{
  "node": {
    "id": "block:operational-amplifier",
    "type": "Block",
    "label": "Finite-gain operational amplifier",
    "properties": {
      "id": "operational-amplifier",
      "name": "Finite-gain operational amplifier",
      "kind": "studio",
      "summary": "High impedance inputs, finite open-loop gain and hard output voltage rails; ideal output drive, no slew or supply-current model",
      "behavior": "Conserving component solved simultaneously with the connected network. High impedance inputs, finite open-loop gain and hard output voltage rails; ideal output drive, no slew or supply-current model",
      "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": "cp",
          "direction": "terminal",
          "unit": "V; A",
          "description": "electrical conserving connection; voltage across and current through the connected branch."
        },
        {
          "name": "cn",
          "direction": "terminal",
          "unit": "V; A",
          "description": "electrical conserving connection; voltage across and current through the connected branch."
        },
        {
          "name": "current",
          "direction": "output",
          "unit": "A",
          "description": "Recorded current measurement from the conserving simulation."
        },
        {
          "name": "voltage",
          "direction": "output",
          "unit": "V",
          "description": "Recorded voltage measurement from the conserving simulation."
        },
        {
          "name": "branchCurrent",
          "direction": "output",
          "unit": "A",
          "description": "Recorded branchCurrent measurement from the conserving simulation."
        }
      ],
      "parameters": [
        {
          "key": "gain",
          "label": "Gain",
          "unit": "V/V",
          "default": 100000,
          "description": "Multiplier from the sensed input to the declared output quantity.",
          "min": 1,
          "max": 1000000000000
        },
        {
          "key": "minimumOutputV",
          "label": "Lower output rail",
          "unit": "V",
          "default": -15,
          "description": "Smallest permitted output voltage of the amplifier abstraction.",
          "min": -1000000,
          "max": 1000000
        },
        {
          "key": "maximumOutputV",
          "label": "Upper output rail",
          "unit": "V",
          "default": 15,
          "description": "Largest permitted output voltage of the amplifier abstraction.",
          "min": -1000000,
          "max": 1000000
        }
      ],
      "equations": [
        "Vout = clip(gain × (Vcp − Vcn), lower rail, upper rail)",
        "Icp = Icn = 0"
      ],
      "example": {
        "title": "Finite-gain operational amplifier worked example",
        "text": "Editable first-party network. supply: voltageV=1; load: resistanceOhm=4. Checks below were verified in the native execution engine.",
        "url": "https://design.lemonergy.com/cosim.html?example=physical-operational-amplifier",
        "label": "Open Studio example",
        "inputs": [
          {
            "port": "gain",
            "label": "Gain",
            "value": 100000,
            "unit": "V/V"
          },
          {
            "port": "minimumOutputV",
            "label": "Lower output rail",
            "value": -15,
            "unit": "V"
          },
          {
            "port": "maximumOutputV",
            "label": "Upper output rail",
            "value": 15,
            "unit": "V"
          }
        ],
        "checks": [
          {
            "port": "target/current",
            "label": "current",
            "atS": 1,
            "value": -0.2499975,
            "unit": "A",
            "tolerance": 2.4999750002499973e-07
          },
          {
            "port": "target/voltage",
            "label": "voltage",
            "atS": 1,
            "value": 0.99999,
            "unit": "V",
            "tolerance": 9.99990000099999e-07
          },
          {
            "port": "target/branchCurrent",
            "label": "branchCurrent",
            "atS": 1,
            "value": -0.2499975,
            "unit": "A",
            "tolerance": 2.4999750002499973e-07
          }
        ]
      },
      "limits": [
        "High impedance inputs, finite open-loop gain and hard output voltage rails; ideal output drive, no slew or supply-current model",
        "Demonstration parameters are not calibrated hardware data. Singular or incompatible ideal constraints and unsupported state ranges stop the run."
      ],
      "references": [
        "physical-amplifier"
      ],
      "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-operational-amplifier"
      ],
      "type": "operational-amplifier",
      "implementationId": "operational-amplifier",
      "url": "https://lemonergy.com/learn/glossary/blocks/operational-amplifier/",
      "documentationUrl": "https://lemonergy.com/learn/glossary/blocks/operational-amplifier/",
      "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-operational-amplifier"
        ]
      }
    }
  },
  "incoming": [
    {
      "id": "edge:usesBlock/native-operational-amplifier/0",
      "type": "usesBlock",
      "source": "workflow:native-operational-amplifier",
      "target": "block:operational-amplifier",
      "properties": {
        "sourceFile": "wiki-blocks.json",
        "position": 0,
        "name": "Finite-gain operational amplifier",
        "type": "operational-amplifier",
        "role": "Conserving component solved simultaneously with the connected network. High impedance inputs, finite open-loop gain and hard output voltage rails; ideal output drive, no slew or supply-current model",
        "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:operational-amplifier/reference:physical-amplifier",
      "type": "cites",
      "source": "block:operational-amplifier",
      "target": "reference:physical-amplifier",
      "properties": {
        "sourceFile": "block-library.json",
        "scope": "Scientific or mathematical background; implementation scope is stated by the block contract"
      }
    }
  ],
  "neighbors": [
    {
      "id": "workflow:native-operational-amplifier",
      "type": "Workflow",
      "label": "Finite-gain operational amplifier worked example",
      "properties": {
        "id": "native-operational-amplifier",
        "title": "Finite-gain operational amplifier worked example",
        "kind": "studio",
        "summary": "High impedance inputs, finite open-loop gain and hard output voltage rails; ideal output drive, no slew or supply-current model",
        "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; load: resistanceOhm=4. Checks below were verified in the native execution engine.",
        "observe": "Inspect the output channels and checks on the block reference page.",
        "limits": "High impedance inputs, finite open-loop gain and hard output voltage rails; ideal output drive, no slew or supply-current model 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-operational-amplifier",
        "label": "Open Studio example",
        "evidence": [
          "docs/glossary/native-block-verification.json"
        ]
      }
    },
    {
      "id": "reference:physical-amplifier",
      "type": "Reference",
      "label": "Lecture 19: The Operational Amplifier Abstraction",
      "properties": {
        "title": "Lecture 19: The Operational Amplifier Abstraction",
        "publisher": "MIT OpenCourseWare, Anant Agarwal",
        "url": "https://ocw.mit.edu/courses/6-002-circuits-and-electronics-spring-2007/resources/lecture-19/",
        "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"
      }
    }
  ]
}