n_eff (effective refractive index) — must be distinguished.
• Bare c is forbidden; always use c_ref.
• Ambiguous sigma: use sigma_cond for conductivity, sigma_std for standard deviation.
• Do not mix phase and amplitude units: rad vs dB must not be interchanged within the same quantity.
• Frequency variable is uniformly omega; f may appear in prose but not in equations.

V. Notation Style & Expression Rules (mandatory)

• Inline + parentheses: wrap all symbols/formulae in backticks; any division/convolution/composed operator must be parenthesized, e.g., Z(omega) = ( V(omega) / I(omega) ).
• Path/measure: any propagation or delay term must declare gamma(ell) and d ell; choose one T_arr dialect and record delta_form in data/reports.
• S↔Z mapping: state port normalization impedance explicitly; after mapping, pass passivity and KK_consistency.
• Dimensional checks: key equalities must pass check_dim = pass; phase is in rad (not omitted).
• Coherence window: inside the window, the first-order approximation arg Z_eft(omega) ≈ ( omega · T_arr ) + φ_T(omega) may be used; outside, use energy composition and label the gates.

VI. HF Incremental Fields & Data Records (aligned with dataset cards)

• Required: alpha_per_m, beta_per_m, T_group_s, E_phase, GDR, ΔZ_rad(omega) (if radiation channel enabled, ensure Re{ΔZ_rad} ≥ 0), Z_c(omega).
• Phase correction: arg Z_corr(omega) = arg Z_raw(omega) - ( omega · Δt_sync ).
• Arrival record (example):
• arrival:
• form: "n_over_c" # or "one_over_c_times_n"
• gamma: "explicit"
• measure: "d_ell"
• c_ref: 299792458.0
• Tarr_s: 1.234e-09
• u_Tarr_s: 6.0e-12
• delta_form: "n_over_c"

VII. Two-Dialect Consistency Gate (hard release gate)

• For the same gamma(ell) and n_eff, the difference between T_arr(n_over_c) and T_arr(one_over_c_times_n) must satisfy
  |T_arr^{(1)} − T_arr^{(2)}| ≤ u(T_arr); otherwise no release.
• Any Z_eft curve must satisfy: min Re{Z_eft} ≥ 0 and KK_consistency = pass.

VIII. Compliance Snippets (copy-ready)

• HF record fragment
• highspeed:
• band_GHz: [f_min, f_max]
• coherence_window: {w1: ω1, w2: ω2}
• dispersion:
• alpha_per_m: [...]
• beta_per_m: [...]
• T_group_s: [...]
• radiation_gate:
• Re_Zrad_min: 0.0
• KK_consistency: "pass"
• Zc_ohm: [...]
• arrival: {form:"n_over_c", gamma:"explicit", measure:"d_ell", c_ref:299792458.0, Tarr_s:..., u_Tarr_s:..., delta_form:"n_over_c"}
• qa_gates: {check_dim:"pass", passivity:"pass", KK:"pass"}
• Phase/group-delay computation (pseudocode)
• phi = arg(Z_eft[ω1:ω2]) # coherence window
• T_group = grad(phi, omega)
• E_phase = max_abs(phi - (omega*Tarr + phi0_opt))
• GDR = max_abs(T_group - median(T_group))
• assert E_phase <= E_phase_gate and GDR <= GDR_gate

IX. Non-Compliant Examples (prohibited)

• Bare c, T, or n; use c_ref, T_fil/T_trans, n_eff.
• Delay without path/measure, e.g., T_arr = ∫ n_eff (×).
• Mixing rad and dB as phase/amplitude units in the same equation (×).
• Z_eft curves that fail passivity or K–K consistency (×).
• S↔Z mapping without stating port normalization or without aligning Z_c(omega) (×).

X. Execution Notes

• At first occurrence, each term/symbol must include a type note (scalar/vector/tensor; real/complex), unit, and the measurable component (magnitude/phase/real part).
• Any cross-volume citation must use the fixed format “work name + version + anchor (P/S/M/I)”, preferably at the article-level anchor.
• The dialect in this chapter becomes normative for Chapters 3–16 and the appendices in high-frequency contexts.