37-EFT.WP.EDX.HighSpeed v1.0 | Chapter 5 — Radiation & Leakage Correction (S50-HF)

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Chapter 5 — Radiation & Leakage Correction (S50-HF)

I. Chapter Objectives & Structure

1. Objective: Define the positive-real equivalent correction ΔZ_rad(omega) for radiation/leakage, establish the radiation mapping and activation conditions of Z_eft, specify metrology records, QA gates, and falsifiability criteria, and align with dispersion, S↔Z mapping, and the EMI/EMC volume.
2. Structure: Symbols & domain → S50-HF mapping & activation → Implementation & records → Falsifiability → Compliance templates → Cross-chapter closure.
3. Shared time-of-arrival dialect (equivalent; explicit gamma(ell) and 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 & mapping: Z_eft(omega), Z_ref(omega), ΔZ_T(omega), Sij(omega), Z_c(omega).
• Radiation & field observables: ΔZ_rad(omega) (require Re{ΔZ_rad} ≥ 0), E_rad(omega,r), H_rad(omega,r), I_CM(omega).
• Geometry & paths: gamma(ell), w_p(omega), γ_side (leakage paths), sigma_seam (seam/aperture effective conductance).
• Hard QA gates: check_dim = pass, passivity (Re{Z_eft} ≥ 0), KK_consistency = pass.

S50-HF — Radiation/Leakage Mapping

S50-HF-1 (Positive-real radiation correction)
Z_eft(omega) = Z_ref(omega) + ΔZ_T(omega) + ΔZ_rad(omega)
with Re{ΔZ_rad(omega)} ≥ 0 and K–K consistency. ΔZ_rad is recorded as an equivalent port-level channel.

S50-HF-2 (Power consistency)
For port current magnitude |I_port(omega)|, the equivalent radiated/leakage power satisfies
P_rad(omega) ≈ (1/2) · Re{ΔZ_rad(omega)} · |I_port(omega)|^2 ,
and grows consistently with near/far-field envelopes |E_rad|, |H_rad|.

S50-HF-3 (Activation conditions)
Enable the radiation channel when any of the following geometric/boundary features is present:

• Discontinuous return/reference planes or unbridged transitions (gaps, apertures, tears);
• Long unterminated stubs or untrimmed via stubs;
• Connector/launch mismatch causing modal leakage;
• Cable common-impedance coupling entering γ_side(cable).
  When enabled, record sigma_seam, the γ_side set, and changes in w_side(omega).

S50-HF-4 (S↔Z & port-normalization consistency)
The transformation from Sij to Z_eft must explicitly state port normalization and Z_c(omega), and after introducing ΔZ_rad must again pass passivity and KK_consistency.

S50-HF-5 (Path–weight coupling)
When the radiation channel is active, w_p(omega) shifts toward external leakage paths γ_side, increasing ΔT_arr; record ΔW = Σ_p | w_p(ω2) − w_p(ω1) |.

III. Implementation & Records (minimum execution dialect)

1. Required fields:
   ΔZ_rad(omega), Re_Zrad_min, near/far-field scan summaries for E_rad/H_rad, I_CM(omega), sigma_seam, Z_c(omega), w_p(omega), ΔW, arrival{...}, binding_ref, deemb, sync(Δt_sync), qa_gates{check_dim, passivity, KK}.
2. Phase correction: arg Z_corr(omega) = arg Z_raw(omega) - ( omega · Δt_sync ).
3. Estimation workflow (indicative):
   • Obtain Z_eft from Sij with stated normalization impedance;
   • Compute an anti-radiation baseline Z_base = Z_ref + ΔZ_T (simulation/fit/post-sealing reference);
   • ΔZ_rad = Z_eft − Z_base; take the positive-real part Re{ΔZ_rad} and verify K–K;
   • Cross-check P_rad against |E_rad|/|I_CM| for monotonic consistency.

IV. Falsifiability Criteria (for S50-HF)

• J-HF-50-1 (Positive-real): If Re{ΔZ_rad(omega)} < 0 or K–K fails, reject the radiation equivalent model or the mapping workflow.
• J-HF-50-2 (Sealing verification): After sealing gaps/shortening stubs, Re{ΔZ_rad} and |E_rad|/|I_CM| must both decrease; otherwise reject the activation criteria or geometry records.
• J-HF-50-3 (Power consistency): If P_rad computed from Re{ΔZ_rad} disagrees in trend with field-measurement envelopes, reject channel parameters or probing setup.
• J-HF-50-4 (S↔Z consistency): If after adding ΔZ_rad you obtain Re{Z_eft} < 0 or fail K–K, reject port normalization/mapping or the Z_c(omega) setting.
• J-HF-50-5 (Path coupling): If changes in ΔW are not directionally consistent with Re{ΔZ_rad} changes, reject the recorded path–weight coupling.

V. Compliance Templates (copy-ready)

• Record template
• radiation:
• enabled: true
• geometry:
• seams: {sigma_seam_S: 0.12, locations: ["J3_gap","L2_return_cut"], length_mm: 18.0}
• stubs: {count: 2, max_len_mm: 3.5}
• launch: {type: "SMA_edge", notes: "taper v2"}
• deltaZ_rad:
• Re_ohm: [ ... ] # ≥ 0
• Im_ohm: [ ... ]
• fields:
• E_rad_peak_dBuV_m: [ ... ]
• H_rad_peak_dBA_m: [ ... ]
• I_CM_A: [ ... ]
• coupling:
• paths: {γ_main: [...], γ_side: [...]}
• weights: {w_main: [...], w_side: [...]}
• ΔW: 0.19
• gates:
• Re_Zrad_min: 0.0
• passivity: "pass"
• KK_consistency: "pass"
• Numerical checks (pseudocode)
• # 1) Positive-real & causality
• assert min(Re(ΔZ_rad)) >= 0.0 and KK_consistency(Z_ref + ΔZ_T + ΔZ_rad)
• # 2) Power consistency
• P_rad = 0.5 * Re(ΔZ_rad) * abs(I_port)**2
• assert corr(P_rad, E_rad_envelope) > rho_gate
• # 3) Path coupling
• ΔW = sum_abs(w_side[ω2] - w_side[ω1])
• assert monotone(ΔW, Re(ΔZ_rad))

VI. Cross-Chapter Links & Closure

• Dependencies: Chapter 2 (Terms & Symbols), Chapter 3 (P10-HF Axioms), Chapter 4 (Minimal Equations & Dispersion).
• Downstream: Chapter 7 (Coherence-window KPIs & gates), Chapter 12 (Layout & Process Rules), Chapter 13 (coordination with EDX.EMI), Chapter 14 (SimStack & cases), Chapter 16 (Design Protocol & Checklist).