Noise Figure and Friis Formula Calculator
Find the total noise figure of a cascaded RF chain from each stage's gain and noise figure using the Friis formula.
📡 What is Noise Figure and the Friis Formula?
Noise figure is a measure, in decibels, of how much a component or stage degrades the signal-to-noise ratio of a signal passing through it, relative to an ideal noiseless component at a standard 290 K reference temperature. The Friis formula extends this idea to a chain of cascaded stages (like an antenna, LNA, mixer, and IF amplifier in a receiver), combining each stage's individual gain and noise figure into one overall system noise figure.
RF and microwave engineers use this calculation constantly when designing receiver front ends for radios, satellite ground stations, radar systems, and wireless base stations, where the system's minimum detectable signal is set almost entirely by the cascaded noise figure of the first few stages.
A common misconception is that noise figures can simply be averaged or added in dB. They cannot, the Friis formula requires converting each stage's noise figure to a linear noise factor F = 10^(NF/10) first, combining the linear factors, then converting the total back to dB. This calculator performs that conversion automatically and shows every intermediate step.
This calculator computes the cascaded noise figure for up to three stages from each stage's gain and noise figure in dB, and plots how the total noise figure changes as the first stage's gain varies, visually demonstrating why a high-gain, low-noise first stage dominates the whole chain's performance.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Typical LNA-Mixer-IF Amplifier Chain
G1 = 15 dB, NF1 = 1.5 dB, G2 = 10 dB, NF2 = 6 dB, G3 = 20 dB, NF3 = 10 dB
Example 2 — High-Gain, Low-Noise LNA
G1 = 20 dB, NF1 = 0.8 dB, G2 = 12 dB, NF2 = 4 dB, G3 = 15 dB, NF3 = 8 dB
Example 3 — Low First-Stage Gain Penalty
G1 = 3 dB, NF1 = 2 dB, G2 = 20 dB, NF2 = 5 dB, G3 = 10 dB, NF3 = 9 dB
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Friis formula for cascaded noise figure?
The Friis formula gives the total noise factor of a cascaded chain as F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2), where F is the linear noise factor and G is the linear power gain of each stage. Converting F_total to dB gives the total noise figure.
Why does the first stage matter most in a receiver chain?
Every later stage's noise contribution, (Fn-1), is divided by the total gain of all stages ahead of it. A high-gain, low-noise first stage (an LNA) suppresses later stages' noise almost to nothing, which is why LNA placement right after the antenna is standard receiver design practice.
How do I convert noise figure in dB to noise factor F?
F = 10^(NF_dB / 10). For example, a 3 dB noise figure corresponds to F = 10^0.3 = 1.995. Always perform the Friis formula's addition in linear F, then convert the final F_total back to dB with NF_dB = 10*log10(F_total).
What noise figure should I expect from a passive component like a cable?
For a purely passive, lossy component at room temperature, its noise figure in dB equals its insertion loss in dB, and its power gain G is less than 1 (a loss). Placing lossy components before the LNA directly raises the system noise figure by roughly their loss in dB.
How does this calculator differ from a full 3-port noise analysis?
This calculator implements the standard simplified Friis cascade formula, which assumes each stage is impedance-matched and characterized by a single scalar noise figure and gain. It does not model noise correlation between stages or frequency-dependent noise figure variation.
What is a typical noise figure for an LNA versus a mixer?
A good RF LNA typically has a noise figure of 0.5 to 2 dB with 15 to 20+ dB of gain. Passive mixers commonly have a noise figure of 6 to 10 dB (close to their conversion loss), which is why they are almost always placed after, not before, the LNA.
Can I model only two cascaded stages?
Yes. Set the third stage's noise figure low or its gain very high (or its noise figure to 0 dB) so the third term (F3-1)/(G1*G2) contributes negligibly to F_total, effectively reducing the calculation to a two-stage cascade.
Why is noise figure always specified relative to a 290 K reference?
Noise figure is defined using a standard reference noise temperature of 290 K (about 17 degrees Celsius), the assumed source temperature, so that noise figures from different manufacturers and datasheets can be compared on a consistent basis regardless of actual operating temperature.
Does stage order affect the total noise figure?
Yes, significantly. Placing a higher-gain, lower-noise stage first always gives a lower (better) total noise figure than placing it later, because the Friis formula divides each later stage's noise contribution by the gain accumulated ahead of it.
What units does this calculator use for gain and noise figure?
Both stage gain and stage noise figure are entered in decibels (dB), the standard units for RF cascade analysis. The calculator converts internally to linear noise factor and linear gain to perform the Friis formula addition.