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Cascaded Noise Figure Calculator

Compute cascaded noise figure and total gain for a multi-stage RF chain using the Friis formula. Add, remove, or reorder stages. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
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) · Matrix
Known limitations
  • No mismatch / image-noise extras. Last-stage gain does not enter F_tot. Arrays max 64 stages. MIXED_INPUT_ENCODING / NONCONTIGUOUS_STAGES.
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Cascaded NF (dB) and total available gain via the Friis formula for an N-stage RF chain.
Scope
Matched stages
Verification
Engine tested · Source checked · v1.1.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
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
Legacy regression
22/22 tests · Production surface contract 4/4
Trust layers
Verification VERIFIED · Production CURRENT · overall VERIFIED
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.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
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 · Manifest
Sources
Sources
Evidence
5 legacy golden · 10 legacy boundary · legacy regression suite · 5/5 oracle-backed golden · 16/16 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.1.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

dB → linear noise factorFi = 10^(NFi / 10)Domain: NFi in dB; Fi is a power ratio, not dB
dB → linear available gainGi = 10^(Gi,dB / 10)Domain: Gi is available power gain (linear)
Friis cascadeF_tot = F1 + Σ_{i=2..n} (Fi − 1) / Π_{j<i} Gj
Total noise figureNF_tot,dB = 10 log10(F_tot)
Total gainG_tot,dB = Σ Gi,dB
iInputs are dB; the engine converts to linear ratios before Friis and converts F_tot back to dB. The last stage's gain does not appear in F_tot — it changes G_tot only. Matched stages; available gain. Not a mismatch / image-noise cascade.

How to use

1

Enter each stage NF and available gain

Noise figure and available gain are in dB. Stage 1 is first in the RF chain (closest to the antenna / source).

2

Add, remove, or reorder stages

Friis is N-stage. Order is part of the answer: swapping two stages usually changes NF_tot even when the numbers are the same.

3

Read total NF and total gain

Earlier stages dominate when they have gain. Changing the last stage's gain leaves NF_tot unchanged and updates G_tot.

Example calculations

Common configurations with formula and result.

ϟ

LNA + mixer (two-stage)

NF 1 / 3 dB · G 10 / 20 dB

F = F1 + (F2−1)/G1
NF_tot = 1.330 dB · G_tot = 30 dB
ϟ

3-stage receiver

LNA 1 dB / 15 dB · mixer 8 dB / 10 dB · IF 3 dB / 20 dB

F = F1 + (F2−1)/G1 + (F3−1)/(G1 G2)
NF_tot ≈ 1.553 dB · G_tot = 45 dB
ϟ

Cable before LNA

3 dB matched loss at T0 (NF 3 dB, G −3 dB) then LNA 1 dB / 15 dB

Matched passive at T0: NF_dB = L_dB ≈ −G_dB
NF_tot = 4.000 dB

Cascaded Noise Figure calculator specification

Version 1.1.1 · Engine tested · Supplemental domain review · Internal · 2026-09-12

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
Friis cascade: convert each stage NF and available gain from dB to linear, then F_tot = F1 + (F2−1)/G1 + (F3−1)/(G1 G2)+…. NF_tot,dB = 10 log10(F_tot). Cascade order is an engineering variable.
What it calculates
Cascaded NF (dB) and total available gain via the Friis formula for an N-stage RF chain.
Inputs
  • NF1,G1,… (UI/share, up to 8, contiguous from 1) or NF_dB[] + G_dB[] (REST/MCP, 1–64); encodings are exclusive
Outputs
  • NF_tot_dB
  • F_tot
  • G_tot_dB
  • G_tot_lin
  • n
Formula
Fi=10^(NFi/10); Gi=10^(Gi,dB/10); F_tot=F1+Σ(Fi−1)/Π_{j<i} Gj; NF_tot,dB=10 log10(F_tot)
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
Units
  • dB
Boundary conditions
  • Missing stage pair → NEEDS_TWO_INPUTS / MISSING_REQUIRED_INPUT
  • NF_dB[] and G_dB[] length mismatch → ARRAY_LENGTH_MISMATCH
  • Non-finite NF/G or linear G≤0 (including gain underflow to 0) → INVALID_NUMBER
  • NF_dB[]/G_dB[] longer than 64 → TOO_MANY_STAGES
  • NF1,G1,… mixed with NF_dB[]/G_dB[] → MIXED_INPUT_ENCODING
  • Field stages with a gap (e.g. NF1+NF3, no NF2) → NONCONTIGUOUS_STAGES
  • Linear G_tot overflow → G_tot_lin null + LINEAR_GAIN_OVERFLOW; G_tot_dB remains finite
Example
NF 1+3 dB, G 10+20 dB → NF_tot=1.330 dB
Validation cases

