38-EFT.WP.EDX.EMI v1.0 | Chapter 6 — Cables, Connectors & Mixed-Mode Coupling (I30-EMI / S40-EMI)

Home ／ Docs-Technical WhitePaper ／ 38-EFT.WP.EDX.EMI v1.0

Chapter 6 — Cables, Connectors & Mixed-Mode Coupling (I30-EMI / S40-EMI)

I. Chapter Objectives & Structure

1. Objective: Establish the mixed-mode (DM/CM) coupling dialect and binding for cable–board interfaces and connector transitions (I30-EMI), define consistent rules for common-impedance coupling, common-mode channels, and port normalization (S40-EMI), and make the frequency trends of I_CM(omega), ΔZ_rad(omega), and weights w_{p,m}(omega) quantifiable and falsifiable.
2. Structure: Symbols & domain → S40-EMI mixed-mode coupling & equivalents → I30-EMI binding & interfaces → Implementation & records → Falsifiability → Compliance templates → Cross-chapter closure.
3. Shared time-of-arrival dialect (equivalent; explicit gamma(ell) & d ell; record delta_form):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

II. Symbols & Domain

• Ports & normalization: S(omega), Znorm(omega), T_mm/Z0_mm (DM/CM), Z_eft(omega), Z_c(omega).
• Fields & currents: E_rad(omega,r), H_rad(omega,r), I_CM(omega).
• Paths & weights: gamma(ell), d ell, {γ_main, γ_side}, w_{DM}(omega), w_{CM}(omega), ΔW.
• Geometry & interconnects: cable return pairing, connector/launch, bridges/returns, shielding continuity sigma_seam.
• Hard QA: check_dim = pass, passivity (Re{Z_eft} ≥ 0), KK_consistency = pass, two-dialect T_arr agreement.

S40-EMI — Mixed-Mode Coupling & Equivalents (Minimal)

S40-EMI-1 (DM/CM mixed-mode mapping)

• From single-ended S_se to mixed-mode via T_mm: S_mm = T_mm · S_se · T_mm^{-1}, then normalize with Z0_mm to obtain
  Z_mm = Z0_mm^{1/2} ( I + S_mm ) ( I − S_mm )^{-1} Z0_mm^{1/2} ,
  preserving power & reciprocity before back-projection to SE domain.

S40-EMI-2 (Common-impedance coupling & CM channel)

• With open returns or unpaired cable returns, common impedance induces DM→CM conversion, observed as co-increasing I_CM(omega) and Re{ΔZ_rad}.

S40-EMI-3 (Connector/launch equivalent)

• Transition mismatch introduces a modal conversion matrix C(omega); design gates on |C_{DM→CM}| and |C_{CM→DM}|; higher |C| raises w_{CM} and Re{ΔZ_rad}.

S40-EMI-4 (Cable–board interface & LISN equivalence)

• Model the common-mode port with LISN/injection networks; I_CM(omega) trends monotonically with ΔZ_rad(omega) and ΔW.

S40-EMI-5 (Shielding & leakage-path consistency)

• Seams/bridges discontinuities activate γ_side; w_{CM/side}(omega) rises; after sealing/bridging both w_{CM/side} and Re{ΔZ_rad} decrease together.

I30-EMI — Cable/Connector Binding & Mixed-Mode Interfaces

I30-EMI-1 (Port & mixed-mode alignment)
S_mm = to_mixed_mode(S_se, T_mm) ; Z_mm = renorm(S_mm, Z0_mm)

• Record T_mm/Z0_mm versions & sources; unify Znorm(omega) & mixed-mode normalization before S↔Z mapping.

I30-EMI-2 (Return pairing & path annotation)
binding_emi = bind_cable(layout, returns, harness, constraints)

• Outputs {γ_main, γ_side}, segment {Δell_i, n_eff(i)}, and initial weights w_{DM/CM,0}; annotate return pairing and bridge locations.

I30-EMI-3 (Port–current–field co-measurement)

• Under consistent normalization & timebase, co-acquire Z_eft/argZ, I_CM, and (if applicable) E/H; write arrival{...} and qa_gates.

