Verified calculation capability

Smith Chart (Impedance Matching) Calculation Capability

RF Smith Chart & Matching Workspace: mode-discriminated Agent API, strict match-steps, Touchstone S11, auto-match, SVG overlays. · Electrical · Rf

Capability ID electrical.rf.smith · version 1.6.3

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

Model

Reflection

Reflection: Γ = (z − 1) / (z + 1)
Series / shunt: z′ = z + Δr + j x · y′ = y + Δg + j b
T-line: Γ′ = Γ · e^{−j 2 θ}
Stub (open / short): Zin = −j Zs cotθ · / · +j Zs tanθ

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`gamma_r`	—	—	output
`gamma_i`	—	—	output
`gamma_mag`	—	—	output
`gamma_angle_deg`	—	—	output
`z_r`	—	—	output
`z_i`	—	—	output
`y_r`	—	—	output
`y_i`	—	—	output
`VSWR`	—	—	output
`RL_dB`	—	—	output
`Z0`	—	Ω	output
`RL`	—	Ω	output
`f`	Darcy friction factor	Hz	output
`load_z_r`	—	—	output
`load_z_i`	—	—	output
`matched`	—	—	output
`already_matched`	—	—	output
`n`	amount of substance	—	output
`Q`	—	—	output
`note`	—	—	output
`path`	—	—	output
`steps`	—	—	output
`solutions`	—	—	output
`best`	—	—	output
`points`	—	—	output

Assumptions / Validity

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

Assumptions

Impedance / matching workspace: passive loads with R≥0 (short and pure reactance allowed on |Γ|=1)
Chart / Z↔Γ / matching steps operate in passive region |Γ|≤1; active-device overlays (stability/gain/noise) are analysis aids and may reference circles that extend outside the unit circle but load markers remain clipped to |Γ|≤1
Looking toward generator; lossless line/stub unless R/‖RLC added; narrowband

Not supported

multi-section Chebyshev / broadband optimizers · full bilateral gain circles with S12 feedback redesign

Example

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

Z0=50, Z=100+j50, f=2440 MHz

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Z↔Γ + match-steps + auto-match + stub + Touchstone + f-sweep + Z(f) + S21/K + stab-geom + chart-xy + gain-geom + noise-geom. 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 · Z↔Γ + match-steps + auto-match + stub + Touchstone + f-sweep + Z(f) + S21/K + stab-geom + chart-xy + gain-geom + noise-geom· View Manifest · CVP overview · Specification
Verified scope: Z↔Γ + match-steps + auto-match + stub + Touchstone + f-sweep + Z(f) + S21/K + stab-geom + chart-xy + gain-geom + noise-geom
Assurance: Engineering
Declared partition coverage: PASS · 16/16 declared partitions (z-gamma, gamma-z, match-steps, auto-match, stub, touchstone, f-sweep, zf-interp, s21-k, stab-geom, chart-xy, gain-geom, noise-geom, url-query, xcal, invalid-domain)
Calculation version: 1.6.3
Verification: 21/21 calculation tests · 9/9 legacy golden · 5/5 legacy boundary · 7/7 legacy property
Production surface contract: 8/8
Versions: Calculation 1.6.3 · CVP protocol 1.0.0-proposed · Evidence 2026-09-07.p14
Verification revision: 2026-09-07.p14 · 53/53 property · digest b586778d9ca9
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · 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: 43/43 golden · 5/5 CVP boundary · 3/3 invalid · 53/53 property · 5/5 metamorphic · 4/4 round-trip · 12/12 O3 · 3/3 cross-interface · 3/3 cross-calculator · 8/8 CVP contract
Supplemental domain review: Internal · Pass · Internal RF review · CalculatorX Internal RF review · 2026-08-09
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.6.3 (workspace artifacts agree)
Review-policy tier: Internally reviewed — catalog token internally_reviewed; supplemental; not CVP status

This calculator CURRENT · Public schema 1.6.3 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 8/8.

Tool id: smith-chart
Engine: smith-chart
REST: POST /api/v1/calc/smith-chart
MCP: execute_calculation with capability_id: "electrical.rf.smith"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.6.3)
Versioned output schema: Immutable pin (1.6.3)

Operations

Declared calculation modes for this capability.

z-gamma
gamma-z
match
match-steps
s11-touchstone
auto-match

References

Human-readable sources plus CVP reference evidence classes.

Sources

Pozar Microwave Engineering — Smith chart / matching
Keysight — Data Format and Scale (Smith / polar) — Smith chart maps Γ to normalized impedance; constant-r / constant-x
IBIS Open Forum — Touchstone File Format Specification 2.1 — Reference specification (Touchstone 2.1); CalculatorX implements a Touchstone 1.x compatible subset

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · O2 expected_values · O2 numerical_behavior · 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.smith"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.6.3) when reproducibility matters. Full protocol notes: MCP docs.