{
  "capability_id": "electrical.thermal.heatsink_rth",
  "tool_id": "heatsink-rth",
  "engine": "heatsink-rth",
  "calculation_version": "1.1.0",
  "generated_at": "2026-09-21T16:00:36.050Z",
  "engine_build": "2026-09-13",
  "test_count": 17,
  "passed": 17,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 4,
      "passed": 4
    },
    "boundary": {
      "total": 5,
      "passed": 5
    },
    "property": {
      "total": 8,
      "passed": 8
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": true,
  "review_kind": "internal",
  "source_checked": true,
  "reviewed_by": "CalculatorX electrical review (EE-001)",
  "reviewer_role": "electrical-engineer",
  "last_reviewed": "2026-09-14",
  "expert_review": {
    "status": "not_applicable",
    "reviewer": null,
    "note": "Internal domain review completed; not a named external expert review.",
    "kind": "internal"
  },
  "internal_review": {
    "status": "approved",
    "reviewer": {
      "name": "CalculatorX electrical review (EE-001)",
      "role": "electrical-engineer"
    },
    "reviewed_at": "2026-09-14",
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "kind": "internal"
  },
  "page": "https://www.calculatorx.com/calc/electric/heatsink-rth",
  "api": "https://www.calculatorx.com/api/v1/calc/heatsink-rth",
  "schema_input": "https://www.calculatorx.com/schemas/electrical.thermal.heatsink_rth.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/electrical.thermal.heatsink_rth.output.json",
  "assumptions": [
    "Steady-state lumped thermal resistance",
    "Rθ constant (not Zth(t))",
    "θJA is an effective / application value, not a JEDEC-board package constant",
    "θJC+θCS+θSA is a single series path; parallel PCB/package paths are ignored",
    "P is device dissipation converted to heat"
  ],
  "limitations": [
    "Steady-state lumped Rθ only; not Zth(t) or CFD",
    "θJA and θJC+θCS+θSA are exclusive models — mixing them is CONFLICTING_INPUTS",
    "Required mode reports θSA,max, not total θJA",
    "θCA / Rth_HS are rejected: θCA already includes the ambient-side path",
    "Parallel PCB/package heat-flow paths are ignored on the explicit stack",
    "P is device dissipation converted to heat, not load or output power",
    "θSA,max ≤ 0 returns HEATSINK_INFEASIBLE and is not a purchasable heatsink"
  ],
  "boundary_conditions": [
    "P < 0 → VALUE_MUST_BE_NON_NEGATIVE",
    "Required mode P ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "Tj_max ≤ Ta in required mode → VALUE_OUT_OF_RANGE",
    "Rth_CA or Rth_HS → CONFLICTING_INPUTS",
    "Mixed θJA and stack fields → CONFLICTING_INPUTS",
    "θSA,max ≤ 0 → warning HEATSINK_INFEASIBLE (result still returned)"
  ],
  "sources": [
    {
      "title": "JEDEC JESD51 series — Integrated Circuits Thermal Measurement Method",
      "section": "Junction-to-ambient and junction-to-case thermal metrics on specified test boards",
      "supports": "Tj = Ta + P·θJA as a thermal-metric estimate; θJA is test-condition specific",
      "kind": "standard",
      "accessed": "2026-09-14"
    },
    {
      "title": "Analog Devices — Practical Design Techniques for Power and Thermal Management",
      "section": "Section 8, Fig. 8.50 — junction → case → case-to-sink → sink-to-ambient",
      "url": "https://www.analog.com/media/en/training-seminars/design-handbooks/Practical-Design-Techniques-Power-Thermal/Section8.pdf",
      "supports": "θJA = θJC + θCS + θSA; required θSA,max = (Tj,max−Ta)/P − θJC − θCS",
      "kind": "reference",
      "accessed": "2026-09-14"
    },
    {
      "title": "Texas Instruments SPRA953 — Semiconductor and IC Package Thermal Metrics",
      "section": "RθJA, RθJC, and application dependence of junction-to-ambient metrics",
      "url": "https://www.ti.com/lit/pdf/spra953",
      "supports": "θJA is not a universal equivalent of the explicit case/heatsink stack",
      "kind": "reference",
      "accessed": "2026-09-14"
    },
    {
