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  "api": "https://www.calculatorx.com/api/v1/calc/antenna-length",
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  "schema_output": "https://www.calculatorx.com/schemas/electrical.rf.antenna_length.output.json",
  "assumptions": [
    "Straight idealized antenna element.",
    "Frequency is the intended resonant/design frequency.",
    "No loading coils or distributed reactive loading.",
    "No explicit ground, nearby-object, conductor-diameter, or end-effect model.",
    "Correction factor k is a scalar length adjustment, not a transmission-line velocity factor.",
    "Quarter-wave mode is the ideal monopole radiator length over a perfect image plane / ground plane (≈ λ₀/4); radials and real soil are not modeled.",
    "Wavelength mode returns L = k·λ₀ (corrected 1λ), which equals free-space λ₀ only when k=1.",
    "S = k·λ₀ is a corrected design length scale, not a physical EM wavelength in a medium."
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  "limitations": [
    "Not a full antenna model — no ground, diameter, end-effect, loading coils, or NEC geometry."
  ],
  "boundary_conditions": [
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    "non-finite λ/L → VALUE_OUT_OF_RANGE",
    "k∉(0,1] → FRACTION_OUT_OF_RANGE",
    "invalid mode → INVALID_MODE",
    "length_factor ≠ velocity_factor when both sent → CONFLICTING_INPUTS"
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  "sources": [
    {
      "title": "NIST / CODATA — speed of light in vacuum",
      "section": "c = 299 792 458 m/s (exact)",
      "url": "https://physics.nist.gov/cuu/Constants/Value/c.html",
      "supports": "λ₀ = c/f",
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      "title": "ARRL — Single Band Dipoles",
      "section": "Empirical 468/f_MHz resonant-wire length; leave extra and trim to SWR",
      "url": "https://www.arrl.org/single-band-dipoles",
      "supports": "Practical wire dipoles are shorter than free-space λ₀/2; this tool uses k=1 unless the user supplies a shortening factor",
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      "publisher": "ARRL"
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    {
      "title": "ARRL — Ground-plane Antennas for 144, 222 and 440 MHz",
      "section": "¼-λ ground-plane antenna; radiator ≈ λ/4 over a ground-plane / radial system",
      "url": "https://www.arrl.org/files/file/Technology/tis/info/pdf/ab18-16.pdf",
      "supports": "mode=quarter ideal radiator length scale; real radials and soil are out of scope",
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      "publisher": "ARRL"
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