Home ／ Docs-Technical WhitePaper ／ 37-EFT.WP.EDX.HighSpeed v1.0
I. Conventions & Dialect (Mandatory)
- All symbols/formulae are in English and wrapped in backticks (e.g., Z_eft(omega), T_group(omega), alpha(omega)).
- Any expression with division/integrals/composed operators must use parentheses and explicitly declare the path gamma(ell) and measure d ell.
- Time-of-arrival (two equivalent dialects; record delta_form):
- Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
- General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
- Use omega as the frequency variable; if f_Hz is used, state omega = 2π f_Hz.
- Units: SI; key equalities must pass check_dim = pass; hard gates: passivity (Re{Z_eft} ≥ 0) and KK_consistency = pass.
- Do not mix phase/amplitude units (rad vs dB) for the same quantity.
II. Observables & Derived Quantities
Symbol | Name | Type/Domain | SI Unit | Notes |
|---|---|---|---|---|
Z_eft(omega) | tension-landscape impedance | complex scalar | Ω | Z_eft = Z_ref + ΔZ_T [+ ΔZ_rad] |
arg Z_eft(omega) | port phase | scalar | rad | first-order in window |
T_group(omega) | group delay | scalar | s | T_group = d/domega( arg Z_eft ) |
E_phase(Ω) | phase linearity error | scalar | rad | KPI (window Ω) |
GDR(Ω) | group-delay ripple | scalar | s | KPI (window Ω) |
ΔW(Ω) | weight drift | scalar | — | `Σ_{p,m} |
III. Paths & Time-of-Arrival
Symbol | Name | Type/Domain | SI Unit | Notes |
|---|---|---|---|---|
gamma(ell) | propagation path | geometric curve | — | ell is arclength; piecewise smooth |
d ell | path measure | differential | m | paired with gamma(ell) |
T_arr | shared arrival term | scalar | s | two dialects; record delta_form |
c_ref | reference propagation limit | scalar | m·s⁻¹ | dimensional baseline |
delta_form | arrival dialect tag | enum | — | "n_over_c" / "one_over_c_times_n" |
w_{p,m}(omega) | path/mode weight | scalar | — | Σ_{p,m} w_{p,m} ≤ 1 |
ΔT_arr | differential arrival | scalar | s | path-switching criterion |
IV. HF Propagation & Modes
Symbol | Name | Type/Domain | SI Unit | Notes |
|---|---|---|---|---|
alpha(omega) | attenuation constant | scalar | Np·m⁻¹ | material/conductor/radiation loss |
beta(omega) | phase constant | scalar | rad·m⁻¹ | beta·L ≈ omega·T_arr + φ_T |
k(omega) | complex propagation constant | scalar | Np·m⁻¹ + i·rad·m⁻¹ | k = alpha + i·beta |
Z_c(omega) | characteristic impedance | complex scalar | Ω | line/mode dependent |
M(omega) | modal basis | matrix | — | projection/merge |
C(omega) | modal coupling matrix | matrix | — | ` |
V. S-Parameters & Normalization
Symbol | Name | Type/Domain | SI Unit | Notes |
|---|---|---|---|---|
S(omega) | N-port S-parameters | complex matrix | — | single-ended/mixed-mode |
Znorm(omega) | port normalization impedance | diagonal/array | Ω | mapping baseline |
T_mm | mixed-mode transform | matrix | — | DM/CM mapping |
Z0_mm | mixed-mode norm impedances | diagonal/array | Ω | corresponding to Z_c(omega) |
Z_ref(omega) | reference impedance | complex scalar | Ω | no-radiation baseline |
ΔZ_T(omega) | tension correction | complex scalar | Ω | kernel & weights integral |
VI. Radiation & EMI Fields
Symbol | Name | Type/Domain | SI Unit | Notes |
|---|---|---|---|---|
ΔZ_rad(omega) | radiation positive-real correction | complex scalar | Ω | require Re{ΔZ_rad} ≥ 0 |
E_rad(omega,r) | radiated E-field | vector field | V·m⁻¹ | near/far-field envelopes |
H_rad(omega,r) | radiated H-field | vector field | A·m⁻¹ | near/far-field envelopes |
I_CM(omega) | common-mode current | scalar | A | EMI key observable |
sigma_seam | seam effective conductance | scalar | S | shielding continuity |
VII. Metrology & Alignment
Symbol | Name | Type/Domain | SI Unit | Notes |
|---|---|---|---|---|
Δt_sync | timebase misalignment | scalar | s | Δφ = omega·Δt_sync |
baseline_id | de-embed/baseline ID | string | — | versioned |
binding_ref | binding record ID | string | — | layout ↔ gamma(ell) |
check_dim | dimensional check | flag | — | must be pass |
KK_consistency | K–K consistency | flag | — | causality check |
passivity | passivity gate | flag | — | min Re{Z_eft} ≥ 0 |
VIII. Implementation APIs & Card Keys
Field/Symbol | Name | Type | Unit/Range | Notes |
|---|---|---|---|---|
map_S_to_Z | S→Z mapping API | function | — | I40-HF |
em_port_align | port/renorm alignment | function | — | I40-HF |
bind_layout_hf | HF binding | function | — | I30-HF |
mode_project/merge | modal projection/merge | function | — | I30-HF |
dataset_card/pipeline_card/env_lock | data/pipeline/env-lock | structs | — | DataSpec |
qa_gates | QA gates | list | — | check_dim/passivity/KK |
IX. Canonical Relations (dialect-aligned, quick ref)
- Group delay: T_group(omega) = d/domega( arg Z_eft(omega) )
- Linear phase (in-window): arg Z_eft(omega) ≈ omega·T_arr + φ_T(omega)
- Propagation consistency: T_group(omega) ≈ L · dβ(omega)/domega
- Amplitude dispersion (matching): |S21(omega)| ≈ exp( − alpha(omega) · L )
- S→Z (N-port): Z_eft = Z0^{1/2} ( I + S ) ( I − S )^{-1} Z0^{1/2}
- Radiated power equivalence: P_rad(omega) ≈ ½ · Re{ΔZ_rad(omega)} · |I_port(omega)|^2
X. Forbidden Aliases & Writing Examples (Compliance)
- Forbidden: bare c, T, n; use c_ref, T_fil/T_trans, n_eff.
- Forbidden: mixing rad and dB in the same equation.
- 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"
- Phase correction (metrology): arg Z_corr(omega) = arg Z_raw(omega) − ( omega · Δt_sync )
XI. SI Quick Reference
Current A; voltage V; impedance Ω; phase rad; time s; length m; attenuation Np·m⁻¹; phase constant rad·m⁻¹; power W; E-field V·m⁻¹; H-field A·m⁻¹; conductivity S·m⁻¹.
XII. Release Hard Gates (Consistency)
check_dim = pass; Re{Z_eft} ≥ 0; KK_consistency = pass; two-dialect T_arr agreement (|Δ| ≤ u(T_arr)); in-window KPIs E_phase/GDR within gates; if ΔZ_rad enabled, Re{ΔZ_rad} ≥ 0 and decreases after sealing.Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
License link：https://creativecommons.org/licenses/by/4.0/