Verified calculation capability

Cascaded noise figure Calculation Capability

Friis cascaded NF and total gain from stage NF/G in dB. · Electrical · Rf

Capability ID electrical.rf.cascaded_nf · version 1.1.1

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

Model

dB → linear noise factor

dB → linear noise factor: Fi = 10^(NFi / 10)
dB → linear available gain: Gi = 10^(Gi,dB / 10)
Friis cascade: F_tot = F1 + Σ_{i=2..n} (Fi − 1) / Π_{j<i} Gj
Total noise figure: NF_tot,dB = 10 log10(F_tot)
Total gain: G_tot,dB = Σ Gi,dB

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`NF1`	Stage 1 noise figure (dB)	—	input
`G1`	Stage 1 available gain (dB)	—	input
`NF2`	Stage 2 noise figure (dB)	—	input
`G2`	Stage 2 available gain (dB)	—	input
`NF3`	Stage 3 noise figure (dB)	—	input
`G3`	Stage 3 available gain (dB)	—	input
`NF4`	Stage 4 noise figure (dB)	—	input
`G4`	Stage 4 available gain (dB)	—	input
`NF5`	Stage 5 noise figure (dB)	—	input
`G5`	Stage 5 available gain (dB)	—	input
`NF6`	Stage 6 noise figure (dB)	—	input
`G6`	Stage 6 available gain (dB)	—	input
`NF7`	Stage 7 noise figure (dB)	—	input
`G7`	Stage 7 available gain (dB)	—	input
`NF8`	Stage 8 noise figure (dB); field encoding max	—	input
`G8`	Stage 8 available gain (dB); field encoding max	—	input
`NF_dB`	Stage noise figures in dB (REST/MCP; 1–64 stages)	—	input / output
`G_dB`	Stage available gains in dB (REST/MCP; 1–64 stages)	—	input / output
`n`	amount of substance	—	output
`F_tot`	—	—	output
`NF_tot_dB`	—	—	output
`G_tot_dB`	Total available gain in dB (always finite when status=success)	—	output
`G_tot_lin`	Linear total available gain 10^(G_tot_dB/10). Null when that ratio exceeds IEEE-754 binary64; see LINEAR_GAIN_OVERFLOW.	—	output

Assumptions / Validity

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

Assumptions

Matched stages
Gi denotes available power gain
NF and gain inputs are dB and are converted to linear factors internally
Classical Friis cascade assumptions apply
For a matched passive two-port at T0 ≈ 290 K, NF_dB = L_dB ≈ −G_dB

Example

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

NF 1+3 dB, G 10+20 dB → NF_tot=1.330 dB

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 · 8/8 declared partitions (nf-g-fields, arrays, n-ge-3, negative-gain, invalid-domain, mixed-encoding, noncontiguous-stages, linear-gain-overflow)
Calculation version: 1.1.1
Verification: 22/22 calculation tests · 5/5 legacy golden · 10/10 legacy boundary · 7/7 legacy property
Production surface contract: 4/4
Versions: Calculation 1.1.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-12.exclusive-encoding-contiguous
Verification revision: 2026-09-12.exclusive-encoding-contiguous · 5/5 property · digest cffdb448177b
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: 5/5 golden · 12/12 CVP boundary · 16/16 invalid · 5/5 property · 1/1 metamorphic · 2/2 cross-interface · 4/4 CVP contract
Supplemental domain review: Internal · Pass · electrical-engineer
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.1.1 (workspace artifacts agree)
Review-policy tier: Internal engineering review — catalog token expert_verified; supplemental; not CVP status

This calculator CURRENT · Public schema 1.1.1 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: cascaded-nf
Engine: cascaded-nf
REST: POST /api/v1/calc/cascaded-nf
MCP: execute_calculation with capability_id: "electrical.rf.cascaded_nf"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.1.1)
Versioned output schema: Immutable pin (1.1.1)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Friis, H. T., “Noise Figures of Radio Receivers,” Proceedings of the IRE, Vol. 32, No. 7, pp. 419–422, July 1944 — Cascade formula
Pozar, D. M., Microwave Engineering, 4th ed., Wiley, 2012 — Ch. 10 Noise and Nonlinear Distortion, §10.2 Noise Figure of a Cascaded System, p. 504

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.cascaded_nf"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.1.1) when reproducibility matters. Full protocol notes: MCP docs.