Verified calculation capability

Coax Impedance Calculation Capability

Z0 of coaxial line from shield inner diameter D, center-conductor diameter d, and εr. Omitted εr defaults to 1.0. · Electrical · Rf

Capability ID electrical.rf.coax · version 1.0.1

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

Model

Z0: Z0 = (η0/(2π√εr)) · ln(D/d)
VF: VF = 1/√εr

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`D`	Shield / outer-conductor inner diameter in metres.	m	input
`d`	Center-conductor outer diameter in metres.	m	input
`er`	Relative permittivity of the homogeneous dielectric; defaults to 1.0 (air).	—	input / output
`Z0`	—	Ω	output
`VF`	—	—	output

Assumptions / Validity

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

Assumptions

Ideal TEM coaxial transmission line
Homogeneous dielectric
Lossless / low-loss approximation
Non-magnetic dielectric, μr ≈ 1
Omitted εr defaults to 1.0 (air/vacuum approximation)

Not supported

Attenuation
skin-effect R
magnetic dielectrics (\(\mu_r \ne 1\))
higher-order modes

Example

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

D=6.6mm d=1.6mm εr=2.25 → ≈56.643 Ω

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 · 2/2 declared partitions (z0, invalid-domain)
Calculation version: 1.0.1
Verification: 21/21 calculation tests · 4/4 legacy golden · 8/8 legacy boundary · 9/9 legacy property
Production surface contract: 4/4
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed
CVP identity: 5/5 property · digest eb5f53204f54
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. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
CVP suite: 1/1 golden · 9/9 CVP boundary · 18/18 invalid · 5/5 property · 2/2 metamorphic · 3/3 cross-interface · 4/4 CVP contract
Supplemental domain review: Internal · Pass · rf-engineering
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.1 (workspace artifacts agree)
Review-policy tier: Internally reviewed — catalog token internally_reviewed; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.1 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 4/4.

Tool id: coax-impedance
Engine: coax-impedance
REST: POST /api/v1/calc/coax-impedance
MCP: execute_calculation with capability_id: "electrical.rf.coax"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.1)
Versioned output schema: Immutable pin (1.0.1)

References

Human-readable sources plus CVP reference evidence classes.

Sources

David M. Pozar, Microwave Engineering — 4th ed., Ch. 2 Transmission Line Theory — coaxial line
Robert E. Collin, Foundations for Microwave Engineering — 2nd ed., coaxial transmission line

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.rf.coax"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.1) when reproducibility matters. Full protocol notes: MCP docs.