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  "slug": "emft-tdr",
  "title": "TDR — Time Domain Reflectometry — EMFT",
  "category": "electromagnetics",
  "category_label": "Electromagnetics",
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  "description": "TDR (Time Domain Reflectometry) sends a fast step into a transmission line and watches the reflection. The distance to a fault (open, short, impedance discontinuity) is half the round-trip time × propagation velocity. Use TDR to find cable breaks, identify the impedance of an unknown line, and verify connector quality. The workbench shows the bounce diagram, the V(z) standing-wave pattern, and the time-domain V(t) at the input.",
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  "content": {
    "formulas": [
      "Reflection coefficient: Γ = (Z_L − Z₀) / (Z_L + Z₀)",
      "Open termination: Γ = +1 (full positive reflection)",
      "Short termination: Γ = −1 (full negative reflection)",
      "Matched load: Γ = 0 (no reflection)",
      "Distance to fault: d = (v·t_round_trip) / 2",
      "Propagation velocity: v = c / √ε_r (e.g., 0.66c for PE dielectric coax)",
      "Resolution: Δd = v·(rise_time) / 2 (e.g., 100 ps rise time → 1.5 cm in PE coax)"
    ],
    "citations": [
      "Pozar, D. M., \"Microwave Engineering,\" 4th ed., Wiley, 2011, Ch. 3.",
      "Johnson, H., Graham, M., \"High-Speed Digital Design,\" Prentice Hall, 1993."
    ],
    "faq": [
      {
        "q": "How do I find an open vs a short?",
        "a": "Open: positive reflection (V jumps up). Short: negative reflection (V drops). The workbench shows both cases as V(t) animations."
      },
      {
        "q": "Why is the round-trip time, not one-way?",
        "a": "Because the step has to travel to the fault AND back. Distance = v·t / 2."
      }
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