Friis Noise Figure (3-stage)

NFtotal = NF1 + (NF2−1)/G1 + (NF3−1)/(G1×G2)

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Result
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Formula

NFtotal = NF1 + (NF2 − 1)/G1 + (NF3 − 1)/(G1 × G2)

Description

Friis' formula calculates the total noise factor of cascaded amplifier stages, showing that the first stage dominates the system noise performance. Each subsequent stage's noise contribution is divided by the cumulative gain of all preceding stages. This is why low-noise amplifiers (LNAs) are placed first in receiver chains: their high gain makes the noise of following stages negligible. The noise factor is the linear (not dB) ratio of output SNR to input SNR. Convert noise figure (dB) to noise factor: F = 10^(NF_dB/10).

Variables

  • NFtotal — System noise factor (linear)
  • NF1, NF2, NF3 — Individual stage noise factors (linear)
  • G1, G2 — Stage gains (linear power ratio)

Practical Notes

A 1 dB noise figure LNA with 20 dB gain followed by a 10 dB noise figure mixer gives system NF ≈ 1.36 dB. Without the LNA, system NF would be 10 dB. Losses before the LNA (cables, filters) add directly to the system noise figure: a 1 dB cable loss adds 1 dB to the noise figure. This is why LNAs are placed at the antenna.

Related Formulas

Wavelength Free Space Path Loss Signal-to-Noise Ratio Nyquist Sampling Rate Link Budget Antenna Gain

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