38-EFT.WP.EDX.EMI v1.0 | Chapter 5 — Seam/Aperture/Stub Equivalents & Shielding Continuity (S40-EMI)

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Chapter 5 — Seam/Aperture/Stub Equivalents & Shielding Continuity (S40-EMI)

I. Chapter Objectives & Structure

1. Objective: Establish equivalent channels for seams/apertures and stubs/open returns, and a shielding continuity metric; provide a parameterized form of ΔZ_rad(omega) with activation/sealing consistency gates so that port–path–field can be quantified, regressed, and falsified in emission/immunity scenarios.
2. Structure: Symbols & domain → S40-EMI equivalents & continuity rules → 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

• Geometry & shielding: sigma_seam (seam effective conductance, S), L_seam (effective length, m), pitch_seam (seam pitch, m), mesh_ratio (shield meshing duty cycle).
• Ports & channels: Z_eft(omega), Z_ref(omega), ΔZ_T(omega), ΔZ_rad(omega) (constraint: Re{ΔZ_rad} ≥ 0).
• Paths & weights: gamma(ell), d ell, {γ_main, γ_side}, w_{p,m}(omega), ΔW.
• Stubs/vias: stub_len (m), backdrill (flag).
• Hard QA: check_dim = pass, passivity (Re{Z_eft} ≥ 0), KK_consistency = pass, two-dialect T_arr agreement.

S40-EMI — Equivalent Channels & Shielding Continuity

S40-EMI-1 (Seam/aperture equivalent channel)

• Equivalent: Parameterize leakage due to shielding discontinuities with sigma_seam and L_seam, yielding at the port
  Z_eft(ω) = Z_ref(ω) + ΔZ_T(ω) + ΔZ_rad(ω; sigma_seam, L_seam, ...) .
• Continuity & optimization: increasing mesh_ratio and reducing pitch_seam, or adding bridges/via fences, makes Re{ΔZ_rad} monotonically decrease.

S40-EMI-2 (Stub/via-activated leakage path)

• Trigger: excessive stub_len or no back-drill activates γ_side; the port shows
  w_{side}(ω) ↑ ⇒ Re{ΔZ_rad}(ω) ↑ .
• Mitigation: after back-drill/trim (backdrill=true), both w_{side} and Re{ΔZ_rad} decrease.

S40-EMI-3 (Return closure & stitched continuity)

• Principle: place bridge/via rings at plane transitions to close returns minimally and suppress γ_side.
• Acceptance metric: denser stitching yields joint improvement in ΔW = Σ_{p,m}|w_{p,m}(ω₂)-w_{p,m}(ω₁)| and E_phase/GDR.

S40-EMI-4 (Meshed/periodic shielding)

• Measures: mesh long seams (raise mesh_ratio) and periodicize (lower pitch_seam).
• Gate: after the design upper bound, Re{ΔZ_rad} reduction saturates; trade off EMI goals vs cost/weight.

S40-EMI-5 (Detection & display dialect)

• Power equivalence: estimate radiation from port quantities
  P_rad(ω) ≈ (1/2) · Re{ΔZ_rad(ω)} · |I_port(ω)|^2 ,
  with monotonic frequency trend to |E_rad|/|H_rad| (record detector detector∈{pk,qpk,avg} IF bandwidth/time constants).

III. Implementation & Records (minimum execution dialect)

• Required fields: sigma_seam, L_seam, pitch_seam, mesh_ratio, stub_len, backdrill, binding_ref, arrival{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form}, Z_eft/argZ, ΔZ_rad(ω) with Re_Zrad_min, field summaries E_rad/H_rad, I_CM(ω), w_{p,m}(ω)/ΔW, Znorm(ω), qa_gates{check_dim,passivity,KK}.
• Phase correction: arg Z_corr(ω) = arg Z_raw(ω) − ( ω · Δt_sync ) , unwrap before fitting.
• Consistency checks: Re{ΔZ_rad} ≥ 0; after sealing/back-drill, Re{ΔZ_rad} and |E_rad|/|I_CM| decrease together; two-dialect T_arr agreement; ΔW trend agrees with Re{ΔZ_rad}.

IV. Falsifiability (for S40-EMI)

• J-EMI-40-1 (Positive-real & causality): if Re{ΔZ_rad} < 0 or KK_consistency fails, reject the equivalent model or normalization.
• J-EMI-40-2 (Sealing/meshing verification): if Re{ΔZ_rad} and |E_rad|/|I_CM| don’t drop after sealing/meshing, reject sigma_seam/L_seam equivalence or geometry records.
• J-EMI-40-3 (Back-drill verification): if w_{side} and Re{ΔZ_rad} don’t decrease after back-drill/trim, reject γ_side labelling or stub parameters.
• J-EMI-40-4 (Return continuity): if stitching/bridging doesn’t improve ΔW and E_phase/GDR, reject the return strategy or path annotation.
• J-EMI-40-5 (Two-dialect agreement): if |T_arr^{(1)}−T_arr^{(2)}| > u(T_arr), reject release.

V. Compliance Templates (copy-ready)

• Record template (YAML)
• seam_stub_equiv:
• band_GHz: [f_min, f_max]
• normalization:
• Znorm_ohm: [50.0, 50.0]
• mixed_mode: {enabled: true, T_mm: "/cfg/T_mm.yaml", Z0_mm_ohm: [100, 25]}
• geometry:
• seams: {sigma_seam_S: 0.12, L_seam_mm: 18.0, pitch_seam_mm: 3.0, mesh_ratio: 0.6}
• stubs: {max_len_mm: 3.5, backdrill: true}
• bridges:{via_fence: true, pitch_mm: 2.0}
• 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"
• impedance:
• Z_eft: {real:[...], imag:[...]}
• deltaZ_rad: {Re_ohm:[...], Im_ohm:[...]} # Re ≥ 0
• fields_currents:
• E_rad_peak_dBuV_m: [ ... ]
• H_rad_peak_dBA_m: [ ... ]
• I_CM_A: [ ... ]
• weights:
• w_main: [ ... ]
• w_side: [ ... ]
• ΔW: 0.17
• qa_gates: {check_dim:"pass", passivity:"pass", KK:"pass"}
• Numerical checks (pseudocode)
• # Positive-real & causality
• assert min(Re(ΔZ_rad)) >= 0.0 and KK_consistency(Z_eft)
• # Monotonicity before/after sealing/meshing/back-drill
• assert mean(Re(ΔZ_rad_after)) < mean(Re(ΔZ_rad_before))
• assert mean(E_rad_after) < mean(E_rad_before)
• # Weights vs radiation
• ΔW = sum_abs(w_side[ω2] - w_side[ω1])
• assert monotone(ΔW, Re(ΔZ_rad))
• # Two-dialect arrival
• 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), EDX.HighSpeed Chapter 13 (EMI Coordination), Chapter 8 (S↔Z Mapping).
• Downstream: Chapter 6 (Cables/Connectors & Mixed-Mode Coupling), Chapter 9 (Metrology & Compliance Dialect), Chapter 11 (Engineering Rules: Shielding/Ground/Returns), plus appendices (data/interfaces/symbols) for release & regression.