{
  "schemaVersion": 1,
  "id": "matched-channel-delay",
  "kind": "channel",
  "model": "labChannel",
  "modelVersion": "1.2",
  "contractVersion": "3.2",
  "params": {
    "reach": 8,
    "loss": 0,
    "rate": 16,
    "dz": 50,
    "dpos": 45,
    "dlen": 0,
    "stub": 0,
    "tr": 12,
    "trTdr": 12,
    "eq": false
  },
  "topology": "Eight inches of uniform lossless 50 Ω line; no discontinuity or stub, CTLE off.",
  "planes": "50 Ω input/output wave-reference planes; group delay before CTLE.",
  "evidence": {
    "type": "analytical",
    "provenance": "First-principles boundary conditions, linear circuit laws or the declared teaching-loop equation; no measured or licensed data."
  },
  "checks": [
    {
      "metric": "maxInsertionDeviationDb",
      "expected": 0,
      "absoluteTolerance": 1e-08,
      "unit": "dB",
      "derivation": "A matched lossless two-port has |S21|=1, so 20 log10|S21|=0."
    },
    {
      "metric": "groupDelay",
      "expected": 1.36e-09,
      "absoluteTolerance": 5e-15,
      "unit": "s",
      "derivation": "Eight inches × the declared 170 ps/in propagation delay = 1360 ps."
    },
    {
      "metric": "impulseSum",
      "expected": 1,
      "absoluteTolerance": 1e-08,
      "unit": "-",
      "derivation": "The discrete impulse weights sum to the unity DC transfer under this FFT convention."
    }
  ],
  "lesson": {
    "prediction": "Can a channel have zero insertion loss while still delaying the signal?",
    "experiment": "Open the scenario, keep its network and stimulus fixed, and inspect the stated observation. Compare with the derived answer before changing one variable.",
    "explanation": "Yes. The ideal transfer is exp(−jωτ): magnitude is unity and group delay is τ. Bulk-delay removal changes the impulse time reference, not the input/output group delay.",
    "transferQuestion": "Does changing symbol rate change the physical delay of this fixed lossless line?",
    "answer": "No. The delay in seconds is unchanged; its length in unit intervals changes."
  },
  "limitations": [
    "Ideal matched lossless model, not a real copper channel.",
    "Group delay is checked at every exported frequency, not only its mean.",
    "Do not compare the peak of individual discrete impulse weights with unity gain."
  ],
  "scenario": "/topics/labs/one-channel.html#lab=labChannel;v=3.2;lc-reach=8;lc-loss=0;lc-rate=16;lc-dz=50;lc-dpos=45;lc-dlen=0;lc-stub=0;lc-tr=12;lc-trtdr=12;lc-eq=0",
  "parameterUnits": {
    "reach": "in",
    "loss": "dB at 8 GHz",
    "rate": "GT/s",
    "dz": "ohm",
    "dpos": "%",
    "dlen": "ps",
    "stub": "ps",
    "tr": "ps",
    "trTdr": "ps",
    "eq": "boolean"
  },
  "stimulus": "Frequency sweep and discrete impulse of a matched lossless channel; fixed PRBS/edge pipeline retained by the lab."
}