{
  "node": {
    "id": "block:mutual-inductor",
    "type": "Block",
    "label": "Coupled inductors",
    "properties": {
      "id": "mutual-inductor",
      "name": "Coupled inductors",
      "kind": "studio",
      "summary": "Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses",
      "behavior": "Conserving component solved simultaneously with the connected network. Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses",
      "ports": [
        {
          "name": "p",
          "direction": "terminal",
          "unit": "V; A",
          "description": "electrical conserving connection; voltage across and current through the connected branch."
        },
        {
          "name": "n",
          "direction": "terminal",
          "unit": "V; A",
          "description": "electrical conserving connection; voltage across and current through the connected branch."
        },
        {
          "name": "s",
          "direction": "terminal",
          "unit": "V; A",
          "description": "electrical conserving connection; voltage across and current through the connected branch."
        },
        {
          "name": "t",
          "direction": "terminal",
          "unit": "V; A",
          "description": "electrical conserving connection; voltage across and current through the connected branch."
        },
        {
          "name": "voltageSecondary",
          "direction": "output",
          "unit": "V",
          "description": "Recorded voltage on the secondary port measurement from the conserving simulation."
        },
        {
          "name": "currentSecondary",
          "direction": "output",
          "unit": "A",
          "description": "Recorded current on the secondary port measurement from the conserving simulation."
        },
        {
          "name": "current",
          "direction": "output",
          "unit": "A",
          "description": "Recorded current measurement from the conserving simulation."
        }
      ],
      "parameters": [
        {
          "key": "primaryInductanceH",
          "label": "Primary self-inductance",
          "unit": "H",
          "default": 1,
          "description": "Self-inductance of the primary winding.",
          "min": 1e-09,
          "max": 1000000000
        },
        {
          "key": "secondaryInductanceH",
          "label": "Secondary self-inductance",
          "unit": "H",
          "default": 1,
          "description": "Self-inductance of the secondary winding.",
          "min": 1e-09,
          "max": 1000000000
        },
        {
          "key": "coupling",
          "label": "Magnetic coupling coefficient",
          "unit": "fraction",
          "default": 0.5,
          "description": "Signed mutual coupling; its magnitude must remain below one.",
          "min": -0.999999,
          "max": 0.999999
        },
        {
          "key": "initialPrimaryCurrentA",
          "label": "Initial primary current",
          "unit": "A",
          "default": 0,
          "description": "Current entering the primary winding at initialization.",
          "min": -1000000,
          "max": 1000000
        },
        {
          "key": "initialSecondaryCurrentA",
          "label": "Initial secondary current",
          "unit": "A",
          "default": 0,
          "description": "Current entering the secondary winding at initialization.",
          "min": -1000000,
          "max": 1000000
        }
      ],
      "equations": [
        "Vp = Lp dIp/dt + M dIs/dt",
        "Vs = M dIp/dt + Ls dIs/dt",
        "M = k sqrt(Lp Ls)"
      ],
      "example": {
        "title": "Coupled inductors worked example",
        "text": "Editable first-party network. supply: voltageV=1; short: voltageV=0. Checks below were verified in the native execution engine.",
        "url": "https://design.lemonergy.com/cosim.html?example=physical-mutual-inductor",
        "label": "Open Studio example",
        "inputs": [
          {
            "port": "primaryInductanceH",
            "label": "Primary self-inductance",
            "value": 1,
            "unit": "H"
          },
          {
            "port": "secondaryInductanceH",
            "label": "Secondary self-inductance",
            "value": 1,
            "unit": "H"
          },
          {
            "port": "coupling",
            "label": "Magnetic coupling coefficient",
            "value": 0.5,
            "unit": "fraction"
          },
          {
            "port": "initialPrimaryCurrentA",
            "label": "Initial primary current",
            "value": 0,
            "unit": "A"
          }
        ],
        "checks": [
          {
            "port": "target/voltageSecondary",
            "label": "voltageSecondary",
            "atS": 1,
            "value": 0,
            "unit": "V",
            "tolerance": 1e-10
          },
          {
            "port": "target/currentSecondary",
            "label": "currentSecondary",
            "atS": 1,
            "value": -0.666666667,
            "unit": "A",
            "tolerance": 6.666666666666666e-07
          },
          {
            "port": "target/current",
            "label": "current",
            "atS": 1,
            "value": 1.33333333,
            "unit": "A",
            "tolerance": 1.3333333333333328e-06
          }
        ]
      },
      "limits": [
        "Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses",
        "Demonstration parameters are not calibrated hardware data. Singular or incompatible ideal constraints and unsupported state ranges stop the run."