10 published on this page · 22/22 tests · Production surface contract 4/4 · View evidence

  • NF1=1,G1=10,NF2=3,G2=20 → NF_tot≈1.330442 dB, G_tot=30 dB
  • NF_dB=[1,8,3], G_dB=[15,10,20] → NF_tot≈1.553288 dB, n=3, G_tot=45 dB
  • NF1=3,G1=-3,NF2=1,G2=15 → NF_tot=4 dB (cable before LNA)
  • NF1=2.5,G1=12 → NF_tot=2.5 dB (n=1)
  • NF1=1 (no G1) → error NEEDS_TWO_INPUTS
  • empty → error MISSING_REQUIRED_INPUT
  • NF1=1, G1=4000, NF2=3, G2=20 → NF_tot≈1.000 dB, G_tot_dB=4020, G_tot_lin=null, warning LINEAR_GAIN_OVERFLOW
  • NF_dB/G_dB length 65 → error TOO_MANY_STAGES
  • NF1=1,G1=10 plus NF_dB=[3,4], G_dB=[15,20] → error MIXED_INPUT_ENCODING
  • NF1=1,G1=10,NF3=3,G3=20 (no NF2/G2) → error NONCONTIGUOUS_STAGES
Sources
Last reviewed
2026-09-12
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.1.1

Background

Interpretation and common distinctions.

Cascade noise figure for an N-stage RF chain with the Friis formula. Enter each stage’s noise figure and available gain in dB, then add or reorder stages — order is part of the answer.

Default: NF 1 dB / 3 dB · G 10 / 20 dB → NF_tot = 1.330 dB, F = 1.3585, G_tot = 30 dB.

Agent / API notes

Capability id: electrical.rf.cascaded_nf · tool id: cascaded-nf · pin 1.1.1.

Human UI and share URLs use NF1,G1,… (max 8, contiguous from stage 1). REST/MCP also accept NF_dB[] + G_dB[] (1–64 stages; longer → TOO_MANY_STAGES). Do not mix the two encodings (MIXED_INPUT_ENCODING). Field stages with a gap (for example NF1+NF3 without NF2) return NONCONTIGUOUS_STAGES. When linear total gain overflows IEEE-754, G_tot_lin is null and LINEAR_GAIN_OVERFLOW is returned; G_tot_dB remains finite.

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Frequently asked questions

Key distinctions behind the calculation.

Must NF and G pairs match?

Yes — each stage needs both a noise figure and an available gain. Incomplete pairs return NEEDS_TWO_INPUTS. Arrays NF_dB[] and G_dB[] must have the same length (ARRAY_LENGTH_MISMATCH). Field encoding (NF1,G1,…) and array encoding cannot be combined (MIXED_INPUT_ENCODING). Field stages must be contiguous from stage 1 (NONCONTIGUOUS_STAGES).

Why doesn't the last stage gain affect cascaded noise figure?

In Friis' formula, each stage's noise contribution is divided by the cumulative available gain preceding it. The gain of the final stage has nothing to divide, so it does not appear in F_tot. It still adds to total system gain G_tot,dB. Changing G2 on a two-stage chain from 20 dB to 5 dB leaves NF_tot at 1.330 dB and drops G_tot from 30 dB to 15 dB — that is the formula, not a bug.

Are NF and G entered in dB or linear?

dB. Internally Fi = 10^(NFi/10) and Gi = 10^(Gi,dB/10). Substituting the dB numbers directly into F = F1 + (F2−1)/G1 is a common mistake and will not match this calculator.

What does a negative gain mean?

A passive matched loss (cable, filter, attenuator) has available gain Gi,dB < 0. For a matched passive network at the standard reference temperature T0 (typically 290 K), NF_dB = L_dB ≈ −G_dB. Putting that loss before an LNA raises system NF almost dB-for-dB — the cable-before-LNA example is 3 dB + 1 dB → 4 dB.