Public evidence

electrical.rf.cascaded_nf

Machine-checked verification for calculation version 1.1.1 · tier expert_verified

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· No mismatch / image-noise extras. Last-stage gain does not enter F_tot. Arrays max 64 stages. MIXED_INPUT_ENCODING / NONCONTIGUOUS_STAGES. · Protocol · Schema · Production report

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)
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

Verification

Legacy regression suite: 22/22 calculation tests · Production surface contract 4/4

Three distinct suites: educational examples on the calculator page, this legacy regression count (22/22 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.1.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-12.exclusive-encoding-contiguous. Calculation version 1.1.1. CVP 1.0.0-proposed. 5/5 golden · 12/12 CVP boundary · 16/16 invalid · 5/5 property · 1/1 metamorphic · 2/2 cross-interface · 4/4 CVP contract. digest cffdb448177b.

Golden (oracle-backed) 5 / 5
CVP boundary 12 / 12
Invalid input 16 / 16
Property 5 / 5
Metamorphic 1 / 1
Cross-interface 2 / 2
CVP contract 4 / 4
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Assurance Engineering

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS

Fingerprint sha256:e499a69bf70cfd80b7dcd608cb849f615e1d54165b1f749836d2a276208a9ac0

Input schema sha256:bfb7a1226de15f901673da5b7e001c641f416e175640fe463850a6d56761ae1d · Output schema sha256:7df2c407d15f6a571ccf19a4e5ad5c0eeeed041efe0b9fcb75ba77483d71de62 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: cascaded-nf
Engine: cascaded-nf
Engine build: 2026-09-12
Evidence core: 2026-09-12T08:53:19.298Z
Rendered: 2026-09-16T22:03:43.723Z
Last reviewed: 2026-09-12

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

Limitations

Mismatch effects are not modeled
Image-noise / special mixer sideband behavior is not modeled
REST/MCP arrays NF_dB[]/G_dB[] are limited to 64 stages (TOO_MANY_STAGES); field encoding NF1…NF8 is limited to 8
Field encoding and array encoding are mutually exclusive (MIXED_INPUT_ENCODING); field stages must be contiguous from stage 1 (NONCONTIGUOUS_STAGES)
When 10^(G_tot_dB/10) overflows IEEE-754 binary64, G_tot_lin is null and LINEAR_GAIN_OVERFLOW is returned; G_tot_dB remains finite

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

Friis, H. T., “Noise Figures of Radio Receivers,” Proceedings of the IRE, Vol. 32, No. 7, pp. 419–422, July 1944 — Cascade formula · 1944-07 · DOI
Supports: F = F1 + (F2−1)/G1 + (F3−1)/(G1 G2) + … with Fi, Gi as linear power ratios (available gain)
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 · 2012
Supports: Matched Friis cascade in the linear domain; available gain; cascade order

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`two-stage`	golden	pass	Expected NF_tot_dB=1.3304418347850302 · G_tot_dB=30 · Actual n=2 · F_tot=1.3584516432910552 · NF_tot_dB=1.3304418347850302 · G_tot_dB=30 · G_tot_lin=1000
`three-stage-arrays`	golden	pass	Expected n=3 · NF_tot_dB=1.5532879789003458 · G_tot_dB=45 · Actual n=3 · F_tot=1.4299761624740048 · NF_tot_dB=1.5532879789003458 · G_tot_dB=45 · G_tot_lin=31622.776601683792
`five-stage`	golden	pass	Expected n=5 · NF_tot_dB=1.1716645959227783 · G_tot_dB=40 · Actual n=5 · F_tot=1.3096838120808023 · NF_tot_dB=1.1716645959227783 · G_tot_dB=40 · G_tot_lin=10000
`single-stage`	golden	pass	Expected n=1 · NF_tot_dB=2.5 · G_tot_dB=12 · Actual n=1 · F_tot=1.7782794100389228 · NF_tot_dB=2.4999999999999996 · G_tot_dB=12 · G_tot_lin=15.848931924611133
`cable-before-lna`	golden	pass	Expected NF_tot_dB=4 · G_tot_dB=12 · Actual n=2 · F_tot=2.51188643150958 · NF_tot_dB=4 · G_tot_dB=12 · G_tot_lin=15.848931924611133
`half-stage`	boundary	pass	Expected NEEDS_TWO_INPUTS · Actual NEEDS_TWO_INPUTS
`empty`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`array-mismatch`	boundary	pass	Expected ARRAY_LENGTH_MISMATCH · Actual ARRAY_LENGTH_MISMATCH
`high-g1-linear-overflow`	boundary	pass	warning LINEAR_GAIN_OVERFLOW
`too-many-stages`	boundary	pass	Expected TOO_MANY_STAGES · Actual TOO_MANY_STAGES
`mixed-encoding`	boundary	pass	Expected MIXED_INPUT_ENCODING · Actual MIXED_INPUT_ENCODING
`noncontiguous-fields`	boundary	pass	Expected NONCONTIGUOUS_STAGES · Actual NONCONTIGUOUS_STAGES
`boundary-zero-g`	boundary	pass	Expected NF_tot_dB=4.116458819258205 · G_tot_dB=10 · Actual n=2 · F_tot=2.580155507429993 · NF_tot_dB=4.116458819258205 · G_tot_dB=10 · G_tot_lin=10
`boundary-nan`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`boundary-gain-underflow`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`property-gain`	property	pass	Gtot 30
`property-nf-lt`	property	pass	1 < NF_tot_dB && NF_tot_dB < 3
`property-more-G1`	property	pass	higher G1 lowers NFtot
`property-n1-equals-nf1`	property	pass	n=1 → NF_tot = NF1
`property-order-matters`	property	pass	swapping stages changes NF
`property-last-G-independent`	property	pass	last-stage G changes Gtot not NF
`property-linear-gain-overflow`	property	pass	G_tot_lin null + LINEAR_GAIN_OVERFLOW when linear gain overflows