      ],
      "references": [
        "physical-magnetic"
      ],
      "availability": {
        "status": "released",
        "label": "Available in Lemonergy Studio",
        "detail": "The bundled example is available in the production release verified on 28 October 2026. The parameters and examples here are synthetic teaching fixtures, not a characterized cell or a validated operating limit."
      },
      "evidence": [
        "docs/glossary/native-block-verification.json"
      ],
      "sourceRepository": "Lemonergy Studio public contract",
      "sourceRevision": "verification-2026-10-27",
      "caseIds": [
        "native-mutual-inductor"
      ],
      "type": "mutual-inductor",
      "implementationId": "mutual-inductor",
      "url": "https://lemonergy.com/learn/glossary/blocks/mutual-inductor/",
      "documentationUrl": "https://lemonergy.com/learn/glossary/blocks/mutual-inductor/",
      "sourceFile": "block-library.json",
      "reviewed": "2026-10-27",
      "releaseEvidence": {
        "environment": "production",
        "status": "verified",
        "revision": "e76cadfc203e15eb41f3478d8b1044a5b851953d",
        "verifiedOn": "2026-10-28",
        "exampleUrls": [
          "https://design.lemonergy.com/cosim.html?example=physical-mutual-inductor"
        ]
      }
    }
  },
  "incoming": [
    {
      "id": "edge:usesBlock/native-mutual-inductor/0",
      "type": "usesBlock",
      "source": "workflow:native-mutual-inductor",
      "target": "block:mutual-inductor",
      "properties": {
        "sourceFile": "wiki-blocks.json",
        "position": 0,
        "name": "Coupled inductors",
        "type": "mutual-inductor",
        "role": "Conserving component solved simultaneously with the connected network. Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses",
        "settings": [
          "Use the block reference for settings and connections.",
          "Bundled example verified on the production release of 28 October 2026."
        ]
      }
    }
  ],
  "outgoing": [
    {
      "id": "edge:cites/block:mutual-inductor/reference:physical-magnetic",
      "type": "cites",
      "source": "block:mutual-inductor",
      "target": "reference:physical-magnetic",
      "properties": {
        "sourceFile": "block-library.json",
        "scope": "Scientific or mathematical background; implementation scope is stated by the block contract"
      }
    }
  ],
  "neighbors": [
    {
      "id": "workflow:native-mutual-inductor",
      "type": "Workflow",
      "label": "Coupled inductors worked example",
      "properties": {
        "id": "native-mutual-inductor",
        "title": "Coupled inductors worked example",
        "kind": "studio",
        "summary": "Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses",
        "steps": [
          "Review the interface, units and model limits.",
          "Open the Studio example and run its bundled model.",
          "Compare outputs with the numerical checks; change one input and run again."
        ],
        "example": "Editable first-party network. supply: voltageV=1; short: voltageV=0. Checks below were verified in the native execution engine.",
        "observe": "Inspect the output channels and checks on the block reference page.",
        "limits": "Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses Demonstration parameters are not calibrated hardware data. Singular or incompatible ideal constraints and unsupported state ranges stop the run.",
        "url": "https://design.lemonergy.com/cosim.html?example=physical-mutual-inductor",
        "label": "Open Studio example",
        "evidence": [
          "docs/glossary/native-block-verification.json"
        ]
      }
    },
    {
      "id": "reference:physical-magnetic",
      "type": "Reference",
      "label": "Mutual Inductance",
      "properties": {
        "title": "Mutual Inductance",
        "publisher": "OpenStax, Rice University",
        "url": "https://openstax.org/books/university-physics-volume-2/pages/14-1-mutual-inductance",
        "type": "Primary educational or metrology reference",
        "scope": "Underlying physical law or reduced-model basis; Lemonergy implementation choices and limits are documented separately.",
        "accessed": "2026-10-27"
      }
    }
  ]
}