{
  "schemaVersion": 1,
  "id": "quarter-wave-open-stub",
  "title": "An open stub transforms into a shunt short at quarter wave",
  "kind": "stub",
  "inputs": {
    "referenceOhms": 50,
    "stubOhms": 50,
    "delaySeconds": 2.5e-11
  },
  "inputUnits": {
    "referenceOhms": "ohm",
    "stubOhms": "ohm",
    "delaySeconds": "s"
  },
  "checks": [
    {
      "metric": "quarterWaveTransmission",
      "expected": 0.0,
      "absoluteTolerance": 1e-12,
      "unit": "-",
      "derivation": "An open stub is a short at f=1/(4td), nulling transmission."
    },
    {
      "metric": "halfWaveTransmission",
      "expected": 1.0,
      "absoluteTolerance": 1e-12,
      "unit": "-",
      "derivation": "At f=1/(2td), the open stub is open again."
    },
    {
      "metric": "eighthWaveTransmission",
      "expected": 0.8944271909999159,
      "absoluteTolerance": 1e-10,
      "unit": "-",
      "derivation": "At f=1/(8td), normalized shunt admittance is j; S21=2/(2+j)."
    },
    {
      "metric": "quarterWaveReflection",
      "expected": 1.0,
      "absoluteTolerance": 1e-10,
      "unit": "-",
      "derivation": "A lossless shunt short reflects all incident power."
    }
  ],
  "evidence": {
    "type": "analytical",
    "provenance": "First-principles network limits or algebraic reduction of the declared teaching loop, independent of production numerical output."
  },
  "prediction": "Can an open-ended branch suppress transmission on the through path?",
  "explanation": "Yes. The impedance seen at the junction depends on electrical length. At quarter wave the open end transforms into a short; at half wave it transforms back to an open.",
  "limitations": [
    "Ideal lossless open stub.",
    "Exact-null evaluation is a floating-point approximation to a singular tangent.",
    "No finite-bandwidth impulse reconstruction is inferred."
  ],
  "relatedPage": "/topics/labs/one-channel.html",
  "availability": "helper-only"
}