38-EFT.WP.EDX.EMI v1.0 | Chapter 7 — Immunity & Injection Channels (S50-EMI)

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Chapter 7 — Immunity & Injection Channels (S50-EMI)

I. Chapter Objectives & Structure

1. Objective: Define injection-channel models and minimal criteria for immunity; establish calibratable response relations and recording dialect for how external fields/ports/cables affect Z_eft(omega), ΔZ_rad(omega), I_CM(omega), and weights w_{p,m}(omega); specify release gates and falsifiability.
2. Structure: Symbols & domain → S50-EMI injection channels & responses → 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

• Injection types: external-field E_ext(omega), H_ext(omega) (chamber/TEM/GTEM), port injection (CDN/BCI), cable injection (LISN/injection networks).
• Ports & normalization: S(omega), Znorm(omega), T_mm/Z0_mm (DM/CM), Z_eft(omega), Z_c(omega).
• Radiation & fields: ΔZ_rad(omega) (constraint Re{ΔZ_rad} ≥ 0), E_rad(omega,r), H_rad(omega,r), I_CM(omega).
• Paths/modes & weights: gamma(ell), d ell, w_{p,m}(omega), ΔW.
• Detectors: detector ∈ {pk, qpk, avg} (IF bandwidth/time constants in dataset card).
• Hard QA: check_dim = pass, passivity (Re{Z_eft} ≥ 0), KK_consistency = pass, two-dialect T_arr agreement.

S50-EMI — Injection Channels & Responses (Minimal)

S50-EMI-1 (First-order response to external fields)

• External E_ext/H_ext drives weight redistribution:
  w_{p,m}(omega) = w_{p,m}^{(0)}(omega) + G_{p,m}(omega) · u_ext(omega) ,
  with u_ext ∈ {E_ext, H_ext}, G_{p,m} calibrated coupling gains.
• Induced port-phase/arrival shifts:
  Δarg Z_eft(omega) ≈ omega · ΔT_arr + φ_Δ(omega) ,
  ΔT_arr relates linearly to Σ_{p,m}Δw_{p,m}, φ_Δ(omega) is slowly varying.

S50-EMI-2 (CDN/BCI/port injection — CM equivalence)

• Port/fixture injection in mixed-mode domain:
  x_mm^+(out) = C_inj(omega) · x_mm^+(in) ,
  DM→CM entries of C_inj determine the rise of I_CM(omega) and the co-increase of Re{ΔZ_rad}.

S50-EMI-3 (Cable injection & LISN consistency)

• Common-mode port described by LISN/injection networks:
  I_CM(omega) = H_cm(omega) · u_inj(omega) ,
  with monotonic trends matching Re{ΔZ_rad}(omega) and ΔW.

S50-EMI-4 (S↔Z & mixed-mode normalization)

• Use the same Znorm(omega) and T_mm/Z0_mm before/after injection for S↔Z mapping:
  Z_mm = Z0_mm^{1/2} (I + S_mm)(I − S_mm)^{-1} Z0_mm^{1/2} ,
  preserve power/reciprocity before back-projecting to SE; after mapping pass passivity/K–K.

S50-EMI-5 (Power & field consistency for immunity)

• Immunity gates hinge on port-equivalent power and field consistency:
  P_rad(omega) ≈ (1/2) · Re{ΔZ_rad(omega)} · |I_port(omega)|^2 ,
  Injection upshifts drive co-increases in P_rad, |E_rad|/|H_rad|, and I_CM; sealing/return closure drive co-decreases.

III. Implementation & Records (minimum execution dialect)

• Required fields: injection:{type, level, site, detector, if_bw, time_const}, S(omega), Znorm(omega), T_mm/Z0_mm (if used), Z_eft/argZ, ΔZ_rad(omega) with Re_Zrad_min, I_CM(omega), (if any) field summaries E_rad/H_rad, binding_ref, arrival{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form}, w_{p,m}(omega)/ΔW, qa_gates{check_dim,passivity,KK}.
• Phase correction: arg Z_corr(omega) = arg Z_raw(omega) − ( omega · Δt_sync ) , unwrap before fitting.
• Consistency: same S↔Z/normalization chain pre/post injection; I_CM trends agree with Re{ΔZ_rad}/ΔW; two-dialect T_arr agreement.

