Noise figure cascade (Friis formula) with a worked example

The Friis formula for noise factor tells you how noise from each stage of a receiver chain contributes to the total:

F_total = F1 + (F2 - 1)/G1 + (F3 - 1)/(G1*G2) + ...

where F is noise factor (linear, NF = 10*log10(F)) and G is available gain (linear). Always convert from dB before applying it.

Worked example (numbers chosen for illustration):
Stage 1: cable/filter with 1 dB loss. For a passive lossy component at room temperature, NF equals its loss, so F1 = 1.259, G1 = 0.794.
Stage 2: LNA, NF 1.5 dB (F2 = 1.413), gain 20 dB (G2 = 100).
Stage 3: mixer, NF 10 dB (F3 = 10), gain -7 dB (G3 = 0.2).
Stage 4: IF amplifier, NF 4 dB (F4 = 2.512).

F_total = 1.259 + 0.413/0.794 + 9/(0.794*100) + 1.512/(0.794*100*0.2)
= 1.259 + 0.520 + 0.113 + 0.095 = 1.987, so NF about 2.98 dB.

Now move the LNA ahead of the 1 dB loss:
F_total = 1.413 + 0.259/100 + 9/(100*0.794) + 1.512/(100*0.794*0.2)
= 1.413 + 0.003 + 0.113 + 0.095 = 1.624, NF about 2.11 dB.

Lessons
1. Loss before the first amplifier adds directly to system NF. Put the LNA as close to the antenna as practical.
2. Once the first stage has enough gain, later stages matter little, but not zero: a high-NF mixer still contributed here.
3. Too much front-end gain hurts linearity. The cascade for IIP3 works the other way: later stages dominate. Balancing gain distribution is the real design task.

Measurement note: the Y-factor method with a calibrated noise source is standard. Account for the analyzer's own noise figure (second-stage correction) and for any loss between noise source and DUT.

Good example. One addition: if the first passive loss is at a physical temperature other than 290 K (for example a cooled or outdoor feed), its noise contribution is not exactly equal to its loss. Use the general expression with physical temperature in that case.