Formula and Method for Noise Figure
Noise figure (NF) measures how much a component or system degrades the signal-to-noise ratio (SNR) of a signal as it passes through, expressed in decibels. It starts from the noise factor F, the linear ratio of the SNR at the input to the SNR at the output: F = SNRin / SNRout. Because every real device adds some of its own noise, the output SNR is always lower than the input SNR, so F ≥ 1 and NF ≥ 0 dB. An ideal, perfectly noiseless device would have F = 1 and NF = 0 dB.
How the calculation works
Enter the input and output SNR in decibels, as measured on a bench or specified on a datasheet. Because decibels are already logarithmic, the noise figure is just the difference of the two: NF(dB) = SNRin(dB) − SNRout(dB). The calculator then converts that figure to the linear noise factor with F = 10^(NF/10), and derives the equivalent noise temperature Te = T0 × (F − 1), where T0 = 290 K is the IEEE standard reference temperature used throughout the RF and microwave industry.
Common mistakes
- Confusing noise factor with noise figure: F is a plain linear ratio (always ≥ 1); NF is F expressed in decibels (always ≥ 0 dB). Do not plug a dB value into a formula that expects the linear F, or vice versa.
- Averaging noise figures directly: NF in dB cannot be summed or averaged across cascaded stages. Convert to linear F (or to noise temperature Te, which is additive) before combining stages with the Friis cascade formula.
- Ignoring the reference temperature: equivalent noise temperature depends on the assumed T0. The IEEE standard is 290 K; using a different reference (such as 300 K or actual room temperature) will shift Te and should always be stated.
Real-world applications
- Low-noise amplifier (LNA) datasheets specify NF, often 0.3-1 dB, to show how little extra noise the first amplifier stage adds to a weak received signal.
- Satellite ground stations and radio telescopes track noise temperature rather than dB because noise temperature adds directly across cascaded stages, simplifying system noise budgets.
- Receiver sensitivity and link-budget calculations combine noise figure with bandwidth and antenna temperature to predict the minimum detectable signal.
- RF engineers apply the Friis cascade formula, Ftotal = F1 + (F2−1)/G1 + (F3−1)/(G1G2) + …, to show that the first stage's noise figure and gain dominate an entire receiver chain's noise performance.