Noise Figure Cascade Calculator (Friis Formula)
Total noise figure, noise temperature and gain of a receive chain of up to three stages (low-noise amplifier, cable, mixer, amplifier), and how much of the noise comes from the stages after the first.
Results
The dashed line marks the value you entered.
What this tool does
In a chain, each stage's noise is divided by the gain in front of it, so the first stage dominates: F = F₁ + (F₂ − 1) ÷ G₁ + (F₃ − 1) ÷ (G₁G₂), with every figure as a plain ratio rather than dB. A low-noise amplifier with 20 dB of gain makes a 6 dB mixer behind it almost irrelevant, whereas the same cable placed before the amplifier adds its whole loss to the noise figure. A passive part, such as a cable or a filter, has a noise figure equal to its loss, so enter its loss as both the figure and a negative gain.
Formula
F = F₁ + (F₂ − 1) ÷ G₁ + (F₃ − 1) ÷ (G₁G₂) · NF = 10 log₁₀ F · T_e = 290 K × (F − 1) (Friis, with F and G as plain ratios)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
nf1 | Stage 1 noise figure (e.g. LNA) | dB |
g1 | Stage 1 gain | dB |
nf2 | Stage 2 noise figure (a lossy part has NF = loss) | dB |
g2 | Stage 2 gain (negative for a loss) | dB |
nf3 | Stage 3 noise figure | dB |
g3 | Stage 3 gain | dB |
NT | Noise figure of the whole chain | dB |
GT | Gain of the whole chain | dB |
TE | Equivalent input noise temperature | K |
SH | Share of the added noise that comes from stages 2 and 3 | % |
Worked example
- Stage 1 noise figure (e.g. LNA)1.5 dB
- Stage 1 gain20 dB
- Stage 2 noise figure (a lossy part has NF = loss)6 dB
- Stage 2 gain (negative for a loss)-6 dB
- Stage 3 noise figure3 dB
- Stage 3 gain25 dB
- Noise figure of the whole chain1.708 dB
- Gain of the whole chain39.0 dB
- Equivalent input noise temperature139.8 K
- Share of the added noise that comes from stages 2 and 314.4 %
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.