How this instrument works
Noise factor F is a ratio of ratios: the signal-to-noise power ratio going into a stage divided by the signal-to-noise power ratio coming out, F = SNR_in ⁄ SNR_out. An amplifier or mixer built from real resistors and transistors always generates a little thermal and shot noise of its own inside the stage, and that noise adds to the signal path without adding to the signal itself, so the ratio can only get worse. F therefore sits at 1 for a perfect, noiseless device and climbs above 1 for everything real. Multiply the base-ten logarithm of F by ten and the same fact is restated as noise figure in decibels, NF = 10·log₁₀(F) — 0 dB for the impossible ideal, a positive number for every actual part.
Harald Friis defined the quantity this way in 1944 precisely because a plain SNR number is not portable: a receiver's output SNR depends on how strong and how noisy the antenna signal happened to be that day, but F and NF describe only what the device itself does to whatever ratio it is handed, measured against a standard 290-kelvin noise source at the input. That is what lets an engineer compare a $2 low-noise amplifier to a $200 one from a datasheet alone, without rebuilding each one's test setup.
The decibel form is convenient for spec sheets but deceptive for arithmetic: stacking two amplifiers in series does not let you add their dB figures, because each later stage's noise contribution is suppressed by the gain of everything ahead of it. Cascade calculations — the Friis formula for chained stages — have to convert every NF back to linear F, combine them with the gain terms, and only then take the log again. Treating decibels as additive here is the single most common noise-figure mistake among people who learned to add dB values for power and carried the habit somewhere it does not apply.
- Measure or read off the input SNR — the signal-to-noise power ratio feeding the stage, as a linear ratio, not decibels — and enter it in Input SNR (linear power ratio).
- Measure the SNR at the same stage's output under the same conditions and enter it in Output SNR (linear power ratio); it will always be the smaller of the two for a real device.
- Read Noise factor F, the dimensionless SNR_in ⁄ SNR_out ratio — 1.0 is the unreachable ideal, and anything above it is what the stage actually cost you.
- Read Noise figure, dB for the same result in the units printed on amplifier and receiver datasheets, ready to drop into a cascade or link budget.
Worked example — an amplifier stage that trims SNR from 20 to 15
A receiver's first amplifier stage is fed a signal whose input SNR is 20, a linear power ratio rather than a decibel figure. After the signal passes through the stage's own gain and picks up the thermal noise generated inside its transistors, the output SNR measures 15. The noise factor is the ratio of those two numbers: F = SNR_in ⁄ SNR_out = 20 ⁄ 15 = 1.33333333333. It is not a tidy round number because the stage genuinely used up exactly one third of the input ratio degrading it.
Converting to the scale printed on datasheets: NF = 10·log₁₀(1.33333333333) = 1.24938736608 dB, which a working engineer would simply read as 1.25 dB. That is a solid figure for a first-stage low-noise amplifier ahead of a satellite downlink or a weak-signal amateur receiver, where every extra tenth of a decibel of added noise makes a faint, distant signal that much harder to dig out of the noise floor.
Questions
Why must the SNR values be entered as linear ratios, not decibels?
Because F is defined as a ratio of two power ratios, and dividing decibel values gives a meaningless number — 20 dB minus 15 dB is 5, not 1.33. Convert each measured SNR to a linear ratio first (linear = 10^(dB/10)) before entering it here; the calculator then converts the final noise factor to dB for you.
Can noise factor F ever come out below 1?
Not for a real amplifying or passive stage under normal operation — the thermal and shot noise generated inside the device can only add to the signal path, never subtract from it, so F stays at or above 1 and NF stays at or above 0 dB. A result below 1 almost always means the two SNR values were swapped or measured under mismatched conditions, not that the device improved the signal.
How is noise figure related to noise temperature?
They describe the same degradation two different ways: noise figure is a ratio referenced to a standard 290-kelvin source, while noise temperature T_e expresses it as an equivalent physical temperature added to that source, related by T_e = 290·(F − 1) kelvin. Noise temperature is the more natural unit for cryogenically cooled front ends, where NF compresses meaningful differences into hundredths of a decibel.
Why can't cascaded noise figures just be added in decibels?
Because each stage's noise contribution is divided down by the total gain of every stage ahead of it, and that scaling only works out correctly in linear form, through the Friis cascade formula F_total = F1 + (F2 − 1)/G1 + (F3 − 1)/(G1·G2) + ... . Convert every stage's NF to linear F, apply the formula, then convert the total back to dB if a single spec number is needed.
Why does the first stage of a receiver dominate its overall noise figure?
Because the Friis cascade formula divides every later stage's noise contribution by the gain already accumulated ahead of it, so a high-gain, low-noise first stage suppresses whatever noise the stages after it add. That is why receiver designers concentrate their effort on the front-end amplifier: a noisy first stage cannot be repaired by a quieter one that comes after it.