Cascaded Noise Figure Calculator (Friis Equation)
Enter each stage noise figure and gain in dB. Fill only the stages you use. This tool computes total cascaded noise figure, total gain, and equivalent input noise temperature.
| Stage | Noise Figure (dB) | Gain (dB) |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
Quick SNR Method
If you know input and output SNR in dB, then NF(dB) = SNRin(dB) - SNRout(dB).
What is noise figure?
Noise figure (NF) tells you how much a circuit degrades signal-to-noise ratio (SNR). In practical RF and microwave design, it is one of the most important performance metrics for low-noise amplifiers, receivers, and front-end chains. A perfect noiseless device would have a noise factor of 1 (linear), which corresponds to 0 dB noise figure.
Engineers usually express this in dB because it is intuitive and easier to compare between devices: lower is better. For example, an LNA with 0.8 dB NF is excellent, while a 5 dB receiver front-end may struggle to detect weak signals in a crowded spectrum.
How the calculator works
This page uses the standard Friis cascade equation. The key idea: the first stage dominates the total noise performance. Later stages matter too, but their impact is divided by the gain that comes before them.
Friis equation (linear form)
Ftotal = F1 + (F2-1)/G1 + (F3-1)/(G1G2) + ...
- F is noise factor in linear units (not dB).
- G is power gain in linear units (not dB).
- Convert dB to linear with
10^(x/10). - Convert linear to dB with
10*log10(x).
Why first-stage gain and NF matter so much
If your first stage has low NF and decent gain, it suppresses the noise contribution of everything that follows. That is why receiver design usually starts with a low-noise, high-linearity front-end architecture: any losses before that first active stage can seriously hurt sensitivity.
A common mistake is placing a lossy filter or long cable before the LNA. Even a few dB of insertion loss ahead of the first amplifier can dramatically worsen system noise figure.
Equivalent noise temperature
Many link budget and antenna system calculations use equivalent noise temperature rather than NF. The conversion is:
Te = (F - 1)T0
where T0 is typically 290 K. This calculator lets you change the reference temperature
if your analysis uses a different convention.
Example workflow
- Enter stage 1 LNA NF and gain (for example 0.8 dB, 18 dB).
- Enter mixer/IF stages and any passive loss as negative gain values.
- Click Calculate.
- Review total NF and gain, then adjust front-end components if needed.
Design tips for better receiver sensitivity
- Minimize loss before the first amplifier.
- Choose low-NF front-end devices and good impedance matching.
- Use enough first-stage gain to bury downstream noise.
- Watch linearity and dynamic range; lowest NF is not always best in strong-signal environments.
- Model realistic temperature, cable loss, and connector loss in your system budget.
FAQ
Can gain be negative in this calculator?
Yes. Negative gain represents passive loss (attenuators, filters, cables). Including these losses is important, especially before the first active stage.
Should I enter values in linear units?
No. Enter NF and gain in dB. The script automatically converts to linear units for computation.
Is this valid for all RF systems?
It is valid for cascaded two-port noise analysis under standard assumptions. For advanced scenarios (frequency-dependent matching, nonlinear effects, or noise correlation), use full circuit simulation tools.