{
  "schemaVersion": 1,
  "id": "matched-t-pad",
  "title": "A matched resistive pad halves the wave amplitude",
  "kind": "pad",
  "inputs": {
    "referenceOhms": 50,
    "seriesOhms": 16.666666666666668,
    "shuntOhms": 66.66666666666667,
    "frequencyHz": 1000000000.0
  },
  "inputUnits": {
    "referenceOhms": "ohm",
    "seriesOhms": "ohm",
    "shuntOhms": "ohm",
    "frequencyHz": "Hz"
  },
  "checks": [
    {
      "metric": "s21Real",
      "expected": 0.5,
      "absoluteTolerance": 1e-10,
      "unit": "-",
      "derivation": "Symmetric matched T pad: series arms Z0(K−1)/(K+1), shunt 2Z0K/(K²−1), K=2."
    },
    {
      "metric": "s21Imag",
      "expected": 0.0,
      "absoluteTolerance": 1e-10,
      "unit": "-",
      "derivation": "Pure resistors introduce no reactive phase."
    },
    {
      "metric": "reflectionMagnitude",
      "expected": 0.0,
      "absoluteTolerance": 1e-10,
      "unit": "-",
      "derivation": "The T-pad input is Z0 when the output is terminated in Z0."
    },
    {
      "metric": "transmittedPower",
      "expected": 0.25,
      "absoluteTolerance": 1e-10,
      "unit": "-",
      "derivation": "Equal real reference impedances: normalized transmitted power is |S21|²=.25."
    }
  ],
  "evidence": {
    "type": "analytical",
    "provenance": "First-principles network limits or algebraic reduction of the declared teaching loop, independent of production numerical output."
  },
  "prediction": "If voltage-wave amplitude halves, is half the incident power transmitted?",
  "explanation": "No. With matched equal real references, transmitted power is one quarter; the resistors dissipate the remaining three quarters.",
  "limitations": [
    "Ideal resistors, equal real reference impedances.",
    "This is a known-attenuation network benchmark, not a lossy transmission-line material model.",
    "The related lesson does not instantiate this exact T pad."
  ],
  "relatedPage": "/topics/fundamentals/s-parameters.html",
  "availability": "helper-only"
}