CVP verified calculation capability

MOSFET Threshold / Overdrive Calculation Capability

Overdrive, square-law Id (cutoff / linear / saturation), or solve model Vth, with optional linear Vth(Tj). Vth is the long-channel square-law parameter, not datasheet VGS(th).

Electrical · Mosfet Capability ID electrical.mosfet.vth version 1.3.1 CVP VERIFIED CURRENT Engineering

Model

Overdrive

Overdrive: Vod = Vgs − Vth
Id sat: Id = ½ · kn · Vod²
Id linear: Id = kn · (Vod · Vds − Vds² / 2)
kn convention: kn = μn · Cox · W/L
Vth(Tj): Vth(Tj) = Vth(Tref) + α · (Tj − Tref)
Solve Vth: Vth = Vgs − √(2 · Id / kn)

Modes: overdrive · id · vth

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`Vgs`	Gate-source voltage	V	input / output
`Vth`	Square-law threshold parameter	V	input / output
`Id`	Drain current	A	input / output
`kn_A_per_V2`	kn = μn·Cox·W/L	—	input / output
`Vds`	Optional drain-source voltage	V	input / output
`temperature_model`	none	—	input / output
`Tj`	Junction temperature	°C	input / output
`Tref`	Reference temperature	°C	input / output
`alpha_V_per`	dVth/dT in V/°C	°C	input / output
`Vod`	Overdrive Vod = Vgs − Vth	V	output
`region`	cutoff: Vod≤0	—	output
`strong_inversion`	Deprecated alias of Vod > 0	—	output
`Vth_Tj`	Model Vth at Tj when linear	V	output
`Vth_Tref`	Model Vth at Tref when linear	V	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Ideal long-channel square-law NMOS model. Not BSIM, velocity saturation, or short-channel.
Vth is the model threshold parameter, not datasheet VGS(th) and not recommended gate drive.
kn = μn·Cox·W/L such that Id_sat = ½·kn·Vod². The ½ factor is not included in kn.
When Vds is omitted, Id uses the saturation equation and region is above_threshold or cutoff.
When Vds is provided: cutoff if Vod≤0; linear if 0≤Vds<Vod; saturation if Vds≥Vod.
Vod > 0 means above the model threshold, not strong inversion.
Cutoff returns Id = 0 A. Subthreshold current is not modeled.
Solve-Vth always uses the saturation extract Vth=Vgs−√(2Id/kn) at the measurement temperature.
Linear Vth(Tj) does not scale kn or μ(T).
Default α = −0.002 V/°C is a Si planning value, not a datasheet TCV of VGS(th).

Example

One numerical check. The calculator page holds worked steps and FAQ.

Vgs=3 Vth=1 Tj=125 α=−0.002 → Vod=2.2, Vth(Tj)=0.8

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Assurance: Engineering
Declared partition coverage: PASS · 4/4 declared partitions (overdrive, id, vth, invalid-domain)
Calculation version: 1.3.1
Verification: 26/26 calculation tests · 10/10 legacy golden · 5/5 legacy boundary · 11/11 legacy property
Production surface contract: 12/12
Versions: Calculation 1.3.1 · CVP protocol 1.0.0-proposed
CVP identity: 11/11 property · digest df4f29a72c29
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 4/4 golden · 5/5 CVP boundary · 5/5 invalid · 11/11 property · 2/2 cross-interface · 10/10 CVP contract
Supplemental domain review: Internal · Pass · electrical-engineer
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.3.1 (workspace artifacts agree)
Review-policy tier: Internal engineering review — catalog token expert_verified; supplemental; not CVP status

This calculator CURRENT · Public schema 1.3.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 12/12.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/mosfet-vth' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"mode":"overdrive","Vgs_V":3,"Vth_V":1},"calculation_version":"1.3.1"}'

{
  "inputs": {
    "mode": "overdrive",
    "Vgs_V": 3,
    "Vth_V": 1
  },
  "calculation_version": "1.3.1"
}

POST /api/v1/calc/mosfet-vth. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: mosfet-vth
Engine: mosfet-vth
REST: POST /api/v1/calc/mosfet-vth
MCP: execute_calculation with capability_id: "electrical.mosfet.vth"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.3.1)
Versioned output schema: Immutable pin (1.3.1)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Sedra/Smith — Microelectronic Circuits — MOSFET DC / square-law saturation and Vth(T)
Toshiba — Power MOSFET Electrical Characteristics — Gate threshold voltage VGS(th)
Nexperia AN11158 — Understanding power MOSFET data sheet parameters — Threshold voltage
Texas Instruments SLUA618 — Fundamentals of MOSFET and IGBT Gate Driver Circuits — Gate drive versus threshold

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"electrical.mosfet.vth"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"electrical.mosfet.vth","inputs":{"mode":"overdrive","Vgs_V":3,"Vth_V":1},"calculation_version":"1.3.1"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.3.1) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.