I30-EMI-4 (S↔Z & ΔZ_rad consistency)
Z_eft = map_S_to_Z_eft(S, Znorm, mode='mixed', T_mm, Z0_mm)

• ΔZ_rad = Z_eft − (Z_ref + ΔZ_T); require Re{ΔZ_rad} ≥ 0 and pass KK_consistency.

III. Implementation & Records (minimum execution dialect)

• Required fields: S(omega), Znorm(omega), T_mm/Z0_mm (if used), Z_eft/argZ, I_CM(omega), ΔZ_rad(omega) with Re_Zrad_min, binding_ref, arrival{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form}, w_{DM/CM}(omega)/ΔW, (optional) field summaries E_rad/H_rad, qa_gates{check_dim,passivity,KK}.
• Phase correction: arg Z_corr(omega) = arg Z_raw(omega) − ( omega · Δt_sync ) , unwrap before fitting.
• Consistency: DM/CM normalization → S↔Z → ΔZ_rad → back to SE domain conserve power/reciprocity; I_CM trend agrees with Re{ΔZ_rad}/ΔW; two-dialect T_arr agree.

IV. Falsifiability (for I30-EMI / S40-EMI)

• J-EMI-6-1 (Mixed-mode consistency): if the loop S_se→S_mm→Z_mm→Z_se breaks power or reciprocity, reject T_mm/Z0_mm or normalization.
• J-EMI-6-2 (Common-impedance coupling): after better return pairing/bridging, if I_CM and Re{ΔZ_rad} don’t drop, reject the coupling equivalence or binding records.
• J-EMI-6-3 (Connector transition): if optimizing launch/ground fingers doesn’t reduce |C_{DM→CM}| or improve KPIs/ΔZ_rad, reject the transition model or geometry.
• J-EMI-6-4 (Path coupling): if ΔW trend disagrees with Re{ΔZ_rad}, reject γ_side annotation or weight model.
• J-EMI-6-5 (Two-dialect agreement): if |T_arr^{(1)}−T_arr^{(2)}| > u(T_arr), reject release.

V. Compliance Templates (copy-ready)

• Mixed-mode & cable binding record (YAML)
• emi_cable_binding:
• ports: ["P1","P2"]
• mixed_mode:
• enabled: true
• T_mm: "/cfg/T_mm.yaml"
• Z0_mm_ohm: [100.0, 25.0] # DM/CM
• returns:
• paired: true
• bridges: {via_fence: true, pitch_mm: 2.0}
• paths:
• - {id:"γ_main", segments:[{len_m:0.010, n_eff:2.14, layer:"L3", neigh:"GND_L2"}], w_init_DM:0.82, w_init_CM:0.18}
• - {id:"γ_side", segments:[{len_m:0.003, n_eff:2.38, layer:"L3", neigh:"slot_L2"}], w_init_DM:0.05, w_init_CM:0.95}
• arrival:
• form: "n_over_c"
• 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"
• Numerical flow (pseudocode)
• # Mixed-mode normalization
• S_mm = T_mm @ S_se @ inv(T_mm)
• Z_mm = map_S_to_Z_eft(S_mm, Z0_mm, mode="mixed")
• Z_se = back_to_single_ended(Z_mm, T_mm) # if needed
• # CM/port consistency
• ΔZ_rad = Z_se - (Z_ref + ΔZ_T)
• assert min(Re(ΔZ_rad)) >= 0.0 and KK_consistency(Z_se)
• # I_CM vs ΔZ_rad / ΔW
• assert corr(I_CM, Re(ΔZ_rad)) > rho_gate and monotone(ΔW, Re(ΔZ_rad))
• # Two-dialect T_arr
• assert abs(Tarr_n_over_c - Tarr_one_over_c_times_n) <= u_Tarr

VI. Cross-Chapter Links & Closure

• Dependencies: Chapter 2 (Terms & Symbols), Chapter 3 (P10-EMI Axioms), Chapter 5 (Seams/Apertures/Stubs), EDX.HighSpeed Chapter 13 (EMI Coordination), Chapter 8 (S↔Z Mapping).
• Downstream: Chapter 7 (Immunity & Injection), Chapter 9 (Metrology & Compliance Dialect), Chapter 11 (Engineering Rules: Shielding/Ground/Returns), and the appendices (implementation APIs, dataset cards) for release & regression.