Cascaded Noise Figure (Friis)
Total noise figure of cascaded RF stages.
How to Use
- Enter NF (dB) and gain (dB) for each of 3 stages.
- First stage dominates — use lowest-NF stage first.
Show Work
Formulas
History of the Friis Formula
Harald T. Friis at Bell Labs published his now-famous cascade noise-figure formula in his 1944 paper "Noise Figures of Radio Receivers". Friis worked on receiver design for the first WWII radar systems and trans-Atlantic telegraph carriers, where extracting signals from the noise floor was life-or-death. His formula captures the key insight that earlier stages in a receiver contribute far more to total noise than later stages — the first stage\'s gain divides the noise contribution of every subsequent stage.
The consequence: receivers are designed "LNA first" — a low-noise amplifier with the lowest achievable NF and enough gain to mask later stages\' noise sits at the antenna input. Cryogenically cooled LNAs (NF < 0.2 dB) power satellite ground stations, deep-space network receivers, and radio telescopes. The Arecibo radio telescope\'s LNA chain had a system noise temperature of ~30 K, equivalent to NF ≈ 0.4 dB — approaching the thermodynamic limit set by the cosmic microwave background.
Modern RF front-end chips (RFMD, Qorvo, Analog Devices) integrate LNA + mixer + IF amp on one die, optimizing the Friis cascade together. Software-defined radio platforms (HackRF, USRP) quote a single-chip NF of 6–10 dB — modest by dedicated-LNA standards but perfectly adequate for consumer and hobbyist use. The Friis formula remains the primary design tool for analyzing these chains.
About This Calculator
Enter noise figure (dB) and gain (dB) for each of three cascaded stages. The tool converts each NF to linear noise factor F, applies Friis\' cascade formula, and returns total NF, total noise factor F, total gain, and the percent contribution of the first stage\'s noise to the total.
Design rule emerges naturally: minimize F1 (use a quiet LNA first) and maximize G1 (enough first-stage gain to crush subsequent stages\' noise). Lossy passive elements (filters, attenuators, long cables) contribute their loss directly to NF with no gain to compensate — minimize them before the LNA. All math runs client-side; no values leave your browser.
About the Cascaded Noise Figure (Friis)
The Cascaded Noise Figure (Friis) gives you a fast, free answer for electronics and circuit design without sending anything off your device. Total noise figure of cascaded RF stages.
How it works
Enter your figures and the result appears instantly, updating the moment you change anything. There is no submit button and nothing to wait for, so it is easy to try a few what-if numbers and compare the results. Just check each box holds the kind of value it expects.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
Friis formula?
F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁·G₂) + …
Why LNA first?
Its gain divides later stages’ noise contribution.
How do I use the Cascaded Noise Figure (Friis)?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Receiver Chain
LNA + mixer + IF amp.
Test Setup
Match source and amp.
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