IV. Falsifiability (for S50-EMI)

• J-EMI-7-1 (Normalization & causality): if either side pre/post injection shows Re{Z_eft} < 0 or fails KK, reject normalization/mapping or port basis.
• J-EMI-7-2 (External-field consistency): increasing E_ext/H_ext without monotonic rises in I_CM, Re{ΔZ_rad}, or |E_rad|/|H_rad| → reject coupling model or injection records.
• J-EMI-7-3 (Port/cable consistency): rising CDN/BCI/LISN levels without co-rising I_CM and Re{ΔZ_rad} → reject CM equivalence or binding.
• J-EMI-7-4 (Phase–arrival): if slope of Δarg Z fails k_φ ≈ ΔT_arr (in-window), reject phase correction or weight model.
• J-EMI-7-5 (Two-dialect agreement): if |T_arr^{(1)}−T_arr^{(2)}| > u(T_arr), reject release.

V. Compliance Templates (copy-ready)

• Injection record (YAML)
• immunity_injection:
• band_GHz: [f_min, f_max]
• injection:
• type: "CDN|BCI|E-field|H-field|TEM|GTEM"
• level: {unit:"V/m|A|dBuV", profile:"sweep|step", value:[...]}
• site: {distance_m: 3.0, coords: "..." } # external-field
• detector: "qpk"
• if_bw_kHz: 120
• time_const_ms: 1.0
• normalization:
• Znorm_ohm: [50.0, 50.0]
• mixed_mode: {enabled:true, T_mm:"/cfg/T_mm.yaml", Z0_mm_ohm:[100,25]}
• 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"
• impedance:
• Z_eft: {real:[...], imag:[...]}
• deltaZ_rad: {Re_ohm:[...], Im_ohm:[...]} # Re ≥ 0
• currents_fields:
• I_CM_A: [ ... ]
• E_rad_peak_dBuV_m: [ ... ]
• H_rad_peak_dBA_m: [ ... ]
• weights:
• w_DM: [ ... ]
• w_CM: [ ... ]
• ΔW: 0.21
• qa_gates: {check_dim:"pass", passivity:"pass", KK:"pass"}
• Numerical flow (pseudocode)
• # Normalization → S↔Z
• S_mm = T_mm @ S_se @ inv(T_mm)
• Z_mm = Z0_mm**0.5 @ (I+S_mm) @ inv(I-S_mm) @ Z0_mm**0.5
• Z_se = back_to_single_ended(Z_mm, T_mm)
• assert min(Re(Z_se)) >= 0.0 and KK_consistency(Z_se)
• # Phase correction & KPIs
• phi = unwrap(arg(Z_se) - ω*Δt_sync)
• k_phi = linfit(phi_after - phi_before, ω).slope
• Tarr = fit_linear_phase(phi, ω).slope
• assert abs(k_phi - ΔTarr) <= 3*u_Tarr
• # Injection consistency
• P_rad = 0.5 * Re(ΔZ_rad) * abs(I_port)**2
• assert corr(P_rad, E_rad_env) > rho_gate
• assert corr(I_CM, Re(ΔZ_rad)) > rho_gate

VI. Cross-Chapter Links & Closure

• Dependencies: Chapter 2 (Terms & Symbols), Chapter 3 (P10-EMI Axioms), Chapter 4 (Minimal Equations & Equivalents), Chapter 6 (Cables/Connectors & Mixed-Mode), EDX.HighSpeed Chapter 13 (EMI Coordination), Chapter 8 (S↔Z Mapping).
• Downstream: Chapter 9 (Metrology & Compliance Dialect), Chapter 10 (Experimental Design & Falsification), Chapter 11 (Engineering Rules: Shielding/Ground/Returns), and appendices (function prototypes/dataset cards) for release & regression.