      "title": "Analog Devices — Thermal Characterization of IC Packages",
      "section": "θCA is case-to-ambient (all case-to-ambient paths); θJA = θJC + θCA",
      "url": "https://www.analog.com/en/resources/technical-articles/thermal-characterization-of-ic-packages.html",
      "supports": "Do not add θCA to θSA — θCA already includes the ambient-side path",
      "kind": "reference",
      "accessed": "2026-09-14"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:4e5f89c5bbd8f444c91daa988c9085b4d4e159aff60af497e4dd5e180c4ce60a",
  "tests": [
    {
      "id": "rise",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "junction_effective_ja",
        "Ta_C": 25,
        "P_W": 2,
        "Rth_JA": 5
      },
      "expect": {
        "Tj_C": 35,
        "dT_C": 10,
        "thermal_path": "JA"
      },
      "expectWarning": null,
      "actual": {
        "Rth_JA": 5,
        "Rth_JC": null,
        "Rth_CS": null,
        "Rth_SA": null,
        "Rth_total": 5,
        "Rth_total_max": null,
        "Rth_SA_required": null,
        "dT_JC_C": null,
        "dT_CS_C": null,
        "dT_SA_C": null,
        "Tj_C": 35,
        "Tj_max_C": null,
        "margin_C": null,
        "mode": "junction_effective_ja",
        "thermal_path": "JA",
        "Ta_C": 25,
        "P_W": 2,
        "Rth_C_per_W": 5,
        "dT_C": 10
      },
      "tol": 1e-12
    },
    {
      "id": "stack",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "junction_heatsink_stack",
        "Ta_C": 25,
        "P_W": 2,
        "Rth_JC": 1.5,
        "Rth_CS": 0.5,
        "Rth_SA": 3
      },
      "expect": {
        "Tj_C": 35,
        "Rth_total": 5,
        "thermal_path": "JC+CS+SA"
      },
      "expectWarning": null,
      "actual": {
        "Rth_JA": null,
        "Rth_JC": 1.5,
        "Rth_CS": 0.5,
        "Rth_SA": 3,
        "Rth_total": 5,
        "Rth_total_max": null,
        "Rth_SA_required": null,
        "dT_JC_C": 3,
        "dT_CS_C": 1,
        "dT_SA_C": 6,
        "Tj_C": 35,
        "Tj_max_C": null,
        "margin_C": null,
        "mode": "junction_heatsink_stack",
        "thermal_path": "JC+CS+SA",
        "Ta_C": 25,
        "P_W": 2,
        "Rth_C_per_W": 5,
        "dT_C": 10
      },
      "tol": 1e-12
    },
    {
      "id": "required-sa",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "required_heatsink_sa",
        "Ta_C": 25,
        "P_W": 10,
        "Tj_max_C": 150,
        "Rth_JC": 1.5,
        "Rth_CS": 0.5
      },
      "expect": {
        "Rth_SA_required": 10.5,
        "Rth_total_max": 12.5,
        "thermal_path": "required_SA"
      },
      "expectWarning": null,
      "actual": {
        "Rth_JA": null,
        "Rth_JC": 1.5,
        "Rth_CS": 0.5,
        "Rth_SA": null,
        "Rth_total": null,
        "Rth_total_max": 12.5,
        "Rth_SA_required": 10.5,
        "dT_JC_C": null,
        "dT_CS_C": null,
        "dT_SA_C": null,
        "Tj_C": null,
        "Tj_max_C": 150,
        "margin_C": null,
        "mode": "required_heatsink_sa",
        "thermal_path": "required_SA",
        "Ta_C": 25,
        "P_W": 10,
        "Rth_C_per_W": 10.5,
        "dT_C": 125
      },
      "tol": 1e-12
    },
    {
      "id": "zero-P-rise",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "junction_effective_ja",
        "Ta_C": 25,
        "P_W": 0,
        "Rth_JA": 5
      },
      "expect": {
        "Tj_C": 25,
        "dT_C": 0
      },
      "expectWarning": null,
      "actual": {
        "Rth_JA": 5,
        "Rth_JC": null,
        "Rth_CS": null,
        "Rth_SA": null,
        "Rth_total": 5,
        "Rth_total_max": null,
        "Rth_SA_required": null,
        "dT_JC_C": null,
        "dT_CS_C": null,
        "dT_SA_C": null,
        "Tj_C": 25,
        "Tj_max_C": null,
        "margin_C": null,
        "mode": "junction_effective_ja",
        "thermal_path": "JA",
        "Ta_C": 25,
        "P_W": 0,
        "Rth_C_per_W": 5,
        "dT_C": 0
      },
      "tol": 1e-12
