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What is noise figure?

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Noise factor F is the ratio of input SNR to output SNR when the input noise is at the standard temperature T0 = 290 K; noise figure is NF = 10·log10(F) in dB. An ideal noiseless device has NF = 0 dB. For cascaded stages, the Friis formula shows that the first stage dominates: F = F1 + (F2 − 1)/G1 + (F3 − 1)/(G1G2) + …, with all quantities linear.[1][2]

How is noise figure defined precisely?

F = (Si/Ni)/(So/No) with Ni = kT0B. Equivalently, F = 1 + Te/T0, where Te is the equivalent input noise temperature. NF depends on the source impedance: a transistor has a minimum NFmin at an optimum source reflection coefficient Γopt, and F = Fmin + (4Rn/Z0)·|Γs − Γopt|²/((1 − |Γs|²)|1 + Γopt|²).[2]

How does the Friis cascade formula work?

Each stage’s excess noise is divided by the total gain preceding it. Example: LNA NF 1 dB (F = 1.259), gain 15 dB (31.6), followed by a mixer with NF 10 dB (F = 10): F = 1.259 + 9/31.6 = 1.544, so NF = 1.89 dB. Without the LNA the system would be 10 dB. Losses before the LNA add directly: a passive lossy component at 290 K has F equal to its loss, so 1 dB of cable before the LNA adds 1 dB to system NF.[1]

What noise figures are typical?

Discrete GaAs pHEMT LNAs below a few GHz achieve NF well under 1 dB; integrated CMOS LNAs are commonly 1.5–3 dB; passive mixers have NF roughly equal to their conversion loss; spectrum analyzers without preamplifiers often have NF of 20 dB or more. Always check the datasheet test conditions.[3]

How is noise figure measured?

With the Y-factor method using a calibrated noise source, or the cold-source method on a VNA. See noise figure measurement.[3]

Frequently asked questions

Can noise figure be negative?

Not for a device at 290 K referenced to 290 K; values below 0 dB indicate measurement error.

Why must the first stage have high gain?

Its gain divides the noise contributions of all following stages.

What is the NF of an attenuator?

At 290 K, equal to its attenuation in dB.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

  1. “Noise Figures of Radio Receivers”. H. T. Friis, Proceedings of the IRE, vol. 32, no. 7, pp. 419-422. July 1944.
  2. “Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
  3. “Fundamentals of RF and Microwave Noise Figure Measurements (Application Note 57-1)”. Keysight Technologies. application note.
Categories: Fundamentals