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Tool 06 · Available

Cascade Gain & Noise Figure

Reorder receiver stages and inspect gain, Friis noise contributions, sensitivity, and headroom.

Typical inputs
Ordered stage gain, noise figure, optional input P1dB, source temperature, ENBW, required SNR, and input level.
Calculated output
Total gain/NF, input-referred contributions, equivalent noise temperature, sensitivity, and indicative compression headroom.
Model status
Release B · documented and numerically tested
Engineering question

How strongly does each stage affect system noise after the preceding gain?

Ordered receiver cascade

Friis calculations use linear factors and available gains. A passive loss row must state its physical-temperature assumption; the default 3 dB filter names 290 K explicitly.

Ordered stages. P1dB is optional and always entered at that stage's input.
StageGain dBNF dBInput P1dBmOrder
Total cascade noise figure1.987783 dB42.000 dB total small-signal gain · T0 = 290 K for NF conversion
Output signal
-18.0000 dBm
Output noise
-56.9771 dBm
Output SNR
38.9771 dB
for entered signal and kTB + cascade NF
Conditional sensitivity
-88.9771 dBm
Equivalent input temperature
168.328 K
Compression headroom
58.000 dB
Signal levels use the entered small-signal gains. Friis contribution is input-referred.
StageOutput signalFFriis contributionCumulative gain
LNA-45.0000 dBm1.4125381.41253815.000 dB
Filter at 290 K-48.0000 dBm1.9952620.03147312.000 dB
IF amplifier-18.0000 dBm3.1622780.13643042.000 dB

Calculation path

  1. Ftotal=F1+F2−1G1+⋯=1.58044100F_{\mathrm{total}}=F_1+\frac{F_2-1}{G_1}+\cdots=1.58044100
  2. NFtotal=10log⁡10Ftotal=1.987783 dB\mathrm{NF}_{\mathrm{total}}=10\log_{10}F_{\mathrm{total}}=1.987783\,\mathrm{dB}
  3. Noise figure conventions for mixers can be SSB or DSB; all rows must use compatible definitions.
Model

What this calculator is doing

Friis noise factor weights each later stage's excess noise by preceding linear gain. Reordering stages changes total NF even when total gain is unchanged.

Decision

How to read the result

Put low-noise gain early when linearity and stability permit. The P1dB result is a screen, not a blocker, IP3, compression-curve, or stability analysis.

Equations & conventions

  • F=F1+F2−1G1+…F = F_{1} + \frac{F_{2}-1}{G_{1}} + \ldots
  • Gtotal[dB]=∑Gi[dB]G_{\mathrm{total}}[\mathrm{dB}] = \sum G_{i}[\mathrm{dB}]
  • F is linear noise factor and NF = 10 log10(F).
  • Gi is linear available power gain preceding a later contribution.
  • ENBW is equivalent noise bandwidth, not necessarily −3 dB bandwidth.

Independently checked example

Checked example: 15 dB/1.5 dB, −3 dB/3 dB, and 30 dB/5 dB stages produce 42 dB total gain and approximately 1.9878 dB cascade NF.

Common mistakes

  • Applying Friis directly to dB values.
  • Ignoring pre-LNA loss or treating output P1dB as an input value.

Assumptions, validity & omissions

  • Gain and noise factors are compatible available-power quantities referenced to T₀ = 290 K.
  • A passive loss row must use the appropriate physical-temperature noise assumption; the named default filter assumes 290 K.
  • SSB and DSB mixer noise figures must not be mixed silently.
  • Stages are linear and stable; P1dB headroom is an indicative small-chain check.

Sources & model provenance

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