    },
    {
      "id": "legacy-ca",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "junction_effective_ja",
        "Ta_C": 25,
        "P_W": 2,
        "Rth_JA": 5,
        "Rth_CA": 8
      },
      "expectError": "CONFLICTING_INPUTS",
      "code": "CONFLICTING_INPUTS",
      "error": "Rth_CA is not a heatsink-path segment"
    },
    {
      "id": "missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "junction_effective_ja",
        "Ta_C": 25
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "P_W is required"
    },
    {
      "id": "boundary-required-p-zero",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "required_heatsink_sa",
        "Ta_C": 25,
        "P_W": 0,
        "Tj_max_C": 150,
        "Rth_JC": 1.5,
        "Rth_CS": 0.5
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "P_W must be greater than zero"
    },
    {
      "id": "boundary-infeasible",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "required_heatsink_sa",
        "Ta_C": 25,
        "P_W": 10,
        "Tj_max_C": 40,
        "Rth_JC": 1.5,
        "Rth_CS": 0.5
      },
      "expect": {
        "Rth_SA_required": -0.5
      },
      "expectWarning": "HEATSINK_INFEASIBLE",
      "actual": {
        "Rth_JA": null,
        "Rth_JC": 1.5,
        "Rth_CS": 0.5,
        "Rth_SA": null,
        "Rth_total": null,
        "Rth_total_max": 1.5,
        "Rth_SA_required": -0.5,
        "dT_JC_C": null,
        "dT_CS_C": null,
        "dT_SA_C": null,
        "Tj_C": null,
        "Tj_max_C": 40,
        "margin_C": null,
        "mode": "required_heatsink_sa",
        "thermal_path": "required_SA",
        "Ta_C": 25,
        "P_W": 10,
        "Rth_C_per_W": -0.5,
        "dT_C": 15,
        "warnings": [
          {
            "code": "HEATSINK_INFEASIBLE",
            "severity": "warning",
            "detail": "Required θSA is -0.5 °C/W (≤ 0). θJC+θCS = 2 °C/W already uses the (Tj,max−Ta)/P budget of 1.5 °C/W.",
            "suggestion": "Lower dissipation P, raise Tj,max, reduce Ta, or improve θJC/θCS."
          }
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-legacy-hs",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "junction_heatsink_stack",
        "Ta_C": 25,
        "P_W": 2,
        "Rth_JC": 1.5,
        "Rth_CS": 0.5,
        "Rth_SA": 3,
        "Rth_HS": 1
      },
      "expectError": "CONFLICTING_INPUTS",
      "code": "CONFLICTING_INPUTS",
      "error": "Rth_HS is not a canonical heatsink symbol"
    },
    {
      "id": "property-dT-identity",
      "ok": true,
      "kind": "property",
      "detail": "ΔT=P·θJA",
      "expect": 10,
      "actual": 10
    },
    {
      "id": "property-zero-power",
      "ok": true,
      "kind": "property",
      "detail": "P=0 → Tj=Ta",
      "expect": 25,
      "actual": 25
    },
    {
      "id": "property-ambient-shift",
      "ok": true,
      "kind": "property",
      "detail": "Tj(Ta+c)=Tj(Ta)+c",
      "expect": 45,
      "actual": 45
    },
    {
      "id": "property-power-mono",
      "ok": true,
      "kind": "property",
      "detail": "P↑ → Tj not lower",
      "expect": true,
      "actual": [
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        45
      ]
    },
    {
      "id": "property-rth-mono",
      "ok": true,
      "kind": "property",
      "detail": "θ↑ → Tj not lower",
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        41
      ]
    },
    {
      "id": "property-stack-sum",
      "ok": true,
      "kind": "property",
      "detail": "θtotal=θJC+θCS+θSA",
      "expect": 5,
      "actual": 5
    },
    {
      "id": "property-required-sa",
      "ok": true,
      "kind": "property",
      "detail": "θSA,max=10.5",
      "expect": 10.5,
      "actual": 10.5
    },
    {
      "id": "property-sa-roundtrip",
      "ok": true,
      "kind": "property",
      "detail": "plug θSA,max → Tj,max",
      "expect": 150,
      "actual": 150
    }
  ],
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