How cascaded noise figure works
Every stage in a receiver adds noise, but noise added after a high-gain stage matters less because the signal is already large. The Friis formula weights each stage's excess noise by the total gain ahead of it, which is why the first amplifier sets most of a receiver's sensitivity.
- Noise factor from noise figure:
F = 10^(NF/10) - Friis:
F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁G₂) + … - Noise temperature:
Tₑ = 290·(F − 1) - A passive loss of L dB has a noise figure of L dB at room temperature.
Worked example: where the LNA goes
A chain of a 28 dB, 0.8 dB NF LNA, a 2 dB filter, a 7 dB mixer and a 20 dB IF amplifier has a system noise figure of about 0.91 dB. Put a 3 dB cable in front of the same LNA and the system noise figure rises to about 3.91 dB: the cable loss adds almost directly. That is why LNAs are mounted at the antenna.
Good to know
- If the first stage contributes less than about 80% of the total noise, later stages are hurting sensitivity.
- Pro converts the result to sensitivity in dBm for your bandwidth and SNR, and to G/T for satellite ground stations.