What is cascaded noise figure?
Every stage in an RF receiver chain — waveguide, amplifier, filter, mixer — adds its own noise. The Friis formula combines them into a single cascaded noise figure referred to the chain input:
F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁·G₂) + …
where Fi = 10NFi/10 is the linear noise factor and Gi = 10Gaini/10 is the linear gain. In terms of equivalent noise temperature (T₀ = 290 K):
T_e = T₁ + T₂/G₁ + T₃/(G₁·G₂) + …
For an amplifier: Ti = (Fi−1)·290 K. For a lossy element at physical temperature Tphys: Ti = (L−1)·Tphys, where L = 10loss/10.
Why the first stage dominates
Stage 2's noise contribution is divided by G₁, stage 3's by G₁·G₂, and so on. A first stage with high gain suppresses all subsequent stages. This is why real receivers put the lowest-NF LNA as close to the antenna as possible — even 0.3 dB of feed loss before a 0.8 dB LNA raises the system NF to ≈ 1.1 dB.
Loss at non-ambient temperature
Losses at temperatures other than 290 K are modelled by Ti = (L−1)·Tphys. A cryogenic feed cooled to 20 K with 0.3 dB loss contributes only ≈ 1.4 K instead of ≈ 20 K at room temperature — a big deal for radio astronomy and deep-space ground stations.
Use the resulting Te in the G/T calculator or the link budget. All computation runs locally in your browser.