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

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

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)

Solve 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).	V	input / output
`Vth`	Square-law threshold parameter (V). Not datasheet VGS(th) and not recommended gate-drive voltage. Required for overdrive and id.	V	input / output
`Id`	Drain current (A). Required for mode=vth.	A	input / output
`kn_A_per_V2`	kn = μn·Cox·W/L (A/V²) such that Id_sat = ½·kn·(Vgs−Vth)². Linear Id = kn·(Vod·Vds − Vds²/2). The ½ factor is NOT included in kn. Required for id and vth.	—	input / output
`Vds`	Optional drain-source voltage (V). Classifies cutoff / linear / saturation. Omit to keep Vod-only bookkeeping; Id then uses the saturation equation.	V	input / output
`temperature_model`	none (default) uses Vth as entered. linear applies Vth(Tj)=Vth(Tref)+α·(Tj−Tref). Omitted infers linear if Tj_C or alpha_V_per_C is set.	—	input / output
`Tj`	Junction temperature (°C). Required for temperature_model=linear.	°C	input / output
`Tref`	Reference temperature (°C) for entered Vth. Default 25.	°C	input / output
`alpha_V_per`	dVth/dT in V/°C. Default −0.002 (≈ −2 mV/°C Si planning) when linear and omitted. Not a datasheet TCV of VGS(th).	°C	input / output
`Vod`	Overdrive Vod = Vgs − Vth (V).	V	output
`region`	cutoff: Vod≤0. above_threshold: Vod>0 and Vds omitted. linear: 0≤Vds<Vod. saturation: Vds≥Vod. above_threshold is not strong inversion.	—	output
`strong_inversion`	Deprecated alias of Vod > 0. Not a physics strong-inversion test.	—	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: 10/10
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 10/10.

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 this capability via same-origin MCP, then call execute_calculation.

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"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.3.1) when reproducibility matters. Full protocol notes: MCP docs.